SMALL WTND—POWERED ELECTRIC GENERATORS AND SYSTEMS

by Vassilis Clitou Nicodemou, M.Sc. (Eng.)

July 1979

A thesis submitted for the degree of Doctor of Philosophy of the University of London and for the Diploma of Membership of the Imperial College of Science and Technology

Department of Electrical Engineering Imperial College of Science and Technology London SW7 2AZ 2. ABSTRACT

This thesis examines some electrical aspects of small wind power systems.

The first part of the thesis deals briefly with the historical background and with a number of basic technical factors.. associated with wind power exploitation.

The second part deals with generators for small wind plants and with aspects of the associated power and control circuits. In the final part, an energy yield estimation method is presented and used to compare a number of different schemes.

Most of the second part concerns the design, manufacture_ and test of several specially built P.M. generators, but sections also deal with the operation and performance of generating systems based on wound field and capacitor-excited induction machines. Control and power matching aspects are considered. The four special P.M. machines comprise two low speed designs intended for direct coupling to windmill rotors and two ferrite-field machines designed primarily for operation with step-up transmissions. The disadvantages and advantages of a number of design features including choice of rated speed, P.M. material and layout are detailed.

Preliminary results in part three of the thesis seem to show that the use of a P.M. generator increases energy yield by only

5-15% compared with that produced by a carefully-chosen wound field machine and that windmill design, windmill operating mode, site, etc. are likely to be more crucial factors in maximising energy yield per total capital cost. 3,

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Dedicated to my parents and all whom I love 4.

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ev0a ūĒ j ux'L%CJ V &Vtl1WV Ya-cgowe )cEXcu&a.

xeivov ynp tatitnv rvēµwv 7cotnae Itpovtwv,

Bjµ:v ;tr..utilEvat, 1jb' ōpvūµCV, Ov )c ' Ē,9gAtJat v."

oi jpoY xep. I: (20).

"be (Aeolus) gave it willingly and presented me with a leather bag, made from the flayed skin of a full-grown ox, in which he had imprisoned the boisterous energies of all the Winds. For you must know that Zeus has made him Warden of the Gales, with power to lay or rouse them each at will."

Homer, Odysseia, X 5.

ACKNOWLEDGEMENTS

This work has been carried out under the supervision of

Dr. H.R. Bolton. For the invaluable help, inspiration, as well as keen interest, valuable guidance and constant encouragement during the course of the work described in this thesis, the author expresses his sincere gratitude to Dr. Bolton.

The author also gratefully acknowledges the valuable and stimulating discussions, useful suggestions and the keen interest maintained during the progress of this work by Dr. L.L. Freris.

Thanks are also due to Dr. E.M,Freeman for his continuous encouragement and the active interest he maintained in the project.

The author wishes to extend appreciation to all his colleagues in the Electrical Machines and Power Systems Section who kindly revised the typescript of this thesis, and especially to Dr. C. Papageorgiou,

Dr. R.A. Ashen and Mr. I.K. Buehring, for their useful discussions and assistance. He would also like to acknowledge the help of Miss. E.

Boden throughout the course of this work.

The author greatly acknowledges the manufacturing work on the

Mark I, Mark II and several test rigs carried out by Mr. R. Moore under the supervision of Mr. C. Jones in the Electrical Engineering Workshop at Imperial College. Thanks are also due to Messrs. R.B. Owen and

C. Johnson for their practical assistance and advice during the work.

The author wishes to thank'. the British Council and the S.R.C. for financial support of the project and a large number of individuals at Imperial College, Rutherford Laboratory, and elsewhere,, for their help, suggestions and opportunities for discussion. 6.

Thanks for financial support are also due to a number of individuals, and in particular my parents.

Finally, the author thanks Mr. R. Puddy for drawing the figures and Mrs. S. Murdock for typing the manuscript.

7. LIST OF CONTENTS

Page

Abstract 2

Acknowledgements 5

List of Contents 7

List of Principal Symbols 13

CHAPTER 1: INTRODUCTION 18

1.1 Brief Historical Review on the Future of Energy, 18 and Wind Power in Particular

1.2 Introduction to the Work described in the Thesis 22

CHAPTER 2: ENERGY RESOURCES AND REQUIREMENTS FOR 23 DOMESTIC APPLICATIONS

2.1 Introduction 23 2.2 Energy Resources and Energy Consumption for 23 Domestic Applications 2.3 Other Applications of Wind-powered Systems 30

CHAPTER 3: MACHINES AND SYSTEMS FOR TRANSFORMATION 36 OF WIND ENERGY INTO ELECTRICAL ENERGY

3.1 Introduction 36

3.2 Wind Power and Windmills 36

3.2.1 Available power in the wind 36

3.2.2 Windmill operation and characteristics 38

3.2.3 Types of windmills 44

3.2.4 Windmills for generation of electricity 49

3.3 Electrical Generators and Systems for Small-Scale 53 Wind Power Application

3.3.1 Effect of operating speed on generator 56 design

3.3.2 Use of special electric generators for 63 small-scale wind-powered systems

3.3.3 Control systems of wind-powered electric 71 generators for maximum extraction of power from the wind 3.4 Capacitor-excited Induction Generator 83 3.4.1 Wind-powered Induction Generator for 88 Maximum Extraction of Wind Power with Variable Capacitor Excitation 3.5 Concluding Remarks 94 8.

Page

CHAPTER 4: SMALL WIND-POWERED WOUND FIELD GENERATORS 95

4.1 Introduction 95 4.2 Rewinding the Armature of the Lorry Alternator 96 4.2.1 Details of the machine 97 4.2.2 Test rig 98 4.3 Tests on the Lorry Alternator 100 4.4 Results and Comments 102 4.4.1 No-load voltage (e.m.f.) Ef, versus field 102 current at constant rotational speed. (Magnetization curve.) 4.4.2 Iron, windage and friction losses (no-load 102 losses) versus field current at 1500 rev.min1 4.4.3 Armature winding temperature rise 104 4.4.4 Constant speed load characteristics of the 106 machine connected to a.c. and•d.c. resistive loads at 1500 rev.min-1 4.4.5 Load characteristics of the machine connected 111 to a d.c. load through a three-phase, half- controlled rectifier bridge 4.4.6 Effect of field current variation on the load 113 characteristics with and without diode bridge rectification 4.5 Operation with a Self-Excited Shunt-Connected Generator 115 4.5.1 Operation with generator 117 4.5.2 Effect of generator imperfections 121 4.5.3 Ideal performance curves 126 4.5.4 Generation using a self-excited generator 128 4.5.5 Determination of coefficient k 128 4.5.6 Experimental measurements 130 4.6 Field Tests on the Lorry Alternator 137 4.7 Concluding Remarks 139

CHAPTER 5: PERMANENT MAGNET ALTERNATORS: LOW SPEED TYPE WITH 140 CIRCUMFERENTIALLY-ORIENTATED PERMANENT MAGNETS ON THE ROTOR

5.1 Introduction 140

5.2 Review of Literature relating to Permanent Magnet Machines 140

5.3 Choice of Principal Features of the First Experimental 145 Generator for Wind Power Application

9.

Page

5.4 Construction of the Mark I Circumferential Rotor 151 Permanent Magnet (P.M.) Alternator 5.4.1 Stator 151 5.4.2 Rotor 153 5.5 Theory 159 5.5.1 Geometry of the alternator 160 5.5.2 The equivalent circuit and phasor diagram of 162 the CRPMA connected to a resistive load 5.5.3 Calculation of the current I and voltage V 166 of the alternator from its phasor diagram 5.5.4 Synchronous reactances of the machine 169 5.5.5 Calculation of the direct-axis magnetizing 172 reactance X ad 5.5.6 Calculation of the quadrature-axis magnetizing 175 reactance X aq 5.5.7 Inductive leakage reactance of the alternator Xe 175 5.5.8 The resistance of the winding of the alternator 176 5.5.9 Equivalent magnetic circuit of the circumferential 177 rotor p.m. alternator at no-load 5.5.10, Magnetic circuit of the alternator and the 183 calculation of the resultant flux in the airgap for-on-load conditions 5.5.11 The e.m.f. of the armature winding of the 185 alternator 5.5.12 No-load e.m.f. of the alternator 186 5.5.13 Definition of the direct-axis demagnetizing 188 m.m.f. of a three-phase winding 5.5.14 The resultant e.m.f. in the airgap of the 189 alternator 5.6 Calculation of the Regulation, Output Power Curves, Load 191 Angle EL and Efficiency Characteristics of the Machine 5.7 Theoretical and Experimental .Results and their Correlation 192 5.8 Saturation of the Stator Teeth of the Alternator and its 197 Influence on the Performance 5.8.1 Calculation of the performance of the alternator 203 with lower line of return of the magnet 5.9 Tests on the Mark I P.M. Alternator 208 5.9.1 Test rig 209 5.9.2 Test procedures 211 5.10 Results and Discussion of Actual Performances of the Mark I 215 P.M. Alternator 5.10.1 Section A results (unskewed machine with 20 turns 215 per coil and an airgap of 0.41 mm) 10. Page

5.10.2 Section B results (unskewed machine with 20 turns 218 per coil and a new airgap of 0.483 mm) 5.10.3 Section C results (skewed machine with 21 turns 221 per coil and the airgap of 0.483 mm) 5.11 Design and Construction of the "Rutherford" Low Speed, 230 Permanent Magnet Alternator 5.11.1 Double—layer fractional—slot windings 236 5.11.2 Design of the double—layer fractional—slot 238 winding of the "Rutherford" p.m. alternator 5.11.3 Theoretical and experimental results and their 244 correlation, for both constructions of the alternator 5.11.4 Calculation of the saturation coefficient of the 248 "Rutherford" p.m. alternator and its influence on the performance of the machine 5.12 First Series of Tests on the'Rutherford" P.M. Machine 252 5.12.1 Test rig 252 5.12.2 Results and discission of first series of test 254 results 5.13 Second Series of Tests' on the "Rutherford" P.M. Alternator 262 5.13.1 Test rig 262 5.13.2 Results and discussion of actual performances of 265 the "Rutherford" p.m. alternator for the second series of tests 5.14 Concluding Remarks 273

CHAPTER 6: PERMANENT MAGNET ALTERNATORS: RADIAL EXTERNAL 276 ROTOR PERMANENT MAGNET (P.M.) ALTERNATORS

6.1 Introduction and Brief Analysis of the Mark II P.M. 276 Alternator 6.2 Construction of the Mark II P.M. Alternator 280 6.2.1 Stator design and construction 280 6.2.2 Rotor design and construction 284 6.3 Theory 290 6.3.1 Geometry of the alternator 290 6.3.2. The equivalent circuit and phasor diagram of the 291 Mark II alternator connected to a resistive load 6.3.3 Calculation of the current L and voltage V of 292 the alternator from its phasor diagram 6.3.4 Magnetic circuit of the alternator on no—load _ 294 6.3.5 Calculation of the resultant flux in the airgap 299 for on—load conditions 6.3.6 Calculation of the e.m.f.s in the machine 300

11.

Pale 6.4 Calculation of the Performance of the Machine 301 6.5 Theoretical and Experimental Results and their Correlation 301 6.6 Tests on the Mark II P.M. Alternator 305 6.6.1 Test rig 307 6.6.2 Results and discussion of actual performances 307 of the Mark II p.m. alternator 6.7 The "Windrive" P.M. Alternator 334

6.8 Concluding Remarks 340

CHAPTER 7: ANNUAL ENERGY YIELD ASSESSMENTAND COMPARISON 342 BETWEEN SMALL WIND—POWERED ELECTRIC GENERATING SYSTEMS

7.1 Introduction .342 7.2 Wind Characteristics 342 7.3 Calculation of the Annual Average Power in the Wind and 349 Annual Energy Yield for Different Wind-Powered Systems 7.3.1 Mechanical transmission losses 353 7.3.2 Definition of the starting rotational speed 356 (cut—in wind speed) of the windmill with a load control for cubic loading 7.3.3 Operation of a wind-powered permanent magnet 359 (P.M.) alternator running at a variable rotational speed at 2.A and C = C p 7.3.4 Control with variable load resistance 361 7.3.4.1 Efficiency values --" 363 7.3.5 Control with variable load current but constant 365 load resistance R. 7.3.5.1 Overall efficiency of the system 365 7.3.6 Operation of a wind—powered wound field alternator 366 running at a variable rotational speed at j? = a and C /( op p = Cpmax . 7.3.7 Computer program for the calculation of the energy 372 yield for different wind—powered electrical systems and their comparison . 7.4 Calculation of the Energy Yield of Different Wind—Powered 378 Electrical Generating Systems with Known Curves of Efficiency versus Speed under Cubic Loading Conditions 7.4.1 Economic Comparison of Small Wind-Powered 384 Generating Systems 7.5 Concluding Remarks 387

CHAPTER 8: CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK 389 12.

Page

Appendix III.1 394

Appendix IV.1 396 Appendix V.1 397 Appendix V.2 403 Appendix VI.1 409 Appendix VI.2 415

Appendix VII.1 421 Appendix VII.2 422 Appendix VII.3 435

References 442

Publications submitted in support of thesis 454 13. LIST OF PRINCIPAL SYMBOLS

A cross—sectional area of the air flow Am area of the magnet B magnetic flux density Bav average flux density per pole B effective flims density per pole ef no—load flux density per pole BNL Br residual flux density of the magnet Bt no—load flux in the tooth Co total cash outflows Cp power coefficient of the windmill plant capital cost Cplant CQ torque coefficient of the windmill Cs discounted cash saving D generator rotor diameter D stator diameter s E generator e.m.f. Ea e.m.f. generated by the armature reaction flux Ef energy of the air flow Ef e.m.f. on the phasor diagram of the generator Eo e.m.f. proportional to field current annual energy produced by the plant OUT Fa fundamental m.m.f. Fad direct—axis demagnetizing m.m.f. F coercive m.m.f. c fuel cost Fcost FIN force on the generator shaft He magnetic coercivity I armature current Id direct—axis current If field current i.e load current Iq quadrature—axis current J armature winding current density KB form factor of the field wave Kd form factor of the direct—axis reaction P coil—span factor of the winding K skin effect coefficient r skewing coefficient Ksk

••

14.

K winding factor wf K d winding distribution factor Kg Carter's coefficient Lam arm length M mechanical advantage of the mesh PA copper losses in the armature winding Pa power in the air flow earing gearbox bearing losses b Pf copper losses of the field winding Pg airgap permeance Pgb gearbox losses generator shaft power, input power to the generator IN P.iron iron losses in the generator P1 leakage permeance per cent gearbox mesh losses Pmesh PNL generator no-load losses Po magnet permeance PQM, output power from the generator in the load Pw delivered power by the windmill. windage and friction losses in the generator yl gearbox windage losses Pwindage bearing torque loss per bear irzg._in- the gearbox Qgb gearbox no-load torque torque on the generator shaft Qgen. Qv torque developed by the windmill R radius of the airgap R total armature resistance a Rf field winding resistance Rg airgap reluctance per pole Rt load resistance R~ leakage reluctance of the magnet Ro reluctance of the magnet R armature winding resistance'per phase K windmill rotor radius Sc pole arc T number of turns per phase Tc number of turns per coil

✓ generator terminal voltage ctive volume of the active parts of the generator a 15.

Vb battery voltage drop Vd rectifier voltage drop Vdc d.c. voltage Vf field voltage Vi internal voltage VNL no-load phase voltage Vph phase voltage w wind speed w average wind speed V cut-in wind speed V, rated wind speed Whearing load on the bearing Wm magnet thickness Xad direct-axis magnetizing reactance Xaq quadrature-axis magnetizing reactance Xt armature leakage reactance Y pole pitch Yc coil span Z armature impedance

a cross-sectional area of the conductor c slot pitch e instantaneous e.m.f. f frequency fbearng friction coefficient of the bearing fg gearbox coefficient of friction h1,h3 slot dimensions i instantaneous output current ig instantaneous value of current in the coil j current density in a conductor kc packing coefficient of the laminations kg gearbox transmission loss k z saturation coefficient Qgeneratora rotor axial length 'Cavn average length of a half mean turn ew length of the end winding length of the conductor per phase ,Qf rotor length taking into account the fringing flux generator airgap length 16.

effective airgap length stack length es isk skewing length magnet radial length er m number of phases m mass of air a n generator shaft rotational speed n windmill shaft rotational speed w p number of pole pairs q number of slots per pole per phase t time 0 t temperature tAl thickness of the aluminium strip th stator and rotor radial thickness tav s average slot width tav w average tooth width 2 wl'W 'W o slot dimensions

a thyristor firing angle O(c temperature resistance coefficient ad pole arc/pole pitch coil span/pole pitch Ljungstrom exponent coefficient load angle

gb gearbox efficiency Igen generator efficiency system efficiency tip speed ratio of the windmill

2d differential leakage permeance %is slot leakage permeance f'o permeability of free space 5'r permeability of material. air density 1 c copper resistivity 0 generator flux armature reaction flux %ad direct—axis flux quadrature—axis flux Sag 17.

0g airgap flux ‘g-/NIL airgap no-load flux per half pole 0NL no-load flux Pro field flux sir residual flux 0(17w) Weibull distribution function 30 angle between terminal voltage and armature current angle between armature current and Ef w generator shaft angular velocity Ww windmill rotor angular velocity CHAPTER 1 18.

INTRODUCTION

1.1 BRIEF HISTORICAL REVIEW ON 'flit; FUTURE OF ENERGY, AND WIND POWER IN PARTICULAR

It is perhaps appropriate to start by quoting some of the major conclusions arrived at by world specialists on energy in their report of the Workshop on Alternative Energy Strategies [1.1J :

1. The supply of oil will fail to meet increasing demand

before the year 2000, most probably between 1985 and 1995, even

if energy prices rise 50% above current levels in real terms.

Additional constraints on oil production will hasten this

shortage, thereby reducing the time available for action on

alternatives.

2. Demand for energy will continue to grow even if govern-

ments adopt rigorous policies to conserve energy. This growth

must increasingly be satisfied by energy resources other than

oil, which will be progressively reserved for uses that only oil

can satisfy.

3. The continued growth of energy demand requires that

energy resources be developed with the utmost vigour. The

change from a world economy dominated by oil must start now.

The alternatives require 5 to 15 years to develop, and the need

for replacement fuels will increase rapidly as the last decade

of the century is approached. 19.

4. Electricity from nuclear power is capable of making an

important contribution to the global energy supply although

world—wide acceptance of it on a sufficiently large scale has

yet to be established. Fusion power will not be significant

before the year 2000.

5. Coal has the potential to contribute substantially to

future energy supplies. Coal reserves are abundant, but taking

advantage of them requires an active programme of development

by both producers and consumers.

6. Natural gas reserves are large enough to meet projected

demand provided the incentives are sufficient to encourage the

development of extensive and costly intercontinental gas transport-

ation systems.

7. Other than hydroelectric power, renewable resources of

energy, e.g. solar, wind power, wave power, are not likely to

contribute significant quantities of additional energy during

this century at the global level, although they could be of

importance in particular areas. They are likely to become

increasingly important in the 21st century.

8. The critical interdependence of nations in the energy

field requires an unprecedented degree of international

collaboration in the future. In addition it requires the will

to mobilise finance, labour, research and ingenuity with a common

purpose never before attained in time of peace; and it requires

it now. 20.

The above conclusions and suggestions are very alarming,

and the time is not far away when major political and social diffic-

ulties that might arise could cause energy to become a focus for

confrontation and conflict.

There would therefore seem to be a case for every country

to set to work now to conserve and find alternative energy sources.

They have to exploit every possible energy source, beginning with the

natural sources provided by the main energy source of our planetary

system, the sun. Wind energy is a largely untapped supply of free and

inexhaustible energy. Item 7 of the conclusions above states that

renewable sources are not likely to contribute significant amounts of

energy during this period, except in particular areas. It is considered

by the author and by many people working on the subject that the wind

regime over the north and west offshore areas of the United Kingdom

•constitute such a 'particular area? as far as wind power is concerned

(see Chapter 2).

Winds are the motion of air about the earth, caused by its

rotation and by the uneven heating of the planet's surface by the sun.

This is caused by a combination of day-night, location, sea-land,

mountain-valley and latitude differentials [1.23 . The wind has been

used as a source of power for thousands of years,. both on land and at

sea. The forces of the wind were worshipped by ancient man thousands

of years ago.

Sailing ships were first reported in Ancient Egypt nearly

five thousand years ago, and their use peaked towards the middle of

the nineteenth century with the development of the fast international

trading clipper ships [1.33. 21.

Windmills for mechanical power on land may have first

appeared in Persia, where archaeologists have found evidence of the

use of wind—driven water pumps for irrigation dating from about the

fifth century A.D.

The development of wind power for different applications involves several different scientific, technological and engineering

disciplines. These are: a) Aerodynamics, b) Mechanical and materials and civil engineering, c) Meteorology and the analysis of the wind, d) Electrical engineering, e) Energy assessment.

Publications have been produced on all aspects of wind power engineering over the past fifty years. The bibliographical book by

Barbara and David Harrah [1.4J includes 143 references from the 1930s up to the early 1970s.

The classical book by Golding on wind power [1.5] includes a brief analysis of all the five aspects mentioned above.

In [1.6] a. broad review is given of different windmill generators of large and medium size. In [1.7] small scale windmills are theoretically analysed from the point of view of energy contribution, whilst in [1.83 small scale windmill systems are described.

There is relatively little literature on the electrical aspects of wind power plants and it is to help fill this gap that the work described in this thesis was undertaken. 22.

1.2 INTRODUCTION TO '1'HE WORK DESCRIBED IN THE THESIS

The work of the Wind Power Group in the department was originally supported by a Central Research Fund grant from the

University of London. It is now supported by the S.R.C. and a number of third—year B.Sc., M.Sc., D.I.C. and Ph.D. projects have been run within the ambit of the group's activities.

The following aspects of the windmill system are covered in this thesis: a) The possible contribution of 'wind power in domestic

applications; b) Windmill generation and electrical system design for

small scale applications; c) Development and design of special P.M. alternators

for wind power applications; and d) Energy yield assessment and comparisons between the

different types of generators and systems.

One of the Ph.D. projects [1.9] examines the aerodynamic and control system aspects, and a recent D,I.C. project E1.103 details the design and operation of a microprocessor—controlled load—scheduling unit.

23. CHAPTER 2

ENERGY RESOURCES AND REQUIREMENTS FOR DOMESTIC APPLICATIONS

2.1 INTRODUCTION

In this chapter a summary is given of the energy resources

and requirements of domestic and other premises and the contribution

that could be made by using wind power for space and water beating.

2.2 ENERGY RESOURCES AND ENERGY CONSUMPTION FOR DOMESTIC APPLICATIONS

To analyse the energy consumption for household use, an

example. is given in Table 2.1 showing the results of energy use in

the United Kingdom in 1970 [2.1J . The energy units used in the

table are GJ = 109J, where 1 GJ = 278 kWh.

From Table 2.1 it can be seen that the 80% of the total

energy demand of the household goes on space and water beating. Of

the total energy demand, 18% is provided by electricity, 57% of

which goes on space and water heating.

The principal household appliances and systems used for

space and water heating are:

a) Electric household appliances, including electric water heaters

and modern storage beaters. It is important to mention that in

almost two million British homes storage heaters are installed

(this is approximately 17% of the 10 year old households in the

United Kingdom) [2.23. 24.

Table 2.1: Total and useful energy consumption for households in the United Kingdom in 1970.

Primary Conversion Net Utilisation Useful energy efficiency energy efficiency energy unction 106 GJ % 106 GJ % 106 GJ

Electricity 38 94 36 Central Solid fuel 126 60 76 heating Gas 143 70 100 Oil fuel i 89 70 62 99 50 Other Electricity 51 Solid fuel 555 30 167, space 117 63 74 heating Gas Oil fuel 39 63 25

Electricity 89 96 86 681 243 Totals Slid fuel 35 Gas .. 260 67 174 Oil fuel 128 68 87

Total space heating, all fuels 1158 51 590,

Electricity 67 99 66 Water Solid fuel 71 47 33 heating Gas 58 70 41 Oil fuel 7 7o 5 Electricity 34 80 27 1 1 Cooking Solid fuel 50 Gas 59 75 44 Oil fuel 5 75 4 Lighting T.V. etc. Electricity 86 35 30

Electricity 187 66 123 72 47 34 Totals Solid fuel ._ Gas 117 73 85 Oil fuel 12 75 9 Total water heating, cooking 388 68 251 and others, all fuels Totals of Electricity 1022 27 276 76 209 768 98 37 277 , energy - Solid fuel 753 449 84 377 . 69 259 demand _ Gas Oil fuel 152 . 92 140 69 96

Total energy demand 2391 65 1546 55 841 25.

Table 2.2: Summary of the electric energy consumption of households taken from Table 2.1.

Function Net energy 106 GJ

Space 89 heating 33

Water 67 24 beating

Cooking 34 12

Lighting, 86 31 T.V. etc.

Total 276 100 26. b) Gas appliances. These now dominate the water and central heating

systems in the United Kingdom. c) Oil—burning appliances. The need for these appliances will

remain where gas is not available (oil—burning central heating

systems). Paraffin stoves are also used for local space beating. d) Solid fuel appliances. In 1970 solid fuel boilers and open coal

fires accounted for nearly half the net energy used for beating

in households. Due to pollution problems and the requirements for

more careful attention and operation, their use has declined and

gas appliances and central heating systems have taken their place.

However, after the 1973 energy crisis they made something of a

comeback, along with wood—burning stoves, which became popular

particularly in rural areas.

District beating. District heating can provide space heating by

steam or hot water for domestic and commercial buildings and

possibly also some process beat for industry. In principle,

district beating schemes save energy by having more efficient

conversion of primary fuels than can be achieved in small heating

units in individual buildings. f) Total energy systems. A conversion system that generates

electricity and produces heat is called a "combined system" or

"total energy system" [2.1].. In principle, such systems can

achieve 85% efficiency, so that 100 GJ of primary fuel could

yield 56 GJ of steam beat and 28 GJ of electricity under ideal

conditions. This theoretical value requires a steady demand that

maintains an appropriate balance between demand for beat and 27.

demand for electricity. This system is widely used in the

Scandinavian, East European countries and in the U.S.S.R., where

the space heating demand lasts for six months of the year.

However, in the United Kingdom conditions are not as favourable

and the average efficiency over a year is lower. g) Heat pumps. Heat pumps are modern appliances which can be developed and used for domestic space heating. Heat pumps based

on atmospheric heat sources in general and on underground water

where available (waste water), can be good economic solutions. h) Solar beating. The viability of commercially made solar heating

schemes for housing is uncertain in the United Kingdom at present.

This type of heating is widely used in the Mediterranean and

Middle Eastern countries for water heating, where eight hours

sunshine per day in winter can provide enough hot water for a

family of three for an entire week.

Wind energy. The complementary nature of wind and solar energy

in the British Isles is illustrated in Fig. 2.1, taken from [2.43.

From Fig. 2.1 it can be seen that more power can be utilised from

the wind than directly from solar radiation. Fig. 2.2 shows the

isovent map of the United Kingdom and Eire, published by the

ERA, of the annual mean wind speeds between 9 and 13 knots

approximately 2.51 (1 knot = 0.514 m.sec-1 or 1.152 miles.hrl ),

which means wind speeds of 4.626 and 6.682 m.sec-1. The isovent

figures in Fig. 2.2 represent the annual mean wind speed in knots

over open sites. The figures shown look very encouraging for

wind power utilisation in the United Kingdom. 28.

6' I.- Global solar radialion_ Wind mtrgy-.- AVfragf daily totals t-t-'--l---+-_#-':':";';'~--; (MJ/m2)

Fig. 2.1: ,t}yeta.je ~(y global irradiation and wind energy available at a wind rotor.

'1

Fig. 2.2: Isovenf map.- --The isovent -figures represent annual mean wind speed in knots over open sites. (Hill-top sites are not included.) (1 knot = 0.514 m.sec-l .) 29.

As shown in the paper by Freris et al [2.6] , for the economics to be at all favourable for small scale wind energy exploitation, the following conditions should be satisfied: a) Location. The mean annual windspeed Vw should be at

least 5 m.sec-1. As is seen from Fig. 2.2, many coastal areas

of the United Kingdom and Eire fall within this category. b) Application. The utilisation of the produced wind

energy should be characterised by simplicity and some cheap energy

storage capacity. Applications which fall within this category

are, in the domestic scene, space and water heating, and on the

farm, building and greenhouse beating and perhaps grain drying,

ventilation and milk—cooling.

The use of wind energy for space and water heating has the following advantages: i) There is a strong correlation between periods of wind

energy availability and periods of high thermal energy demand.

In [2.5] it is shown that the ratio of wind energy available in

January to that of July is expected to lie between 2 and 3. ii) Cheap short—term storage can be incorporated in the

form of standard night storage beaters. In [2.7] it is shown

that for a location in Denmark for which profuse meterological

data exist, the power output exceeds the average annual power

for 42% of the time. If now a storage facility is added, power

equal to average or above is sustained for 62% and 72% of the

time for storage capacities of 10 hours and 24 hours average power, 30.

respectively. Thus, even a small storage facility improves

considerably the ability of the system to sustain the average

power.

Assuming conversion of wind energy into electric

energy, the latter can simply be dissipated in resistive elements.

This requires an inexpensive electric system particularly suited

to a permanent magnet alternator. In the proposed scheme,

Fig. 2.3, the alternator output is rectified and then routed to

off—peak storage beaters or to an immersion beater. Controller A

conditions the alternator output so that at all times the windmill

operates at a fixed tip—speed ratio and thus at maximum conversion

efficiency. Controller B routes the energy to the appropriate

load and ensures that minimum off—peak energy is extracted from

the mains to top up any deficiency in the storage heaters and

hot water tank during calm periods.

Full details of the operation and construction of controller A are given in [2.7] and in 1=2.83 the controller B, which can be based on microprocessor technology, is explained.

2.3 OTHER APPLICATIONS OF WIND—POWERED SYSTEMS

Today's consumers and industry expect to receive goods and services on demand rather than when they are available. Hence, there is- much reluctance on the part of many industries to make use of wind energy unless acceptable energy storage capabilities have first been perfected to supplement the wind's variability.

4 Timing signals Wind speed V Half-controlled Thyristor bridge pulsing t ~ rectifier unit t Power measurement Controller A

Y

Load switching Controller B unit

A • Temperature signals White meter r Standby Storage Immersion convector heater(s) heater Clock heater

Mains Mains

Fig. 2.3: Block diagram of wind energy conversion system. 32.

The agricultural industry is dependent on nature's variables

— sun, wind, and the rain. For the most part, farmers have been able to adapt to these variables by raising different crops in different areas. With a similar form of management, it may be possible to utilize the wind's variability to produce energy.

It is essential if wind power is to be successful, to recognize and evaluate carefully specific issues, such as the wind's availability, the economics for a particular use or proposed system, and the efficiency of the design. In addition, developmental work must be done in the area of energy storage and in perfecting simple energy transmission systems.

The Institute of Gas Technology (IGT) in the U.S.A. 2.113 is evaluating 5 to 50 kW windmills for farm application. The IGT studies can be utilized in conventional a.c. and d.c. applications in generating hydrogen as a combustible fuel. Their proposed system can be used to produce both hydrogen and oxygen that can be stored and later electrolytically recombined to generate power when the wind is insufficient to operate the windmill. The reserve power considerations may take the form of fuel cells, engine sets, or even conventional batteries. The electricity storage may be in the form of hydrogen in a a battery. It is likely that hydrogen would be stored as a compressed gas or a hydride.

For the most part, wind energy conversion systems (WECS) are considered clean systems with respect to air quality control. However, energy storage units used in parallel with WECS can be a source of air pollution. For example, batteries or electrolysis units can emit dangerous acid vapours. 33.

The use of small WECS for heating of premises is likely to be restricted mainly to areas having fairly high annual mean wind speeds and to premises at or near sites with a reasonable level of

"exposure". The erection of WECS equipment may also be constrained by: a) noise and vibration, b) T.V. interference, c) danger to people and property due to possibility of stress failure

of components such as blades, tower structure, etc.

The magnitudes of such factors, although primarily dependent on the size and rotational speed of the WECS, also depend on the windmill type and on the materials used. In general, the larger the rated kW level, the greater the distance required between windmill and dwellings, etc. Hence WECS at a reasonable power level is easier when large gardens, smallholdings and farms, etc. are involved rather than the small gardens common in towns and cities.

In the case of use of large-scale WECS of remote hilltops, moorland and offshore sites, etc. the above—mentioned hazards can be less of a problem though new factors can occur, such as obstruction or danger to navigation or to aviation traffic control due to electro- magnetic wave interference.

Further points of comparison between "large" and "small"

WECS are: maintenance needs, level of capital cost per rated kW, and the nature of the back—up supply. "Do—it—yourself" maintenance can sometimes provide an adequate basis for small systems (thereby improving the overall economics of a system), whereas maintenance on 34. large WECS may require teams of skilled personnel and a certain amount of expensive equipment. The law relating capital cost per rated kW to rated kW (i.e. size) for WECS is not thought to follow the simple shape common for conventional generating plant (i.e. the larger the plant, the lower the cost per rated kW). Sub 20 kW WECS are certainly more expensive per kW than larger systems, but the difference may be reason- ably small due to the cheaper materials and methods of construction, etc. allowed when stress levels are low plus the usual absence of grid connection costs, wayleave costs, etc.

National kWh allowances granted for large WECS by supply authorities can be quite low due to the lack of firmness associated with wind energy, whereas the householder or farmer may not reckon that lack of firmness with his wind energy—generated heat is anything of a snag since be already has back—up plant (e.g. boiler, mains electricity).

Modern electronic techniques may allow small plants to be controlled cheaply using sophisticated control strategies.

Small—scale WECS have so far been used mainly in isolated weather and communications stations, farmsteads and outposts.

Continuity of electricity supply has usually been necessary in these installations and storage batteries, small internal combustion—engine- driven generators etc. have had to be paid for, The overall cost per electrical kWb is then high and can only be justified on remote sites where normal power supplies are unavailable and fuel is expensive.

With regard to the use of small windmills for dwellings, the Building Research Establishment has concluded from a study [2.3] that capital costs on existing commercially available units would not 35. match present fuel bill savings, making it extremely unlikely that

consumers at present would view such investment as worthwhile at

current costs. Fuel cost increases and the development of effective

but cheaper small systems (with no electrical batteries, etc.) may change the picture.

In Chapter 3 more details are given on different types of WECS.

Sections 1.2 and 2.2, references [2.5, 2.6, 2.7 and 2.8 J together with the basic principles outlined in Section 3.2 enable a a fairly well defined set of generator requirements to be built up.

Many of the factors are dealt with in detail in Section 3.3, but it is perhaps helpful to list at this stage the more obvious requirements for the electric generating and heating systems.

1. The system should make sense economically. This

implies that the effective cost per kWh of heat produced by the

system be comparable with, or less than, the cost of the user's

currently available beat source. In some cases it might be

possible to justify the use of a wind power system producing more

costly energy on the grounds of the future fuel cost trends. The

exact accounting method used may vary depending on the category

of user. Low cost per kWh for a wind system is very much a

global type of figure of merit and clearly involves several

factors, such as: (a) capital cost of plant; (b) plant

efficiency; (c) rates of interest; (d) maintenance; and

(e) insurance requirements, etc; some of which factors involve

quite complex calculations. A typical cost assessment method is

given 'in Ref. [2.6] and in Section 7.4.1. 35a.

2. Heat availability.

3. Reliability of plant.

4. Simplicity of plant hardware.

5. Level of disturbance to environment (see page 33).

Selection of specific system for detailed study had been made before the start of the project and this is therefore not the place to examine the precise reasons for the choice of configuration studied.

Pages 29 and 30 and reference X2.61 summarise the advantages of the particular system chosen, but it is perhaps worth adding that this is unlikely to represent the only good solution to the "wind heating" problem.

Important alternative solutions could easily involve, for instance: i) Heat churn on the tower with fluid circuit to the house. ii) Hydraulic pump on the tower with throttle (and possibly heat exchanger) (tried by WESCO). iii) Heat pump on the tower with fluid circuit to house.

Table 2.3 gives a very rough comparison between the systems, but it is impossible to gauge the extent to which the alternative systems would satisfy the above requirements better than the chosen electrical solution without a reasonably comprehensive system study. An appropriate system study could well form part of a future project. Suffice it to say that in none of the non—electrical systems is there freedom from snags, although capital costs may be lower.

Qualitative factors leading to the selection of the electrical system alternative are given on page 64 (third paragraph). Transmission Transmission Heating system Control Power take—off hardware losses cost complexity gearing 1

Normally Electric wires low medium medium normally yes yes Heat churn pipes maybe high no low low no Hydraulic pipes maybe high no medium and throttle medium no normally Heat pump pipes maybe high no high high yes

Table 2.3: Comparison between different wind—powered heating systems. 36. CHAP'TBR 3

MACHINES AND SYSTEMS FOR TRANSFORMATION OF WIND ENERGY INTO ELECTRICAL ENERGY

3.1 INTRODUCTION

This chapter gives a brief introduction to wind power and windmill systems. Windmill characteristics and behaviour are introduced. A very brief historical review of the different types of windmills applied to generation of electricity is included. Brief descriptions and first order analysis of electrical systems for small plants are given.

Finally, the experimental results of a variable capacitance excited induction generator scheme are presented. These tests show that an induction generator can be matched over a reasonable range of wind speeds of a windrotor. However, sacrifices in power output size, range of rotational speed (build—up) and capacitor costs tend to occur. No attempt was made to give a theoretical backing of the experimental results due to the lack of time and the already existing literature on the subject [3.40] .

3.2 WIND POWER AND WINDMILLS

3.2.1 Available Power in the Wind

The energy associated with the wind is in the form of kinetic energy. The energy of the air flow Ea, having a cross—sectional area of A, is determined according to the expression:

37.

2 Ef - ms a 2 (3.1)

Since the mass of air mw flowing with a velocity of Vw through the area A in a second is:

mw, =t A Vw (3.2)

the energy flowing in one second is numerically equal to the power Pa:

p.A. w3 2 (3.3) where .Īo is the air density, equal under normal conditions to 1.23 Kg.m 2 (at t = 15°C and p = 760 mm.Hg).

Therefore, the power of the wind changes with the cube of its velocity.

Normally, the cross-sectional area of the wind is circular in shape for propeller type windmills (see Section 3.2.3). Thus:

2.V3 Pa 2JD.TL.R (3.4)

where R is the radius of the windmill.

The windmill can transform into useful work only part of its energy. This extraction efficiency is normally defined as the power coefficient Cp. 38.

3.2.2 Windmill Operation and Characteristics

Power coefficient C is defined as the ratio of the power delivered by the windmill (Pw) to the total power (Pa) available in the cross—sectional area of the wind stream subtended by the wind rotor. Mathematically, this is expressed by the equation

P w Pw Cp (3.5) Pa ip .Tt .R 2.V 3 w w

From [3.1]the ideal windmill is a windmill with an axis of rotation parallel to the velocity of the wind, having an infinitely large number of very narrow blades, whose profile drag is equal to zero and the circulation of velocity along the blade is constant, rotating with an infinitely high angular velocity taw and finally, being distinguished by the fact that the loss in airflow velocity in the plane of the windmillls rotation is constant along the entire swept surface.

The actual windmill is a windmill having a finite number of blades and angular velocity taw co ). Losses occur at the tips of the blades and wake rotation is caused by the finite angular velocity W

(and hence extra power loss).

As claimed by [3.1] , the theory of the ideal windmill was first developed by V.P. Veychinkin in 1914 and after 6 years

N. Ye. Zhukovskiy gave the solution for the coefficient C and founded a number of important propositions of the ideal windmill D.23.

The classical theory of N. Ye. Zhukovskiy establishes that for an ideal windmill C = 0.593 [3.1] , which was also shown by Amax 39. 11 A. Betz, of Gottingen in 1927 [3.33 . According to the theory of

G. Kb. Sabinin, C = 0.687 Amax [3.1, 3.3] . This discrepancy was caused by the fact that in

determining the axial force of pressure of the flow in the windmill,

Sabinin determined the impulse of the forces not at the place where

the vortex solenoid was formed, but in the place where it adopted a

cylindrical form and has an area larger than the swept surface.

Detailed analysis of windmill aerodynamic calculation is

not included in this thesis because this was not the aim of the author's

work. More detailed analysis is given in [3.5] .

From momentum theory for the actual windmill it is found

[3.1, 3.2] that the total torque developed by the windmill is:

3 = z CQTCR A V Qw w w (3.6)

CQ is the torque coefficient of the windmill and is a function of the

tip speed ratio X, where:

()w R V (3.7) w

The form of the characteristic of CQ depends on the number,

width and aerodynamic profile of the blades and the angle of attack

or inclination.

The power extracted from the windmill will be equal to:

Pw = Qw.Ct) w (3.8)

Substituting expression (3.6) into expression (3.8), we obtain: 110.

P, = 2 . CQ .TC Rw3..P vw 2 . W w (3.9)

But from expression (3.7)

Vw (3.10) , w

Substituting (3.10) into (3.9), it becomes:

CQ 3 pw = i . AJ) Tt22 w .V (3.11)

Therefore from expressions (3.5) and (3.11):

Cp = CQ . (3.12)

The power coefficient of the windmill is a function of its torque

coefficient CQ and tip speed ratio A

Fig. 3.1 shows typical CQ and C characteristics of a three—

bladed windmill rotor.

The major points of the curves in Fig. 3.1 defining the major

parameters of the characteristics will be: (i) C is the optimum op relative torque coefficient, which the windmill develops with (ii) the

optimum tip speed ratio aop at which the power coefficient is at its

maximum value, (iii) C = C , (iv) CQ is the starting torque max o coefficient developed by the windmill rotor during starting, i.e. when

= 0; (v) A max is the synchronised speed at which CQ = 0;

(vi) CQ is the maximum torque coefficient developed by the windmill max rotor at (vii) X. (viii) The relationship CQ ACQ is called the max op 41.

Co Cp 0.1

Comax

Ca

I

I 0.1

I

I

I Coop -CF

I i I 0.08 04 1 4 1 I ! I •

0 3 I ! I \/- • Coo 0.2 /1 I / 1 I / I I 1 -0.1 ( I -~ 1 i/ ~ 1 1 / 1 IX I X Op 1' max '' 0 2 4 6 8 10 r 12 TIP SPEED RATIO X

Fig. 3.1: Typical CQ and Cp curves of a three-bladed horizontal-axis windmill: 42.

overload of the windmill [5.1] . This means that the windmill can run

between the range of XII and X without being stalled. max

From examining the characteristics of windmills having

variable rotational speeds (see Fig. 3.2) and also the results of

theoretical and experimental investigations, the following conclusions

can be drawn, as noted in [3.1] :

1. The greater the number of blades, their width and angle

of attack, the lower the rotational speed of the windmill and the

value of 'Ā m , and the higher the value of C and the curve ax CQ(X) has a sharply dropping form.

2. In high-speed windmills, the value of CQ is several 0 times smaller than CQ , and the synchronized speed is 2-2.5 times op higher than normal.

3. The power of the windmill, other things being equal,

depends only to a. limited extent on the number of blades and the

solidity of the rotor or= S/A (the relationship of the blade area

to the swept surface). The form and profile of the blades, their

position in the airflow and the diameter of the windmill have

more important effects on the power.

4. The relative initial torque coefficient decreases

faster as blade number goes down than rotational speed increases.

Thus, with an increase in a op by twice,CQ decreases by 6-7 times. 0 At the same time, pickup, defined by the relationship CQ /d,o 'o op in a six-bladed rotor is 3.3 times greater than in a two-bladed one.

5. For a given wind rotor the rotational speed of the

windmill is directly proportional to its tip speed ratio and

wind velocity and inversely proportional to diameter. Ca cp

0·20~----~----~------~----~----~------

1. 2-bladed rotor 2. 3-bladed rotor 1----1-4---1-----+----4 3. 6- bladed rotor 4. 1B-bladed rotor . Ca Torque coefficient

0.16 t----+-f---+----t~--+------Cp Power coefficient -----t

0·12 t----f--fHt----t--it----f----+---+-----l

0·08

o 2 4 6 8 10 12 TIP SPEED RATIO A

Fig. 3.2: Typical C and C curves of horizontal-a~is windmills Q p with different number of blades. 44.

When selecting and computing layouts for windmills, it is necessary to consider the aerodynamic characteristics of windmills and the loading characteristics of the working machines. For instance, for driving a low-speed pump having a high starting load torque, it is better to use a multi-bladed windmill; this allows a reduction in the value of the minimum working wind velocities, and a reduction in the gear ratio of the reduction gear and in mechanical losses, even though the value of C is rather lower. However, for combination Amax with an electrical generator having a high rotational speed, a low starting torque and a smooth increase in load, it is often more effective to use a high-speed windmill. As stated in [3.1] , during recent years, due to the use of blades with highly improved aerodynamic profiles and different automatic systems, an increase in the effective- ness of utilization of high-speed windmills has been successfully achieved, which was in part expressed in an improvement in their starting characteristics, an increase in power, a reduction in imbalance of rotation and so forth.

3.2.3 Types of Windmills

From [3.6] , use of the term owindmillt should be restricted to machines for milling (grain-grinding, etc.) and not for those gener- ating electricity or pumping water. However, being short and evocative the word tends to be used to describe what may more correctly be called wind generators, aerogenerators, wind-driven turbines, wind- plants and 'wind machines, to mention but a few. 45.

Many different types of windmill have been designed and constructed during the course of windmill history. Today, the most common windmills are classified according to their axis of rotation relative to the direction of the wind. There are basically two types of windmill: • a) Horizontal-axis, where the propeller (or rotor) on a

horizontal shaft or axis moves in a plane perpendicular to

the direction of the wind. b) Vertical-axis, where the rotor on a vertical shaft or axis

has its effective wind catching surface moving in the

direction of the wind. This type includes those using

Darrieus and Savonius ' rotors [3.3, 3.4, 3.7] .

Designs may vary considerably within each class. With horizontal-axis windmills, blades are usually coupled directly to the output of the system through a shaft on which the rotor sits. Other arrangements utilize a circular rim that is attached to the blade tips.

This rim then drives a secondary shaft that is mechanically attached to the power output network.

One class of horizontal-axis windmills is designed so that the blades rotate in front of the tower with respect to the wind direction. These are generally referred to as upwind windmills.

Another variation, called downwind windmills, has blades rotating behind the tower.

Fig. 3.3a [3.4] shows some of the different types of horizontal- axis windmill rotors and horizontal-axis windmill designs (Fig. 3.3b). 46.

SINGLE-BLADED

DOUBLE- TRIPLE- BLADED BLADED

(U.S. FARM WINDMILL DESIGN) (BICYCLE DESIGN)

Fig. 3.3a: Typical blade configurations for horizontal-axis windmill rotors.

WIND -a. DIRECTION

-r.

UPWIND DESIGN DOWNWIND DESIGN

Fig. 3.3b: Upwind and downwind horizontal-axis windmill designs. 47.

The first windmills (Persian and Chinese)[3.3, 3.4] were of the vertical—axis type; however, they were never incorporated in

any large—scale operations like the horizontal—axis systems. The one

major advantage that these systems have over the horizontal—axis units

is that they do not have to be reorientated into the direction of oncoming

wind as the windstream direction changes. This advantage essentially

reduces some of the complexity in design and at the same time reduces

the gyro forces on the rotors that in the former systems cause stress

on blades and other components when yawing.

Savonius rotors, which were invented and used in the 1920s

and 1930s in Finland, are the most common design among the vertical—axis

windmills.

The Darrieus—type rotor was first introduced in France by

G.J.M. Darrieus in the 1920s. The Darrieus has relatively low starting

torque but a high tip—speed ratio-and maximum power coefficient near

to that of a horizontal—axis windmill. A combination, of ā, Savonius rotor (low power coefficient, but high starting torque) with a

Darrieus rotor can give a highly competitive windmill [3.13] .

Fig. 3.4a and 3.4b shows the diagrams of the two above—mentioned windmills.

The cycloturbine [3.6] , developed by Pinson Energy

Corporation, is a straight bladed Darrieus. A similar type of rotor is being developed by Exeter University [3.45] As a result of its cyclically varying pitch blades it has the advantage of being self— starting. Another interesting and recent development of the vertical— axis windmills is the twin—bladed variable pitch rotor shown in

Fig. 3.4c. The twin blades are hinged to the cross arm and are allowed to vary their angle of lean to suit changing windspeeds [3.14]

48.

SIDE VIEW OF SAVONIUS MOTOR

LOW 111, PRESSURE AREA WIN D ` - STREAM /0 \ROTATION DIRECTION

`POWER SHAFT

HIGH -~► PRESSURE AREA -~ .

TOP VIEW

Fig. 3.4ai Savonius S-shaped vertical-axis windmill.

Fig. 3.4b: Darrieus rotor vertical axis windmill.

ROTATING TUBULAR INNER SHAFT TIE WIRE AEROFOIL SECTION BLADE HINGE

GUY WIRE TERNATOR .

Fig. 3.4c: "Musgrove" type vertical axis windmill. Variable pitch rotor configuration at low wind speed (left) and at high wind speed (right). 49.

This decreases bending stresses caused by high rotational-speeds.

This design takes the name of its inventor, Dr. P. Musgrove, of

Reading University. The "Musgrove" type windmill, shown in Fig. 3.4c,

can be self-starting [3.14] when three or more blades are used.

3.2.4 Windmills for Generation of Electricity

Space and time do not allow a full review of all the different

windmills which have been built, tested and designed for large, medium

or small wind power applications for generation of electricity. Warne

and -C alnan [3.8] give a very good review of large and medium size

windmills for generation of electricity from 1930 to 1976. In [3.6]

an interesting review is given, mainly of small scale windmills

currently used for generation of electricity.

Large scale windmill electrical generators are generally

expected to work in parallel with the grid, whereas medium and

especially small scale machines tend to be used for isolated loads

(e.g. for beating , providing power to radio installations, fox.

cathodic protection of major oil and gas pipelines, for supplying with

power automatic meteorological stations and distilling installations).

In [3.1] a series of modern small scale windmill generators used in the

U.S.S.R. is described. In the U.S.S.R., grouped wind-electrical stations

made up of 10-15 machines of 25-30 kW each, working for a common

consumer are considered to be more economic than single large

machines. However, in the U.S.A. and other countries greater

. preference is given to large single-machine stations. The best known

large windmill built in 1941 and known as the-Smith-Putnam wind turbine, 50.

possessed a rated power of 1.25 MW [3.7] . Recent machines in the

U.S.A. show the same tendency of building large single-units, e.g. the

ERDA-NASA 100 kW prototype at Plum Brook Station, Sandusky [3.8, 3.9]

and the experimental 200 kW wind turbine at Clayton, New Mexico [3.10] .

The paper by Jorgensen et al [3.11 gives an interesting

analysis of the selection of large wind-driven generators, system

optimization, control system design, safety aspects, economic viability

on electric utility systems and potential electric system interfacing

problems.

However, the most successful unit till now in the history of

wind power utilization of energy was the Gedser Windmill, power 200 kW,

built in Denmark in 1957 [3.8, 3.12

The largest windmill built to date was completed recently

at Tvind in Denmark by a group of teachers, students and pupils and

is a bold, practical and sophisticated project. It is a 2 MW windmill,

designed for grid connection and domestic heating of the school

buildings and local dwellings [3.15]. The most extraordinary thing

about this project is that it was built by amateurs, without prior

experience of civil, mechanical, aerodynamical and electrical

construction.

The United Kingdom is one of the richest areas in the world

from the point of view of wind speeds suitable for generation of

electricity (see Chapter 2). However, the development of wind power

has not boomed in this country, though enthusiasts in the subject exist and grow in number every year. In the past five years, quite a number of research groups, universities, organisations, firms and individuals 51.

have become very actively involved in wind power. One of the recent

British achievements in the area of wind power is the construction and

operation of the Aldborough aerogenerator built by Sir Henry Lawson-Tancred

[3.16] . The machine is rated at 30 kW in a 8.9 m.sec-1 wind speed.

The machine mainly feeds its power into the grid via a hydraulic

pump/motor system.

The principal large scale windmill electrical generating

system.. configurations are:

a) A variable-speed constant-frequency system with frequency

converter. These are sometimes troubled by mechanical resonances

within the operating speed range [3.173.

b) Constant-speed constant-frequency systems. With a

constant rotational speed, the windmill rotor does not extract

maximum power from the wind.

Item (b) can be achieved by blade pitch regulation by

hydraulic speed regulation or clutch and/or by regulation of generator

electrical characteristics (pole and rotor resistance regulātiōn,

especially for induction generator schemes). Also, if the windmill

generator is connected to an infinite bus bar, then the system itself will "pull" the windmill unit into synchronism, e.g. single induction

generator input can be matched with the wind rotor's output torque [3.41] .

For item (a), several alternative techniques have been tried

or proposed to extract power at the mains frequency. These are:

(i) Single-phase a.c. generator d.c. field excitation-rectifier-

inverter. 52.

Single-phase high frequency a.c. generator, a.c. field

excitation-rectifier-inverter-filter (field modulated system)

[3.20, 3.21] .

(iii) Three-phase alternating current commutator generator [3.19] .

(iv) Three-phase slip-ring double output induction generator [3.17] .

A variant of the last scheme employs a three-phase slip-ring induction generator with the stator output fed to the mains and rotor output to space or water beaters of variable or fixed resistance [3.18] .

It is also worth mentioning the work by SOdergard [3.22] , where he suggests a d.c. generator/thyristor converter as a possible alternative to a.c. alternator for large wind-electric generators. His comparison output and efficiency figures for the two generators are convincing; being in favour of the d.c. generator/inverter system if the assumed efficiency figures for the two cases are correct.

However, the author does not believe that a d.c. generator is more robust, reliable and cheaper than an a.u. alternator.

Another interesting scheme used in Quirk's windmill unit employs a bruehless wound field alternator with a pilot exciter having field excitation on the stator. The exciter armature winding and rectifier bridge are shaft-mounted. 53-

3.3 ELECTRICAL GENERATORS AND SYSTEMS FOR SMALL SCALE WIND POWER APPLICATION

Section 3.3 quotes freely from [3.23] and [3.46] , on which the author of this thesis was a co-author.

The choice of generator and electrical system configuration

depends greatly on the plant size, whether grid connection is intended and, if not, what type of electrical load is to be used. With small

wind-powered systems, a choice from a great variety of electric

generator and system configurations must be made, and Table 3.1 lists

a number of generator types which have been used or suggested for use

with small wind-powered systems [3.23] .

Table 3.1: Generator types.

-N Approximate data Type of for small machines cost Type sliding Control Efficiency at Wt. full load contacts /x p.u. p.u. a 0-1 KW 1-10 KW

1. D.C. 'dynamo' with wound commutator d.c. field 5 2 80 1), field / 90 ii) with permanent commutator magnets various ./ 4 2 90 93 2. Alternator with wound i field slipp ring s d.c. field v/ 3 1.3 80 90 ii) with permanent L/ magnets none various 3 1.3 90 93 3. Induction none slip various ti/ 1/1.5 1 85 90 machine rings 4. Field modulated alternator 3. fq~ slip rings a.c. field x - - X8.0 <9.O 5. Roesel generator none a.c. field x 5? 1.5? 8C) <90 6. Commutator a.c.`"' commutator a.c. field v/ 5? 1.3? 4 <9D generator ( 3.f3] c8d Inductor 7. d.c. field x 1.8? al, generator/7140-7 5? 54.

In their paper, Johnson and Walker [3.43 suggest a scheme

with an a.c. alternator driven by a windmill at variable speed and

supplying an induction motor which drives an air conditioner at

variable frequency. Their experimental results seem to be satisfactory.

The best choice depends mainly on the windmill type, wind

regime, power level and type of load, but in most cases the front

runners will be an alternator of some type or an induction generator.

If the generator is to be connected to three—phase mains and a

virtually fixed (±7%) windmill speed can be countenanced, the induction

generator is likely to be preferable. When the electric system is

isolated from the mains, then an alternator, though more expensive than

an induction generator, is likely to prove more economic when the

adjustable capacitor bank necessary for the induction generator and the

better efficiency of the alternator, are taken into account.

The task of providing fixed output frequency with variable shaft speed is a difficult one. Electronic frequency conversion is still expensive. The use of a variable ratio transmission (e.g. variator cone or Daf belt system) is certainly worth considering for

1 to 30 kW systems but may not prove reliable enough or efficient enough at part loads.

A special generator feature should perhaps be mentioned which would allow a compromise to be reached between the windmill's need (if maximum energy is to be extracted) to run at a variable speed and the generator's need (when supplying constant frequency power) to run at a fixed or (for an induction machine) near—fixed speed. This is the two— speed design. Induction machines can be designed to operate efficiently around two or even three speeds. Alternators can be designed to operate at two speeds. Typical speed ratios are 2:1, 4:6. 55. Table 3.2: Advantages and disadvantages of generator types.

1 2 Generator type given Advantages Disadvantages in Table 3.1 1(i) Easily controlled. Expensive; brush maintenance required; brush friction and field losses reduce effic- iency; d.c. output only. 1(ii) No field losses. Expensive; control requires; system handling main output power; d.c. output only. 2(i) Slip rings handling output power Field losses reduce effic- rather than commutator handling iency; frequency proportional output power, therefore less to shaft speed. maintenance, less friction and less costly than d.c. machine; easily controlled; rectification to d.c. easy. 2(ii) No sliding contacts; therefore Expensive; control requires extremely low maintenance system handling main output required; high efficiency pols-. power; frequency proportional ible; robust; rectification to to shaft speed. d.c. easy. 3 Cheap; robust; easily available. Only efficient when frequency is approximately proportional to shaft speed; high rotor losses; machine requires reactive power, hence less efficient generally than others; mains connection or to adjustable bank of capacitors. 4 Frequency independent from shaft Not easily available special speed. field control system design; expensive. 5 No sliding contacts; frequency Not easily available; special independent of shaft speed; design; expensive. robust. 6 Frequency independent of shaft Not easily available; special speed; no special field control; design; expensive commutator works on mains frequency; self— maintenance. excitation possible. 7. Robust; no sliding contacts, easy Power/weight/speed much lower control via field winding; could than that of alternatives; obtain high frequency output for frequency proportional to subsequent conversion to constant shaft speed; special design. 50 Hz via electronic cyclo— converter; robust. 55a.

Space does not permit a full discussion of the relative merits of the different types of generator given in Table 3.1, but some of their pros and cons are given in Table 3.2.

Within the project attention was paid to three of the more promising of the generator types, viz: P.M. alternator, wound field alternator and induction generator. A system study would have been possible here in reachinga decision on the choice of generator, but such a study would need: to have been a very extensive and lengthy one if the conclusions were to be able to be treated with any confidence. The input data to such a study could only be based on the performance, cost- and availability of commercially available machines, and, given the scope of the machine laboratory's skills, this seemed a second—best alternative to a course of action involving an attempt to develop more cost—effective versions of the machine type that seemed to have the greatest potential advantages, viz: the P.M. generator. The main thrust of the project was therefore concerned with the development of some new P.M. generators. Some important subsidiary studies were also made of induction and wound field generators, tests being made on commercially available units of these types. A system study based on data from the most recently available machines of each type in Table

3.1 could form a useful part of a future project since it is perhaps unwise to disregard, at this stage, any of the generator types, in suitably modified form, as having no potential to be an effective and economical part of a small wind plant. 56.

3.3.1 Effect of Operating Speed on Generator Design

Windmill rotational speeds are rather low when compared to most

generator drives, e.g. diesel engines, steam turbines, etc. There are

some notable exceptions, however, the hydro—generator and bicycle

dynohub being the most important modern examples at opposite ends of the

power spectrum, and the early alternators driven by reciprocating steam

engines being the most well known example from earlier times. Why are

low rotational speeds usually avoided? In most generators, the shaft

torque results from a circumferential shear stress on the curved surface

of a cylindrical rotor. The stress results from an interaction between

the magnetic field crossing from rotor to stator, and the currents in

the windings. The total circumferential force on the rotor is found by

integrating the B x J product over the rotor surface (B is magnetic flux

density, J is winding current density in total Amps per metre of

circumferences).

The designer tries to maximise values of B and J but is

constrained by cost (if high B magnetic materials, high temperature

• insulation used), heating levels (caused by high iron and copper

armature winding losses) and space (deep slots give high leakage

reactance slots and teeth must share the periphery). Hence, for most

machines of a given genus, B and J fall within fairly narrow and well

defined limits, though it must be mentioned that allowable J values 57. rise with pole pitch. Slot leakage varies as slot depth/pole pitch.

Hence, slots can be deepened as pole pitch increases, though heating

problems usually limit J to varying as the square root of pole pitch.

The torque on the shaft of the generator Qgen will be:

5$B . J . ds Qgen = (3.13)

= K.—.B J. "L Qgen a

9 TL.Dy . na . B . J (3.14) Qgen = K 2 where K allows for the B and J distribution, and:

D — generator rotor diameter,

L — generator rotor axial length. a

Generator shaft power PIN will be:

TL2D2 PIN K . E.. B . J . VJ (3.15)

where: W — generator shaft angular speed in rad.sec-1.

Output power from the generator will be:

(3.16) POUT = PIN ' 1lgen where: '1'1— efficiency of the generator. 58.

= 2 POUT .63 (3.17)

Ka '1 where: K.Z gen

If B and J are assumed constant, equation (3.17) can be

written:

POL, = K" . D2 . Ea . (3.18)

where: K" = Ko. . B . J

It can be seen that for a given machine POUT varies

directly with speed. Hence, a low speed implies a low power output.

Hence, with a direct drive from a windmill we must apparently either

make do with a derated machine which is rather large, expensive and

heavy for its power, or we must use gearing or some other speed increasing

transmission to raise generator speed. In fact there is another

possibility: to use a generator with a large DA ratio. If the active

parts of an alternator are considered to consist of stator and rotor

annulus rather than a stator annulus and a rotor solid cylinder, then

the volume Vactive (and hence, weight) of the active parts can be

expressed in the form:

(3.19) Vactive2Īt . 2 • 2t b. Ea

where: tb«D

tb — equal stator and rotor radial thickness.

Vactive Hence: D (3.20) a 2TG.tb 59- and:

POUT - K Vactive " D (3.21) where:

K"' = K",/2Trt h

This shows that it is possible to compensate for a low W by adopting a large D. The volume and weight of the machinefs active parts for a given can be kept to reasonably low figures. POUT Clearly, if it is desirable to rate a machine at a speed which is, say, 105 of "normal" (e.g. 300 rev.min l),.a D which is five times "normal must be considered if POU`N "active is to be left at its "normal" value.

Increasing D by 5:1 implies reducing ea by 5:1 if is to Vactive be left unchanged. Hence, the aspect ratio of the machine changes in the ratio 25:1, say, from a D/Pa of 0.5 to one of 12.5 (e.g. D goes from 0.5 to 2.5, /a goes from 1 to 0.2 units). Note that the volume

Vactive is that of just the active parts of the machine (iron, copper, magnets, etc.). The volume of the entire machine cannot be kept constant in the way that Vactive can, as D/P changes to match lower speeds. Clearly the total volume VT is related to D2. a rather than Dfa, so that total volume might increase from 0.52 x 1 (0.25 cubic units) to 2.52 x 0.2 (1.25 cubic units) to take the above example, i.e. the total volume, for D and raised to'keep and pa Vactive POUT constant is inversely proportional to operating speed W. Why are such aspect ratios not used to increase power/weight on standard speed machines? The reasons are probably: 6o.

1. Supply frequency. This is given by:

f - Hz (3.22) - 2TG . p where: p - number of pole pairs, and: La - (3.23) 211 - 60 where: n - generator shaft rotational speed, rev.min 1.

Hence if it is required to generate at 50 Hz and, say,

1500 rev.min 1, the machine must have four poles. If the number of poles is constant, pole pitch Y increases with D. A high Y is generally disadvantageous because it results in long end connections on the windings (therefore more bulky) and deep core iron sections to carry the large pole fluxes the long distances from one pole to the next. Hence standard speed, standard frequency machines generally possess low DAa.

2. Centrifugal forces are too high at standard speeds.

3. The machine shape is sometimes less convenient to manufacture and install. More structure (therefore extra weight) is needed to hold the large D stator and rotor; the total volume and centre height for the shaft is larger, etc. Small airgaps may cause difficulty.

On a low speed machine, however, (1) and (2) do not apply.

Item (3) does apply, and care must be taken to ensure that this is taken into account when comparing the low speed option with a geared, high speed option. 61.

The electrical design of large DAS machines differs little

from standard practice. In both cases there is a need to keep the

ratio of pole pitch/I below 2 to avoid undue end winding losses and

the pole pitch itself within the range 4 cm. to 15 cm. (for 1 to 10 kW

machines) to avoid excessive slot and field leakage, and overhang losses, respectively.

The mechanical design problems differ in that: (i) low rotational speed results in less effective fan cooling, (ii) the stator

and rotor stiffnesses are low and extra structural stiffening and alignment measures are needed.

On a horizontal—axis windmill, a very large D would cause excessive disturbance to the wind, though the desirable D values in practice do not seem to fall into this range. On a vertical—axis windmill; large D is of little consequence from the aerodynamic point of view, since the alternator is "sideways on" to the wind if located on the tower and out of the wind if at the base of the tower.

It is interesting to observe that pre—war wind power work in

Germany [3.24] examined the possibility of using so—called "ring generators" of extremely large DA. These possessed outside diameters of 18% to 73% of the windmill blade diameters and the rotor elements were fixed directly to the blades, which consisted of two counter— rotating systems. See also Noah windmill [3.25] . Although the thin annular shape of the generators kept wind disturbance down to reasonable levels, the idea was not taken up after initial tests, due presumably to construction difficulties. Table 3.3: Pros and cons of generators running at lover or rated speeds.

A - B C High speed alternator Purpose-built low-speed High-speed alternator operating at low speed alternator with step-up

1) Alternator is derated; 1) No derating; alternator 1) No derating; low hence, large heavy alternator weight/power probably heavier alternator weight/power. for a given power. than C, but considerably lighter than A; power/cost is reduced. 2) Can be standard machine; 2) Can be standard machine; losses, weight, maintenance extra losses, weight and 2) Usually special design; extra and cost of step-up must be cost; maintenance of losses and weight; maintenance considered. step-up avoided. of step-up avoided.

3) Low friction, windage losses. 3) Friction, windage and step- 3) Low friction, windage losses. up losses may affect 4) Neat mechanical layout; no efficiency, particularly at lubrication or belt breakage part-load. problems; cost, weight and bulk of step-up transmission avoided; no transmission losses; therefore higher kW p.a. 63.

What are the pros and cons when comparing low speed

derated generators with normal DA, purpose-built, low speed generators

with high DA, and high speed generators with step-up transmission? Some of the factors are shown in Table 3.3.

Options A or C are likely to be chosen when no specially

designed alternator is available. Option B is preferable, given the

availability of a specially designed alternator at a cost and weight which is either comparable with C or is within the range in which extra

alternator cost with respect to C is more than offset by better

efficiency, saving of step-up cost and weight, and lower maintenance requirements.

Of course, it is possible that some combination of A, B and

C is best for a particular system. A machine built for operation at

an intermediate speed (say 500 or 1000 rev.min-1) plus a low ratio step-up might represent an optimum solution.

3.3.2 Use of Special Electric Generators for Small-Scale Wind-Powered Systems

One of the principal aims of the project was to develop an

electrical generating system isolated from the 50 Hz mains, suitable for small (i.e. less than 10 kW) windmills. It was decided to

concentrate on a system in which the main electrical load would take the

form of electrical "storage heaters" which would be topped if necessary

by mains power (see also Chapter 2). Control of frequency was not

therefore required and voltage control only constrained by the need for maximum extraction of useful power from the wind. Although many 64. aspects of the system under development are rather different from alternative schemes involving battery—charging, main—synchronisation of high—power levels, the thinking behind many other aspects, particularly those stemming from the unusual nature of wind as a power source, are common to all wind schemes.

Although the "load end" is less critical to the success of a scheme than the wind rotor end, there has been a surprising lack of attention in the literature paid to the problems of designing suitable electric or hydraulic/electric systems0for electricity— generating wind—powered installations. The topic is covered only briefly by most of the classical texts on wind power and although a number of articles do exist [3.26] , few of them deal with any of the more recently developed options available to the system designer.

In Chapter 5 details are given of low speed wind—powered electric generators. Although hydraulic/electric systems have much to offer especially at medium power levels (10 to 50 kW), it was decided to concentrate on a purely electric scheme: a) because the cost per kW of components (particularly when

"peripheral" components are included) for a low power hydraulic

system was expected to be high and outweigh savings elsewhere; b) because the evolution of an optimum purely electric system was

a worthwhile objective in itself in order to allow valid

comparisons' to be made between electric and hydraulic/electric

systems employing the best of current technology.

Of course, some of the components developed for a purely electric system, particularly the alternator and the controller system, 65. could find applications in other wind systems since some design criteria are common.

There are probably two principal questions to ask when considering electrical generator options for a small wind—powered system: (a) what are the desirable criteria.on which different generators can be judged? (b) how far do commercially available generators meet these criteria?

Desirable characteristics of any generator include low cost per output, high efficiency, temperature rise on full load within allowable limits, etc. Many of these lead to conflicting design situations and compromises are usually necessary. Over the years, a large number of generator designs have been evolved, the emphasis (or bias) in each being fixed so as to meet the specific demands of each application, e.g. on a vehicle electric generator, low cost, high reliability, ability to withstand rugged environment, are most important whereas with a large turbo—alternator, high full—load efficiency and high power/weight are most important.

Some of the specific demands in the wind power case are unusual. They can perhaps be listed as:

1) Need for high efficiency over as wide a range of conditions as

possible.

2) Desirability of good performance at low shaft speed range.

3) Desirability of low starting torque of generator (low cogging

torque).

4) Need to withstand exposure to atmosphere. 66.

Items (3) and (4) are easier to cope with than (1) and (2).

Item (3) is absent from the wound field generators but it is essential

in the case of permanent magnet generators because of the constant

presence of the magnetic field in the rotor of the machine. Weather-

proofing is a standard feature of many commercially made electrical

motors and generators. To understand the difficulties associated with

(1) and (2), it is perhaps best to consider a number of basic features

common to almost all generators.

There are perhaps two points to consider with regard to

generator efficiency:

(a) Implications of the need to avoid low efficiencies at low

power levels:

Generator efficiency = output power/input power

Output power = input power - loss power

Generator efficiency = 1 - loss power/input power.

The losses in a machine can be divided into those which vary

with load current PA (these are mainly the copper losses in the

output winding), those which vary with speed PNL (mainly no-load

losses bearing windage and brush friction losses), and in a machine

with a field winding, those which vary with field current Pf (mainly

field copper losses and iron losses, the latter being dependent also

on speed). Hence:

(3.24) 7+gen = 1 - (PA PNL + Pf)./PIN

While PA reduces with power and PNL with speed, Pf will in general tend

to zero as wind power falls if If falls with wind power and speed. But 67. in the case when Pf is kept constant with power and speed, then the ratio loss.power/input power increases at low wind power levels, so reducing efficiency.

(b) Implications of the need to obtain high overall efficiency at rated power. Clearly this requires low levels of all losses.

While PNL turns out to be normally reasonably low in most machines,

PA as well as Pf can be appreciable at rated power, especially in small machines (i.e. less than 10 kW) and in low speed machines, since:

PA oC I2Rs (3.25)

POUT OC E.I OC k.n.I (3.26) therefore,

OC PA/POUT I/(k.n), and thirdly, in machines designed for minimum size and/or minimum cost:

Winding resistance/phase It OC 1/slot area therefore,

OC L/E.slot area. PA'OUT

Decreasing slot area helps to minimise copper weight and machine size and cost, but thus decreases efficiency.

The potential advantages of permanent magnet field excitation for alternators and d.c. machines, viz: zero field losses, absence of field connections (for alternator elinimation of slip rings and hence virtual absence of maintenance) has in the past been offset for all but very small machines by: 68.

1) High cost per performance of permanent magnet materials

compared with wound fields.

2) Difficulty of controlling the machine since magnet

control using an auxiliary winding is difficult and defeats the

original object.

In recent years, magnet cost per performance has progress- ively decreased and magnet performance itself progressively increased as better materials have been developed. Larger and larger motors with permanent magnet excitation are appearing on the market. These are mostly for applications: a) involving constant speed (i.e. no control needed); b) where control is effected by means of control circuitry in the

armature supply.

The latter option was forbidden in the past to all but high cost installations due to the requirement for the control circuitry to handle the bulk of the input power to the motor. The availability in recent years of power tbyristors and transistors, and their progressively-reducing cost per kW has now made armature control a popular one for most variable speed industrial and other drives (e.g. washing machine, fork lift truck, continental urban railway drives).

When d.c. generators and alternators are considered, constructions incorporating permanent magnet excitation and control circuitry in the output are less common, although examples can be found, e.g. motor cycle alternator, where a zener diode across the battery automatically diverts excess output when the battery is fully charged. 69.

The pros and cons of permanent magnet (P.M.) generator usage are indicated in Table 3.4 [3.233.

P, M, and Table 3.4: Comparison betweenAwound field alternators.

ADVANTAGES f DISADVANTAGES

Somewhat better efficiency. Smaller choice of already— manufactured machines. No brushes, etc; therefore almost no maintenance and Normally not possible to longer M.T.B.F. control field. Always 'builds up'. Control circuit, if required, normally has to handle output No field supply or control power. circuit required; therefore fewer slip rings and wires Armature winding faults rather on the tower (H.A.). more troublesome. No risk of 'loss of field'.

The opportunities for using "as—purchased" or modified versions of existing P.M. machines are given in Table 3.5. D.C., P.M. synchronous and induction motors can generally be run without modification as generators, but often the opportunity arises of using a machine at rated speed or voltage conditions which differ from those on the nameplate. See also [3.23]

Table 3.6 lists a selection of commercially available small windmill systems using P.M. alternators. Information from [3.6] and private communication. 70.

Table 3.5: Commercially produced P.M. machines usable as wind generators. Note: Data obtained from manufacturerst publicity material.

Typical data Type of P.M. machine Rated speed Efficiency` Rated power r.p.m. at full power A) D.C. motors Low voltage car or 10-60 W 2-4000 40-65 h~"d etrimmer motor (tow Yo~YRGF McTvdt s LTD) Servo motor 0-2 kW 0-4000 40-85 (/NLA0 tro,E. SHED LTD) Disc servo motor 0-2 kW 2-4000 40-65 ikOL NORGEN Co)lt e, Philips washing 75 W 800 60 machine motor

B) Alternators Exciter type (e.g. Newton-Derby, 0-12 kW 3000 80-95 Georator tNobrush') Motor cycle 180 W 6000 20-70 alternator (zv,/9S L*,D) Dynohub cycle 5-15 W 300 40? alternator

C) Machines rebuilt with ferrite P.M. motors

Car alternator 140 W 1500 50? (G 'cAs kiwi ) h.p. induction 2 1500 70? motor (N(CO «D) 76 W

Table 3.6: Commercially available systems using P.M. generators.

Rated P.M. generator Wind Rated wind Manufacturer rotor speed, m/s kW r.p.m.

Aerowatt H.A. up to 4.5 800? 7 Dunlite/Pye H.A. 2 750 11 Elektro H.A. up to 5 800? .20 Zephyr (U.S.) H.A. up to 15 300 _ 13.4 Trimble H.A. 5 90 10 A.W.T. (U.S.) H.A. up to 3 4500 11

71.

3.3.3 Control Systems for Wind—Powered Electric Generators for Maximum Extraction of Power from the Wind

From expressions (3.11) and (3.12) the extracted power from the wind rotor will be:

3 w = z /3T1.R 2.Cp. v3 (3.27)

Taking into account that at X , C = C. (see Fig. 3.1), the op P Pmax maximum extracted power from the wind will be:

P = 0-ER 2 C ,V 3 (3.28)

max max w

Therefore the maximum extracted power from the wind changes proportional to the cube of the wind speed.

From equation (3.7),

R V w A (3.29)

From expression (3.23) the wind rotor angular velocity can be expressed as:

2TC C~w = 60 nw = 3030w (3.30) where n is the windmill shaft rotational speed in rev,min w 1.

Substituting equation (3.30) into expression (3.29), it becomes:

w 30 ), nw (3.31)

If the windmill is running at the constant values of ?. op r and C at any winv}Ispeed Va, substituting expression (3.31) into Pmax 1 (3.28), it becomes: 72.

TT .4 1.7 Py = 1,P n 3 (3.32) max 30' k"op Pmax w

where:

TL R 5 k w zy 303 Ad Cpmax P

is a constant. Therefore:

Pw = k n 3 (3.33) max w w

Assuming that kg is the transmission ratio of the gearbox,

the generator shaft speed becomes:

n = k .n g w (3.34)

Substituting expression (3.34) into (3.33), it becomes:

P = kg n3 (3.35) wmax w where,

kg = k . w w k g (3.36)

Therefore the generator/control,lead combination should be designed so that the input power PIN to the generator changes in proportion to the cube of its shaft speed in order that maximum energy be extracted from the wind (if transmission losses are neglected for the moment):

3 IN = w = kwn . (3.37) max max

From Section 3.3.2 it is known that the input power to the generator shaft is, 73.

P PIN = NL PA Pf + POUT (3.38)

Therefore regulation and control on one or any combination

of the three parameters of expression (3.38), which depend on

generator shaft speed, can achieve the law given in expression (3.37),

i.e. the generator input power matches the windmill's maximum

characteristic at variable rotational speed.

A simplified equivalent circuit for an alternator or d.c. generator is shown in Fig. 3.5. See also [3.23J . A d.c. current

If in the "field" winding (or a permanent magnet) sets up a field flux pi. When relative motion exists between the armature conductors and the field flux, an e.m.f. is produced. For a given generator:

_ ..n E E (3.39) where E is the e.m.f. produced in the armature winding, kE is a design constant. If the armature is connected to some load circuit, the voltage V at the armature terminals will differ from E due to the voltage drop I.Z across the armature impedance. If the machine is a d.c. generator, Z is merely the total armature resistance Ra, and,

V = E — I.Ra (3.40)

For very small alternators (< 200 W) working at moderate frequencies, Z is predominantly resistive. An assumption,

Z = Ra (3.41) will be made for simplicity in what follows. If the generator is connected to a fixed load resistance R~ (Fig. 3.5 or Fig. 3.6a), the power delivered to the load (neglecting losses in the output controller, if any) is: 74.

r------i I I I I I Z I

Drive

Generator Load

Fig. 3.5: Simplified equivalent circuit of an electric generator.

(a) 3—phase resistive loading. (b) Battery loading.

Fig. 3.6: Loads of electric generators. 75.

v2 POL, = RE (3.42)

The armature current in terms of E is:

I Ra + Rt (3.43)

Therefore from expressions (3.40) and (3.43), expression (3.42) becomes:

R2 R o (1 (3.44) POUT = E - Ra + Ile)-

The load on the generator shaft, therefore on the wind rotor, is:

PIN = E2/(Ra + R, ) (3.45)

(neglecting iron, mechanical and field losses, if any). If the machine is operated with fixed flux %, as is normally the case with P.M. generators,

E = kn.n (3.46)

2 and both PL and P IN vary as n . At high speeds I must normally be limited, due to winding heating problems, to a limiting value Imax; then from expressions (3.43), (3.44) and (3.45) the PIN and POUT then vary linearly with n.

If the generator is connected (via a rectifier in the case of an alternator) to a battery load (Fig. 3.6b), the instantaneous output current will be:

Or i — d + Vb),%Ra (3.47) 76. where e is the instantaneous e.m.f. and Vd and Vb are the rectifier drop and battery voltage, respectively. Clearly if the peak value E of e is less than Vd+Vb, the rectifier remains blocked and i = 0. For a d.c. generator I is given by (for I >0):

I = CE — VbJ /a (3.48)

For a resistance—dominated alternator it can be shown that:

Vd °t i - ^Vb — OL ~ I ticos (2 2) (3.49) mean Ra where:

Otl = sin 1(Vd + Vb)/E (3.50) and:

C42 = Tt— Ocl (3.51)

The output power is:

OUT = Vb.Imean (3.52) and:

53) PIN = Imean(Vb + Imean.Ra) (3. neglecting also all other losses.

Curves showing the variation of input power to the generator for resistive and battery loads are shown in Fig. 3.7a superimposed on a typical family of windmill—output—power Pw curves. It can be seen that with a resistive load, the generator will prevent start—up at low wind speeds, will tend to cause early stalling for decreasing wind P, Watts P, Watts 2000----~----~----~----~----~--~----- .2·000r---.,.----r---~---.r------+----

Generator input Wind rotor power~-f_-+---I-~-fC----' power Wind rotor power -+----I--HI---I----I output output Generator 1500r-____T- ____+- ____~~--~--~~-;~np~u-tPower, 1500~--~~---+-----*----~~--~----+---~

1000~--~-----r--~~-r--+---~~~~----~ 1000r---~-----+----~~~--~~--~--~

Battery load Batterr load

I Rl load -1--~~~~--_+~~~~--~ RL load

-.J -.J. 14 15 msec-1 ~ 15 msec-1 o 380 570 760 950 1140 1330 o 380 570 760 950 1140 WIND ROTOR SPEED,nw,rev min-1 WIND ROTOR SPEED, nw,rev min-' Power versus speed curves for alternator and Fig. 3.7b: Power versus speed curves for alternator and windmill with narrow C curve. .. 1 . p windmill with wide Cp curve.

78.

speeds and that the windmill will tend to operate beyond its C Amax point at high wind speeds. Since the generator's power capability only

increases as n-9 at best, it is incapable of absorbing the converted

wind power (proportional to C.n3) at high wind speeds. The starting

situation is improved with battery loads but operation near C still Amax occurs over a narrow range of wind speeds only.

Fig. 3.7b shows the situation when the C versus

characteristic of the windmill is very peaky. Clearly stalling can

take place even after sudden increases in wind speed to levels which

could give satisfactory steady state operation.

One could opt to make do with this state of affairs and

accept the reduced energy yield that would result; with battery loads

the reduction might be fairly small. However, in most cases,

particularly with resistance loads, it is worth improving things by

adding some form of control.

At high wind speeds there are only three options for control

of the extracted power from the wind:

(i) use a large generator so that the maximum power capability of the

windmill at the maximum relevant wind speed lies within that of

the generator.

(ii)allow the operation beyond the C point even for the maximum Amax wind speed.

(iii)use aerodynamic means to reduce the converted wind power Pw.

Option (i) may be costly and may lower energy yield due to

increased mechanical losses. Option (ii) can be satisfactory with 79. sub 100 W and other small systems where blade stresses, even on run- away with high winds, are within reasonable limits, and can be adopted on larger systems where shut—down by orientation out of the wind or the use of mechanical shaft brakes is possible. Option (iii) is frequently adopted and a number of ways of minimising the added complexity and cost have been found.

At low wind speeds, the task is generally to reduce generator output, (a) to aid starting, and (b) to match the n3 ideal windmill characteristic. A number of methods is shown in Fig. 3.8:

Field current control. If the field flux is varied as:

= (3.54)

n3%2 output volts and current into a fixed resistance load vary as and power as n3. The method can also be applied to battery charging systems. The method is, of course; normally confined to wound—field machines (see also Chapters 4 and 7). b) Load control. If the load resistance Re is varied as:

K1 R Ra t n - (3.55) i.e. Ri reducing as n increases, then POu, and PIN again vary as n3. This method is often implemented by sectionalising the load and switching sections in and out using contactors to give a stepped— approximation to the required 111 versus n characteristic. c) Regulator circuit in the output. D.c. to d.c. chopper circuits for d.c. systems and tbyristor regulators for a.c. systems are now widely used for power control in industry. They can also be 80.

used for small generator control, particularly when field control is

difficult. Costs and losses need not be high. The chief difficulty

at present is that suitable circuits are not available off—the—shelf.

The a.c. regulators fall into two groups:

(i) a.c. to a.c. phase—angle—controlled regulators,

(ii)a.c. to d.c.—controlled rectifiers.

Their detailed behaviour is complex, but in both, the

thyristor switching elements control the level of power throughout by

their ability to behave as open circuits until triggered by a pulse from an external source. The delay period DC/2Ttf between the start

of each period of normal conduction and the instant of triggering controls the mean throughput power. In the case of a three—phase controlled bridge rectifier (Fig. 3.8c(ii)), the throughout power POUT with a resistance load varies very approximately as:

Ot POUT = POUT(' — TL) (3.56) where (Xis the delay angle (or firing angle) and P is the throughput OUT power when OC is zero and the bridge behaves as a diode rectifier.

Hence if:

57) PŌUT = k2n3 (3. is required, and

2 POUT = k3 n (3.58) then OC must he controlled as

a = 7T(1 - II ) (3.59) r

81.

4= 1 r Ī-1

1 ~ iv Field i Load I Li control 1 (a) field control I— L------.1 I D.C. Generator or L • Alternator

RI r r--- —1 r i l s t li 1 1 1 I t i 1 I

Pi o T I I. T 1 L L--- ~i----- ~------~ (b) load control

(c)(i) output regulator (a.c.)

L _,. NNW -- L J --- -

(c)(ii) output regulator (controlled rectifier)

r -t I I I I I 1 ~able 44— Load (e) reactance control

L ____ _ L___ _I

r r------, (g) reactance control using shunt 00111711 inductors. L — I t I i 1 I L----- Fig. 3.8: Methods of control of electric generators for wind power application. 4 4 4 a=Q p p p p.u p.u. p.u.

3 3 3 _. ___ P=kn3

2~------+------+4-4~~~ 2r------+------~~--~-1 2~------r------+#------~

1~------+---~~~--~-~~ 1r------+---~~~------~

°0 1/ ' 2 3 °0 2 3 1 2 3 n p.U. np.u. n p.U. a) Field control. b) Load resistance or battery c) Thyristor output regulator with voltage control. fixed IO,ad. CD Fig. 3.9: Typical alternator power versus speed curves for different modes of control. •to 83.

where nr is the generator shaft speed at rated power. The thyristors

are "phased back" for n < nr. Test results on a generator system using

such a regulator are included later.

d) On/off or "high/low" switching. Torque per inertia ratios in

wind plants are usually low enough to allow the use of two state load

or field current switching systems using contactors, relays or

thyristors. The mark:space ratio is varied to vary the mean power. The

high/low method is used in the field circuits of most car d.c.

generator systems. Method (c) can to some extent be regarded as a

speeded—up version of bang—bang or on/off methods.

e) Other methods. For the sake of completeness, a number of other

methods should be mentioned. They involve the use of, (i) fixed or

controllable reactances placed in the output circuit, (ii) flux

bucking and boosting windings on a P.M. machine's field poles, fed via

slip rings, (iii) toroidal bias coils wound around the core of a P.M.

alternator's stator fed with d.c. and used to saturate the stator core.

Fig. 3.8g shows a typical circuit of the e(i) type. At low speeds and

frequencies the shunt acts as a short circuit and reduces output

power. Fig. 3.9 shows output characteristics for field—controlled, load—resistance controlled and control rectifier systems.

3.4 CAPACITOR EXCITED INDUCTION GENERATOR

An interesting system for small scale wind power applications is the capacitor—excited induction generator. Induction motors of all sizes and powers are readily available on the market (see Appendix III-1).

They are cheap; robust; reliable and bandy. However, care is needed 84. with their application for wind power because the required excitation control circuit might dominate the overall cost and reliability of the system..

Basett and Potter [3.27 in their paper in 1935 showed that the indiction machine can be operated as an independent or isolated generator at a predetermined voltage and frequency, with excellent waveform, by means of capacitive excitation.

Here are some of the conclusions which were arrived at in this paper:

1. The induction machine with capacitive excitation will

build up its voltage exactly as does a d.c. self—excited shunt

generator, the final build—up value being determined by the

saturation curve of the machine and by the value of reactance of

the excitation capacitance.

2. Wave shape of the induction generator with capacitive

excitation is sinusoidal.

3. Frequency of the output is directly proportional to the

rotor speed minus the slip speed.

4. Machine constants can be compensated for quite well by

means of series capacitance in the lines, resulting in a fairly

flat external characteristic under unity power factor load

conditions.

5. The induction generator can be made to handle almost any

type of load, provided that the loads are compensated to present

unity power factor characteristics to the generator. 85.

6. Use of the induction generator with capacitive excitation

may be made in installations of small capacity where single or

three-phase power is required, and where the cost of a synchronous

generator and auxiliaries is prohibitive.

7. Small series capacitive reactances required for

"compounding" can be obtained by means of series transformers with

the capacitors connected to the high voltage sides of these trans-

formers.

A later paper by Wagner [.3.28]. gives the theoretical perform-

ance verified with experimental results of a self-excited induction

generator by capacitors connected across its terminals under different

load conditions.

A paper by Glazenap [3.29] analyses a three-phase self-excited

induction generation through capacitors and working with an unbalanced

load, even with single or two-phase loads. The analysis and experimental

results have shown that the problem can be readily solved if small

capacity machines are used (3 kW).

Barkle and Ferguson in their paper [3.30] analyse the self-

excited induction generator with capacitors connected to the mains

system, presumably the mains supply was not able to supply the required

VARs to the generator.

An interesting paper by Rechberger [3.31] describes the use

of capacitor-excited induction generators to small hydro-electric plants.

Eastbam in his paper [3.32] gives a generalized theory of induction generator where also the variable pole-pitch control system is mentioned. 86.

Hadley in his article [3.33] gives the experimental results

of a three—phase capacitor induction generator connected to a three—

phase resistive load at various rotational speeds. In the article it

is shown that a three—phase machine connected in "delta", excited by

a single shunt capacitor in a compound connection and feeding a

single—phase resistive load, gave the best results.

In the paper by Bokhyan [3.343a special L,C shunt is

described for the voltage stabilisation of a self—excited induction

generator.

Panda and Ray [3.35] show an analysis of the induction generator

performance verified with experimental results. It is shown how the

open circuit characteristics of the induction machine can be determined

by: (a) using static capacitors, (b) parallel connection of the machine

to the mains, and (c) exciting the machine with the help of a

synchronous condenser.

Sipaylov et al in their paper [3.36] came to the conclusions that:

(1) Capacitor excitation of three—phase induction generators

is possible for squirrel cage motors having a wide range of

winding parameters.

(2) To minimise capacitor values, machines should be selected

where possible possessing low per unit magnetizing current and low

leakage reactance.

(3) If an unbalanced capacitor arrangement is used, decrease

or increase of capacitance around certain critical values results

in reductions in the zone of self—excitation. 87.

In their paper, Cbizhenko et al [3.37] give a theoretical analysis of a compound connected three—phase induction generator supplying a resistive load through a rectifier bridge. In their analysis they use the circle diagram of the induction machine. Experimental results are not included in the analysis.

Recent papers also look to the connection of induction generators to rectifiers, as in the paper by Novotny et al [3.38] .

There the authors analyse the inverter—machine mode system which functions as a stable self—excited induction generator capable of supplying d.c. or a.c. power to a resistive load following the removal of the d.c. supply to a voltage—source—inverter initially driving the induction machine. Experimental results confirm the validity of the analysis and illustrate the behaviour of the self—excited systems.

The paper by Arrillaga and Watson [3.39] shows a similar system to the previous paper where theoretical and experimental results are provided showing that the self—excited induction generator can operate in the linear region of the magnetization curve while feeding a variable d.c. load at constant voltage through a controlled—rectifier unit.

During the last two years some papers have been published on the application of the self—excited induction generators to small wind power systems.

One of the first papers was by Mohan and Riaz [3.40] . They suggest a scheme using a wind—driven, capacitor—excited induction generator running at variable speed and supplying beating loads for residential electric beating. It is suggested that the power output can be controlled over a substantial range of speeds to match the windmill speed—power characteristic, by adjusting the excitation—capacitance 88.

In their paper Debontridder et al [3.41] are analysing a system consisting of a mains-connected induction generator driven by a windmill of the vertical-axis type.

Ooi and David in their paper [3.42J give another interesting scheme where the induction generator driven by a windmill takes its

VARs from a synchronous-condenser and feeds a load with constant voltage and frequency. A slip-ring induction generator is investigated, its voltage being regulated by the synchronous condenser and its frequency by a Scherbius drive circuit. Slip-energy recovery is also mentioned with preliminary test results. For slip-energy recovery see also [3.18 .

3.4.1 Wind-Powered Induction Generator for Maximum Extraction of Wind Power with Variable Capacitor Excitation

As is mentioned in [3.40] , the electric power output of an induction generator can be controlled over a substantial range of speed to match the windmill speed-power characteristic.

In this section a brief experimental programme of work carried out on capacitor-excited induction generators by the author is described.

A 7.5 kW at 720 rev.min l (750 rev.min 1 synchronous 50 Hz) three-phase squirrel-cage induction motor was used. The machine was rated at 415 V and line current 16.8 A, with the winding of the machine connected in delta. 89.

Fig. 3.10 shows the test rig used to test the machine. The d.c. motor (1) with a maximum power of 7.5 kW at 1500 rev.min 1 drives the induction machine (2), through a step—down 2:1 belt transmission (3).

For safety reasons a safety cage (4) was fixed round the transmission system. Because the induction machine could not be dynamometer mounted on gimballs, the d.c. drive motor was fixed in this way and a spring balance (5) was used to measure the output torque to the induction machine. The losses on the transmission were very small and therefore neglected. A tachogenerator (6) driven by a pulley and belt system (7). from the induction machine shaft measured the rotational speed. The machines were assembled on a metal platform.

Initially the magnetic characteristic of the induction machine was obtained using the methods described in [3.35] . The reason for obtaining the magnetic characteristic of the machine was to determine the maximum and minimum capacitance values for the build—up of the machine at nominal rotational speed. Precautions were taken to ensure that the voltage did not build up to a value exceeding the rated voltage of the capacitors (415 V), e.g. for rated speed (750 r.p.m.)and frequency

(50 Hz) the capacitance per phase had to exceed 40 t,LF.

Fig. 3.11 shows the power diagram of the variable capacitance self—excited induction generator connected to a constant resistive load.

It was decided to run the machine under conditions of variable variable speed but constant load resistance and to vary the capacitance so as to keep the input power to the generator following a cubic law with respect to speed (from expression P kg .n3. To (3.37)): IN w max achieve this, the following procedure was used: 90.

Fig. 3.10: 'Test rig of the induction generator.

I~ V POUT .A.C. TEST SET

RESISTIVE LOAD INDUCTION MACHINE Imach MAIN SWITCH Ri A

CAPACITOR id THREE-PHASE SWITCH f PLUG BOARD Fig. 3.11: Power diagram of the capacitor— excited induction BANK OF generator. CAPACITORS 91.

a) The machine was run at its full rotational speed of 750 rev.min 1; b) The bank of capacitors was adjusted so that the line voltage

built up to the maximum value of 415 V; c) The resistive load was switched on and adjusted in parallel with

the capacitors to give the maximum allowable current in the machine,-

Imach (15 A) . The values were Re = 100n, and C = 6011F; d) The input torque of the machine was measured and the parameter K g calculated as 0.985 x 10-5; e) The capacitance was adjusted at each of a number of lower speeds

to give an appropriate level of input power. Rt was kept fixed.

Fig. 3.12 shows the theoretical curve (ideal cubic) and experimental values of input power and efficiency versus rotational speed.

The correlation between them is reasonably good and it is apparent that the induction generator operated in this way can provide output power over a fairly wide range of speeds (750 rev.min 1 to 200 rev.min 1).

The capacitance varied from 60 p,F to 480 p.F per phase. Although the machine was run only at a number of discrete speeds (750, 700, 600,

500, 400, 300 and 200 rev.min 1) and capacitance values (60, 80, 100,

140, 220 and 480 LF) the change of powers was quite smooth. This suggested that with a windmill system having a bank of capacitors and typically six three—phase contactors, a reasonably good cubic—loading characteristic for the windmill can be achieved. The measured efficiency of the system as shown in Fig. 3.12 never exceeds 75%. It is important to mention that the cost of the capacitor is proportional to its rated voltage and capacity. For this type of scheme, high capacitance per phase is required only when voltages are low (4801,LF, 92. p C Watts 11 ~F

5000 1·0; 500----r----,------r----....., I Rl =100Q Input power Efficiency • Theoretical 0 o Experimental Output power •X Capacitance l:::.

4000 o·a; 400 ----+-I----i!----+----+-----+-----+-I------I

3000 0·6i300~---~~-~----+----~---~--~~~~~

2000 O·4;200-----~---~----~----+---~~-4~~--~

1000 0'2; 100 ---+---~-___+__I__Ptt.~----+---+--~

o~----~--~~----~----~------~----~----~------o 200 400 600 800 SHAFT SPEED, n, rev min-1 Fig. 3.12: Performapce of the self-excited variable-capacity induction generator _ working on a cubic loading characteristic of a windmill. 93.

50 V) and vice versa (601.1F, 415 V). Even so, the cost of the capacitors and contractors may exceed that of the generator itself. The pros and cons of having fewer stages or a smaller total capacitance value would be worth assessing. It could be that just a single-stage unswitched could be justified where a restricted operating speed range and reduced energy yield was acceptable.

Another factor which might be important is the generated power size of the machine, which proved to be very low for this particular induction machine.

The machine possessed a relatively large magnetizing current

(large number of poles, 8 poles) and the reactive component in the total stator current was hence fairly large. Hence the output power was less than rated when full goad current was circulating in the stator. The machine was rated at 7.5 kW, ?50 rev.min 1

but at the resistive load the maximum output power achieved was only 3 kW,

750 rev.min-1 (a reduction of 60%). Overloads would of course be possible for short periods.

It may be noted that lower minimum speeds than the one tested (2/7.5 of rated speed) are possible but very large capacitance values are required which would probably not be economically viable in view of the low wind power levels involved.

The maximum measured efficiency value of this particular induction machine (75o)is not representative of the corresponding figure for machines with lower magnetizing currents (e.g. lower pole 94.

number, higher speed machines). In particular, a two— or four—pole

machine may often have a relatively low magnetizing current and

therefore the reactive component in the total stator current will be

small and hence a smaller efficiency drop and little derating) will

occur in the generator as opposed to the motoring mode. On the other

hand, larger ratio gearing perhaps with larger transmission losses

will be needed.

3.5 CONCLUDING REMARKS

In this chapter some different wind—powered systems have

been described and the tremendous variety in the choice of generator types and systems for small wind plants has been indicated.

The induction generator scheme with capacitor excitation for wind power applications allows the use of easily—available, low cost and robust induction machines (see [3.441 ), but introduces problems of build—up and loss of excitation, capacitor and contactor cost. CHAPTER 4 95.

SMALL WIND-POWERED WOUND-FIELD GENERATORS

4.1 INTRODUCTION

Wound-field a.c. or d.c. generators can be used for a big power range of wind-powered generating systems. Wound-field alternators synchronised to the grid can be used for large scale wind plants, as was mentioned in Chapter 3, but smaller wound-field alternators feeding isolated loads, or synchronised to the mains are an attractive alternative to induction, d.c. or permanent magnet a.c. generators in small wind plants. The main advantages of wound-field alternators are:

1. voltage regulation is easy, since the control quantity - the field current - involves only a low power d.c. regulator and output voltage may generally be varied over a wide range without complication (cf. induction generator, where this is not possible); 2. the large market for "stand-by" and portable generators means that availability, breadth of choice, efficiency and cost factors are favourable over a large rated power range.

An interesting report of recent work involving a wound-field alternator and a Darrieus windmill is given in reference C4.8] .

The principal disadvantages for small systems stem from the presence of a second winding in the machine, slip-rings and brushgear, field supply wires (and often slip-rings) on the tower, and the need for a field regulator. Reliability may be reduced and costs and losses increased (see ref. [3.23] and later in this chapter).

There is a large range of wound field generators available commercially at each power level and the selection for a particular 95a. wind power application is not very easy unless some selection basis

can be formulated. The several generating control schemes given in

Section 3.3.3 indicate the multiplicity of choice in this matter.

It is understood that the larger the machine, the higher its

efficiency. Therefore for small generating systems the selection of a wound field machine should be justified by other reasons than high

efficiency value. These, for instance, can be:

a) simple control system,

b) very low cost,

c) ease of operation.

The types of and design biases given to wound field machines vary a great deal, not least in the matter of efficiency. Ref. [3.23]

examines the general question of field losses and their effect on efficiency under varying wind conditions.

In this project, study was made of two lorry alternators and a single 5 kVA, 6—pole salient pole laboratory alternator. The contrast between the latter machine's performance and those of the lorry alternators demonstrated the large range in efficiency found in machines of the wound field type, the full—load, rated speed measured efficiencies being 90 and 68% respectively. The robustness and easy availability of vehicle alternators has encouraged their use for small wind plants, in spite of their efficiency figures, and the remainder of this chapter is confined to the study of a programme of work on the two alternators of this type mentioned above.

Work on the lorry alternators was encouraged by the need to be able to test the recently—completed windmill rig (Figure 4.21) in 95b

advance of a somewhat delayed delivery of the Mark II P.M. alternator

from the workshop.

It is important to bear in mind, when comparisons with other

generator types are being made, that the efficiency levels evident are

below those which could be achieved by other alternators (say those

designed for use in stand-by generating sets), and the reader is

referred to Tables 3.1 and 3.2 (for extremely summarized typical data)

and to page 393 (for a general conclusion).

Field-control aspects of the usage of wound-field alternator

(both of the conventional and the brushless types) in small wind

plants could form an interesting future project. A number of

commercially available electricity-generating windmills (e.g.

Electro, P.I. Specialist Engineers) are thought to employ field

switching regulators of the 'vehicle type' and reference [4.8J looks

briefly at this type of control. Control-aspects of wound field

machines were only briefly dealt with due to time pressures in the

present project, except for the self-matching schemes described in

Section 4.5.

The lorry alternators were of the high speed (1000 to 5000

rev.min 1), wound-field type with an "interdigitated" rotor construction

and an important part of the work concerned the effect on performance of

_operation at lower speeds. Before commencing the testing programme, the

armature was rewound to produce a no-load phase voltage of 100 V at the

new nominal speed of 1500 rev.min 1. Details of the rewinding process

are given later.

The tests fell into three groups: (a) measurement of standard

characteristics; (b) measurement of characteristics with the alternator 95c output connected to resistive loads through diode and thyristor

bridges; and (c) measurement of power, etc. versus speed characteristics with a constant resistive load and an unregulated shunt field connection.

Each group of results relates of course to operation with a particular system design. The first group relates to a system in which field control is used to match windmill and load characteristics and in which the load takes the form of a three—phase a.c. resistive circuit.

The second group with diode bridge rectification relates again to a field—controlled system, but one in which a d.c. output is required.

The third group of tests was carried out with a thyristor bridge.

The final group of tests relates to a completely self—controlled system. It is thought that such a system was worth examining because it is possible by suitable design of the magnetic circuit of a shunt— connected generator (d.c. type or alternator with shunt field supplied via diodes or from a rectified output) to achieve a roughly cubic power versus speed characteristic, even when the load resistance remains constant. This could of course match the characteristic of a windmill running under constant tip speed ratio conditions (see Chapter 3).

See also 4.13 .

Constant voltage (battery) loads were not looked at, though some aspects of the performance of a battery charging system could be deduced from the results presented here.

In the first half of this chapter the author quotes freely from E4.10] , on which the author of this thesis was a co—author.

Because of lack of time no attempt was made to give a theoretical analysis of the generator—rectifier, diode or thyristor system. 96.

4.2 REWINDING THE ARMATURE OF THE LORRY ALTERNATOR

Originally, the machine was wound to produce 60 A on a 24 V

vehicle system. For tests during a previous undergraduate project 04.2 the machine was rewound to give a phase voltage of 121 V at 3000 rev.min 1. Unfortunately, this winding did not occupy the whole

slot area and this resulted in a high armature resistance (thin wire)

and hence high temperature rises in the winding. It was therefore

decided to rewind the machine again. The new armature winding was

designed to give an open circuit voltage of 100 V with a field current

of 1.25 A and a rotational speed of 1500 rev.minn 1. 97.

Note that the principal relationship enabling one to calculate the number of turns per coil Tc to give a new open circuit voltage E2 2 at a speed n2 and field current If , knowing the previous number of 2 turns/coil Tc to give an original open circuit voltage El at nl 1 and If, is:

f E Tc 2 n2 I E2 = 1 (4.1) Tc a n ' fĪ 1 1 assuming magnetic linearity. Also armature resistance losses equal

I2R and current density

_ J a (4. 2) where a is the cross-sectional area of each conductor; and I is the phase current.

4.2.1 Details of the Machine

a) Stator

The stator is made of laminated steel with 36 unskewed semi- closed slots. The axial stack length is 0.05 m. The winding is a

"mesh" type with Lewkanex-coated wire, able to withstand 160°C temperature rise. It is a three-phase winding with 12 poles and one slot per pole per phase. The number of turns per coil is 38, the diameter of each conductor is 0.61 mm, and two are connected in parallel.(effective diameter '0.61 mm). The winding is star-connected. 98- b) Rotor

The rotor has an interdigitated or claw pole or Lyndell-type construction. It has 12 poles and the maximum continuous field current is about 3 A. The average resistance of the winding measured via the slip rings was about 20 Q.

The slip ring assembly of the machine consists of two brass rings and two carbon brushes. The field can be supplied either in shunt via a field regulator or by an independent external d.c. source.

In this case, the d.c. supply in the laboratory was used with a separately excited circuit.

4.2.2 Test Rig

As shown in Fig. 4.1, the alternator (1) was driven directly through a flexible coupling (2) by a d.c. drive motor (3) which simulated the windmill. The alternator was dynamometer mounted on gimballs (4) so that the alternator input torque could be measured by means of a load-cell (5) on the stator case. The load-cell was attached to an arm of 0.3 m length (from the centre of the alternator).

The load cell was calibrated and it was found that its sensitivity with a 20 V supply was 8 mV per kg.

An a.c. tachogenerator (6) was attached to the shaft end of the d.c. motor and this developed 1 V per 100 rev.min-l. The whole rig was assembled on a steel platform (7). FIELD TERMINALS 3-PHASE TERMINALS

-OA -0 g -0C

Fig.~4.1: •Test rig of the lorry alternator. 100.

4.3 TESTS ON THE LORRY ALTERNATOR

These can be listed as following:

a) no—load voltage (generated e.m.f.) Ef at fixed speed versus

field currents;

b) iron, windage and friction losses at fixed speed versus field

current;

c) armature winding temperature rise versus time for fixed armature

current;

d) load characteristic with an a.c. resistive load at fixed voltage

and speed;

e) load characteristic at constant field current and rotational speed

for a d.c. resistive load fed via a diode bridge;

f) load characteristic versus rotational'speed for different load

resistance fed via a thyristor bridge at constant field current

and different firing angles;

g) load characteristics versus rotational speed at different load

resistances and field currents, for an a.c. resistive load;

h) load characteristics versus speed at different load resistances

and field currents for a d.c. load fed via a diode bridge;

i) load characteristic with self—excited, shunt connected field.

The main power circuit diagram of the alternator is shown in Fig. 4.2a. LORRY ALTERNATOR THREE PHASE RHEOSTATS R PLUG BOARD

FIELD EXC IT. t~ I MAI N LOAD SWITCH SWITCH A.C. TEST SET OSCILLOSCOPE RESISTIVE LOAD

+200V - D.C. SUPPLY 0

Fig. 4.2b: Diode bridge.

1.0552

0 Fig. 4.2a: Main power circuit diagram. • 102.

This range of tests enables assessments to be made of the

performance of the Wind Energy Conversion System (WECS) for a large

number of electrical system configurations and operating modes.

4.4 RESULTS AND COMMENTS

This section gives details of the ways in which the tests

were carried out, together with results and comments.

4.4.1 No—load Voltage (e.m.f.) Ef versus field current at constant rotational speed. (Magnetization curve.)

The results of the tests are shown in Fig. 4.3. It must be

noted that the machine starts to saturate a.t If = 1 A and that at the

1500 rev.min1 test speed, the rewound machine can generate up to

130 V on no—load. The e.m.f. would of course change in proportion to the speed.

4.4.2 Iron Windage and Friction Losses (No—load Losses) versus Field Current at 1500 rev.min-1

The no—load loss was measured during the previous test by monitoring the input reaction torque on the alternator stator. Hence:

2TC 81 . F . L . n PIN = 60 • 9. (4.3) where: PIN is the input power in W, FIN is the force in kg, Lar is the length of the arm in m, and n is the shaft rotational speed in rev.min—1 . Et PNL Ef • n* Watts Volts ' Volts/rev min-1 X PNL No-load losses 280- 140; 0.093 Et No-load e. m.f.

240-120;0.08

200.100; 0.067

160-80; 0.053

120- 60; 0.04

80-40; 0.027

40-20;0.013

1 2 3 4 FIELD CURRENT, If Amperes 104.

When the field current is increased, the friction and

windage losses of course remain constant but the iron losses increase.

Fig. 4.3 shows that at If = 0 the friction and windage losses

are about 20 W (iron losses approximately zero when If = 0). The no—load losses at 1500 rev.min-1 reach constant 290 W for If > 3.25 A.

From this it is concluded that the iron losses are quite large even when the machine is working at its nominal field current of 1.8 A (about 200 W) and this is an important factor affecting the on—load efficiency of the machine.

4.4.3 Armature Winding Temperature Rise

For the temperature rise tests a Kelvin bridge ohmmeter was used to measure the average resistance of one phase of the winding.

Measurements were made at five minute intervals, the entire rig temporarily being brought to standstill (for 30 sec.) for each measurement.

The following formula was used to calculate the temperature rise:

At° = t° — 20° _ (R /R — 1).1 (4.4) st s20 4°C'c where: Rs and Rs are initial (Rs = 1.2S2) and subsequent winding 20 t 20 resistances, respectively, and 04c is the temperature resistance -1 coefficient for copper (CCc = 0.004° C ). At °C I •I=6A 140 •

• 120 •

100 •

80 X t --X- I = 2.5 A X~~X~'

60 • vx,e/elsr.-----..4(4-----"--1.)(

40

20 X

0 n 10 on q0 - an qn An 70 BO 90 1( TIME, minutes Fig. 4.4: Temperature rise curves of the armature winding of the alternator at 1500 rev.min—l. 106.

Two temperature rise curves of the winding are shown in

Fig. 4.4 for two different load characteristics, 2.5 A and 6 A. The

machine was tested without any forced cooling. Clearly at 6 A the

temperature rise would lead to rapid degradation of the insulation.

For the insulation used in this machine the temperature rise should

be within 100°C at maximum power and normal working conditions.

Therefore it can be concluded that the machine can work for

long periods with a load current of about 3.5 A without damaging the

insulation. From Fig. 4.5 it can be seen that this current corresponds

at 1500 rev.min-1 to a load of 1.1 kW when the machine is connected to

an a.c. resistive load.

4.4.4 Constant Speed Load Characteristics of the Machine connected to a.c. and d.c. Resistive Loads at 1500 rev.min-1

The machine was connected to the main power circuit as shown in Fig. 4.2a and the field current was adjusted throughout the test to maintain the phase voltage constant at about 100 V. The load current was varied by adjusting the load resistors, and care was taken to ensure that symmetry was maintained between phases. (This was also checked by checking that the current in the neutral, see Fig. 4.2a, was roughly zero.)

Fig. 4.5 shows the field and output currents versus output power at the speed of 1500 rev.min-1 and phase voltage of 100 V.

The overall generator efficiency of the machine is also shown there, where, from expression (3.26), If 11 Iac Amps Amps x

3.0 0.6

X

5 0

2.O 0.4 _4 % s / _t kPac~

-3 / 0,

‘2a~,c'' 1.0 0.2. 2 I s

11 s i I 0 0 300 600 900 1200 1500 Watts Fig. 4.5: Output power and efficiency curves of the alternator connected to an a.c. resistive load. 108.

(4. igen = POUT'(P IN+Pf) 5) where: is the outout power measured on the wattmeter, multiplied POUT by three (for three phases), P is the input mechanical power which IN is obtained from the load cell reading and equation (4.3), Pf is the field losses given by:

2 Pf If Rf (4.6)

Taking the rated power of the machine as 1.1 kW, it is found that the efficiency at 1500 rev.min 1, 100 V phase voltage, is about 65%, which is not a very encouraging figure.

Figs. 4.6a—c show the waveforms of the phase and line voltages for no—load and on—load conditions. There is considerable distortion due, it is thought, mainly to the non—sinusoidal field distribution and to the unskewed stator slots.

For the d.c. load test the machine was connected to the resistive load through a three—phase diode bridge shown in Fig. 4.2b.

Fig. 4.7 shows the output current versus the d.c. voltage and also versus output power of the machine at a constant speed of

1500 rev.min1 and a constant field current of 1.8 A. The efficiency characteristic of the system is also shown.

It is noticed that the efficiency of the system is generally a little lower than when the machine is working with an a.c. resistive load. 109.

Fia. 4.6a: No-load phase and line voltage waveforms.

Fig. 4.6b: On-load phase and line voltage waveforms, I = 1A.

Fig. 4.6c: On-load phase and line voltage waveforms, I = 5A. 110. N

cn 15 u

co cr N O Ō Ō

Fig. 4.7: D.C. output power, voltage and efficiency curves of the alternator connected to a d.c. resistive load. 4.4.5 Load Characteristics of the Machine Connected to a d.c. Load through a Three—Phase, Half—Controlled Rectifier Bridge

The purpose of conducting tests with this arrangement, in which field current is maintained constant and the load power varied by means of phase—angle control of a "line" commutated thyristor/ diode bridge between the alternator and the load, is to simulate the corresponding P.M. alternator system. Actually the two systems are not completely analogous because the permanent magnet field system does not act quite as a constant m.m.f. source, but the correspondence is reasonably. close.

Measurements were taken as speed was varied with If, firing angle & and RA being kept constant.

The test was then repeated for different firing angles and load resistor values.

The approximate OCvalues used were: 00, 400, 600, 950, 1050 and the RQ values were 40S/, 60SI and 95SZ.

Figs. 4.8a to 4.9c show the efficiency and power character- istics of the alternator versus rotational speed.

Figs. 4.8 show the overall efficiency curves of the alternator taken using expression (4.5).

Figs. 4.9 show the same set of output power versus speed curves as in Figs. 4.8, but a new set of efficiency curves calculated using the relation:

(4.7) Tt gen = POUT'P IN

(b) • iPPe Watts (a) F1rIng angle o a • O' A 0 •40' • I • • i 0 • 0.6 oa .60. • x a • 95• i •

• a .105• 1000

04 x G4 x • x i

-600 -600- i 1, -~------

0.2 02 ' i I

.200 _ t '

1 1200 1600 1200 1600 ` 0 400 eoo 400 400 600 SHAFT SPEED. n, rev m n' SHAFT SPEED, n, rev min-' • Fig. 4.8: Output power and efficiency curves of the alternator connected to a d.c. resistive load. (a) Re = 40 , (b) RQ = 60 , (c) R€ = 95 4

(a) (b) (c) • P 1Natts Firing in;!.

O M.. 0* A . 40* 08 O a . 60' X a.95' .l000 ~ • a-105•

04 800

•600

02 -400—

-200

0 O 400 1300 1200 1600 400 BOO 1200 1600 0 400 600 1200 1600 ' SHAFT SPEED, n, rev min' SHAFT SPEED. n, rev min' SHAFT SPEED n rev min"' 1-4 N Fig. 4.9: Output power and overall efficiency curves of the alternator connected to a d.c. resistive load. • (a) R = 40 , (b) RQ -- 60 , (c) RP = 95 . 113.

Hence, these efficiency curves neglect the power loss in the field winding and simply give the ratio between the output electrical power in the load and the input shaft power. They are helpful for the case of tests on the windmill rig for definition of the wind rotor power coefficient.

Comparing the two sets of efficiency curves, it is clear that field losses affect the overall efficiency considerably, particularly at low speeds;p ds ; e. g. at 1500 rev.min—1 and OC = 0, 12 68%. gen — 40%'i gen —

It is also apparent that efficiency too is seriously affected by OC. Hence, whether the output power is low due to low speed and/or to phasing back the thyristors, only low efficiencies can be expected with this type of alternator. This is inevitable, given the relatively high magnitude of the "no—load" losses. The increase of the level of higher harmonics in the alternator due to tbyristor commutation will give a substantial decrease of efficiency.

4.4.6 Effect of Field Current Variation on the Load Characteristics with and without Diode Bridge Rectification.

A series of tests was carried out with the machine connected to different constant a.c. resistive loads (Ri = 20/, 40S/ and 75S2) and with different constant field currents (If = 2 A, 1.8A and 1.4 A).

Figs. 4.10 show the overall efficiency curves and power characteristics plotted against the rotational speed of the alternator.

Figs. 4.11 show the same curves with the alternator connected through a diode bridge to different constant d.c. resistive loads with the load resistance of 55A10 78S-2 and 15552, and with the same field currents as in the previous tests. (a) (b) (C) 1.Id current • it •2A P.c Watts Oe X It •18A O 1r •16A A It •14A

0.4

02

400 800 1200 1600 800 1200 1600 800 1200 1600 SHAFT SPEED. n, rev m n'' SHAFT SPEED, n,rev min' SHAFT SPEED, n, rev min"' Fig. 4.10: Power and overall efficiency curves with a.c. resistive load, where (a) Rt = 25 , (b) Re. 40 , (c) R, - 75

Pdc. Watts (a) (c) ri e10 current • It .2A '1 Pe8.Watts X Ir •18A o-e o Tr •1SA A Ir •14A

0.4

02

400 000 1200 1600 400 800 1200 1600 400 800 1209 1600 SHAFT SPEED.n, rev min"' SHAFT SPEED n rev min' SHAFT SPEED, n, rev min"' Fig. 4.11: Pōwer and overall efficiency curves with d.c. resistive load, where (a) Re = 55 , (b) RQ = 78 , (c) Re = 155 . 115.

Unfortunately the range of field current rotation chosen

was almost entirely within the saturated region of operation and

therefore there was little change in flux and e.m.f., and hence little

change in output power. Nevertheless, the test results show that this

method of control is effective and that little sacrifice in overall

efficiency occurs when output power levels are reduced by decreases

in field current.

4.5 OPERkTION WITH A SELF—EXCITED SHUNT—CONNECTED GENERATOR

Section 4.5 quotes freely from 5.13, on which the author

of this thesis was a co—author.

The control of small wind power systems is complicated by

the variability of the energy source and by the need to operate the

windmill itself at variable speed if good wind energy conversion

efficiency is to be`obtained [4.3] . The various lines of approach in a single machine, isolated load system were given in Section 3.3.3. It is sometimes forgotten that a further possibility exists. This is

to leave the windmill generator and load without control means under

normal conditions and design them so that efficient operation occurs naturally. The design task is to ensure that throughout normal

operating range the windmill is loaded by the generator and load just

enough to enable it to run at optimum rotational speed (i.e. the speed at which the power extracted from the wind at its current velocity is a maximum). Briefly, this usually means that the load torque on the windmill be arranged to vary as the square of the shaft rotational speed and that stable operating points be obtained where generator 116.

load torque and windmill drive torque equate. This can sometimes be

achieved by careful choice of generator e.m.f./speed, terminal voltage

load current or e.m.f./excitation current characteristics and the

advantages in terms of simplicity and reliability are obvious.

Examples of "naturally" matched wind generator systems are

found in the literature. Perhaps the most successful large windmill

system built so far — the Gedser windmill [..4.4:1— employed a certain

degree of natural matching and incorporated a fixed pitch windmill and

a simple induction generator connected to the mains. Systems incorporating

uncontrolled induction generators have also been examined elsewhere

[4.5, 4.6, 4.73 . A number of battery charging schemes [4.3] used

matched d.c. generator systems. Schemes incorporating capacitor

excited induction generators with isolated resistance or induction

motor loads [4.5] and P.M. alternators with resistance or battery loads

are also possible. It may be noted that in most cases such windmill

systems are not entirely free of control means since special measures

for starting and overspeed protection are often necessary.

This section examines systems using self—excited, wound—

field generators supplying resistive loads (e.g. heaters). It was

found possible with certain assumptions to draw up a theoretical basis

for such systems and here are included experimental results from the

lorry alternator. 117.

4.5.1 Operation with Generator

The behaviour in terms of speed of generators supplying

resistive loads is here examined in more detail. Fig. 4.12a shows a

d.c. generator with separate excitation feeding a load of constant

resistance R . If armature resistance is negligible and the field

current is held constant, V varies directly with n and the power POA in the load is proportional to n2 (see also Section 3.3.3). This does not match the n3 power curve for the windmill. However, if field excitation

is now varied so that the field flux increases with speed according to

relation (3.54), then:

V = kv ..~i n (4.8)

= kv k0 3/2

and the power in the load is

2 V2 (kv kk) 3 P — . n P (4.9) OUT Rt. R

If, for the time being, generator and gearbox losses are neglected, it is apparent that a windmill to generator match is now

possible since kv, k0or RR can be chosen to give a generator shaft

power versus speed curve that is identical to the windmill shaft power curve. The question now arises of how the correct flux versus speed relation can be achieved. Two self—excited arrangements will be considered: (a) plain shunt connection, Fig. 4.12b, and (b) plain series connection, Fig. 4.12c.

If the field is connected in shunt across the armature and a constant field resistance is assumed, then the field current, 118.

Fig. 412a: Separately excited.

If Rf GEAR BOX *Ri

Fig. 4.12b: Shunt.

GEAR BOX Rif A ~YV T V

Fig. 4.12c: Series.

Fig. 4.12: Excitation Schemes. 119.

If = V/Rf n3/2 kv k0 Rf (4.10)

Since the flux must vary as k,An, the appropriate magnetisation

characteristic,

it = f(If )

must be

= kf 34- (4.11)

where kf is a constant. Substituting equation (4.10) gives-

3 k _ kf Rf ~. ~- bit

(4.12) as required, kft being given by

_ k312 f (4.13)

Can a magnetisation characteristic corresponding to equation

(4.11) be achieved in practice? Fig. 4.17 shows a cube root curve of the type required and it may be observed that it is remarkably similar to a normal magnetizing curve, especially as regards the saturation region. However, the real magnetisation curve for a machine always possesses a straight line "airgap" portion corresponding to operation at low flux levels where the m.m.f. drop in the iron is negligible compared to that in the airgap, whereas the cubic curve has no straight

120.

line portion. Hence generator operation at low speed would not be

expected to be ideal, particularly as regards "build-up" capability,

but there is a fair chance that operation would be good enough for

practical purposes.

If the field is connected in series with the armature, all

losses are again neglected, and considering including the value of Rif Rf of the series field winding, then

3/2 V kv k n I = If R (4.14) ef RQf

and the magnetisation characteristic between and If to give the required

O = k i/ relation is again:

=

A relation for ke in the series case is found by substituting for I : f

= kf3 •tj if

Hence Icy is now given by:

k 3/2 kv (4.15) f R~f

It may be noted that if the magnetic circuit of the machine remains linear over the operating range, active field control is then 121.

required if a cubic power versus speed curve is to be obtained. For

the shunt generator the fieldts effective resistance must vary

according to:

kt 2 f R = V = K k n3~ f If v

kt 3/2 = k kf n (4.16) kv kis n

where lc' for the linear case is defined by:

= kf If (4.17)

A controller, perhaps of the car "regulator" type [4.8] ,

would normally be used to vary Rf but a non-linear resistor in the

field circuit giving Rf varying kRV3/2, where

3 kR = kf (4.18)

would also achieve this.

4.5.2 Effect of Generator Imperfections

It is possible to make allowances for some of the imperfections

of a real generator, while still preserving an analytic rather than numerical approach. The new assumptions are:

1. Constant ratio between mechanical ..input and armature output,

i.e. constant "armature efficiency".

2. Armature resistance and brush drops negligible compared with

generated e.m.f. 122.

3. Constant field and load resistances Rf and R.

4. Armature reaction and transient effects are negligible.

5. Magnetization characteristic is again of the form given by

equation (4.11).

6. Constant gearbox efficiency.

7. "Build—up" problems are neglected.

Assumptions 1, 2 and 6 involve somewhat less error in the context of variable speed, cube—type loading than might at first sight be thought. Since flux, voltage and armature current all decrease with speed (the flux as 1/17, the others as n3/2), both iron losses and armature losses decrease as power throughput falls. Hence the ratio of losses to power input would be expected to remain reasonably constant for all but very low speed operation. Similarly armature resistance drops stay small at low speeds in comparison to generated e.m.f. since at low speeds, armature currents are small. Comprehensive efficiency data for step—up gearboxes is very scarce but it is probable that like the iron losses in a generator, a gearbox's friction losses stay in very rough proportion with power throughput over much of the operating range when the speed varies as the cube root of the power throughput.

The input power PIN to the machine is now no longer equal to the load power POA, but from expression (4.5) is given by:

1 PIN = (PP gen 123.

If the gearbox efficiency is Tlgb, then

PIN - w '1gb (4.19)

Hence:

(4.20) Pw = (POUT + Pf) 1

where its, the overall efficiency of gearbox and generator, excluding

the effect of field losses, is given by:

21) Its = 'gen (4.

The windmill output when running at C is still given by Amax expression (3.37). For the shunt-excited machine,P +Pf is given by: OUT

POL, f = V2 R + P (R + Q )/RfRt

Hence equating Pw from equations (3.37) and (4.20):

kg n3 = V2(Rf+RL)/ils Rf RE

Thus V must still vary as n3/2 for cubic windmill loading.

Writing V in terms of generator parameters and n gives:

kw = (kvko)2 (Rf+Rt)/TL RfR (4.22) s t

Substituting equation (4.13) for ko, then:

f/2 kg = (kvk ✓kv/Rf)2 (R f+RP)/Yt sRfRB

kg = kv3k f3(Rf+f)/cLsRf2R$

kg 3(Rf L)/11 sR (4. = k +R f2R1 23) 124.

where the new coefficient k is:

k = kvkf (4.24)

The expression (4.23) enables suitable values to be chosen

for Rf and Rn in order to match a generator of known k and Tis to a

windmill and gearbox of known kwg or in order to help fix the design

of a new generator in which case k as well as Rf and RI are under the control of the designer.

Since,

V=

a magnetisation characteristic of the type

= kf3V 1f

is again required for cubic loading if field resistance is to be left unchanged. When k is fixed and 72, s is known, it is possible to use relation (4.23) to obtain a quadratic equation for Rf (which includes the resistance of any field ballast resistor) in terms of load resistance RI and other parameters.

Rewriting expression (4.23) for the shunt—excited generator gives:

kg-Il R R - k3 Rf k3 Rt .0 (4.25) s e f2 -

The real root of the quadratic equation (4.25) is:

k3 + k6 + 471.s(kg )3 k3 R~ Rf - (4.26) 2'1, kw RL ▪ P • s 125.

• The value of the square root in equation (4.26) is greater than the value of k3. Hence only the positive sign in front of the square root need be considered.

Clearly the value of the required field resistance Rf depends on the value of the load resistance.

For the series—excited generator:

2 Pt 1 11 f = $f V2 = R (4.27) tf

Equating Pw as before:

V2 kg n3 — v sREf

V must again vary as n3/2 and '0 as 3T. Substituting for V as before, gives:

2 kg , (kv k) — V Ref

Substituting equation (4.15) for k1, then:

w k (k 113/2113/2t/k v/R'jf)2/~-sR'$f

• k k 3 R2 ✓3 f /'' s lf

• k (4.28) 3/1 sR'~f where k also is

k = kvkf 126.

The relation (4.28) again enables values of RQf (which includes the field winding resistance) and k to be chosen for a windmill and gearbox of known kg

Clearly,

REf k3~92s (4.29)

4.5.3 Ideal Performance Curves

Fig. 4.13 shows curves of normalised Ø,_ V, I, POUF, V , Q, w Pw and efficiency 71s versus speed for a typical "ideal" system incorporating a shunt generator having 'ig = 0.75, Rf = l0RRt. en Gearbox efficiency 11 gb is taken as 0.9. The assumptions of Section

4.5.2 are made. Superimposed on Fig. 4.13 are four dotted lines indicating windmill torque versus shaft speed for two constant windspeeds and two typical types of windmill. The way in which these lines cross the generator torque line indicates that the speed stability of the system at constant windspeed will depend on the shape of the windmill characteristic. With some "peaky" characteristics (type B) the steady— state operating point is not well—defined and speed instability would be expected. However, with the drooping characteristics of water— pumping type windmills (see Fig. 3.2) or with characteristics (such as type A) possessing any sort of plateau around the maximum torque point, speed stability should be good. Fraction. 1.0 r---r-----r---t------t"--;---r---r-----.-----,r----:.-.!'...... -:----t---~---r------1 of value at rated conditions o·g t---t---t---t---r---t----1f----+----:l~~~AI,f--~--+-~

0'7 " B 115 0·6 •

0·5 A

0·4

0·1 0·2 0·3 0·4 0·5 0'6 0·7 0·8 o·g 1·0 1·1 1'2 1·3 p. u. Shaft speed Fig. q.13: Normalised characteristics of an ideal self-excited windmill g~ne'rator. 128.

4.5.4 Generation using a Self—excited Alternator

The advent of compact rectifiers has been largely responsible

for the almost universal adoption for d.c. power generation of the poly-

phase alternator plus rectifier bridge in place of the d.c. generator.

The lower maintenance requirements of alternators are particularly

advantageous in small wind generation schemes and Fig. 4.14 shows the

layout of typical systems incorporating self—excited alternators. The

theory of Section 4.5.1 and Section 4.5.2 is generally applicable to

these systems, if allowance is made for the difference between the d.c.

voltage beyond the rectifier bridge Vd.c. and the alternator phase voltage Vph, e.g. for the Fig. 4.14a a system with a star—connected,

three—phase alternator connected to the load via a full diode bridge:

V 31 V dc it ph (4.30)

Assumption 2 of Section 4.5.2 is of course made slightly more

approximate since additional voltage drops now occur across the

alternator's armature reactance and across the diodes. Commutation

delay will also decrease Vdc. Reactance effects will tend to be

significant at high speeds, and diode drop at low speeds, though for

small alternators (say up to 1000 w) running at frequencies up to say

60 Hz, armature X /R is low and little error should be involved. a a

4.5.5 Determination of Coefficient k

For prediction of system performance, knowledge of the coefficient k is required. The defining equation (4.24) gives k as:

k = kv kf 129.

Idc

GEAR Vdc BOX I

Rf

Fig. 4.14a: Shunt—excited with d.c. load.

Fig. 4.14b: Series—excited with d.c. load.

Fig. 4.14c: Self—excited with a.c. load.

Fig. 4.14: Self—excited alternator schemes. 130.

k = --a-- T n If

= 1 n f

Hence, ideally

V = k.n 3~ (4.31)

It has been assumed that the terminal voltage V is negligibly

different from the open circuit voltage V (both measured beyond the

rectifier for the case of an alternator). The coefficient can thus be

obtained from a calculated or measured magnetisation curve for the

generator. This is done by using the method of least squares to fit

a best

NL V = k 141 - (4.32) nNL

line to the magnetisation curve. The k corresponding to this best

line is the required value (which can be obtained with the aid of log-log

graph paper). Often it is possible to sacrifice accuracy of fitting

over certain parts of the range of magnetisation for the sake of

obtaining good fitting and hence good power matching elsewhere (e.g. in

the mid-magnetisation and speed range). In this case, points over an

appropriately restricted range can be fed in to the least squares

method. See Appendix IV-1.

4.5.6 Experimental Measurements

Measurements were made on three systems, based in turn on:

(a) the 1.5 kW, 12 pole lorry alternator, with the rewound armature 131.

(see Section 4.2) and field connected in series (Fig. 4.14b);

(b) a 1 kW, 12 pole vehicle alternator with unmodified windings and connected in the Fig. 4.14a configuration; (c) a 5 kW, 6 pole alternator of conventional salient pole construction connected in the

Fig. 4.14a configuration.

In all the above systems the alternators were driven by a d.c. drive motor which simulated the windmill.

Fig. 4.15 shows experimental curves of per unit shaft power versus per unit speed for each system, together with the ideal

P = kg n3 w w curve. One per unit power and speed figures for the three systems are:

1.15 kW, 1500 rev.min 1; 1.15 kW, 3000 rev.min 1; 4.1 kW, 1000 rev.min1 respectively.

It may be observed that in general the shaft power varies with speed in a manner which is not too far away from the required cubic law.

During the tests, it was found that the ability of the generator to build up its flux from a residual value was in some cases rather poor. The problem is of course made more severe by the presence of the permanently connected load resistance and by the significant voltage drops across the rectifier diodes even at quite small currents.

Minimum speeds for build—up for the three systems were 500, 2750 and

500 rev.min1 , respectively. An investigation was made of the effect of using a 12 V battery across the field of the system (b) alternator to assist build—up. The circuit layout, shown in Fig. 4.18, includes two blocking diodes, one effectively to disconnect the battery when the I Theoretical wind power Pw I Theoretical wind power Pw IU-o-- Unmodified vehicle alternator ū —x— Rewound vehicle alternator with no battery -o- Salient pole alternator INPUT POWER p.u. LQ-.- Unmodified vehicle alternator INPUT POWER p.u. with batt 1- 1.0

0.9 0 9

0 08

0• 7 0-7

0 0.6

0 i 05

0• 1 0.4

'O 03

• x 0- 0.2

0• 1 0.7

O 01 02 03 04 0 5 06 07 08 09 1-0 01 0.2 03 04 05 06 07 08 09 1.0 p.u. SHAFT SPEED au. SHAFT SPEED

Fig. 4.15: Input power versus speed characteristics: experimental results. 133. d.c. load voltage exceeds the battery voltage, and the other to dis- connect the battery from the load resistance when the battery voltage exceeds the d.c. load voltage. The speed for build-up was reduced by this means to 2000 rev.min 1 (curve (iv) on Fig. 4.15). There was a certain amount of hysteresis in the power versus speed characteristics, presumably due primarily to magnetic hysteresis in the generator rotor particularly for system (b). Self-excitation was maintained during speed reductions for system (b) down to speeds of 1500 and 1777 rev.min-l.rwith and without the battery, respectively.

In order to achieve still lower build-up speeds, it is clearly desirable to increase the field ampere-turns per output voltage (for the shunt generator) or per output current (for the series generator).

To avoid excessive field beating at full load, a special rewound derated design would normally •be needed, though it is possible that the large air velocities available for cooling at full load might enable rewound versions of standard machines to be used without temperature rise limits being exceeded.

Fig. 4.16 shows a comparison between measured and predicted shaft power for system (a) as a function of speed, the predictions being made using the approach outlined in Section 4.5.2. The magnetisation curve for the system (a) alternator, taken from Fig. 4.3, is shown in

Fig. 4.17 together with an ideal

nNL curve fitted over the range 0.7 < If < 3.8 Amp. The value of k, found using a measured magnetisation curve and the method of Section 4.5.4, 1 was 0.139 Volts rev.min 1 Amp The values of load and field 134.

POWER p.0 EFFICIENCY Watts 4

- / Output power from 9 3 / the windmill P" n 1000 _ 1 —• _ Input power to the alternator — -- Power to the resistive load // ------Efficiency of the system %/

4' I 750 - i # ij P I~

~~ ~~~ _ -- -0---/- 'C

500 0 5 'P.% ' 11 i i r r • i

i a / // T / / I 1 r / 1 I i /I' 1 r / r I T r x / 250

,' / 1 / , i I ///I.

I i /Ii0 0 0 500 1000 1500 SHAFT SPEED, rev min-1

Fig. 4.16: Power/speed characteristics of system with a series excited alternator. Comparison between predictions and measurements.

0.3

- - r

i

1 Fitted curve of the form /

01 / -- — -- Experimental magnetization / curve

/ / . / / / /

00 1 2 3 FIELD CURRENT, If , Amperes

Fig. 4.17: Magnetisation characteristic of alternator with fitted curve. 136.

+ Idc

Rt Fig. 4.18: Circuit with auxiliary battery for initiating self—excitation.

Fig. 4.19: The lorry alternator mounted on the windmill rig. 137.

resistance were 21 and 89.Q respectively, and the average efficiency

'it s determined from a number of standard load tests with separate

excitation (see Section 4.4.6) at a number of constant speeds, was

taken as 0.65. It can be seen that the agreement between prediction

and measurement is fair, except (in percentage terms) at speeds below

the build-up speed. The maximum discrepancy in absolute terms

(85 Watts at 700 rev.min—l) is reasonably low.

4.6 FIELD TESTS ON THE LORRY ALTERNATOR

The lorry alternator was mounted on a windmill rotor through a commercially available, packaged step-up gearbox of ratio 5:1.

Figs. 4.19 and 4.20 show photographs of the assembly of the windmill- gearbox-alternator. The use of the gearbox unfortunately made the test results useless because: (a) attempts to define its efficiency were unsuccessful due to the misalignment of the input and output shafts of the gearbox, and (b) the level of friction of the oil seals gave rise to unacceptably high losses.

On tests at the Silwood Park test station, starting only commenced when wind velocities exceeded 5 m.sec-1 , even when the alternator was on no-load. As soon as any load was applied, the windmill stalled. Due to the rarity of high windspeeds, the field tests on this windmill assembly were abandoned.

Fig. 4.21 shows the 2.5 m diameter cambered plate blade rotor mounted on the tower at the field station at Silwood Park

(see more information about the windmill and field tests in [4.9] ). 138.

Fig. 4.20: Gearbox—lorry alternator assembly.

Fig, 4.21: The cambered plate windmill at the Silwood Park field station. 139.

4.7 CONCLUDING REMARES

In this chapter the performance of wound field alternators

has been examined. An inherently self—regulated class of resistance-

- load generation schemes suitable for windmill application has been

looked at. Measurements show that, subject to certain criteria related

to residual voltage level and shape of magnetisation curve, generator

input power can be made to vary with speed in a manner which should

enable the windmill to operate at near—optimum tip speed ratio over

a wide range of wind speeds.

This might well be a system worth considering when low first

cost and simplicity are important.

The design bias given to vehicle alternators — low first

cost, extremely rugged construction, low efficiency, high operating

speed, high waveform distortion — does not match the requirements of a

wind generator particularly well. However, the tests show that if

low first cost is of overriding importance, then a rewound generator

operating at reduced speed with moderate gearing should be able-to form

part of an effective WECS. Clearly the step—up system used must be

carefully chosen for absolutely minimum levels of friction and losses

if satisfactory output levels are to be obtained.

140.

CHAPTER 5

PERMANENT MAGNET ALTERNATORS: LOW SPEED TYPE WITH CIRCUMFERENTIALLY-ORIENTATED PERMANENT MAGNETS ON THE ROTOR

5.1 INTRODUCTION

As demonstrated in Chapter 3, machine permanent magnet

excitation has particular advantages (over coil excitation) for small

alternators (up to 10 kW) for wind power application, and a large part

of the activities covered in this thesis concerned the design,

construction and testing of these machines.

This chapter examines one of the types with a ocircumferential'

layout of magnets in the rotor. An attempt was made to draw up a

theoretical basis for prediction of the behaviour of such alternators,

and to correlate the results with measurements.

The equivalent magnetic circuit and phasor diagram from two-

axis machine theory were used extensively by the author in p.m.

alternator analysis and are described together with details of design

features and experimental test results for two low-speed circumferential

rotor, p.m. alternators.

5.2 REVIEW OF LITERATURE RELATING TO PERMANENT MAGNET MACHINES

There have been a number of papers and patents published on

application of permanent magnets in electrical machines. Some of the

more important post-war ones are considered in chronological order. 141.

One of the first such papers was by Brainard and Strauss.

Brainard (in Part I) deals with the mechanical 'construction of

synchronous machines with rotating permanent magnet fields and Strauss

in Part II deals with the magnetic and electrical design of the

machines [5.1, 3.23. In Part I are included construction details of

'radial' magnet p.m. generators rated at from 0.1 kW 12000 rev.min 1 to 75 kW 1714 rev.min 1. The use of the magnetic material Alnico V is considered and these magnets are attached to the rotor with pole shoes to protect them from demagnetizing armature reaction. A laminated rotor stack with buried magnets is described. Part II deals with the magnetic and electrical design of the machines, incorporating graphical representation of the magnetic circuit and an analogous electric circuit replaces the magnetic circuit of the armature field in the direct axis.

Some of the parameters of the machine are calculated, but these are not verified by means of experimental measurements.

Goss [5.3] gives some designs of small p.m. motors and generators. He describes p.m. machines developed in the late 1930s and

1940s which used magnets outside the rotor (welded on the stator), d.c. tachogenerators with or without damping windings or other auxiliary windings. Multi-pole alternators are described with smooth non-salient pole 'ring' magnets on which the polarity is impressed during magnet- ization. A redesign of these machines is shown using the Lundell-type rotor construction with a single axially-magnetized magnet between two discs with interdigitated fingers.

The paper by Ginsberg and Misenheimer [5.4] describes a simplified method for calculating the performance of p.m. generators using empirical equations and concepts familiar to the designer of conventional 142. a.c. generators. Leakage equations are presented for radial rotor p.m. generators. The calculated parameters of the generators have good correlation with experimental results. However, the performance of the machines is based on the graphical solutions of the permanent magnet material characteristics.

In the paper by Merrill [5.5] , an interesting layout of a p.m. motor is given where the permanent magnets lie under the bars of a squirrel cage inserted into the rotor hub.

In the paper by Mole [5.6] , several types of p.m. generators are described among which is a type using a. one—piece rotor casing for small multi—pole generators. This paper also describes the Lundell rotor configuration using a permanent magnet ring. The 9 conventionalo p.m. generator construction, normally used for large machines, is also described either with poles separated by air or cast in aluminium.

Puder and Strauss [5.7] describe the pechanical design of a salient—pole p.m. alternator for high—speed use. Performance curves derived from the graphical characteristics are presented but are not compared with experimental results.

An important paper written in the late 1950s by Hanrahan and

Toffolo (Parts I and II, early 1960s) [5.8, 5,9] describes a calculation method for the salient—pole p.m. alternators using an equivalent magnetic circuit, and the Blonde' diagram neglecting the armature resistance. The derived formulae are not verified by experimental results and in some cases the derivations are over— summarised and unclear. It is thought that the neglect of the armature resistance is not adequately jusrified because for the case of small p.m. alternators its influence on the performance of the machine is substantial. 143.

A number of interesting patents were published in the late

1960s and early 1970s. Most of them have modified versions of the

conventional radial rotor configuration formed by introducing more complex shapes of rotor lamination. These designs enable easy manufacture and construction of p.m. machines [5.10, 5.13, 5.14, 5.15,

5.163 Patent [5.11] .by Gratzmuller gives an interesting layout for a variant of the Lundell—type rotor using a cascade of axially magnetized discs (which may comprise small..cylindrical magnets) and claw poles.

The number- -of discs and claw poles can be chosen so that the required power output of the machine can be achieved, but the disadvantage of such layouts is the appreciable level of rotor leakage between the claws (or fingers) of opposing polarity.

A patent by Siemens AG- _[5.12] describes some configurations of circumferential rotor p.m. alternator layouts. Unfortunately, the rotor lamination layouts are quite complicated and, like the other types mentioned above, are only economic in mass production conditions where the high tooling costs (pattern—making costs with Gratzmuller types) can be offset by large production runs. Performance data is not available.

The paper by Rao and Batra [5.17] gives theoretical calculations of the reactances of the salient pole p.m. alternator derived from the equivalent circuit of the machine and its equivalent magnetic circuit.

These formulae are also given without experimental results.

A graphical derivation of the design of p.m. generators is also given in a paper by Ahmad et al 5.18] where, although an attempt is made to give an example for calculation of the design, this is done without comparing it with an existing machine. 144.

In [5.33, 5.343 the design and experimental results of a permanent—magnet synchronous motor are given, employing new test and design methods.

Ford, in his review on brushless generators for aircraft

[5.35] , gives interesting designs of several types of machines where the small p.m. machines are highly suitable and recommended for use in missiles and aircraft.

In a recent review on permanent magnets, Gould [5.36] gives • a detailed account of the latēst=:developments in magnetic materials.

In Ashen's work [5.37, 5.38, 5.39] magnetic materials are analysed and calculated performances are verified with experimental results. The use of permanent magnet materials for high—torque brushless motors is mainly considered.

The booklet by Mullard [5.19] details the design and construction of a.c. motors with radially—orientated ferrite magnet excitation.

Receat papers and work deal with magnetic material character- istics and calculations of performance of p.m. machines by using finite difference or finite element techniques [5.20, 5.21, 5.373. These techniques of course deal in great detail with the behaviour of the magnets, but are often too lengthy to .use for design purposes.

In the U.S.A. and Europe, several types of p.m. alternators are commercially available and some of these have been modified for wind power application. Examples are the Zephyr range of machines

(series 647 V1,5—PM) with rated outputs up to 15 kW at 300 rev.min 1, and the Nobrush p.m. alternators which are mainly used for exciter applications and rated up to 10 kW 1200 rev.min1. 145.

In the United Kingdom p.m. alternators are made by Newton

Derby (fairly costly, high rated speed, exciter type) and Clarke

Chapman (for Trimble Windmills; recently developed low—speed type with ferrite magnets). No design details or performance curves are available of either type.

The Swiss firm, Elektro, produce aerogenerators up to 5 kW rated. P.M. alternators are used in some of the units. It is believed that these are of the older type of design using steel alloy magnets, but again details are not available.

This chapter and following one review designs of two different types of p.m. alternators which were mainly designed, developed, manufactured and tested at the Electrical Engineering Department of

Imperial College. The author has contributed to the design, development, manufacture and testing of these machines.

5.3 CHOICE OF PRINCIPAL FEATURES OF THE FIRST EXPERIMENTAL GENERATOR FOR WIND POWER APPLICATION

Work at Imperial College on p.m. alternators for wind power applications started in 1976 under an M.Sc. project [5.223. Within that project, a low speed 2.5 kW generator was designed, built and partly tested and these sections (5.3 and 5.4) present some of the factors considered during the design stage. Some of these were detailed in [5.22 and [5.40] . The design was thought to represent an advance on previous p.m. designs in its use of a very high airgap flux density, achieved by adopting polymer—bonded rare—earth permanent magnets with their magnetic axes orientated circumferentially. It was hoped that 146.

power output per speed and frame size would thus be better than in

previous p.m. machines. As it turned out, power output figures not too

far short of those expected were obtained, but the cost of the permanent

magnets made the machine rather too expensive alongside conventional

wound field alternatives.

The generator was designed for use in the scheme shown in

Fig. 2.3. Hence, mains connection'of the generator was not envisaged.

The storage heater load would be connected to the mains for topping up

but it was intended that at no time would the generator and mains be

paralleled on the same load. There was hence no constraint on

generator output frequency.

It was decided to attempt a low speed design capable of being -1) connected directly to the windmill shaft (rated speed 300 rev.min

without a step-up transmission. No machine of this type appeared to be

commercially available. The benefits of a low speed design were certainly

worth having if the attendant potential penalties (weight, cost, bulk)

could be kept within reasonable limits.

The design represents what could be achieved within a very

tight time schedule. Ideally, stator laminations having an internal

diameter of approximately 35.56 cm and fairly dmall radial thickness

should have been used for this low speed, high pole number design.

Only standard induction motor laminations of internal diameter 25.4 cm

(and rather large radial thickness) were immediately available and this 1 meant that if a maximum output at 300 rev.min of 3 kW was to be

achieved, a high field flux density was essential if the alternator's

axial length and weight was to be kept within reasonable limits. In

order to obtain this high field density, it was decided to use the 147. circumferential magnet layout (see Fig. 5.1) in which the flux produced by each rotor pole comprises the fluxes produced by two rather than just one of the magnet blocks on the rotor, and to use the high performance magnetic material, Hera. This is a mixture of rare earth/cobalt alloy and an inert polymer. The polymer "dilutes" the extremely high perform- ance rare earth/cobalt alloy. The magnetic characteristics (see Fig. 5.2) are still superior to most other materials and cost, while somewhat higher than Alcomax type alloys and considerably higher than hard ferrites, is 20:1 down on the cost of the pure rare earth/cobalt alloy.

The material is easily machineable and has a low density. A slight drawback is the uncertainty about performance changes after prolonged operation at temperatures above 100°C. Magnet cost turned out to be responsible for about one—third of the total cost of the alternator.

The final price per kW of the manufactured machine would therefore certainly be high and justifies the search for improved designs.

The choice of pole number is affected by a number of factors.

The most important ones are:

1. Shaft speed/frequency constraints, if any.

2. Ease of construction: too small a pole pitch implies a high pole number and a large number of field poles, etc.

3. Problems stemming from high pole pitches (low pole number).

These are: (i) bulky, lossy end windings, (ii) heavy core— iron sections, (iii) large armature m.m.f. per pole.

Item 3(iii) is critical in permanent magnet machines since too large an armature m.m.f. can demagnetise the magnets. Note that STATOR TRANSIL 92

SLOTS OF THE ARMATURE WINDING

AIR GAP `/~~ / 1 _ ~~" `~`~II — ~`~~~~;J~ MILD STEEL

ALUMINIUM STRIPS HERA

ROTOR AIR

Fig. 5.1: The cross—sectional view of the circumferential rotor p.m alternator. •CO

INDUCTION (B)TESLA-1.4 Hera • • • • • Alcomax III R> ā bO -13 O Alnico o % • -12 •,.- 0 Oriented Barium Ferrite L/D VALUES 0 m \ • -1•' • .____ Recoma • °•s • -0.9 • • a 0. -0.8 a V • • •O7 • o 03 • ~ -0.61 0.2s` • • • r 1 ` 1 • 1 ::::; •• • i...... • 045, ••~ -0.3I1 ' • 04.... •• •1 0.2• • •1 ♦ • 0.05— ,1 S. • 0.1 -• I~ '1 1• I I V i I • 1 I •1 I I 1 1 I I 1 1 l 1 I I 600 500 400 300 200 100 0 10 20 30 40 50 60 70 80 90 100 110 120 130 DEMAGNETISED FORCE (H) k Am1 ENERGY PRODUCT (BH) kJm3

Fig. 5.2: Comparative properties of magnetic materials. 150.

armature m.m.f. per pole increases with pole pitch for constant stator

current loading.

4. Problems stemming from low pole pitches (high pole number).

These are: (i) poor waveform due to constraints on (a) field shaping,

(b) provision of slots per pole per phase greater than one, (c)

sufficiently high skew angle; (ii) relatively high armature leakage

flux and field leakage flux, caused by relatively short paths between

poles.

Item 3(iii) was perhaps the most important one and led to the adoption of the relatively high pole number of 16. This gave a slots

per pole per phase of 1, given the stator slot number of 48.

Fractional slots per pole per phase designs were not considered at the time. A pole number of 8, 6 or 4 giving slots per pole per phase of

2, 3 and 4 respectively, would almost certainly have been forbidden

due to item 3(iii) - but the use of a fractional slot per pole per phase design (as direct drive gramophone turntable motor or wind generator of ref. [5.23 ) would in hindsight perhaps have been worth considering as this would probably have reduced cogging and waveform distortion. Details relating to the general mechanical design are given in Sections 5.4.1 and 5.4.2..

No attempt was made to achieve a sinusoidal output waveform as this did not seem necessary, given the isolated resistance load, and most of the shaping measures would have involved delays during construction and reductions in total r.m.s. output (due to chording, etc.).

Poor waveform did in fact cause slightly increases losses and

thyristor control problems (see Sections 5.10) so improvement here and in respect of the closely related cogging torque effect would have been

worthwhile at the start. 151.

5.4 CONSTRUCTION OF ME MARK I CIRCUMFERENTIAL ROTOR PERMANENT MAGNET (P.M.) ALTERNATOR

The permanent magnet alternator has many common features with the conventional types of rotating electromagnetic machines, as illustrated in the half-section of the assembly of the machine in

Fig. 5.3. In the typical arrangement shown, there is an outer stationary member (stator) and an inner rotating member (rotor) mounted in bearings fixed to the stationary member. The stator and rotor are separated by an airgap. A main magnetic flux 0 passes across the airgap from the rotor to the stator in a closed magmetic circuit, as shown in Fig. 5.1.

In the case of a permanent magnet alternator the armature winding is the same as in a conventional machine, but the main magnetic flux 0 is provided by permanent magnets instead of windings through which a d.c. current flows.

In Figs. 5.5 to 5.10 are shown photographs of the different parts of the circumferential rotor permanent magnet alternator.

5.4.1 Stator

The stator of the machine is conventional (see Fig. 5.3).

The laminations (1) were, as usual, made out of electrical sheet steel

("Transil 92") and held together by a pair of ring-shaped clamp-plates

(4) and longitudinal mild steel bolts (7). Duralumin end plates (6) which form part of the machine's case are separated from the clamp- plates (4) which hold the laminations, by means of a number of cylindrical duralumin spacers. The spacers and end plates replace the cast pair of "end belts" of a commercially produced machine. On the 152.

Fig. 5.3: Half-section of the Mark I p.m. alternator. 153.

experimental machine the use of castings was avoided for reasons of time. The outer periphery of the machine can be covered by a sheet metal cylinder (not shown in Fig. 5.3) if full weatherproofing is required. A system of tubes passing through holes in items (4) and

(6) and interspersed between the spaces would then be added to act as a heat exchanger if required. External air would pass through the tubes while internal air circulates around the tubes in the space between items (1), (4), (6) and (7).

The copper coils of the "mesh" type winding of the stator are placed in the slots. The slots are insulated with 0.25 mm insulation

(class E) slot liners and fixed firmly by Paxolin wedges.

To each phase winding a thermocouple and a thermistor were attached for temperature measurement and protection purposes.

5.4.2 Rotor

The rotor of this machine is based on a magnet configuration which, though not unknown, is not commonly used. The rotor field winding is of course absent and the magnets are arranged with their magnetic axes oriented in a circumferential direction. Mild steel "pole—pieces" carry the magnet fluxes up to the airgap. There is no "rotor core" iron as such, since this would short circuit the individual magnets.

The advantage of the configuration is that the fluxes from a pair of adjacent magnet blocks combine in the pole pieces to form the

"pole flux", thus increasing the flux per pole and hence the output voltage. The disadvantage is that each magnet is called on to force 154.

flux across two airgaps in series and the configuration therefore

tends to be suitable for high coercivity magnets only and tends to be a

little more leaky than designs using the "radial" configuration. The

configuration also requires that the rotor structure (end plates, etc.)

be non—magnetic to avoid magnetic short circuits.

The pole pieces were bolted on to a pair of duralumin end

plates. A steel shaft was used as this is reasonably remote from the

magnet assembly.

The permanent magnet blocks (1) (see Fig. 5.4), sandwiched

between the pole pieces (9), were held in place partly by magnetic

forces on to the neighbouring pole pieces and partly by means of

duralumin strips (3) which were screwed on to the duralumin end plates.

The duralumin strips and end plates formed a primitive type of damper

for the rotor.

A simple aluminium fan was fitted above the end of the rotor

to assist in circulating air through the machine.

A cylindrical aluminium sheet was placed inside the magnet,/

pole—piece. assembly to prevent ferrous particles in the internal air

(which passes through holes in the rotor and plates) from adhering to the interior surfaces of the magnet block and raising leakage levels.

In order to protect the permanent magnets from the slight possibility of demagnetization when the rotor is removed from the stator, a circular mild steel ring was designed to serve as a keeper. original ,/segment

1 1" ~ 8

•

Fig. 5.4: Rotor assembly of the Mark I p.m. alternator. 156.

Fig. 5.5: The unskewed stack of the Mark I machine.

Fig. 5.6: The stator laminations of the skewed Mark I machine. 15 7.

Fig. 5.7: The steel pole pieces of the alternator rotor.

Fig. 5.8: The end plates of the alternator. 158.

Fig. 5.9: The stator with its winding and the rotor of the alternator.

Fig. 5.10: The mounted Mark I p.m. alternator from the side of the drive and the terminals of the winding. 159.

5.5 THEORY

To design any machine a prediction theory of performance is required. In this section a steady state prediction theory is given of the performance of a "circumferential rotor" permanent magnet machine.

In fact the final suggested theory presented here was obtained after the construction and the initial design of the machine, though a basis was laid in work reported by Allyn [5.22] . Considerable difficulties were encountered during the evolution of the final theory, due mainly to the use of magnet excitation and to the unusual magnet layout, but it is hoped that the theory presented is now reasonably error-free.

The theory was not developed to cover the following: (i) damper parameter and damping phenomena, and (ii) transient phenomena.

These would normally be quite large omissions since these aspects are crucial to the alternator's behaviour during asynchronous running, with unbalanced or non-ideal loads, following switching operations or short circuits. A case for developing a more comprehensive theory certainly exists and the reasons for not doing so within the project are as follows:

(i) With machines of novel layout considerable effort is

needed even to obtain a steady state theory. It was decided that

to confine the project just to the formulation of a comprehensive

prediction theory, and its verification, and this is what would probably

have been involved, would be unwise given the need to devote time to

the other aspects of the WECS project. I.e., the way in which the

available time was spent should match, to a certain extent, the

priorities of the overall project, not just those of the field of

p.m. machines. 160.

The transient phenomena in small alternators with small

pole pitches are of much less significance than in larger machines

of few poles. There is hence less need for transient prediction

theories.

In p.m. machines there is no field winding in which

voltage spikes due to switching transients can give trouble. Hence

damping needs, and damping prediction, are less vital.

A full theory is, of course, necessary for accurate prediction

of performance with thyristor load.

5.5.1 Geometry of the Alternator

It is very important to classify the type of the machine.

Though the surface of the rotor of the machine (see Fig. 5.1) is smooth,

the rotor's structure, in particular the sequence of high permeability

iron pole pieces and low permeability (slope of BA characteristic)

magnets give rise to considerably saliency.

Fig. 5.11 shows the magnetic characteristic of the material

"Hera" where it is noticed that:

Br __ 0.55 10-7 ~r ~ ~o H __ 400000 4.377 x TL x c

therefore

= 1.094 . 110 which is almost equal to the relative permeability of air, where:

',Lo is the permeability of free space and I r is the permeability

of material. B A Wb• rrī2 0.6

Br Bos 0.5 Bo M anufacture

0.4

0.3 Probably non-reversible portion of BH line 02 Ass umed "low" BH line for predic tions 0.1

\BS,Hs Hc H

100 200 300 Ho Hos 400 1 kA, m

Fig. 5.11: Magnetic characteristic of the alternator magnets (type "Hera"). 162.

5.5.2 The Equivalent Circuit and Phasor Diagram of the CRPMA connected to a resistive load

An equivalent circuit is developed which represents the machine

under steady-state, balanced, polyphase conditions. In order to

simplify matters, an unsaturated machine is initially considered.

Neglect of saturation is rather a drastic simplification, but

modifications are introduced later which make some allowance for this.

As ref. 5.31] states: The resultant airgap flux in the

machine can be considered to comprise the phasor sum of the component

fluxes created by the field and armature-reaction mmfs, respectively,

as shown by phasors yo, j~a and % in Fig. 5.12. These fluxes cause

generated emfs in the armature ways. The resultant airgap voltage E

can then be considered as the phasor sum of the excitation voltage E

generated by the field flux and the voltage Ea generated by the armature reaction flux. The component emfs E° and Ea are proportional

(saturation neglected) to the field and armature currents, respectively,

and each lags the flux which generates it by 90°. The armature-reaction

flux-%a is in phase with the armature current I and consequently the

armature-reaction emf Ea lags the armature current by 90°.

The flux produced by an mmf wave in the uniform-airgap machine is independent of the spatial alignment of the wave with respect to the field poles. The salient-pole machine, on the other hand, has a preferred direction of magnetization, caused by the "saliency" of the field poles.

In the case of the circumferentially orientated p.m. machine the iron pole segments represent the field poles of the salient-pole machine and the magnets the interpolar space. The field current here 163.

is absent but the excitation voltage Eo is related to the operating

point of the magnets of the machine.

For a machine with salient poles the fluxes and corresponding

voltages diagram in Fig. 5.12 remains unchanged. However, the flux

density no longer bears the same ratio to the mmf at every point, and

therefore must be determined by resolving the armature mmf into

components on the direct and quadrature axes. Each component of mmf

produces a proportional flux along the same axis ''ad and 0aq, but the

factor of proportionality is different for the two axes.

Assuming that the permanent magnet alternator is connected to

a resistive load, the armature current I is in phase with the terminal

voltage V.

The component phasors and 0aq Dad in the space phasor diagram in Fig. 5.12 correspond to component phasor currents Id and Iq in the

time phasor diagram of currents (Fig. 5.14). Fig. 5.13 shows the

equivalent circuit of the circumferential rotor permanent magnet

alternator, at its direct axis, and Fig. 5.14 shows the phasor diagram of the machine.

The airgap voltage E differs from the terminal voltage by the armature—resistance and leakage reactance voltage drops, as shown to the right of E in Fig. 5.13 where Rs is the armature resistance, Re is the armature leakage reactance and V is the terminal voltage.

In Fig. 5.14 the phasor (CG) Eo represents the field flux.

The voltage induced by the direct—axis component of flux is represented by GE and is equal to jXadĪd, where Rad is the direct axis magnetizing Resistive load'

Fig. 5.13: Direct-axis equivalent circuit of a salient-pole alternator with a resistive load.

jX.jd

Fig. 5.12: Phasor diagram of component fluxes and corresponding voltages.

Fig.. 5.14: Phasor diagram of a salient-pole alternator with a resistive load. 165.

reactance. Similarly the voltage induced by the quadrature-axis

component of flux represented by GH is equal to jXagĪq, where Xaq is

the quadrature-axis magnetizing reactance. CA is the phasor Ef

representing the voltage which depends on the field flux, the direct-

axis armature current Id and the quadrature-axis magnetizing reactance

Xaq. AJ represents the voltage induced by the component I, and can be

considered as a reactive drop in the quadrature-axis magnetizing

reactance Xaq. It leads the current by 90o and is equal to jXagĪ.

CJ represents the internal voltage Vi induced by the resultant flux.

The voltage phasor diagram is completed by adding the resistance

drop R Ī s and the leakage reactance drop jXQĪ to the internal voltage Vi. The resultant is equal to the terminal voltage V, which makes an angle with the vertical axis and the excitation voltage Eo.

The theory of the construction of this phasor diagram is quite general and applies for any condition of steady operation. The shape of the diagram does of course vary considerably at different loads, and the point B moves along the semicircle with the diameter CA always having a right-angle between the direction of JXgĪ and V phasors.

For different loads we have different diameters CA and hence different semi-circles.

Problems arise in constructing the phasor diagram when p.m. machines are involved and a special method for unity power factor loads was developed for doing this during the Aliyu M.Sc. project._

The essence of the method was again used in the present project, but additional work was done: (a) to eliminate some errors which were discovered, (b) to check the theoretical basis 166.

of the method and make it more convenient to use, and (c) to derive

algebraic relations from the final phasor diagram and write a

corresponding computer program.

The diagram is built up as follows:

1) Assuming a value of Id, calculate the resultant emf E

which is the vector CE (calculation of E, see Section 5.5.10).

2) Subtract from the vector CE the vector XQĪd, vector

DE. At the point D, then

3) Add the vector XgĪd vector DA;

4) With the line CA as diameter, draw a semi—circle.

5) From the point D draw a perpendicular which meets the

semi—circle at the point B.

6) The vector BA is the vector XqĪ and vector CB is the

sum of the vectors V+RsĪ from where,

7) Subtracting the vector RsĪ the terminal voltage of the

alternator V is obtained.

8) Assume a new value of Id, etc.

5.5.3 Calculation of the Current I and Voltage V of the Alternator from its Phasor Diagram

In [5.8] relations are given without full derivations for the terminal voltage in terms of load current, no—load emf and machine 167. constants. Attempts were made to check these but were unsuccessful,

and there was some doubt about the validity of the relationships. A

decision was made to obtain performance relationships independently in terms of the magnetic circuit parameters and the geometry of the

phasor diagram of the alternator. The latter is shown in this section.

In the phasor diagram, Fig. 5.14, the triangle BAC is similar to the triangle ADB and BDC. Similarly the following relations are obtained:

ACAB and ACBC AB = AD BC = DC from which

AB = v5TTAT (5.2) and

BC = AC.DC (5.3) where AB represents phasor jXgĪ, AC represents phasor Ef, AD represents phasor jXgĪd, BC represents phasor V+RsĪ and DC phasor represents

Ēf jXgĪd.

Hence relation (5.2) becomes:

•

jXgĪ = Vf.jXg1Td

Id I = i . x (5.4) g relation (5.3) becomes:

V + RsĪ = VEf•(EfJXgĪd)

V = 1/Ef.(Ef—XgId) — Rs.I (5.5) 168.

It can be seen from relationships (5.4) and (5.5) that the

values of current I and terminal voltage V can be obtained knowing the

parameters of the machine Ef, Xq, Rs in terms of the direct-axis

components of current I.

Therefore the load angle 6 from Fig. 5.14 equals:

ā = arc cos(Id/I) (5.6)

From Fig. 5.14 Ef can be defined in two principal ways:

(1) Ef = + jXagId Eo iXadld (5.7)

2) Ef = E + JXagId (5.8) where Eo is the open-circuit emf, i.e. the emf behind the direct-axis magnetizing reactance Xad (see Fig. 5.13). and E is the resultant airgap emf after the direct-axis magnetizing reactance Xad.

From relationships (5.7) and (5.8) it is observed that two methods can be used for the calculation of the performance character- istics of the alternator. Briefly, these consist of:

(i) Working from the no-load emf Eo and using the direct- and quadrature axis reactances of the machine, and

(ii) Working from the resultant airgap voltage E and using the quadrature-axis magnetizing reactance Xaq. 169.

5.5.4 Synchronous Reactances of the Machine

By definition 5.24, 5.28-5.32] the synchronous reactance is

the reactance offered by a synchronous machine to a balanced three—phase

voltage of rated frequency applied to its stator winding when the rotor

is unexcited and rotates at synchronous speed; if the axis of the

resultant armature reaction field coincides with the pole axis, it will

be the direct—axis synchronous reactance and if the axis of the resultant

armature reaction field is perpendicular to the pole axis, it will be

the quadrature—axis synchronous reactance.

The leakage reactance XI, is relatively small and the

synchronous reactances depend mainly on the reluctances met by the armature

reaction mmfs of the corresponding axes.

In wound rotor salient—pole machines the reluctance offered

to the direct—axis armature reaction mmf is less than that offered to

the quadrature armature reaction mmf and therefore, in them X ad > Xaq and consequently Xd > Xq (Xd = Xad+XZ, Xq = Xaq+Xi).

In a circumferential rotor, permanent magnet machine there is

no low reluctance path connecting adjacent steel pole pieces (as was

mentioned in Section 5.5.2) and less reluctance is therefore offered to

the quadrature—axis armature reaction mmf than to the direct—axis

armature reaction. (The magnets have a high reluctance, as mentioned

in Section 5.5.2,and inhibit direct—axis armature fluxes, whereas

quadrature flux can circulate into and out of the steel pole pieces

quite easily.)

Fig. 5.15 shows a two—pole circumferential rotor permanent

magnet machine where the direct— and quadrature axis reactances are shown.

Figs. 5.16 and 5.17 show, respectively, the direct— and quadrature—axis flux paths of the machine. 170.

Fig. 5.15: The paths of the magnetic reactances of a two—pole circumferential rotor p.m. alternator. 171.

Fig. 5.16: Flux path of the quadrature—axis reactance of the circumferential rotor p.m. alternator.

Fig. 5.17: Flux path of the direct—axis reactance of the circumferential rotor p.m. alternator. • 172.

5.5.5 Calculation of the Direct—Axis Magnetizing Reactance Xad

Two approaches are possible for the calculation of the

direct—axis magnetizing reactance: (1) derivation of an equivalent magnetic circuit for the machine, with lumped mmfs and reluctances,

and (b) use of segmented reluctance motor theory [5.25] .

The latter approach is possible because the alternator rotor's structure (apart from the presence of magnet blocks instead of air between the pole pieces) is essentially identical to that of a segmented rotor reluctance motor. Since the magnet permeability is so near that of air, the rotor, as seen by stator mmfs, looks virtually identical to that of a segmented rotor reluctance motor of appropriate pole number, etc. Another way of putting it is to say that the change in the net flux in the machine that occurs when armature currents are allowed to flow is virtually identical with the change that would occur if the magnets were replaced by air.

A snag occurs with nomenclature. The segmented reluctance motor's direct axis is usually thought of as lying along the centre- line between the steel segments whereas in the circumferential rotor p.m. alternator, the direct axis is located on the centre—line of the steel segments i.e. centre—line of the field flux emanating from the pole).

Hence the alternator's Xad is calculated using a modified version of the segmented reluctance motor's X formula and the aq alternator's X calculated using a modified version of the segmented aq reluctance motor's X ad. 173.

Thus in segmented rotor motor nomenclature Xad > Xaq in

circumferential rotor-alternator nomenclature Xad < Xa q

The relation for the alternator's direct-axis reactance is: T.K sin0( Tt ad }I. ( X = 48. o 2pW)2•f•~R'~s(~'d + .ted ). g

— [l+(n -1).(20c 3_ad4)3 .cosorTL1 (5.9)

where,

sink 2 cos()r = (5.10) Oc2 TL 2 + P [b'/(W/ 2)] • (LJR)

1.1.0 = 4TG.10-7 Wb. (At.m)-1

and 11 is the effective airgap of the alternator (see Section 5.5.9); p is the pole pairs of the alternator; f is the frequency in Hz;

T is the number of turns per phase; k is the winding coefficient w (see Section 5.11); and R is the radius of the airgap of the machine and is equal to (Ds-$g)/2; DS is the diameter of the stator;

4E' is the effective airgap of the machine (see Section 5.6.9);

CCd = S- /Y• Sc is the pole arc; Y is the pole pitch; 4 is stack length; h' is the effective value of the pole depth, and is equal to W r + ad.2 +tA1; Wm is magnet thickness and t is the thickness of the Al aluminium strip.

by approximates the calculation of fringing fluxes of the pole. For values of Y, Wm, Sc and € see Fig. 5.18. 174.

`k

IRON POLE-PIECE MAGNET 4Vm

Fig. 5.18: Geometry of a pole—piece of the alternator.

IRON POLE-PIECE MAGNET

Fig. 5.19: Three—dimensional paths of the leakage flux of a pole pitch of the alternator. 175.

5.5.6 Calculation of the Quadrature—Axis Magnetizing Reactance X aq

The formula for Xad in [5.25] was found to be identical with

the formula for the Xaq of a conventional salient pole machine. With

the rotor in the q position (see Fig. 5.16) the experimental machine

looks like a conventional salient pole machine as far as armature fluxes

are concerned since there is no tendency for fluxes to pass from one

pole to the next. Hence it is immaterial whether the poles are

connected by high permeability material or not. The formula is:

sinaaTT T.8 2 R Xaq = s 48. ~lo. ( p .) .f T .c (OC d — TI ) (5.11) T

5.5.7 Inductive Leakage Reactance of the Alternator Xt

Armature leakage reactance is assumed to be identical to that

of a conventional machine. This is given by [5.24] :

$ T 71e~. X~ = 41Tf 111,0p20 sq ( ils + q. + Xd) (5.12)

where As is the equivalent permeance for the slot leakage fields, and

for the type of slots in this machine (see Fig. 5.1 ) is:

2h3 hl + 0.623 Xs — 3(W +W ) + W (5.13) 1 2 0 where q is the number of slots per pole per phase.

The end winding leakage is calculated mathematically with

greater difficulty than the slot leakage. . A number of formulae for different cases of end—winding arrangement have been found by empirical methods. 176.

In the case of a double—layer diamond winding the following

formula is used:

Xe ie = where

Ī3=—ye/Y

Yc is the coil span and % d is the permeance of the differential leakage flux, which in this case can be considered equal to zero. This is because it is reduced from the slot openings on the stator, the damping strips on the rotor which play the role of a squirrel—cage type winding and the saliency of the machine.

5.5.8 The Resistance of the Winding of the Alternator

The resistance of the winding per phase is given by the expression in [5.26 :

c R (5.14) s r' c'a where . is is the length of conductor per phase = 2T £av; Qav is the average length of a half mean turn; a is the cross—sectional area of -7 .Q m); the conductor; p is copper resistivity (A = 1.724.10 ° 20°C Kr is skin effect coefficient, assumed to be x 1.05; Lav = Ls+ 2.ew4 Lew is the length of the end winding.

For a double layer winding:

= + 1.8Y Q ew 1.5 177.

5.5.9 Equivalent Magnetic Circuit of the Circumferential Rotor P.M. Alternator at No-Load

The use of equivalent magnetic circuits for p.m. machine

analysis is evident in [5.2, 5.8] . The nomenclature and certain aspects

of the broad approach used in this section followed those of [5.8]

although a considerable number of detail divergences from [5.8] were

introduced, many of them stemming from the different rotor design and

p.m. material used.

In Section 5.5.3 the current I and the voltage V of the machine

are derived from the open-circuit emf Eo (no-load voltage) or from the

resultant airgap emf E and the parameters of the machine. In order to

define the two emfs it is necessary to know either the "no-load" or the

resultant airgap fluxes of the machine.

In previous works [5.7, 5.18] the magnetic parameters of the

machine were obtained by a partly graphical approach. Here a decision

was made to obtain these parameters from the magnetic circuits of the machine without using the graphical method.

A developed view of the machine showing the paths of the field fluxes is shown in Fig. 5.1. The shaded portions of the drawing represent iron parts (except the magnets) of negligible reluctance when compared with the airgaps. The magnetic circuit of one of the paths in the machine is shown in Fig. 5.20a, when there is no load.

The reluctances in Fig. 5.20a are effective values. RLe is the reluctance of the equivalent leakage path and II' is the reluctance of the equivalent airgap across it half-pole segment. Pole-segment reluctance is assumed negligible compared to Ro, the internal reluctance

178.

Fad

(pg —41 Ro 0

Rte

Fig. 5.20a: Equivalent magnetic circuit of the circumferential rotor p.m. alternator at no-load.

Og A

Fig. 5.20b: Modified magnetic circuit at no-load.

Rg +R°

Pg A + Fo; - 0 Fig. 5.20c: Resultant equivalent magnetic circuit of the alternator at no-load.

Rg+Ro

Fig. 5.20d: Resultant equivalent magnetic circuit of the alternator on-load. 179.

of the magnet. Since iron saturation is neglected and Ro is constant,

the circuits are linear. Moreover for stabilized operation, Fo and 00 are constant. The permeances are the reciprocals of the corresponding reluctances.

The permeance of the magnet is taken from the magnetic characteristic of the magnet. The demagnetization curve given by the manufacturers of the magnet "hers" taken from Fig. 5.2 is given in

Fig. 5.11 with coordinates flux density and flux mmf per meter (B to H).

The B-H characteristic of the material corresponds to the 0r "residual flux" and F c the "coercive mmf".

The magnet was "stabilized by exposing it to the maximum demagnetizing influence that it will encounter in normal working conditions. As long as the magnet is not subjected to a greater demagnetization, the flux density remains within the reversible band of operation. Most permanent magnet generators are designed to be air- stabilized, i.e. stabilized by separating the rotor and stator in air.

The magnet can be demagnetized to any point (Bs, Hs) on the dashed curve given by the manufacturers. Operation occurs around minor hysteresis loops, so that the magnet flux density remains below the maximum of B = B. These major loops can be approximated by a straight line, called the line of return, originated at Hos and having a slope roughly equal to that of the major loop at Br. The intersection of the line of return with the B-axis gives Bos'

The line of return gives the magnet "terminal" flux and mmf for any condition of stabilised operation. Hence, the line of return is like a "volt-ampere" characteristic of the permanent magnet; 00 is 180. the magnetic short—circuit flux and so the open—circuit potential is given by the intersection of this line with the H—axis. Operation outside the major loop is impossible.

In the case of ferrite and rare—earth based magnets (including

Hera), recoil lines (or lines of return) can usually be assumed to lie along the main B—H characteristic. This contrasts with the situation with Alcomax and Alnico materials where recoil lines usually lie considerably below the main B—H characteristic.

So for Hera magnets,

0o = Br.m (5.15) A .2. t = Qr a (5.16) Fo = Hc.Wm (5.17)

Am, g and ka are parameters of the geometry of the magnet; see r Fig. 5.18.

Since the line of return is straight, the stabilized magnet may be represented by a constant mmf Fo source in series with a constant reluctance Ro (the negative reciprocal of the slope of the line). This is shown in Fig. 5.11 and is the basis of the method used for the design of this machine.

Permeance of the magnet,

Po = 9foJFo (5.18)

Airgap permeance across the half pole arc, see Fig. 5.18, from [5.27] is: Sc. ~ P'g = P o 2 .gf (5.19)

181.

where ~f is the rotor length taking into account the fringing flux, and o f — Es'

From [5.26] , the effective airgap of the alternator is:

eg = Kg. Q'g (5.20)

where KE is Carter's coefficient which takes into account the influence

of the non—uniform airgap; Q g is airgap length; and

(5.21) K0 = C — ~g

where c is slot pitch; and (Woe )2 B _ 5 +W Qg

Fig. 5.19 shows a rough sketch of the three—dimensional

leakage flux path from the magnet. A formula for the calculation of the leakage permeance assuming elliptical paths is given in [5.27] and is probably sufficiently accurate here:.

WT 2(xm " m2 P = ln 1 + + + Km m ) L µ0Tt W (5.22) m

_ La + 2 $r (5.23)

Fig. 5.20a shows the no—load magnetic circuit of the machine.

This can be modified using Thevenin's theorem to obtain the equivalent magnetic circuit shown in Fig. 5.20b: where

Rg = 1/Pg (5.24)

g + RI = 2R,g = Rg (5.25)

PI 1 — 2 Pg = 210 (5.26) 182.

From expressions (5.19) and (5.26):

Sc. tf Pg = µo 4.Z1 (5.27)

Equivalent mmf from Thevenints theorem:

Fo.R/e Ft Fo — R +Re (5.28) o e Equivalent reactance from Theveninrs theorem: R r _ o. R'Ee Ro Ro+Ro (5.29) e

Finally, the magnetic circuit takes the form shown in Fig. 5.20c, from where:

+ Rt).O = Ft (Rg g Fr 0 _ o g R g + Rō (5.30)

By substituting expressions (5.28) and (5.29) into equation (5.30):

F° + Rze 110.111e Pg o R + Rae Rg + Ro + Rae

Fo.Rte 14'g R:Ro + + ō (5.31) RgRge R0

Ro = 1/P

Rg = 1/13g — (5.32) Rae 1/Pe

Substituting expressions (5.32) into (5.31): 1 F. Pa g = 1 1 1 PgPo + PgPP, + PoPP

Po+P +P~

PoPgPi. 183.

Let us say that:

Po + Pg + PE = Pt (5.33) then: P P _ o-' (5.34) gN Fo Pt where from equation (5.18):

00 Fō o = P (5.35) 0gNL = ~o pt

Expression (5.35) is the no—load flux from one magnet through the two airgaps.

5.5.10 Magnetic Circuit of the Alternator and the Calculation of the Resultant Flux in the Airgap for On—Load Conditions

When the alternator is loaded, armature currents give rise to an mmf whose major component is in a demagnetising direction. The load is assumed to be purely resistive. (Hence the load power factor cos t = 1, i.e. the angle between the terminal voltage of the machine V and the current I is zero.)

The demagnetizing armature mmf Fad (see Section 5.5.13) may be introduced into the magnetic circuit of the machine as shown by the dashed lines in Fig. 5.20a. Fig. 5.20a is modified into its equivalent circuit as shown in Fig. 5.20d. From Fig. 5.20d:

(R g+1190 O — Ft + Fad = 0

Fo d = — Fad (5.36) g R + Rō ▪ P

184.

Substituting expressions (5.28) and (5.29) into equation (5.36): o F .Rte Ro+RQe Fad tag Ro.Rte R + g + Ro+Rt e

- Fad +Rte) ōRQe (Ro = (5.37) ōRbg + Rg RLe + 0R2e Substituting expressions (5.32) into equation (5.37):

1 `1 F - 1 FadPo P + z fig - 1 1 1 PgPo + PgFt oPE

1 F 1 1 Po idg PQ +Po +P (5.38) P0PgPt Substituting expression (5.33) into (5.38):

P P P _ ~ ~ + Po ~g Fo Pt Fad Pt (5.39)

Finally:

P P ~g =~o p d (Pp Po (5.40) t - Fa Pt

It may be noted that the first member of the right-band side of the

equation (5.40) is the no-load flux in the airgap of the machine for a

half pole arc, as in expression (5.36). The expression (5.40) can be put in the form:

0g (5.41) ~°NL ~°ad

Yad is the demagnetizing flux in the airgap for a half pole arc. 185.

5.5.11 The EMF of the Armature Winding of the Alternator

The general expression for the fundamental emf of an a.c.

machine armature winding as given in [5.26] is:

E 4.KB.T. w.f.~ (5.42) where KB is the form factor of the field wave and for a sinewave field

KB _ TC (5.43) 2

K K .K w wf s

The winding factor of the alternator is:

K = K .K wf wd (5.44) where w is the winding distribution factor, and from [5.263: d TC si — K n 2m (5.45) wdq sin Tt q where m is the number of phases.

In the case of a fractional slot winding in expression

(5.45), q becomes as follows:

bd + c q = qf

For definition of the values of b, d and c see Section 5.11.1.

K is the coil—span factor of the winding, and from [5.25]

K = sin(") (5.46)

Ksk is the skewed coefficient of the slots of the stator of the alternator. 186.

Fig. 5.21a shows the unskewed slot and Fig. 5.21b the

skewed slot machine by a slot pitch c. From [5.26] :

t sin( Yk . 2) (5.47) Ksk — 8 sk TC Y ' 2

where esk is the skewing length, which in this case equals c;

and is the resultant flux per pole calculated from the magnetic

circuit of the alternator.

5.5.12 No—Load EMF of the Alternator

From equation (5.42) the no—load emf of the alternator Eo

can be derived:

Eo = 4.1%.T.Kw.f.0n. (5.48)

where is the no—load flux per pole. From the magnetic circuit on 0NL no—load and Fig. 5.1 (equation (5.35)): P (5.49) °NL = 2 "o Pt

Substituting expression (5.49) into the equation (5.48), the no—load emf of the alternator is obtained;

P Eo = 4.KB.T.K ~.f.2.0 . "t P Eo (5.50) rt 187.

Axial line of the rotor Centre lines of the slots of the stator r-

Rotpr

Y

Fig. 5.21a: The unskewed stator slot of the alternator.

Axial line of the rotor r Centre lines of the slots of the stator C

SE-

Y

Fig. 5.21b: The skewed stator slots of the alternator (skewed-by one slot pitch). 188.

5.5.13 Definition of the Direct—Axis Demagnetizing MMF of a Three—Phase Winding

In [5.24] the amplitude of the fundamental mmf wave of a three—phase winding is given by: T.K F 3 v2_ wI a TL p (5.51)

The value of Fa is derived from the expression:

F = 2 TC.if ct C (5.52) where Tc is the number of turns per coil; it is the instantaneous c value of current in the coil; and F represents the mmf necessary for et setting up the magnetic flux through one airgap.

In the magnetic circuit of the permanent magnet alternator the' direct—axis demagnetizing mmf Fad is introduced, which is equal to:

a. sin Fad = F 1) .Kd (5.53) where pis the angle between the stator current I and the induced emf

Eo of the winding. In this case because the alternator is assumed to be connected to a pure resistive load, and angle T equals angle 6. See the phasor diagram, Fig. 5.14.

The factor Kd determines the degree of decrease in amplitude of the fundamental harmonic of the direct—axis armature reaction due to airgap non—uniformity and to the presence of air space between the pole pieces and is called the form factor of the direct—axis reaction:

OC dTr. + Tr sin ad Kd — TC or sin ad TL Kd ad + Tt (5.54) 189.

It is very important to notice that the value of Fad which is given in relationship (5.53) is for one airgap per pole. See

relationship (5.52). In order to introduce Fad to the magnetic circuit of the alternator, it has to be multiplied by two. Hence, from (5.51):

f- K Fad 6 . T . w Kd . I . sin TG2 P T (5.55) where I . sins) = Id (5.56) where Id is the direct—axis component of current I.

6 v K I Fad TL T p d d (5.57)

This is the value of the direct—axis demagnetizing mmf introduced in the magnetic circuit of the circumferential rotor permanent magnet alternator. See Fig. 5.20a.

5.5.14 The Resultant EMF in the Airgap of the Alternator

The resultant emf in the airgap of the machine E which is shown in Fig. 5.7 is obtained from the expression:

E = 4.KB .T.K . f.0 (5.58) where 0 is the resultant flux in the airgap per pole.

From expression (5.41):

= 2 . ~g = 2.(0 (5.59) — g~ad ) Substituting relationship (5.40) into (5.59):

190.

(~ P = 2. L6o Pt - Pg t (5.6o) . Fad t '(F + Fo)]

Substituting equation*(5.57) into equation (5.60) and then (5.60) into

expression (5.58); the resultant emf in the airgap of the machine in

terms of the direct-axis current Id can be obtained:

T. 2 K E = 8.K .T.K .f.~ --g ( v) P B wPdo.P - 48 .K .KB.f.P (P~ +Po),Id t t (5.61) Expression (5.61) can be put in the form:

E = Eo - Ead (5.62)

The emf Ead induced in the stator winding by the direct-axis reaction

mmf Fad can be thought of as the self-inductance emf of the stator

phase winding due to its magnetic field, the mutual inductance of other

stator phases taken into account. For negligible saturation the emf Ead

is proportional to Fad and consequently, to the direct-axis current Id:

Ead = Xad.Id (5.63)

where the proportionality factor Xad is the direct-axis armature

reactance of the circumferential rotor permanent magnet alternator.

From expression (5.61):

48 (Taiw )2 X _ .K . f —~(P +Po ) (5.64) ad TG p d KB Pt l o

The expression for Xad, (5.64), calculated from the magnetic

circuit of the machine should be approximately the same as the

expression for Xad of a reluctance rotor machine given in expression 191.

5.6 CALCULATION OF THE REGULATION, OUTPUT POWER CURVES, LOAD ANGLE 6 AND EFFICIENCY CHARACTERISTICS OF THE MACHINE

For the calculation and plotting of all these characteristics a computer program was used. The program is shown in Appendix V-1.

The "Graf" subroutine was used for plotting the required curves.

The "Function" subroutine of the program was fed with all the equations and relations mentioned in the previous sections to obtain the theoretical curves of the alternator. The "Function" is such that the performance of different alternators with different parameters can be obtained. This gives the opportunity to see very quickly the effect on regulation, power, angle 6 and efficiency curves of the alternator.

The equation used to obtain the power output of the machine is:

3•I.V POUT = (5.65) since cos cp = 1

Assuming that the armature winding is connected in star, then:

V = Vph I = I~ where IE is the load current per phase, and Vpb is the phase voltage.

For the efficiency calculation:

'11 _ OUT (5.66) L PNL PA POUT where: PA = 3.I2.Rs (5.67)

PNL is the power required to drive the alternator at no load. 192.

From experimental results on this alternator it was found that

the no—load losses can be determined in terms of the rotational speed as:

PNL = KNL n3 /2 (5.68)

KNL is a constant taken from the PNL = f(n3/2) experimental curve

(KNIece 0.0124). For the case of a universal expression given in terms of

the Mark I alternator's active volume V 0.00316 m3, active = PNL can be given as:

_ Vactive 3/2 PNL = VI KNL n (5.69) active

_ TL.R2 active — .4s (5.70)

The values of I and Vph were derived from the expressions

(5.4) and (5.5), respectively.

It is not possible to calculate for a given I, or vice versa, because the relations are expressed in terms of Each calculation is therefore based on an assumed initial value of The load angle S as well as V emerges in the calculation and this enables the actual phase current I to be determined.

5.7 THEORETICAL AND EXPERIMENTAL RESULTS AND 'r11EIR CORRELATION

In this section the correlation is shown of the experimental and theoretical results which were obtained with the methods given in

Section 5.5.3. As shown in Section 5.5.3, there are two possible methods for the calculation of the performance of the machine: 193.

1. Using the no-load emf of the machine E0 (equation 5.50),

derived from the no—load magnetic circuit of the alternator and the

direct and quadrature—axis reactances (equations (5.9) and (5.11)),

defined from the formulae given in [5.25] .

2. Using the quadrature—axis reactance derived as in method 1

but the resultant emf in the airgap of the alternator, therefore the

direct—axis reactance, are derived from the on—load magnetic circuit

(expressions (5.61) and (5.64), respectively).

The principal quantities calculated were the regulation, power, efficiency and load angle S. The results relate to the alternator in its final state, i.e. after airgap enlargement, skewing and rewinding

(see Section 5.10.3). Results were calculated using both methods.

Parameter values:

It was found that the calculated X = 8.65S2 at 300 rev.min1 , aq the calculated resistance of the winding Rs = 0.742 per phase, which is not fax from the measured Rs = 0.715E2 per phase.

The two values of calculated were 4.15c2 and 4.25 ad respectively. This agreement is quite close and the two methods are probably identical. The average value of the Xad from the two methods was fed into the program.

Unfortunately, the agreement between the theoretical and the experimental curves is not very good. See Figs. 5.22(1)a, b, c, d,

Table 5.2 and Appendix I. For the 300 rev.min-1 the no—load phase voltage is 113 V as opposed to a measured value of 100 V. The theoretical maximum power output of the machine is higher than the experimental one by

35.7% (2140 W experimental to 3327 W theoretical). (Limited by volt droop.) 350r---~--~----~--~---r----r----~--~--~

X e:xperimental points nt 300 rev miri' 1201----f--~---f.--+__~ THEORETICAL CU~VES -0300~----~---+-----+---4---~~---~--~----+~~ 1- 300 rev min-' .2-250revrr.in-· ..- 3-200·· 4-~50· • X tf) 100X---+---+--- ~~-100 •• 6- 50· • tf) ~ ~250~----4----+-----+-----~--~~~~-~----~' __~ r­ I ~ --1 :?: g 80 ~-I--+--...!.f----t--::::~~--I---~.--+--~ .. W· ~ GOI---~-~---4----+__--~-

:..J~ g 40~----~---+----~--~----~--~~-~--~ ~ I <{ I J: 20 -- : a..

°d----~--~---~G----~8-----1~0---~12~-~,~---~~--~~8 LOAD CURRENT, AMPS ,(a)

et: 1·2 \ Q 1·2 J_ L1 - Z " U <:: 20·4 ,. y ~ I W 00'4 1 [} 00 . I ~ 40 eo 120 1GO 200 240 280 320 360 0· TOTAL OUTPUT POWER. WATTS x 10'. 00 2 4 6 e iO ~2 14 16 is . (C) \ LOAD CUrd~ENT, AMPS Fig. 5.22(1): . Curves of the Ma.rk I p.m. 01 ternator with a high line of return of the magnets assumed and no saturation taken into account. (0) voltage regulation, (b) power output, (c) efficiency, (d) load angle. . 195.

Table 5~2: Parameters and design of the Mark lop.m. alternator ~th magnets of high line of return.

High line of return 0 P.M. ALTERNATOR DESIGN MARK I I of the magnet

~l.~ M> ~ r", o \ / ~ ~ ./ ~,,' ~ ...... , Dso ~~ Lr ~ ~La--" D ~11 12 Os ! 9 t e ~~woth1 'l-ltll...-\ r- Lm ..- .

No. of phases m - 3 Os - 266 mm ls -57 mm Lm =0 145 mm t wav -9.0Sm - No. of slots Z =- 48 Dso =360 mm Lg= 0.48)1 ~Wo= 3mm w1= 9 mm

No. of poles 2p= 16 la= 52 mm wm=lO mm W2= 11.7mm h1=1.7 mm

No ot turns/coil Tc = 21 lr= 46 mm y= 52 mm h2::' 2 mm 0 h3=23~5 2 No. of Slot~ q = 1 Conductor cross = 24. 7 mm slot = 29~ c =17 .4mm pole/phas s~ctiona' area area mm I Typeot . double-layer Hera Stack steel=Transil 92 Type of magnet = winding · "mesh" 240 Br 0.55T Ho - 400kA'Jri~ Bsat= 1. 2T Winding • = Hsat=ATm-l connection' A

R.P.M.~ 300 Cos~= 1.0 KWd'=- 1.0 Kp= 1.0 KSk= 0.955 Kz= 4.2 55 4>NL =1. 98mWll BNL::' 1.05 T Bt= 2.16 T Htn=kAT~ Temperature rise = 75°C Calculated Calculated unsatur. satur. Test Un satur. Satur. Test

2.78kW 2.14kW 0.7422 0.742~ 0.715 SZ POUT 3. 327kW· ·R s

V 77 V 69.5 V 55 V Xad 4.2 Q 4.03S'2 -

Imax 14 A 13.3U 12 A XaQ 8.62 Q. 2.05 Q. -

VNL 113 V 104 V 100 V Xl 1.25 Q 1.25£2 -

Isc 20 A 19.8A - Xd 5.46Q 5.28Q -

1) 86% 86% 85% XQ 9.8752 3.31Q - 0 0 o 0 57 42 - Overall weight: 120 Ib· - 54.5 kg

\. 140----~--~---r--~TX--EX-P-ER-IV.-.E-N-TA-L~PO~!-NT~S-~~T~30~0-r~-m~i~~~'--I t!:!.fORETICAL CURVt!S 1-300 rflV mina' o 120 --~---+----t----H 2-250 • .. 3- 200 _. .. ;240r---+----r---+--~~~ 4-150 .. lJ) ~- 100 - ~,oo --x­ e- ~O .. .. ~200r-~+---~--~ __~r_7'_~--+_--~---~~~~--~ ~ ~ r-2_,--_ wo. eo.--;---'~- ffi 1601----+----+---r ~ r-3-;-_-L_ ~ ~ 60 --t-~-+-- ...a.. 120t---+---y g r-4-T---~--_L ...a.:::> :::> 80·!---·I...". o

6 B 10 1 14 LOAD CURRENT. AMPS (b)

1·04 i , ---_. f----- I '·2 "L '-0 ~. I . ~ , , o I ;2 OB w" /,V ~:>i /ilFr=j~: 6 0 .6 Z et VI/" ~ f----. f- 00·4 et ", .. 9 VI 2 _- --r--- 02 ~ ~ ~ ·'T 80 120 160 200 240 280 3~ 300- 2 4 6 8 10 12 1.4 ~ 16 20 TOTAL OUTPUT POwER WATTS x10 LOAD CURRENT, AMPS (c), . (d) Fig. Curves of the Mark'1 p.m. al terna.tor with a high line of return of the magnets assumed and with saturation taken into account: (a) 'voltage regulation, (b) power output, (c) efficiency, (d) load angle. 197.

The efficiency characteristics in Fig. 5.22 show that the

alternator has a maximum efficiency of approximately 93% to 86% from

half maximum power to the maximum power. This is very encouraging because

the windmill electrical generator is not normally working at its full

load. The experimental efficiency of the alternator at full load drops

to 85%.

In the following sections suggestions are made as to why the theoretical and experimental performance of the alternator differ.

5.8 SATURATION OF THE STATOR TEETH OF THE ALTERNATOR AND ITS INFLUENCE ON THE PERFORMANCE

Since iron saturation in the alternator was neglected, the derived expressions will be correct only for unsaturated conditions.

It is therefore important to check whether any part of the iron circuit of the alternator is saturated.

It is unlikely that the iron pole—pieces are saturated due to their fairly large cross—section. Reference [5.26] gives a simple empirical method for dealing with saturation which involves the use of a saturation coefficient in the performance of a wound field alternator.

The no—load flux per pole is calculated from the required no—load terminal voltage VNL: V NL (5.7 °QL 4KB.f.T.K J 1)

Bef KB — B (5.72) av where Bef is effective flux density per pole and Bay is average flux density per pole.

198.

The no-load maximum flux density in the airgap of the

alternator per pole can be derived from:

-BNL = O 6. Y. s (5.73)

In this case 0 is the no-load flux given in equation (5.49):

B cc a = Bav (5.74) max

Fig. 5.23 shows the change of values of KB and 0(6 in terms

of the saturation coefficient of the alternator k . When k = 1 (no z z saturation) for a conventional salient pole generator, the waveform is

sinusoidal. There was no pole-shaping and hence the no-load waveform

tends to be a trapezoidal one. However, for simplicity, sinusoidal

conditions were assumed when saturation was absent, so that:

ab = 2/It (5.75) and TG (5.76) 215

From the calculations it was found that:

0NL = 0.00198 Wb

Y = 0.052 m

ts = 0.057 m

So from expression (5.73):

B = 1.049 T

Flux density of the tooth at no-load on its maximum value:

B BNL.c B (5.77) t t av k c . w 199.

ab

as 1.12 - 0.84

0.10 - 0.80

1.08 - 0.76

1.06 - 0.72

1.04 - 0 68 KB

1.02 - 0.64

1.00- 0.60 1.0 20 3.0 KZ

Fig. 5.23: The change of the values of SB and OCb in terms of the saturation coefficient k z . 200. where kc is packing coefficient of the laminations and equals 0.93;

c is slot pitch, and equals 0.0174 m; tw :is average tooth width and is 0.00908 m.

• Bt = 2.16 T.

The value of 2.16 T is very high for the electric steel

(Transil 92) used in the alternator. From Fig. 5.24 saturation begins at about 1.2 T. This saturation occurs in one of the teeth of the stator pole pitch at no—load assuming that the flux is distributed equally through the teeth. When the alternator is on—load, any quadrature—axis current will give an mmf which reinforces the field flux for one of the teeth in each stator pole pitch and, hence, gives a further increase in saturation (see Fig. 5.16).

Obviously, these levels would not occur in practice as the flux spreads out into neighbouring teeth and air paths.

It is difficult to find the performance of the machine when it is in a saturation condition because of the non—linearity of the magnetic circuit and modified values of reactance, etc. are necessary. In [5.26] the saturation coefficient is defined as follows:

When the flux density of the tooth is higher than the saturation flux density of the steel, a line x is drawn on the magnetic characteristic of the material, as shown in Fig. 5.24, line Kx is taken from Fig. 5.29(a): tav s K — k .t (5.78) c w where tsv is average slot width and equals 0.0104 m, and Kx is 1.2. 201.

line Kx ,

Induction (Tesla) Hx100

2.0

Hx10

• 1.5 HX1.0

1.0 •1 Nx

TRANSIL 92 TYPICAL CURVE D.C. MAGNETISATION THICKNESS: -020" (O.50mm) TEST METHOD: D.C. PERMEAMETER

/ ASSUMED DENSITY: 7.65 gicc 01 i 0. . I 0 5 10 15 (Oersteds) 397.9 735.8 1193.7 (ATm') - Magnetising Force Fig. 5.24: Magnetizing characteristic of the lamination steel. 202.

Then a line parallel to the line of EX from the point Bt on

the B-axis is drawn. The intersection of this line with the magnetic

characteristic gives the new values of Bt and Ht . In this case it n n was found that the line meets the magnetization line at: x

Ht = 55 kATm 1

This new value of Ht can define the mmf in the stator tooth from: n Ft = Ht .h3 (5.79) n

where h3 is the length of the tooth, and is here 0.0235 m; Ft =

1292.5 AT.

The no-load mmf per pole is derived from:

-NL' g FNL (5.80) leo FNL = 403.6 AT

Finally, the saturation coefficient kz is given by:

k FNL + Ft z (5.81) FNL

k = 4.2 z

With the value of kz new values of kB and Oc6 are obtained

from Fig. 5.23; therefore new for a given Vim. This is of course N possible for a wound field alternator where the VNL can be varied and depends on the field excitation.

Finally, the saturation coefficient kz is introduced into expression for Xaq,. i.e. Xaq under saturation conditions is: x aqunsat Xaq k (5.82) - z 203.

Unfortunately in this case the kz is quite high and is not

in the Fig. 5.23, but an estimation of the behaviour of the KB curve

can show that for this particular k z

KB -=-- 1.02.

The new values of KB and Xaq are introduced into the computer

program and new curves of the machine are shown in Figs. 5.22(2) a, b, c and d. The results are also shown in Table 5.2.

It is noticed that the introduction of the saturation coefficient improves the correlation between theory and practice but still leaves some discrepancy. Several reasons may be responsible for this:

(a) under—estimation of magnet leakage; edge—leakage permeances were neglected: (b) unknown demagnetization; BH curve of the magnet not corresponding to the manufacturers design: (c) non—sinusoidal distribution and waveforms: (d) temperature rise of the winding and the magnet.

5.8.1 Calculation of the Performance of the Alternator with Lower Line of Return of the Magnet

It was decided to check whether the lower performance of the machine was due mainly, not to the saturation, but to a possible low BH characteristic of the magnet material, i.e. one falling below the manufacturer's specification—sheet curves. Fig. 5.25(1) shows the new performance of the machine with values of Bo = 0.48 T and Ho =

350000 AT.m 1. In Fig. 5.25(1) the no—load phase voltages are very nearly the same, but the theoretical regulation curve is not as high as previously (section 5.8) and the. discrepancy between the predicted and the measured power output is 15.6% (theoretical output at 300 rev.min-1 equal 2537 w). /

.k --- ~ V --+--'·---+-+-iXE~Pj~~.;;~~~r~'·nts "\ ~~~~~ THEO~TICALCURV~ I Y X 2! _.L ! I \ I 1- 3eU rev rnin- I ...... 2-2eO • .' V~ '{ 3-2e~' • /V* 4-150 • • j- af _3. ~. \f\ L1 +-L V"'" i'-" 11 LI/ . i "~.- - Ix/ .,,17l I i--r t-f:,...... L~ALV /~ I ' ~ "\I\~ 1 I I 5 ~ k-"'-~ . -...... '-. \. I WV- -.

--t.~ -- i- N '~J j- . \.~ \ ~rl ~ '\ 2 4 6 e 10 12 14 1€ 1S LOAD C~~~ENT.AMPS.

2-4 I I I I I 'I 2-0 - I I I o r-' ~ '--I ~ 1·6 I I --f- r.J I I I 1/ --1 1 ~ 1·2 t I - ~

Table 5.3: Parameters and design of the Mark I p.m. alternator 1ntb magnets of low line of return.

Low line of return P.M. ALTERNATOR DESIGN MARK I on t.hp. m:urnp.+,

1-15- . .fij} ~~ ~ ~ ~ /~\SbfJJ1J~, Dso ~~ Lr ~ ~La-' tJ ~W1 ~h2 Os .I 9 t c ~I-wo +"h, -rI~..-.\ r- - Lm ... .

No. of phases m - 3 Ds - 266 mm Ls· 57 mm Lm = 145 mm twav J:J • o&m

No. of slots Z =' 48 D50=360 mm 19= 0.48:;n wo= 3 mm w, = 9 mm

NQ of poles 2p = 16 La= 52 mm wm=lO mm w2= 11. 7mm h,= 1.7mm ." NQ of turns/coil Tc = 21 lr= 46 mm y= 52 mm h2::' 2 mm h3 = 23.5

I) No. of Slot~ q = 1 con~uctor cross = 2. 47 mm ~ slot == 29~ pole/phas sectional area area mm C =17.4mm Type of Double Type of magnet = Hera Stack steel =Transi 1 92 . winding· 1 aver "mesh" _ 350 _ 240 Br 0.48T 8 t= 1.2 T Winding • = Ho - kATm-1 sa H5at-ATm3 connection • A R.P.M.= 300 Costp= 1.0 KWd = 1.0 Kp= 1.0 KSk= 0.955 Kz= 2.08 10.2 $NL = 1. 73mWb BNL::' 0.916T Bt= 1.89T HtnTcATm-1 Temperature rise== 75°C Calculated Calculated Unsatur. satur. Test Unsatur. Satur. Test POUT 2.54 kW 2.12kW 2.14 kW Rs 0.742.2 0.74252 0.715.Q.

V 67.5 V 20 V 55 V Xad 4.2 Q. 4.085.(2 -

Imax 12.5 A 11.8 A 12 A Xaq 8.62.Q 4.14.Q -

VNL 100 V 93 V 100 V Xl 1.25.0 1.25.Q. -

lsc 18 A 17 A - Xd 5.46(2 5.34Q - 11 86% 85% 85% Xq 9.87.Q 5.4 a - 0 57° 43° - Overall weight: 120 1b - 54.5 kg EXPERIMENTAL POINTS AT 300 rw mil\-1 x 240r---,----r----r---~--~--~--~~--~--~ }t4EOflE'!ICAL CYRVE~ 120 ,- 300 r."min-' ''0 a- 2~O· • 3-200· • X .-150 • ~200r---;----r----r---+-~~---+~~' 100 . ~-'oo· • 0- 50· • ~ lI'I ~ ~160t----~---r----~--~~ o eo ~ > W "r- ~ 120f--+--+--..oC---,A-- w· 3 (!) 60 ~ ~ 4 g 40 W 5 ~ J: 20 n-

00 :.! 4 G 6 ~ ~ LOAC? CURRENT. AMPS (a)

0: 12 ' 12 ~ ~ ffi 1'0 I "0 V I ~ <: woe ,«O'OB /- J: 7(~~'~5 4 0:: l- '''' 1: ~ LL 6 006 L I ~f06 / >- I1 ;-:; (!) U Z /' Z 0,4 W04 , ~ , « L o o './' 6: () '/ tt 02 I . -I 0·2 ~ :> ; V a.: ./ eo 120 160 200 240 280 320 360 2 4 6 8 10 12 14 16 18 TOTAL OUTPUT POWER, WATTS x10' , LOAD CURRENT, AMPS (d) / I\:) (c) o Fig. 5.25(2): Curves of the Mark I p.m. alte~nator with a low line of return of the magnets and with saturation 0\ taken into account: {a} voltage regulation, (b) power output, (c) efficiency, (d) load angle. • 207.

The -check on the saturation of the stator tooth with the new line of return at no—load gives, for:

¢NL = 0.00173 Wb

From expression (5.73):

17 T —NL = 0.9

From expression (5.77):

Bt = 1.89 T

The saturation level is somewhat less than previously. In this case the saturation coefficient was found to be:

k z 2.08 therefore:

kB = 1.05.

Fig. 5.25(2) shows the new performance of the alternator, taking into account a low line of return for the magnets and the saturation effect.

It is very difficult to tell which line of return is the true one. The question can be answered only if magnetic measurements could be taken on the rotor magnets themselves.

It was decided for future design calculations to assume a low line of return (see Fig. 5.11) and if the tooth is still saturated then to introduce new values of KB and Xaq which are derived from the known saturation coefficient kz.. Table 5.3 shows the performance and design of the Mark I p.m. alternator at these conditions, i.e. with the low line of return and the introduction into the calculations of the saturation coefficient. 208.

As is seen in Fig. 5.25(2) and Table 5.3, the calculated no-

load voltage might be lower than the experimental one, with the

introduction of the saturation coefficient, but the overall shape of

the regulation, power and efficiency curves is quite satisfactory.

Because in the calculation of Xad is included the value of KB, then

Xad is slightly different from the one for unsaturated conditions.

5.9 TESTS ON 'nib MARK I P.M. ALTERNATOR

Two constructional modifications were made to the alternator during testing and the results are correspondingly divided into three sections, A, B and C. In its original state, the alternator had an unskewed stator with 20 turns per coil and an airgap length of 0.41 mm.

Section B results were measured after increasing the airgap length of the machine by 15% to 0.438 mm (see also Section 5.10.2), by turning down the rotor diameter. Section C results were measured after rewinding the machine and skewing the stator laminations by a slot pitch; a new winding was put in with 21 turns per coil of four wires with diameter 0.9 mm each. The results are discussed in detail in

Sections 5.10 to 5.10.3.

The principal tests carried out were:

1) Voltage and output power versus output current at the constant speed of 300 rev.min 1 (variable, three-phase resistive load).

2) Voltage and power versus current at the constant speed of

300 rev.min 1 (variable d.c. resistive load fed via diode bridge rectifier). See Fig. 5.30. 209.

3) Temperature rise of the winding versus time at constant speed

and load.

4) Variation of output current and input torque versus speed for

constant d.c. voltage loads beyond a diode bridge (see Fig. 5.30).

5) Output and input powers at different constant resistances

versus rotational speed for an a.c.,resistive load and a d.c. resistive load fed via diode bridge rectifier.

The last group of tests was carried out at the Twente

University of Technology in Holland. The results of the tests enables efficiency versus output and rotational speed curves to be derived for various conditions.

5.9.1 Test Rig

The alternator was tested in the laboratory with a d.c. drive motor replacing the windmill. The available d.c. motor could not give the required maximum torque at the rather low speed of 300 rev.min 1, so a step-down transmission was used. The rated power of the d.c. motor was 3.5 kW at 1450 rev.min-1 and it was decided to use a Fenner timing belt drive incorporating a 5:1 step-down.

The alternator was dynamometer-mounted on gimbals so that alternator input torque could be measured by means of a spring balance on the stator case. Figs. 5.26 and 5.27 (photograph) show the rig of the tested alternator, where: (1) d.c. motor, (2) Fenner timing belt drive, (3) the under test p.m. alternator, (4) tachogenerator,

(5) supporting bearings, (6) driving shaft, (7) solid coupling, (8) the

210.

10

sr* MI OW

Fig. 5.26: The laboratory rig for the tests on the Mark I p.m. alternator.

Fig. 5.27: The laboratory rig used for the tests on the Mark I p.m. alternator. 211.

three-phase terminals and the neutral of the alternator, (9) safety

cage, (10) spring balance, and (11) steel base of the rig.

5.9.2 Test Procedures

The main power diagram used is shown in Fig. 5.28, where:

(1) p.m. alternator, (2) main switch from the alternator, (3) three-phase

plug-board, (4) load switch, (5) variable resistor (load), (6) oscill-

oscope, and (7) a.c. test set.

The system incorporated an earthed neutral point in order to decrease pick-up in the oscilloscope. The three-phase plug-board was used in order to have measurements of the currents flowing in each of the three phases. This is important because the load had to be symmetrical in the case of the a.c. load to avoid extra noise caused by the sensitivity of the alternator, especially in the unskewed state, to unsymmetrical loads.

During the constant speed (therefore constant frequency) tests, speed was held constant by making suitable adjustments to the d.c. drive motor control. The three-phase diode bridge used for the tests with d.c. loads is shown in Fig. 5.29. For the temperature rise tests, the same technique was used as in Section 4.4.3.

The waveforms of the phase current and the phase and line voltages for different conditions are shown in Figs. 5.32a to 5.34d.

These were obtained using a differential-input oscilloscope. The harmonic levels in the voltage waveforms were determined with a wave analyzer. 9

15A

B RESISTIVE Y LOA D A FUSES

DIODES

I 0 04

Fig. 5.29 Rectifying diode bridge connected to a resistive load.

1.O5S2

Fig. 5.28: The main power circuit. 213.

RESISTIVE LOAD

P.M. ALTERNATOR DIODE BRIDGE

Fig. 5.30: Diagram of the Mark I p.m. alternator connected to a d.c. resistive load.

D.C. GENERATOR

PM. ALTERNATOR DIODE BRIDGE

Fig. 5.31: Diagram of the Mark I p.m. alternator connected to a d.c. constant voltage load. 1 214.

0

Fig. 5.32a: No—load phase voltage Fig. 5.32b: No—load line voltage (Section A) waveform. waveform (Section A).

Fig. 5.32c: On—load phase voltage Fig. 5.33: On—load phase voltage and current waveforms and current waveforms (Section A). (Section B).

0 t t

Fig. 5.34a: No—load phase—voltage Fig. 5.34c: No—load line voltage VQ1 waveform (Section C). VIS waveform (Section C).

Fig. 5.34b: On—load phase voltage Fig. 5.34d: On—load line—voltage and current waveforms and current waveform (Section C). (Section C). 215.

5.10 RESULTS AND DISCUSSION OF ACTUAL PERFORMANCES OF 'lilt: MARK I P.M. ALTERNATOR

This section presents the results obtained.

5.10.1 Section A Results (Unskewed Machine with 20 Turns per Coil and an Airgap of 0.41 mm)

By increasing the load of the machine, i.e. changing the load

of the machine, i.e. changing the load resistors and keeping the speed

of the machine constant at 300 rev.min1 , the regulation and power

characteristics were obtained as shown in Fig. 5.35. Fig. 5.35 shows

output voltage and power versus load current at 300 rev.min 1, the

three—phase a.c. load being varied by adjusting the bank of rheostats.

A brief test was carried out at this stage to see if any

marked transients occurred after load switching. Maximum load was

suddenly connected and then suddenly disconnected by means of a three—

phase switch. Ultra—violet recorder—traces of voltage and current showed

that the overshoots of current and voltage are minute and that the decay

to zero occurs within only one or two cycles.

The very short time constants implied by these results are

almost certainly due to the "stiffness" of the field supply system

(magnets) and the small pole pitch (hence low X/R ratios) of the alternator.

The temperature rise curve of the winding is shown in Fig.

5.36. This test is essential for any electrical machine because it indicates the temperatures at which the insulation materials have to work. Temperatures beyond the classified levels, if maintained for any length of time, lead to rapid degradation of the insulation system. P Watts 1000 I I AC.POWER OUTPUT/phase 900L-----~----~----+_--~·r_--~~==~ IgSO'41mm

A.C.POWER I aoo L----t----.J----t---:-~1'f7~_'\ OUTPUT! phase 19- 0·483 mm . I 1.12A. Ig =- 0·41m.rt 700 70 ~ V ---- !. Volts 00 V 100 6 60 ./ n - 300 re'.! min-1 ~ 1=10·25A. 90- 500 50 7 ~ • lo=O·483mm V/" 80 400 40 / /; / 70 300 30

J 1,t 60 200 20 1/ \ I· \

50 100 10 .1

__ 4J ~ ~----..-L-----_+--_-~----l+9=~0-.4~ o 5 10 15 100 200 300 Load current I, Amps . Time. min Fig. 5.35: Regulation and power output character­ Temp erature rise characteristics· of the istics of the Mark I p.m. alternator with an a.c. loud (Sections A and B). ~ark I p.m. alternator (Sections A and B). 217.

For insulation of the class used in our machine, the temperature rise

should be within 100°C at maximum power and normal conditions. Luckily,

in wind power applications, maximum cooling and maximum power conditions

coincide.

Waveforms of current, phase and line voltages which were obtained at no—load and on—load conditions are shown in Figs. 5.32a, b and c respectively. The waveforms are found to be quite different.

This is thought to be due to the higher level harmonics in the airgap of the alternator caused partly by the slotting and pole number chosen and partly by suspected saturation. The third harmonic of the phase voltage on load was found to have the value of 24% of fundamental.

The machine was designed and built very quickly and the design (a), though convenient from the constructional point of view (one slot per pole per phase, unskewed, full pitch winding, unshaped field),

(b) giving unity winding factor, was expected at the outset to give rise to considerable waveform distortion. Distortion associated with mains supply is undesirable due, briefly, to the interactions which result between the undistorted sinusoidal conditions normally present and the source of distortion itself. The experimental alternator was never intended for mains connection and distortion is less of a nuisance.

However, it does give rise to: (1) slightly higher winding and iron losses, (2) difficulties with thyristor triggering when thyristor controlled rectifier bridges are used on the alternator output; and there is therefore some incentive to reduce distortion where possible by the traditional means (skew; short—pitched windings; field shaping, etc.). The saturation effect in the machine was thought to result from a too—narrow tooth width in the lamination design (see Section 5.9.1). 218.

This again was inevitable, given the use of laminations available in

the laboratory and the rather high flux per pole, and led to the

decision to increase the airgap since this reduces both field flux

(only slightly with high coercivity magnets) and armature reaction

(by a larger amount).

5.10.2 Section B Results (Unskewed Machine with 20 Turns per Coil and a New Airgap of 0.483 mm)

Most of the Section A tests were repeated and the results (regulation, power output and temperature rise) are shown in Figs. 5.35 and 5.36, respectively.

Opening up the airgap reduces the flux per pole as stated above, and this has reduced the no—load voltage and maximum power.

Unfortunately, the regulation curve has not been improved (an improvement was expected due to lower armature reaction reactances) and the maximum power output is 9.3% down.

However, the voltage waveform is much improved, as shown in

Fig. 5.33. The phase voltage waveform on—load is much smoother than before (Fig. 5.32c). The third harmonic in this waveform had the value of 2.5%. This improvement indicates that the suspicion about the influence of the armature mmf and the saturation in the machine was correct.

The regulation and power output curves with diode bridge and d.c. resistor load are shown in Fig. 5.37, together with curves obtained previously with the a.c. load. Vp, Pr 1)ac :' 4 '\I Volts Watts-t---i---t----t--r---+__ VdcYac;R.~w~a~tt~! __~ ____-' ______'- ______r- ____:r ____ --' , I Volts

2700--~----+------4------r-----r-----J

POWER OUTPUT '2400--+-----+-----+------t-}~·~~~~1

220,110 2100 --1-----J.----f--r--t---t---.

" .\fJ, 6 1200 -t----t--I---t---+---+-,f--t---l\r ~:\~

19 =0·483mm 160,80 1200--+--J~~----t-"'~----rn :: 300 rev min-t

40 800-4-~-+------~--r~+_-+ __~ __~ 19 = Q-483mm 140,70 900 ,}, n :: 300 rev min-t

\'1 \ ')

~~~-----~--~- 10 I ., 5 10 I 15 Load current ac Amps 9-?" __ °1,4'-' 0;6 0;8 1-,0 1J J ,Fig. 5.37:" Jl,egulation and power output ·characteristics 2 4 6 B 10 12 '14 ~~...... of the Mark I p.m. alternator with a.c. and Load current . I Amps . I Fig. 5.38: d.c. resistive loads (Section B). Regulation, power output and efficiency. . \. charadtel'istic curves of the mark I p. m• . al te rn'at or- '(Se'ct!oi}' C). '\ ' .... 220.

On a d.c. load the machine can give a measured maximum power

output 22.7% less than it gave on a three-phase a.c. load. This is

thought, briefly, to stem from the fact that with a rectifying three-

phase system only two of the phases are conducting at any instant,

leading to less uniform conditions inside the machine. Another reason

is that the distorted waveform gives less rectified output than a pure sinusoidal waveform.

A further undesirable feature of the alternator was the rather high "cogging" torque. "Cogging" torques are caused by magnetic attraction effects between rotor and stator efficiencies. In a permanent magnet-excited machine, the field cannot be'bwitched-off" and the cogging torque is always present (independent of output current). Cogging is exhibited by cycle dynamos, etc. and consists of a rotor-angle-dependent torque which alternates about zero as the rotor revolves. It is desirable to eliminate cogging in order to minimize noise and vibration and, for windmill applications, in order to minimize also the starting torque requirement and hence minimize the wind speed for starting

(assuming separate starting means are absent).

The alternator was designed with one stator slot per pole per phase, i.e. three stator slots per rotor pole. Hence all the rotor pole pieces come into alignment together, with sets of three stator teeth, thus maximizing cogging. It would undoubtedly have been better, given more time, to have used a different slotting design but as an interim measure it was decided to skew the stator laminations by one stator slot pitch, thus smearing out the rotor edges over an angle of 27/ number of slots. The skew would also reduce output distortion levels. 221.

5.10.3 Section C Results (Skewed Machine with 21 Turns per Coil and the Airgap of 0.483 mm)

It was necessary to extract the windings before skewing the

laminations and opportunity was taken of adopting a new winding with more turns of a thinner wire in order to restore the no—load voltage of the machine to its original level of 100 V. The number of turns per coil calculated to achieve this was 21 turns per coil.

The stator of the machine before and after skewing are shown in diagrams in Figs. 5.18 and 5.19. See also the accompanying photographs of the unskewed and skewed atator, Figs. 5.5 and 5.6, respectively..

The new winding of the machine was wound with four conductors of 0.9 mm having class F insulation for temperatures up to about 160°C. The attached photographs show the new winding in its stator, Fig. 5.9.

The tests were repeated again. The skewing of the alternator gave satisfactory results. The waveforms were generally smoother than before (Figs. 5.34a-5.34d). The measured efficiency characteristic calc- ulated from the output power, torques and speed figures is shown in

Fig. 5.38 together with the regulation and power output characteristics for an a.c. three—phase resistive load.

Tests were again carried out with a rectifier load. Fig. 5.38 shows the differences between the efficiencies of the machine on differing types of load. Fig. 5.39 shows the power levels on the a.c. and d.c. sides of the rectifying bridge. It is apparent that the losses in the bridge are about 18-20 W. As stated previously, a rectifier load is less favourable for machine operation and the maximum power available is reduced. This affects its efficiency as shown in Fig. 5.38. On an a.c. load the P = 2140 W and on a d.c. load the P = 1770 W (a max max difference of 370 w). 222.

The results of a temperature rise test on the new winding of

the machine are shown in Fig. 5.40 and are quite satisfactory.

Because the alternator is intended for use in wind generation

it is very important to know the behaviour of the alternator at different

rotational speeds. Figs. 5.41 and 5.42 show the obtained results for the

regulation and power characteristic of the alternator at different

constant speeds with d.c. load. Tests were also carried out with constant

voltage d.c. loads fed via a rectifier bridge.

A separately excited d.c. generator (see. Fig. 5.31) was used and

Figs. 5.43 and 5.44 show the changes of current and torque of the alternator

in terms of its rotational speed at different constant d.c. voltages. The

standstill torque in all cases was 4.8 Nm (the residual togging torque of

the skewed alternator, a reduction of 65% from the unskewed alternator).

Figs. 5.45-5.50 show curves of input, output power and

efficiency versus speed for different constant (resistance) a.c. and d.c.

loads. The shape of the power versus speed curves shows that the power changes with the square of the speed when the machine is on low loads but this relation of power and speed changes when the load increases

(small values of load resistance). This is because the voltage drop in the machine increases with the load and therefore the voltage is not directly proportional to the speed, i.e. power to the square of speed.

The efficiency curves appear to show that with a d.c. load, the alternator works with a higher efficiency. Unfortunately, the instrument- ation used for these particular tests was not functioning properly and the results obtained, in particular the power output, were almost certainly in error. Because the alternator works with higher losses with a d.c. load, where the losses of the rectifier bridge are also included, the efficiency is almost certainly lower than the efficiency with an a.c. load.

P Watts 2000 Pat.__—_ a.c side FFai td c .eiQe 7

•-.. •

1600 At

100 I.12A 1200 80

60

800 40 7

1 20 •

400 0 100 200 300 Time, min

4 8 12 16 20 Idc A 2 4 a 10 i2 Load current lac Amps

Fig. 5.39:. Power output curves on the two sides of Fig. 5.40: Temperature rise characteristic of the the rectifying bridge of the Mark I p.m. Mark I p.m. alternator (Section C). alternator. Vdc Volts

Pacwatts 200 18 3001 rev min1 -,

. i 150

300 rev min' 150

200 rev min' 1000

100 "00 rev ruin' J

500 100 rev min'

80 rev min 50 1 00 rev min'' d:•••00•0001.„-- . .

80 rev min' ir 0 2 a 6 a 10 12 14 tN Load current Idc Amps •

0 . 2 - 4 6 8 10 12 1i Load current IdC Arnps Fig. 5.411: Regulation characteristics at different speeds Fig. 5.42: Power output characteristics at different speeds of the Mark I p.m. alternator with a d.c. of the Mark I p.m. alternator with a d.c. resistive load. 1 resistive load. I,Am s

14 rN-m

12 :~< ; 60 t·,

11 10

8 40

6 ~ .

4 20

2

o 100 200, 300 O~.----~~----~----~~----~----~----~ 1 100 200 300 Shaft speed n, rev min- S.hatt speed n. rev min-1 Fig. 5. U: Change of current at differen't speeds of the Fljg., 5.44: Ch~nge of the invut, ~~rque at d~fferent speeds of Mar}c I p.m. alternator with d. c. c.onstant the Mark I p~m. alternator with a d.c. coristant voltage load. voltage load. I\:) I\:) U1. 226.

~

... jl2''JQ Fig. 5.45 / Input power versus speed at different constant, a.c. resistive loads of the I 1&Ao ! " Mark I p.m. alternator. 1/ /,2SQ 'I

1000 / I lif/ v \00._

~ ~IA'/ V lOOQ .~~' I ~Q) ~~L Po"r Watts o 100 200 300 400 <:'JOO Shaft speed,n, rev min-' [ . :---_.-,-

I I2'S~ I

Fig. 5.46 1Soo / V Total outPut.power versus speed at I different constant a.c. resistive 2SQ loads of the Mark I p.m. alternator. j' 1000 11 V _L / V V· 5011 / / / V VV .~ R1~ o 100 200 :300 400 :---. St-.aft s;>ced. n, rcv mln"'

I ~~2'JQ ~ .. ~Q 0-8 e-e- X i -I r- o· 7n'~t11 ~IOOQ- It'~' lL· . I 0'6r--t.'" Fig. 5. 117 It,"'~' , o· 'Jr-'~' V Efficiency curves versus speed at different constant a.c. resistive 0'" JILj "'1 loads of the Mark I p.m. alternator. J-u"H- ",/I' ,, '2 r o 0111 , .U , o"l-t;r '11 r I I I I 0 !:' 100 200 300 400 Shaft spced,n, rev min-' 227.

Fig. 5.48 Input power versus speed at different constant d.c. resistive loads of ~be Mark I p.m. alternator.

200 ~CO 400 Stoaft speed,n. rev min·' ,-

Fig. 5.49 1~~-+--~---r--+----~' Total output power versus speed at different constant d.c. resistive loads of tbe Mark I p-.m. al ternato ______1OOOI

f I I I~J . ~u,. ~~~~- Fig. 5.50 I' ,. . tU' I Efficiency curves versus speed at different II~ constant d.c. resistive loads of tbe Mark I 11 , r--.II'Ll· - p.m. alternator. I, it; /1 "i t-I,,," I ,,"'1 I' 0·3 ~j" ,'f"':" ,t I L 0-2 :1:: I' ~ - r'"'11 , 01,::1------.---. '" o 100 200 300 400 Shaft speed. n, rev min·' 228.

Unfortunately, technical difficulties with the windmill of

Imperial College, sited on the roof of the Electrical Engineering

Department, have prevented quantitative tests from being carried out

with the alternator mounted on the windmill. Qualitative observations indicated, (1) that the mechanical mounting of the alternator arrangements were satisfactory, and (2) that the residual cogging torque enabled windmill rotation to commence at about 2.2 m.sec-1 wind speed and to continue as long as the windspeed kept above 1.3 m.sec-1. The maximum metered output power from the windmill rig was 1.5 kW, before tests were abandoned.

Photographs show the whole windmill assembly de—erected with the shroud removed (Fig. 5.51) and erected with the shroud in place

(Fig. 5.52).

This first part of the chapter has dealt with the first experimental p.m. alternator intended to satisfy the requirements of a direct drive windmill system. The machine gave high values of efficiency and appreciable power output at very low rotational speeds. After modifications had been made, the cogging torque was reasonably satisfactory for the experimental three—bladed windmill on which it was mounted, but excessive for the low solidity, high aspect—ratio, high speed, single—blade windmill of the Twente group.

A fairly full report 05.40: was written on the Mark I work and Sections 5.3 to 5.10.3 above quote freely from this report. 229.

I

Fig. 5.51: The Mark I p.m. alternator mounted on the windmill assembly with the shroud removed.

Fig. 5.:52: The Imperial College windmill generator mounted on the roof of the Electrical Engineering Department. 230.

5.11 DESIGN AND CONSTIJCTION OF THE "RUTHERFORD" LOW SPEED PERMANENT MAGNET ALTERNATOR

Parts of this section quote freely from a report 5.413 in

preparation on this alternator.

Due to the willingness of the Rutherford Laboratory to assist university research by providing manufacturing, design and testing expertise and resources, a decision was made to design and manufacture a larger alternator of the Mark I type. The proposed 10 kW machine was based on the probable future need for a wind system of this power level, given its capability, in locations having mean wind speeds of 10 mph and above, for providing at least 75% of the thermal demands of typical well—insulated homes. The alternator was designed to match a vertical—axis windmill of "Musgrove" design, also built at Rutherford

Laboratories. The speed of typical 10 kW windmills, when operating at full load, is 150 rpm. It was decided to attempt a design having a rated speed of 150 rpm. -see-photograph 5.74b.

The overall layout of the "Rutherford" p.m. alternator is very similar to the Mark I p.m. alternator but due to the higher power and lower shaft speed a larger value of DAL is necessary. The overall diameter that emerged following the choice of rotor diameter was not considered to be excessive for a horizontal—axis windmill of appropriate power rating. In the case of the vertical—axis windmill, the alternator location and orientation results in almost no disturbance to the wind.

The choice of pole number of the alternator is dependent on a large number of variables which are given in Section 5.3. There was no requirement for the alternator to be synchronised to a 50 Hz supply. If this had been the case, a 40— or 50—pole choice would have been mandatory 231.

for 150 and 120 rev.min-1, respectively. Hence a pole number between

30 and 50 was thought appropriate.

The rotor construction of the "Rutherford" p.m. alternator is

similar to the Mark I p.m. alternator, though the bearing arrangement is

different, as is shown in the cross—section of the machine in Fig. 5.53a. Fig. 5.53b shows the stator slot and tooth dimensions and Fig. 5.54 shows a photograph of the machine during its construction at "Rutherford" laboratories.

The magnets/ radial depth was chosen so that there is not an over—increase of rotor leakage flux and the pole flux is 0.967 T (see

Section 5.11.4), high enough to just saturate the stator teeth. Due to the large number of iron pieces required to be machined to form the rotor poles, a strong case can be made for a laminated rather than solid steep rotor construction.

At first the rotor end plates were made of dural, but this gave some trouble due to the different expansion rates of the stator stack and the dural rotor end plates. The airgap of the machine tended to close when the alternator was cooling after test runs. New rotor end plates were then used, made of a non—magnetic stainless steel. Later on in

Sections 5.11.3, 5.12.2 and 5.13.2 it is shown that this operation, though reducing the closure of the airgap, did not eliminate it entirely, and also resulted in a slight increase of the rotor leakage flux and hence reduction of voltage and power levels of the alternator.

The stator design of the alternator was based on the stator design of a conventional machine as in the case of the Mark I alternator. 232.

890 mm

SHAFT ROTOR

AIR

DURAL STATOR CASING STACK AND DURAL WINDING END PLATE MAGNET ROTOR END PLATES BEARING HOUSING (Dural or non-magnetic stainless steel ) BEARINGS Fig. 5.53a: Cross-section of- the "Rutherford" permanent magnet alternator.

All dimensions in mm. Not to scale

Fig. 5..53b Slot and-tooth-dimensions of the "Rutherford" p.m. alternator.

Fig. 5.54: "Rutherford" p.m. alternator during its construction. 233.

The electrical design of the alternator was determined after

looking carefully at several trial designs. Predictions were made using

the computer program given in Section 5.6. A 0.4 mm airgap was feasible,

given the large rotor diameter, and was near optimal magnetically.

As stated in 5.41] , the mechanical design of large diameter

length, small airgap machines is difficult because: (a) rotor

concentricity and alignment tolerances are tight, (b) the stiffness of

the stator lamination pack to radial distortion is relatively low, and

(c) thermal expansion problems may occur.

The solution adopted in the "Rutherford" machine's mechanical

design is shown in greatly simplified form in Fig. 5.53a. The main frame

consists of a fabricated assembly comprising a 19.05 mm rolled-dural

cylinder and a single-webbed 19.05 mm dural circular base-plate. Two

bearings located at one side of the rotor only are used and their housing

is built into the base-plate. The laminations are glued together with

epoxy resin. The lamination pack is located radially by means of

accurately turned bands. The bearing assembly is carefully designed to

allow a minimum of tilt. A double-ended shaft arrangement was adopted

to facilitate dynamometer mounting during testing.

The number of stator slots in a three-phase machine is usually

three, six, nine, etc. times the number of rotor poles. This enables one

or two or three, etc. overlapping coils per group, all connected in

series and all belonging to one phase to be placed in successive slots

in the stator, there to be threaded, by the flux from each rotor pole.

When a relatively small pole pitch is used, as in the present case, a

small q is generally inevitable, since if individual slots and teeth

are made too small, the winding packing factor becomes low, the cost of 234.

punching, winding and connecting go up and and teeth become brittle.

In the Mark I design, a q of one simple coil giving a group containing a simple coil and three coils belonging to the A, B and C phases, respectively, in each pole pitch of the rotor periphery. The snag with a q of one, or any integer, is that cogging torque is maximized. As the rotor rotates all the rotor pole edges align simultaneously with slot edges and the reluctance alighment forces, due to the permanent field, reinforce. In the Mark I machine cogging torque was reduced by skewing the stator lamination stack. A skew of one slot pitch (i.e. circumferential twist over the stack length is one slot pitch) should theoretically reduce the cogging torque to zero. However, flux fringing at the stack ends gives a modified effective stack length and some trial and error on the stack length and skew level is necessary to produce zero torque (see also Chapter 6). This would have been time-consuming and difficult on the Rutherford machine. Also, skewing reduces output due to mismatch between the parallelogram shape of the coils and the rectangular distribution of the field, and the enhancement of both rotor and stator leakage effects.

Hence an alternative to skewing is desirable, and the one considered, perhaps the only one available, is the use of a non-integral number of slots per pole per phase q. Cogging forces, although not zeroed, are reduced, briefly, because fewer poles align simultaneously with stator teeth. When a non-integral q is used, it is inevitable that the size of individual coil groups varies between integer values above and below q. The calculation of the total emf generated by all the series-connected coils of a phase winding is complicated by this non-uniformity and care must be taken to ensure that the three-phase emfs remain balanced, i.e. equal in magnitude and differing by 120° in 235.

phase (see Sections 5.11.1 and 5.11.2). As with skewing, a non—integral

q reduces output slightly. This is due to phase differences between emfs

in the different coil groups in a phase winding.

A number of possible designs were examined, some using skewing, some using non—integral q and some using both methods, and it seemed that for the magnet blocks available and the airgap diameter chosen, a

48—pole, unskewed design would be preferable. A larger number of poles would lead to worse stator tooth saturation, given the pole flux set up by the magnets (with an allowance for leakage and a provisionally assumed slot/tooth width ratio on the stator). A smaller number of poles would reduce output due to the reduced airgap (or pole) flux density. As was stated previously, similar arguments were involved in fixing the pole number on the Mark I machine. Similar sized magnet blocks were used and it is therefore not surprising that both machines have a similar pole pitch, since the pole pitch rather than the number of poles controls the nature and extent of a large number of first and second order effects in the machine. A fair degree of confidence could be assumed for prediction about the "Rutherford" machine based on the existing theory and measurements for the Mark I machine.

The slot width to tooth width ratio was then fixed at a value which avoided an excessive tooth flux density and slot current density level under worst case conditions. The depths of the slot and the iron behind the slots were similarly fixed. In hindsight, a slightly deeper slot would have been worthwhile to hold copper losses down a little more at full output. However, the machine would have been made heavier and more expensive, and the winding process more lengthy. On the contrary, a wider tooth would increase the slot area, therefore increase copper losses. 236.

The choice of q narrowed to 11/12 or 10/12 and 11/12 was

selected since this gave a larger maximum output. After freezing the

lamination design, it was discovered (see Section 5.11.1) that a 48

pole, 11/12 q, three—phase winding is among those than can 9 officially1

be balanced. Although a change in the rotor design could have been made,

dropping the pole number, e.g. to 46,_or:. raising it to 50, would have

involved the penalties mentioned above.

5.11.1 Double—Layer Fractional-Slot Windings

As stated by M.G. Say E5.29: , this type of winding is sometimes used for alternators and a.c. motors. It is mainly used in order to: a) reduce the cogging torque levels in the machine and smooth its

rotational torque in the case of a.c. motors; b) smooth the voltage and current waveforms of the machine, which are

distorted by the non—distributed pole flux and the higher harmonics

due to the stator slotting.

All the coils in the stator have the same dimensions and this type of winding has fractional values for the number of slots per pole per phase, q. The fractional value of q can be written as follows:

q = b + c/d (5.84) where b is an integer, and c/d is a proper fraction.

From £5.26D the following two requirements have normally to be satisfied in order that the fractional slot winding can be balanced: 237.

1) 2p/d has to be an integer, where 2p is the number of poles of the

machine;

2) d/m has to be a fraction, where m is the number of phases of the

machine.

It is said that in a fractional slot—winding there are big and

small groups. The value of b gives the number of coils in the small

groups and b+l the number of coils in the big groups. A method is

shown below for designing a fractional slot winding:

a. The number of coils in the small and big groups is found.

b. The series of c numbers is written as follows: djc; 2d/c;

3d/c; ; cd/c = d.

c. Into each fraction of this series is substituted the nearest

bigger integer. A new series of numbers is obtained: N1, N2, N3, ..., d.

This series of numbers indicates the position of the big groups

of all the phases along the periphery of the stator for one sequence of

the winding.

There is no need to give more detailed explanation of this method

of construction of a fractional slot—winding because in the case of the

"Rutherford" machine, since this method does not apply because q <1 and

the small groups are missing.

Checking this particular winding for balance conditions, it is found that q = 1112, and therefore b = 0, d = 12 and c = 11. It can be seen that the winding satisfies the first rule, i.e. 2p/d = 48/12 = 4, which is an integer. However, the second rule cannot be satisfied, because d/m = 12/3 = 4, which is not a fraction as required. 238.

The construction of the machine hence does not satisfy the

requirements of symmetry and so theoretically the winding cannot be

balanced.

The next section shows the method which was used to achieve

a reasonable degree of balance.

5.11.2 Design of the Double—Layer Fractional—Slot Winding of the "Rutherford" P.M. Alternator

The winding can be designed with the help of coil emf vector

diagrams. The stages were as follows:

1. The electrical angular slot pitch is given by the expression:

= 36o° x P (5.85)

where p is the number of pole pairs and z is the number of slots of the

stator. Therefore:

= 3°6 o x — 65A545° Y 132 and the phase angle of the emf induced in each coil by the field flux was calculated from:

36o° x N (5.86) Yc z where N is the number of slots per coil. Therefore:

At Yc = l x 3 = 8.181°

Hence the phase angles of the first few successive coils were: 8.181°,

73.636°, .139.0909°, 204.74°, 270.0°, etc. (e.g. the positions of the- coil sides for coil No. 1 were 0° and 196.364°). See Fig. 5.55. 239.

84.5454 90° 95.4545 .4545 144.5454 C l B, 3 155.45 24.5454

204.5454 B 335.45 C 324.5454 215.45 275.45 264-5454

270°

(1) (2) (3)

slot number coil number

• A 0.0000 S. • 65.4545

130.9090 8.181 A1A2 A3 . . . 2> 73.636B;B2 'B3 196.3636 • B 261.8181 139.09 C1C2 C3

327• 2727 204.54414243

IS 32.7272 5) 270'0 B1 B2 C3

335.45 A1C2A3 98-1818 ~_ ~~ -

7> 40.9 B1B2B3 A 163 6363 ~- ~ B 229.0909 - - --- — — — /3106-363 C1C2 C3.

171.818 Ā4A21 3 294 5454

10> 237-272 B1B2 B3 A 0-0000

65 45 / `` /11\ 302.727 Ci C2 C3 13 /~ 8181

Fig. 5.55: Angular distribution of the coils of the winding of the "Rutherford" p.m. alternator. 240.

2. Decisions were then made on which phase each coil should be connected into. The decisions were based on Figs. 5.55(1), (2) and (3).

Fig. 5.55(1) corresponds to the conditions in a conventional machine, all coils with emfs having phase angles between —30° and +30° being put into the A phase etc. When the diagram in Fig. 5.55(1) was used for the entire winding of this machine, a large level of imbalance was found to result (23%). A similar result occurred when any other orientation of the boundary angle rose. The reason for this is that the imbalance in a sequence of eleven coils is reinforced in successive sequences.

It was therefore decided to use differing compositions in successive sequences. Using Fig. 5.55(1) as a basis, the sequences of eleven coils connected into twelve groups'of 1 or 0 coils per group is as follows:

Coil No. 1 2 3 4 5 6 7 8 9 10 11 Phase A Bs C A' B Cl B' C A' B C' Coils per 1 1 1 1 1 1 0 1 1 1 1 group

It seemed that for minimum disturbance one should adopt a choice basis which used the minimum amount of Fig. 5.55(1) reorientation necessary to achieve just a single change in the position of the group containing zero coils. Fig. 5.55(2) involves a twist of 5.45° anti- clockwise, giving:

Coil No. 1 2 3 4 5 6 7 8 9 10 11 Phase A B' C A' B C' A C Al B C' Coils per 1 1 1 1 1 1 1 0 1 1 1 group 241.

To achieve symmetry, it seemed sensible to use also a third

sequence based on a reorientation of 5.45° clockwise (Fig. 5.55(3)):

Coil No: 1 2 3 4 5 6 7 8 9 10 11 Phase A BY C Al B A BY C Al B Co Coils per 1 1 1 1 1 0 1 1 1 1 1 group

3. The B2 coils in the machine were divided into 12 sequences of

11 coils each.

4. The emfs from a set of three sequences, one of each type, were then summed and examined for balance. The emf values were 10.43046 < 0°,

10.4953 <239. 5°, 10.4953 <120.46° for the A, B and C phases, using a Iv one volt per coil basis. The imbalance of this set IVa + = 0.9947, or bi 0.5%. The Vc and Vb phase angles are ±120° ±0.45° with respect to Va.

This was thought to be satisfactory. A possibility remains that the set of three sequences is perfectly balanced and that the low level of calculated imbalance results merely in the residue of calculation errors.

5. Four identical sets were then assembled from the 132 coils of the entire winding, half of the winding connection diagram is shown in

Fig. 5.56 and in Table 5.4 are shown the coil connections of the whole winding.

6. One feature of the alternator specification was that the winding should allow series/paralleling to give half volts double current operation.

The fact that the winding divides into four identical sets means that a pair of sets can be connected in parallel with the remaining pair with only minimal circulating current occurring. Clearly one could even go to a connection where all four sets were in parallel.

6 6 6 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 i 11 N 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 1 la A ESC A` B C'. B C ti C' A BC/ B C A C A' B C' A B'C A' B A B C A' B C' A B C 1 4 6 7 8 9 11 1 13 14 15 16 1I 18 1 2• 21 2 2 24 25 26 27 28 30 32 33 34 35 5 1 /\ oft% 29

ti • : ~ / `~~ 9 OI 2 13l !4' ;Ō 17! !9~ O. 1; 12! 3 I4I 151 6 1?I 9 21 m 4 1 1 y y .a • * y 1 • I-4 1~ Is slesi ' V ' & 4 i A 4 !I4t ' t 1 11 I j ' 1 I I • I I Ili . t) p et- 1)..,.1) .5...... ~•X K Cr M 1 Lt. ewl H3 0 11 A I I • 1 I 11 1 1 1 , 1 K V • 1 • 1 • n 1I_--+J L - L. -j • 0 • 7Y2 Z2 0 Ca 1-1 Al Bi Ci p 1 b ,2 3 ,A ,5 6 7 ,9 8 i 3 ,7 1 B 1 3 3C 3B 3 4 4B 4 4A 4g 4C 4'4 4B 4 4 5C 5 5B 5C 5A 5B 5C 5A 58 5A 6B 6C 6A 6B. 6C 6 6B 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6

H. (XI 0

cs cD

u' fD I• 1-04 III I I 0 I L 1_11 II 10+ _J 1_ __I I _.J ā ō bi X1 Y, Z1 A2 B2 C2

aoTeuaa:je of of th e f e racti

onal —sl ot ot wi g g n ndi of th of e e : 'Saig es

10 11 12 14 13 15 16 17 19 18 21 20 22 3 4 6 2 7 5 8 9 Coil No. .61F Winding No. 15S 12F 18F 20S 23F 26S 28F 31S 37S 34F 45F 42S 48S 51F 53S 56F 59S 64S 9F 4S 1F 1S Connect to

Coil No. 18S 15F 12S 20F 23S 26F 28S 31F 34S 42F 37F 48F 45S 51S 61S 53F 64F 56S 59F

9F 4F A X l 1

1

PHASE A Coil No.

108S • 100F 103S 111F 114S 117F 119S 125S 122F 127F 130S Winding No. 69S 70S 67F 75S 78F 81S 86S 84F 89F 94F 92S 97s Connect to

Coil No. 100S 108P 103F 114F 111S 117S 119F 127S 125F 122S 130F 75F 70F 78S 84S 81F 89S 86F 92F 97F 94s

A X 2 2 2

Coil No. Winding No. 13S 16F 1OF 24S 21F 29S 27F 35S 32F 38F 43F 40S 49F 46s 60F 54F 65F 628 57s 7S 5F 2F 2S Connect to

Coil No. 10S 16S 13F 24F 21S 29F 27S 32S 4OF 38S 35F 46F 43S 49S 54S 62F 6os 65s 57F

7F B 5A Y 1 1 PHASE B

1

Coil No. 101S 1o6S 104F 109F 115F 112S 120F 126F 123E 131F 128S Winding No.. 68F 71F 68s 73S 79S 76F 87F 82F 90S 98F 95S 93F Connect to

Coil No. 104S 101F 106F 112F 109S 115S 120S 123F 128F 131S 126S 79F 76S 73F 71S 90F 82S 93S 87S 98S 95F B Y 2 2 2

Coil No. Winding No. 11S 14F 19F 17S 22S 30F 25F 36F 33S 39S 44S 41F 47F 50S 66s 63F 52F 58F 55S 6s 3s 8F 3F Connect to

Coil No. 14S 17F 11F 22F 19S 25S 30S 39F 36S 33F 41S 47S 44F 63S 52S 50F 55F 58S 66F

8S 6F c Z. l t PHASE

1

Coil No. C 102F 105S 110S 107F 116S 113F 124F 118F 129F 121S 132S Winding No. 69s 69F 72S 77S 74F 83S 80F 91F 85F 96F 88S 99S Connect to

Coil No. 105F 102S 107S 113S 118S 110F 116F 129S 124S 132F l21F 74S 72F 80S 83F 96S 91S 88F 85S 77F 99F

c Z 2 2 2

244.

5.11.3 Theoretical and Experimental Results and their Correlation, for both Constructions of the Alternator

As previously mentioned, the "Rutherford" p.m. alternator was modified following the first set of tests by replacing the dural rotor end plates by non-magnetic stainless steel ones. In this section are given the theoretical and experimental results before and after the modification (Case A and Case B).

The single set of theoretical results was taken from the existing computer program as described in the previous sections (see also

Appendix V-2) by feeding in the parameters of the "Rutherford" machine.

The parameters of the machine were left unchanged by the modification, but changes did occur in the test results (see also Sections 5.12.2 and

5.13.2).

For the calculation of the performance of the machine the low line of return of the magnet was used (see Section 5.8.1).

Parameter Values:

It was found that the calculated Xaq = 22.4Q at 150 rev.min-1, the calculated resistance of the winding R5= 1.32Q per phase in comparison to the measured one Rs = 1.38§/ per phase (both values at cold conditions).. The two values of Xad described in Section 5.8 were

10.7S2 and 9.9S/ , respectively.

The agreement between the theoretical and experimental curves of the alternator in both cases is only fair. See Figs. 5.57(a), (b),

(c) and 5.58(a), (b), (c) and Table 5.5. At 150 rev.min1 the no-load phase voltage is 351 V as opposed to a measured value of 287 V (18% 245.

~O~--~--~--~----~-r------~Ucal Exrcri'fl4!f'ltal ~ POInts 12~0~--~--~--~--=-~~-~------~ , X 1J~!:Ir ... "",,-t 2 0 108 x 3 0 6!:1 .. ~ 68 " ~,00~-~-_r-~~-~--+_~_4-_4--~ & GI .,·7& • IS IIi2 H~-& • ~ ~ a: eol----+---+:.f-~.. --I__-~o_ll_+-__+_--__I w 3:' ~ 601----F--/ I- ::> a.. 40 ~ o -1 ~ f2 26 32

0 0 4 8 ~ 16 20 24 28 32 ~D CURRENT. AMPS __ (a) :Regulation ~'{b}---'Power . output

f2~ ,~----~--~--~--~~--~--~--~--~ 2-0 c::~ '-Ol--~---+----I'----If--+----!----+--~ W ; ~ '~ c <{ 08 'If.~~-:o,....:=-+-J..Jj re '·6 W ::I: 6 L!.j I- • -./' ~ 0-61--t-+1 /Mr----4_--4_---t---~~--I---~ a 1~2 z <{ t; L V @0-4~-/J+---_+_--_4_---J!__-~--~--+-__I ~o·e d ) (J ..J V Li: 0-4 /" . tb 0·2~-4_--4_--~+---1_~+--~--~,-~ v L 20 40 60 eo 100 120 140 160 00 4 8 12 16 20 24 28 . 32 TOTAL OUTPUT POWER, WATTS x 102 LOAD CURRENT, AMPS (C) Efficiency (-d)1oad angle -.------~-- Fig. 5.57: Case Ai curves for differen:t rota,tional speeds with no saturation taken into account, for the "Rutherford" p.m. alternator.

Tneoretica' EXDl!'rjmenta' N curve. poInts S2,~o 1 X '~OreY mln"' 2 0 120 · )( 3 a 90 · .. ~ eo ~'00 0 30 · & · ~:= a:"ao w !: ~ 60 I- ::> e: 40 :::> 0

28 32 8 12 16 20 28 32 .- (a) LOAD CURRENT, AMPS (b) Pmver . output

- I Fi~. 5.58: Case B, curves for WK-....,~2~ It.~ ~ 0 3 x ;...-- C;:>1 different rotational speeds with ~'II )b ~ y. I ,no saturation taken into account, ~v.. . for the "Rutherford" p.m. V/ alternator • .//, I

20 40 60 eo 100 120 140 160 lOTAL OUTPUT POWER. WATTS x 102 (c) Efficiency 246.

Table 5.5: Parameters and Design of tbe "Rutberford" p.m. Alternator.

P.M. ALTERNATOR DESIGN I "Rutberford"

~I--I.:- M> ~ ~ "" ~ ,/\ --r I .... Dso ~~W21 ~.... h3 . h2 Lr ~ ...-La--- .~J ~ .t ! 9 Ds t j]f-,-Wo t . e h1 'lJ1fI~ r- ..-- lm - . t 9.83 No. of phases m - 3 Ds -780 mm ls - 56 mu: Lm =~160mm W;w- mm 8.43 Yw~ = No. of slots Z =- 132 D50=890 mm Lg= 0.4 mm 0 3.9mm W1= mm .

No of poles 2p= 48 La= 48 mm wm=12.3mn w2= 10.46mm h1=1.3mm 1.4 ~4.~7 No of turns/coil Te ·= 18 lr= 48 mm y= 51 mm h2::' h3= mm 2 2 No. of Slot~ q = con~uctor cross = 2.65 mm slot =272mm 18.6mm pole/phas 11/12 sectional area area c = Type of . Double-layer Type of magnet = Hera Stack steel =Losi1 450 winding· Fractional sllJ t 500 Br :; H = 350 -1 Winding • O.48T o kATm Bsat= 1.4T Hsat=ATm -1 connection· A R.P.M.-150 Costp= 1.0 KWd= 0.955 Kp= 0.99 KSk= 1.0 Kz= 1.87 11 ~L= 1.76mWb BNL::' 0.967T Bt = 1.97 T Htn= kATml Temperature rise == 75°C ... Calculated Calculated Un5atur satur. Test Unsatur. Satur. Test

11.2 kW 9·.3 kW 1.32 ~ 1.32.Q. 1.38.Q POUT 13.3 kW RS

V 2.53 V 2.24 V 195 V Xad 10.3-'2. 10.3.Q -

Imax 17.5 A 16.6 A 15.75 A Xaq 22.4.Q 12.0.Q -

VNL ~51 V 334 V 287 V XL 3.56 Q. 3.56.)2 -

I Isc 25.75A 24.5A - Xd 13.9.Q. 13.9,Q -

1) 90% 89% 87% Xq 25.9Q 15.5Q - 0 0 0 57 47 - Overall weight: 496 1 b - 225 kg 247.

difference) in Case B, and at 135.5 rev.min 1 the theoretical no-load

phase voltage is 317 V, in comparison with the experimental one 286 V

(9.8% difference) in case A. The total maximum power output of the

alternator at 150 rev.min 1 gave 13.3 kW theoretical and 9.3 kW

experimental, which is a difference of 30% (Case B) and at the speed of

135.5 rev.min 1 11.9 kW theoretical to an experimental value of 8.3 kW, a difference of 30.2% (Case A). If the differences between the theoretical and experimental results are compared, then it can be seen that for Case A the no-load voltage is higher than the one in Case B, but the output power shows no big difference.

The efficiency characteristics shown in Figs. 5.57(c) and

5.58(c) for case A and case B, respectively, indicate that the alternator has a maximum efficiency of 95% (0.95 p.u.). Efficiency at a given speed then falls off as load increases. It can be seen also that the efficiency of the machine at maximum power points on the family of constant speed lines drops with decrease of speed, but to not less than 80% (0.8 p.u.).

The efficiency was calculated as shown in Section 5.6. The active volume of the known Mark I p.m. alternator was used as well as its Kib value as a basis for predicting the no-load losses of the "Rutherford" alternator.

The comparison between the experimental results and the calculated ones of the efficiency curves shows that this approach gives reasonably good estimates. The calculated no-load losses at 150 rev.min-1 were about

494 W, where the measured losses for case A were 450 W.

Fig. 5.57(d) shows the predicted curve of load angle versus load current does not depend on the rotational speed. Fig. 5.57(d) shows that for loads up to the maximum output power (load currents I up to 17 A), the load angle ei rad ( < 60°). 248.

The following section gives a very rough estimate of the

saturation level in the stator teeth of the alternator and the influence

of saturation on the performance of the machine.

5.11.4 Calculation of the Saturation Coefficient of the "Rutherford" P.M. Alternator and its Influence on the Performance of the Machine

The method given in Section 5.8 can be used to find saturation levels and calculate the saturation coefficient. From the calculations of the parameters of the machine it was found that:

= 0.001% Wb; NL L = 0.056 m; Y = 0.051 m; c = 0.0186 m; av and t = 0.00983 m. w

Assuming a sinusoidal flux distribution in the airgap, then from equation (5.73):

0.968 BNL T

Therefore, from expression 5.77):

Bt = 1.97 T.

The teeth of the machine are thus heavily saturated.

From expression (5.78):

E = 1.0 x

As was done in Fig. 5.59(a), a line x = 1.0 is drawn on the Losil 450 magnetisation curve. A parallel line is drawn to the curve from the point Bt = 1.97 T. This line Kx = 1 meets the magnetisation curve at point A. Hence: 2.5 1Htn Kx=1.0 I

J . I c/n Li1 A 2.0 I Mom Kx =1 Ww Bt _ .0 I Mann 411=0 MINN w OVOID =NM .11M•lw > A

z w B T X 1.5 2.4 0 0.5 J L 23 1.0 U_ 1.5 f-- 2.2 20 w z 2.5 0 • 2.1 3.0 •4 1.0 Kx Bt =1.6 KX 2 Btn 20 A

1.9 (a)

05 MAGNETIC FIELD STRENGTH, H,A/m„ H 6 104A 1 • - 0 1 Htn 4 100 1,000 10,000 100,000 Fig. 5.59: Magnetisation curve of the steel, Losil 450. 250.

Ht 11 kATm 1 n

Hence from expression (5.79) and the tooth length:

h3 = 0.02427 m

Ft = 267 AT

From expression (5.80) the no—load mmf per pole is:

FNL = 308 AT

Therefore from expression (5.81):

kZ 1.87

From Fig. 5.23, KB = 1.056.

Fig. 5.60 and Table 5.5 show the new performance of the

alternator for Case B at saturation conditions. It can be seen that the

new predictions are nearer the experimental values, though the differences

are still appreciable.. At 150 rev.min 1 the no—load voltage is 351 V, in

comparison to the experimental value of 287 V.(18% difference). The maximum power output figures differ by 16.4% (11.6 kW theoretical;

9.3 kW experimental).

It is suspected that the reason for the residual discrepancies may be primarily caused by an underestimate of the rotor leakage levels, due to the neglect of fringing leakages of the magnets. The introduction of the saturation coefficient into the calculations reduces the value of the load angle by 17.5%. i .: N 0 "C"- X 1~~---+----~--~-----~--~----~--~ ~ ~100r----r----+----I-

0:: W'200 W 8Or----r----~/_ (9' 3=

0:: f2 1.2r----~----_r_--__r---,._-__T---_r_-__., 2·4 ~ 0:: W 2·0 ~

a.: 00 ~ 20 40 60 80 100 ·'20 '10 --+---8 .12 .6 20 24 TOTAL OUTPUT' POWER, WATTS X 10 LOAD CURRENT, AMPS . (c) (d) Fig. 5.60: Curves of the "Rutherford" p.m. alternator with saturation taken into account: (a) voltage regulation~ (b) power output, (c) efficiency, and (d) load angle. 252.

5.12 FIRST SERIES OF TESTS ON TEE "RUTHERFORD" P.M. ALTERNATOR

The first series of tests was undertaken at the Rutherford

Laboratories. The results are discussed in detail in Section 5.12.2.

The principal tests carried out were:

1) Voltage and output power versus output current at different constant speeds of 19.5, 41.75, 66, 85, 108 and 135.5 rev.min-1 (see

Figs. 5.57(a) and (b), which also include the theoretical curves).

These experiments were carried out with different constant three—phase resistive loads.

2) Heat run (temperature rise versus time) at constant load current and speed. The measurements were taken with a thermometer located on the stator stack and with thermocouples on the attached stack and on the winding.

5.12.1 Test Rig

At the Rutherford Laboratories a sufficiently large variable speed drive motor was not available so the alternator was mounted on the table of a boring mill, as shown in Fig. 5.61, and was dynamometer— mounted. Unfortunately the drive was not powerful enough to drive the alternator at its full power and speed of 150 rev.min-1. The maximum speed which could be achieved was 135.5 rev.min 1 and the maximum power output was 8.4 kW. The input torque to the alternator was measured by means of a spring balance attached to a torque arm on the alternator stator and to a fixed metal column in the workshop. The boring mill had a variable drive which enabled it to drive the alternator at 66, 85, 108 253.

SPRING BALANCE PM.ALTERNATOR

DRIVE FROM BORING MILL

(rLY I

Fig. 5.61: Test rig of the alternator at the Rutherford Laboratories.

P.M. ALTERNATOR R SW TCH RESISTIVE LOAD

Fig. 5.62: Power diagram of the alternator during tests at the Rutherford Laboratories. 254.

and 135.5 rev.minl .(on load). Fig. 5.62 shows the power circuit used.

The rotational speed of the alternator was measured with a pulse counter.

The three voltmeters enabled adjustments to be made to the load to

maintain balance between the three phases. Two a.c. test—sets were

connected in the two wattmeters connection for measuring current; line

voltage and power output. The ammeter in the neutral wire gave the

zero sequence current.

5.12.2 Results and Discussion of First Series of Test Results

Firstly, the cogging torque of the machine was measured and it

was found to be approximately 27 Nm. This might sound a big value for wind power application, but it should be compared to the rated full load torque of the alternator, 740 Nm.

Fig. 5.63 shows curves of power loss, torque and voltage versus speed under no—load conditions. The no—load voltage curve shows that the voltage is directly proportional to the speed, as expected.

In Fig. 5.63 it is clearly seen that as soon as the machine starts rotating, the torque drops from its value of 27 Nm to a value of 1.5 Nm, which is mainly friction losses. The maximum no—load loss was about

400 W at the speed of approximately 137 rev.min-1. The alternator was then run on—load with the constant speeds mentioned in Section 5.12.1 and with three constant resistive loads of 8 g, 10.5 Q and 17.50. per phase.

Fig. 5.64 shows the derived voltage curves versus rotational speed for these three constant resistive loads. It can be seen that at higher load currents, the voltage does not change proportionally with the speed due to the I.Z voltage drop in the machine. 255.

TNL p VPhaseNL NmVā Volts

PN 40 400

VNL 30 300 -300

•TNL x

•

20 200 -200 ~

10 100 100 •

i x

1

I r r ix

AMMO 50 100 150 SHAFT SPEED, rev min-1

Fig. 5.63: No—load, voltage torque and losses of the alternator. '\

Vphase~----~-----~----~----~----~------Volts

200~-----~·----~-----~-----+----~----~

150~----+-----4-----~-~---A-----~-----~ 6000 6O-I-_i1-----+__---i--

100~----+-----~~~-~----~----~-----~ 4000 40~·_i~---+__--~~r--j~+----4_----~

2000 20 -_il----I--I---r---t-

50 100 . 150 °o~----~----~--~~----~----~---~ 1 50 100 150 SHAFT SPEED, rev min- SHAFT SPEED, rev min-1

Fig. 5.64: Voltage curves versus speed for . Fig. 5.6"5: Output power and efficiency curves versus different resistive loads. speed for constant resistances. 257.

Fig. 5.65 shows the output power and the derived efficiency

curves versus speed for these constant loads. It can be seen that the

power changes with the square of the speed and the efficiency stays more

or less constant for a wide range of speeds. The higher the value of the resistance (i.e. the lower the load current) the higher the value of the

efficiency of the machine. The maximum value of the efficiency was 93%, and at the maximum obtainable speed the lowest was 82%. The high values of efficiency at very low speeds are an important factor for machines for wind power applications which most of the time run at lower rotational speeds than their nominal.

Fig. 5.66 shows curves of input and output powers versus speed for the constant resistance of 10.5g2 and the corresponding efficiency curves versus speed and output power. The output power efficiency curve shows very clearly that the efficiency of the alternator over the whole range of loads stays between 82% to 87% for that particular resistance.

Fig. 5.67 shows the input torque curves versus speed for the three constant resistances. The starting torque at zero speed represents the cogging torque of the alternator. Naturally the torque increases with the increase of speed and load (low resistance).

Fig. 5.68 shows the different power losses in the machine versus speed for two different resistances. It is quite clear that at higher resistances (low loads) the losses are dominated by the iron, friction and windage losses (no-load losses) and at low resistances (high loads, high load currents) they are dominated by the copper losses.

Fig. 5.69 shows the losses in the machine for constant rotational speed versus load current. Highlighted here is the behaviour of the two 110 Watt I Nm Pin Ra10.5S2 1000 100 800 k 7) Ra10.5S2 Ra8S2

n PJ — .

. Ra10.5S2 -600

• Pout ' 'alb• S2 — • Ra17.5(2

5000 50 400 7) Ra10.52

.

I/ 200

I i 50 100 °% 0 50 100 150 0 50 100 150 SHAFT SPEED, rev min"' SHAFT SPEED,rev min'1 Fig. 5.66: Input and output power curves of the Fig. 5.67: Input torque versus speed for different load alternator with its corresponding efficiency resistivity. curve versus speed and output power. p p Watts watts

1qOOO~----~------~----~------+-----~~----~ 1QOOO~----+-----~----~----~-----+--__~~

I •

5000~----+------+-----41

o~~--~----~~----~----~ 4 8 12 16 20 :t 50 100 150 1 ~ 1 LOAD CURRENT. Amps SHAFT SPEED t rev min- Fig. 5.69: Losses of the alternator versus load .\Fig. 5.68: Power losse~ of the alternator versus current for two constant rotational sp~ed at different constant r~sistances. speeds. 260.

main losses in the machine where the no—load losses are constant with

constant speed but increase as the speed goes up, and the copper losses

which increase with the load current but not with the speed.

Finally, the alternator was run at a constant load and speed 1) (16 A at 108 rev.min and the temperature rise was measured. In the

alternator during construction two thermocouples (iron/constantan) were

attached, one on the stator stack and the other in the winding. During

the heat run a thermometer was attached to the stack of the machine.

Fig. 5.70 shows the thermocouple diagram used to measure the

temperature. The measured voltage was multiplied by 18.94 to give the

temperature value in °C.

Fig. 5.71 shows the temperature increase of the machine where the'- ambient temperature was 21.5°C. The machine originally produced a power

output of 6.6 kW at 108 rev.min 1 at this ambient temperature. When the temperature rose to a maximum of 75°C after 75 minutes, the output power dropped to 6.24 kW. When the machine was cold the efficiency was 79% and when hot it was 77%.

The thermometer indicated a maximum iron temperature increase of

55°C but, as seem from the temperature rise curves in the iron and copper, the iron and copper temperature rises tended towards more similar values as time went on, presumably due to the normal beat diffusion phenomena between the different parts of the machine.

As previously mentioned, events after the beat run showed that during cooling the airgap closed due to the different expansion coeff- icients of the stator iron and the dural rotor end plates, and it was decided to replace them with non—magnetic stainless steel ones. 261.

THERMOCOUPLE COLD JUNCTION

IRON CONSTANTAN IRON

D.C. MILLIVOLTMETER

Fig. 5.70: Thermocouple circuit diagram for measuring temperature.

~tOC

60------~~--~----~----~-----r-----r----~

STATOR IRON­ 50~----~----~----~- (Thermometer measurements )

40~----+-----+-----+---~~----~~~~----~----,

Thermocouple } measurements

10~~~~----+------~------~-----;------+------r-----'

10 20 30 40 50 60 70 80 TIME,min

. Fig. 5.71: Temperature rise curves of the alternator. 262.

5.13 SECOND SERIES OF TESTS ON THE "RUTHERFORD" P.M. ALTERNATOR

In order to be able to obtain maximum output at maximum speed

(150 rev.min l) it was decided to test the machine at the heavy current

laboratory at Imperial College, where a d.c. drive was available.

The principal tests carried out at this stage were very similar

to the previous ones. Because the d.c. drive could be adjusted over a

wide range of speeds, the tests were carried out with speeds of 15, 30,

45, 60, 75, 90, 105, 120, 135 and 150 rev.min 1. Measurements were also

taken for a series of constant load resistances: 116 g), 79 SZ, 45 SI

24.6Q, 1512, 10.85Q, 7.4Q, 4.8 Q and 2.65Q per phase.

5.13.1 Test Rig

The test rig diagram is shown in Fig. 5.72. The d.c. motor of

17.5 hp at 1625 rpm was stepped down in two stages to give the required

rotational speed of 150 rpm to the alternator. The first stage was a

5:1 step down to the belt system. The second stage consisted of a 5:1

worm reduction gear box. As shown in the diagram of Fig. 5.72, the

alternator was in a horizontal position having a supporting bearing on one

side and a solid coupling on the other fixed to the gearbox. The

supporting bearing and the solid coupling enabled dynamometer mounting of

the alternator. The torque to the alternator was measured by a spring—

balance attached to the case of the machine through a steel arm of 0.61 m

length. The rotational speed of the alternator was measured from an a.c.

tachogenerator through a step—up transmission. The spring balance is not shown in the diagram, but it can be seen in the photograph of the rig in

Fig. 5.74a. In Fig. 5.74b the "Musgrove" type vertical—axis windmill mounted at the Rutherford Laboratories can be seen. 263.

SOLID COUPLING

TACHO- GENERATOR

Fig. 5.72: Test rig of the "Rutherford" p.m. alternator at the Electrical Engineering Department of Imperial College.

0 OSCILLOSCOPE

PM. ALTERNATOR I,V,W AC SET I ,V,W RESISTIVE A.C. SET LOAD I,V,W A.C. SET SWITCH

Fig. 7.73: Power diagram of the "Rutherford" alternator tests at Imperial College. 264.

Fig. 5.74a: The Rutherford alternator test rig at Imperial College.

Fig. 5.74b: The "Musgrove" type vertical-axis windmill. 265.

Fig. 5.73 shows the power diagram used to carry out the tests

on the alternator. Three a.c. sets were used to check the balance of the

load and to measure phase voltages, current and power in the three phases

at once. The oscilloscope gave the voltage waveforms and the ammeter in

the neutral measured the zero sequence current.

5.13.2 Results and Discussion of Actual Performances of the "Rutherford" p.m. Alternator for the Second Series of Tests

The modified alternator was at first checked for its cogging torque. It was found that it had a value of 18.22 Nm, 32.5% lower than the initial case with the dural end plates. It is known that the level of the cogging torque depends on the value of flux which passes from the rotor to the stator teeth. As far as possible, this airgap length was kept at the same as before, and a decrease of the airgap flux is hence suspected. This is suspected to be due to an increase of rotor leakage or a reduction of flux density of the magnets. The latter is unlikely since appropriate precautions were taken to minimise the possibility of demagnetisation during the reconstruction.

Fig. 5.75 shows the measured no—load losses and phase voltage of the alternator versus speed. Comparing the no—load voltage given in

Fig. 5.63, it can be seen that no—load voltage in Fig. 5.75 is about 9% less. This reduction of voltage indicates that the modification has some effect.

The results of voltage, output power and efficiency curves versus output are shown in Fig. 5.58 for the different speeds of 30, 60, 90, 120 and 150 rev.min1 . 266.

PNL VNL • Experimental Watt$AVoItSNO-LOAD LOSSES x PNL = KNL n3/2

PNL

300 300

VNL •

• 200 200 •

• 100-100

00 50 100 150 Shaft speed, rev min-1

Fig. 5.75: No—load voltage and power loss of the alternator versus speed. 267.

As can be seen from Fig. 5.58(b), the maximum power output was

9.3 kW at 150 rev.min-1, with an efficiency of 87%.

The test results of the no—load losses were checked against the

law given in expression (5.68) earlier. As can be seen from Fig. 5.75, the results are quite satisfactory.

Fig. 5.76 shows output power and efficiency curves versus speed.

The range of resistances from 79.51 to 12.4g. corresponds to the range of maximum output powers of 2.94 kW to 9.3 kW at 150 rev.min 1.

Figs. 5.77 and 5.78 show the waveforms of the phase and line voltages and off—load. Fig. 5.77(a) shows the phase voltage waveform of all three phases at no—load when the alternator is running at a speed of about 30 rev.min-1. It is important to mention the identical nature of the three waveforms by amplitude and the phase shifts between of 120°; this indicates that the fractional slot winding was balanced within the limits of the measurement accuracy. As stated in E5.40 , the

"Rutherford" machine, like the Mark I machine, has no pole shaping, so the airgap field is essentially uniform above each pole. The flux per pole is maximised with this arrangement, but the emf waveform in each conductor is trapezoidal rather than sinusoidal. Although the third harmonic in the flux distribution and in the emfs will be absent with an appropriate choice of pole width to pole pitch ratio, in general the attainment of a reasonably good terminal voltage waveform is required is entirely dependent on these techniques, i.e. skewing, distribution and crowding of stator winding. It was not intended that the'Rutherford" p.m. alternator should be run in parallel with other machines, nor that its output should be particularly free from harmonics. Harmonics matter little either for battery or for resistance loads. However, there was pout kWl A

R~ y,,,;10•8552 TI

10

R-24.611 XR1a,,,~ 246Q R-79R I phase R.10•8552

/ i . // I / 1/ /

ii I

1 , 1 1 • 05 1 1, 11 ,I x-79Q i' 1 1

I ;,

1

u 50 100 150 50 100 150 Shaft speed, rev min'' f Shaft speed, rev min'i Fig. 5.76: Output power and efficiency curves versus speed for different load resistances. 269.

111111/ MO/ (a) Al Tbree-phase voltages A, B and C at 30 rpm at no-load. 11.1.1111111,01111 111111111

1111111111111111,11111

1111 PAIIIR 1,21 kingialintraltilljo-load phase and line voltages LiTiortnigillekil at 30 rpm. EWA 1111102 111: 11111111 MI MEE MIMI

111111 1 1111111761311011111111APon-5A resistive load, phase and la line voltages at 30 rpm.

MERE 1111 =IMill

Fig. 5.77: Voltage waveforms of the "Rutherford" alternator. 270.

ME

RIM 211. MAk (a) MINNIMMERMIttno-load phase and line voltages rev.min-1.

MEMMEMMU R

=REM=

pimilmmel Am pram mall i IliIII IIÌOn 10 A resistive )load, Pha and M M UMW nvoltages in.- M

M&MWEEMM E

WAINER 1111 MEE EMI=■

MUM klin1111

(c)

1211111011111111111111111,11111111voltages at 120 rev. min 1.

UNNMEMMUNIVI

MMMENOEUMM

MUMMEOME W

Fig. 5.78: Voltage waveforms of the Rutherford alternator. 271.

some incentive to try to avoid excessive harmonic levels, (a) to minimise

troubles with any rectifiers or capacitors, (b) to avoid excessive iron

losses due to armature mmfs of high frequency, (c) to minimise metering

and interference problems. As it turned out, the measures taken to

minimise cogging torques (use of fractional slotting, equivalent to

distributing and chording the winding) were also adequate in cutting down

harmonics in the terminal voltage to a very acceptable level, as shown in

Figs. 5.77(a) and (b), and Fig. 5.78(a). The ripples shown on these

waveforms are due to the slotting harmonics and these could be further

reduced by skewing.

When an alternator is loaded, the terminal voltage waveform may

change because: (i) the movement of the rotor through armature reaction

flux may modulate it at frequencies different from the fundamental which

will cause additional harmonic frequency emfs in the winding, and (ii)

additional volt drops occur in the winding due to the passage of load

current through it. The nature of the volt drops, and hence the nature

of the terminal volts change, is dependent on the waveform of the load

current and on the resistance and inductance values of the winding

impedance. In the case of the purely resistive load, the load current

waveform will be identical to that of the terminal line voltage. With

inductive loads, harmonic current level will be reduced, with capacitive

loads accentuated.

Figs. 5.77(c) and .5.78(b) and (c) show the voltage waveforms

of the "Rutherford" p.m. alternator when loaded. It can be seen that the higher the frequency and the higher the load, the higher the

distortion in the waveforms. 272.

The measured resistances of the winding gave a value of 1.38g2,

1.37Q, 1.36 c2 for phases A, B and C respectively.

A two hour heat run was performed at full load and speed. The

temperature rise of the winding was not more than 75°C.. The power output

of the alternator dropped to 8.4 kW at constant load current and constant

speed and the efficiency dropped to 83.5%. This decrease of load and

efficiency is due to an increase in the copper losses and a decrease in the magnet flux due to beating. The new value of the winding resistance was 1.89n and the thermocouples in the winding and stack of the stator showed temperatures of 75°C and 62.5°C respectively.

An attempt was made to measure the short circuit current of the alternator but the test was abandoned due to large vibrational effects on the dynamometer. The value of 19.75 A at 30 rev.min-1 was achieved.

The alternator winding was finally connected into a parallel configuration as explained in Section 5.11.2. The winding was checked for circulating currents in its two parallel windings for each phase.

It was found that at full speed the value was not greater than 0.3A in each phase.

It was also decided to connect the alternator to a load of a leading power factor by connecting capacitors in parallel with the load resistors. Unfortunately the test could not be carried out at full power due to the failure of the d.c. drive to give the required input power to the alternator. It is expected that a power factor of —0.8 can give an 1. output power of 10 kW at 150 rev.min A typical test has shown that an 80 'IF/phase capacitance in shunt with the alternator gave an increase of about 9% in power output at the speed of 60 rev.min 1 with a load 273.

resistance per - phase of 122. However, the efficiency of the alternator

changed from 90% without the capacitors to 86% with the capacitors.

5.14 CONCLUDING REMARKS

In this chapter the design and calculation and performance

predictions have been presented for two circumferential rotor.permanent

magnet alternators, together with test results. Hera magnets were used

in both machines. The design of such machines has shown that high

performance can be achieved at low speed and relatively low volume/power.

High efficiency levels can be achieved for a wide range of rotational

speeds and loads.

For wind power applications these alternators can have the

following advantages:

(a) Do not require external source for excitation;

(b) Can be directly coupled to the windmill without any transmission;

(c) Can generate power as soon as the windmill begins to turn;

(d) Can give this power with high efficiency. levels;

(e) As robust, therefore can withstand the severe environmental

conditions on or at the base of a windmill tower;

(f) Need almost no maintenance, therefore can be used in remote areas

with little or no maintenance service;

(g) Long life. '274.

However, they have to cope with the following disadvantages:

(1) They require external control or careful matching of the alternator,

windmill, and load;

(2) The field cannot be switched off and cogging torques may occur;

The voltage is not controllable and, for instance, cannot usually

be kept constant;

Rather distorted output waveform can occur, which can give trouble

to thyristor control units for load control (note though that

conventional alternators also produce distorted waveform);

Larger diameter than a standard speed machine;

(6) Rather high cost per rated power; for the Mark I machine, cost of

magnets 045, cost of steel £14 and cost of copper £9. Estimated

ex factory cost £670. For the "Rutherford." machine, cost of

magnets 080, cost of steel £220and cost of copper 00.. Estimated

ex factory cost £2200.

Some of these points are specific to these two machines, rather than to all low speed p.m. alternators. It is thought that there is considerable scope for improvement with further designs with respect to items 2, 4, 5, and 6 but that there would always be some penalty in cost and weight terms for low speed operation.

The penalty for these two machines is probably too severe in many cases to be worth paying. In the next chapter, Chapter 6, improved designs of p.m. alternators with a lower penalty in extra cost and weight terms are discassed and are found worth adopting. 275.

If load power is to be matched with available wind power, the

absence of a field control facility means the need for load switching or

the provision of a thyristor control unit in the output. It is realized

that either of the control options is likely to be more expensive than

field control (since the output power itself rather than just the field

power is being controlled) and it may be that the compensations in terms

of zero field losses (therefore higher efficiency, lower running

temperature), absence of brushes and field winding (therefore lower

maintenance, minimal transients, and potential savings in assembly cost)

will in some cases fail to outweight the penalties. The work discussed in

Chapter- 7 enables firmer conclusions to be reached on this point.

From the previous discussions and the experience of these two

machines one.can._come to the conclusion that direct drive is the best

option for "high speed", single blade windmills (up to 1000 rev.min-1)

and a low ratio step—up plus special medium speed alternator (see

Chapter 6) combination as the best option for low speed (less than 1) 300 rev.min windmills in the many applications where the first cost is

likely to loom large in the minds of purchasers. In many other cases it is hoped that the attractions of an alternator running at windmill shaft speed, not needing any gearing, not requiring any field supply, producing efficiencies of 70 to 90% over most of the load range would outweight the disadvantage of a higher first cost.

The methods presented in Chapter 7 were evolved to help enable quantitative comparisons to be made between the economics when using different types of generator. 276.

CHAPTER 6

PERMANENT MAGNET ALTERNATORS: RADIAL EXTERNAL ROTOR, PERMANENT MAGNET (P.M.) ALTERNATORS

6.1 INTRODUCTION AND BRIEF ANALYSIS OF Tib MARK II P.M. ALTERNATOR

The experience and difficulties with the circumferential rotor, low speed, permanent magnet alternators led to the development of two further prototype alternators which would overcome some of the disadvantages given in Section 5.14. It was decided to use a cheaper type of magnetic material and to accept the inevitable reduction in power per size that would result. One of the high performance orientated barium ferrites (Magnadur 330) was selected. The materials BH curve is shown in Figure 6.1[6.0 . It was then decided to use a radial orientation of the magnets with an absence of "pole shoes" in order to minimize synchronous reactance. High Xq in the Mark I machine had led to a fairly steep voltage (regulation) droop and to rather poor commutating performance (hence appreciable reductions in maximum power output) with rectifier loads. The use of a design in which rotor iron was absent from the vicinity of the air gap would give low Xq and Xd due to the low (111) of the ferrite material. There are two sr snags with this type of design:

(i) there is an absence of flux density eamplificationf as usually

occurs with circumferential designs;

(ii) the magnet has little protection against armature demagnetizing

mmfs. 277.

B (mT) 400

Br

I Bo / / 3 / 00 / / i / / / / / / / 200 O /

/ • rh") / / / 100 / / / / / / / / / ~ r // / // / / / / 300 250 Ho 200 150 100 50 -H (A/m) x103

Figure 6.1: Typical demagnetisation curve at 25°C of • Magnadur 330 and 370. 278.

Since (i) means that the machine's rated power per rotor DL product is

reduced; snag (ii) that demagnetisation may be more likely under heavy

load or short circuit conditions. An 'inside out' configuration of

stator and rotor was used to minimise the effect of snag (i), a

fairly small pole pitch (hence low armature Al per pole) and a fairly

'thick" nagnet shape (in the direction of magnetisation) used to

stave off the effect of snag (ii). The inside—out configuration

(stator inside rotor) maximises the airgap diameter for a given overall

diameter because the field magnet and rotor backing iron assembly can

be much less deep radially than the stator's radial depth (see Figure

6.2). It was decided to design an alternator for a rating of about

7 kW at 1500 rev.min-1. A pole number of12 was chosen to keep the

pole pitch at a suitably low value. It was also decided to choose a slot per pole per phase of one and use skewing to reduce the togging torque and improve waveforms. This made the total number of slots 36.

Some further points should be made about the inside—out configuration:

(i) The mounting:of the magnets inside the rotor "cup" will not give

centrifugal force problems since the centrifugal forces keep

them in position.

(ii)A disadvantage which should be considered is that the stator which

is the source of the beat cannot dissipate its heat directly to

the surrounding air and has to transfer it by conduction through

the shaft and the mounting ring to the body of the windmill or

via forced air through the stator.

A heating problem was expected and has been solved, as shown later in Section 6.2. Aluminium sheet

Slots of the armature windin

Stator Losil 450

All dimensions in cm

Figure 6.2: Radial external rotor p.m. alternator layout. 280.

This chapter deals with two external rotor, radially

orientated, permanent magnet alternators. The performances of the

machines were predicted theoretically and found experimentally. The

Mark II machine was designed, manufactured and tested at the Electrical

Engineering Department of Imperial College. The smaller size machine

was manufactured privately by "Windrive".

6.2 CONSTRUCTION OF THE MARK II P.M. ALTERNATOR

As was mentioned before, the construction of the Mark II

machine is different in layout from the conventional machines. A

section of the assembly is shown in Figure 6.3. The outer rotating

member (rotor) is mounted on the shaft, which is fixed on bearings

through the inner stationary member. The stator carried the iron core

and the bearing housings. The rotor is made of a soft iron "cup" which

in its inside diameter carries the magnets. The main magnetic flux.O

paths are illustrated in Figure 6.2. The armature winding on the

stator is conventional.

6.2.1 Stator Design and Construction

Because the stator is not a conventional one, some skill is

required in its design to make the manufacture easy and to minimize

material usage. In the cross-section of the machine in Figure 6.3 the

laminations (made of Losil 450 electrical sheet steel) (1) had slots for the armature winding (2) on their outside periphery and on the inside periphery they accommodated the iron housing (3) of the two ball 281.

~-_____73/~- 197mm ------I~

~ 12 V

23 Figure 6.3: Assembly of the Mark 11 p.m. alternator •

.------

Figure 6.4: The Mark 11 p.m. alternator dismounted. 282. bearings (4). The lamination stack was clamped by two iron rings (6),

one welded on the housing of the bearings and the other a sliding fit

on the housing outside surface. Each ring had 20 holes, four of which

were used to clamp the rings using tension bolts (7). The laminations

were kept concentric by four steel tubes (8) through which the clamping

bolts passed. The rest of the boles were used as ventilation ducts (9)

for cooling the stator stack, etc. At one end of the bearing housing

a steel mounting ring (10) was threaded on. This holds the dural end

plate (11) and fixes the machine onto the windmill structure in the

case of a direct drive mounting. The other end plate (13) was held by

aluminium pipes and long brass bolts (12). The outer periphery of the

machine was covered by a sheet—aluminium cylinder (not shown on

Figure 6.3), for full weather protection.

A "mesh" type winding of copper wire is used. 0.5 mm

insulation (class E) card is used as slot insulation, together with

paxolin wedges. Under one of the wedges halfway along the stack a

thermocouple was attached for temperature measurements. The terminals

of the winding and the thermocouple wire (14) pass through a hole in

the end plate of the machine. The winding of the machine is a

conventional double layer winding which is divided into two halves for

parallel and series connection.

The machine was designed with one slot per pole per phase, as

mentioned previously, and it was decided to eliminate cogging by skewing the slots of the stator. To achieve this the stator was initially

assembled minus windings, .with a stack having an,axial length equal- to that of the magnets. The rotor was assembled with the magnetized magnets in position. The required airgap of 0.4 TT was achieved by machining 283.

down the lamination stack by several thousandths of a mm. The slots

were then skewed by one slot pitch. The cogging torque was measured

using a spring balance and was found to be equal to 5.5 Nm.

Adjustments to the skewing angle above and below one slot pitch were

then tried but the cogging torque increased. The 5.5 Nm level was not

satisfactory and it was decided to try changing the stator stack length

while keeping the skew angle the same, i.e. one slot pitch. When the

stack length was increased to 78 mm, the cogging torque was virtually

eliminated. This procedure proved that the cogging torque on a p.m.

machine can be eliminated by correct solution of stack length/magnet

length (or stack 'overhang' length), and skew angle. Factors involved

here include:

(a) the strength of the magnets,

(b) airgap length,

(c) distance between neighbouring magnets,

(ð) slot pitch,

(e) number of slots per pole per phase,

(f) the fringing magnetic flux which affects the effective

length of the machine.

A theoretical basis for the correct choice of skew angle and

stack overhang would obviously be worth developing.

Figure 6.4 shows a photograph of the rotor and the finished stator of the machine. 284.

6.2.2 Rotor Design and Construction

The 'inside out' configuration, though not unknown, is not

commonly used. It is similar to the arrangement and layout of a bicycle

''dynamohub' generator or 'tubular axle' traction motor.

There are no mild steel pole shoes on the radially—orientated

magnets so each pole flux passes directly from the magnet surface across

the airgap to the stator iron, dividing itself into two paths as shown

in Figure 6.1. The mild steel rotor core closes the magnetic circuit

fluxes.

The advantages of this configuration and layout are as follows:

(a) Compactness due to the external rotor layout,

(b) Increase in power/size due to the increased peripheral airgap length and 'torque arm' length,

(c) Reduction in rotor leakage in comparison to the circumferential p.m. alternator.

It was decided not to use pole shoes for manufacturing reasons and to reduce the weight and quantity of material. A demagnetization test was carried out on an annular ferrite magnet and proved very satisfactory.

The Magnadur 330 magnets were cut from unmagnetized, unmachined blocks of dimensions 156 mm by 99 mm by 25 mm, three such blocks being cut to obtain the twelve required magnets. Because of the ferrite material being very hard and brittle, special diamond tools were used to cut it and machine it to the shape shown in Fig. 6.5. A special grinding diamond wheel was used to grind the curvature of the magnets. After the magnets had been ground to the required shape, they were magnetized. 285.

It is extremely important that the magnetizing field strength

used is not less than the specified minimum, otherwise the maximum

performance of the material will not be achieved. If the magnet to be

magnetized is assembled in a circuit which shields the magnet, then the

required field strength will be greater than the stipulated minimum shown

in the appropriate data sheets of the manufacturer, by the amount

required to saturate the shielding positions.

Modern magnetic materials like ferrites and Hera require

considerably greater magnetic field strength than earlier materials. To

obtain the maximum effect from the magnetizing current the magnetic

circuit should be closed during magnetization by an iron return path

capable of carrying the saturation flux.

Calculations were performed which showed that the magnets could be magnetized by using a special jig, and d.c. supply from the available d.c. generators in the laboratory. The d.c. generator could provide a current'of 50-60,A. Figure 6.6 shows a photograph of the magnets with the magnetizing jig made of mild steel and a coil of about 400 turns.

The pole shoes which clamped the magnet in position were given the shape of the magnet surfaces. The d.c. generator supplied the coil through 1 A fuse wire. When the circuit was made, the 60 A current fused the wire immediately. Each magnet was magnetized individually and stabilised in air by removing it from the jig. Care was taken to get the correct polarity using a compass. The permanent magnet blocks (12) (see

Figure 6.3) attached to the rotor "cup" (16) were held in place partly by magnetic forces between them and the rotor core and partly by two aluminium rings (17) clamped together by brass bolts passing through the gaps between the magnets. The magnets were kept equally spaced by grooves in the aluminium rings. Simple aluminium fan blades (18) were attached around the periphery of the outer magnet clamping ring. The 1 2,

All dimensions in mm

~{4K, I ! S 5 p 6 7 8 9 I 11• Ilr-ss S, • s e / - 12 13 14 IS 16 I1 1e L9 20 21 22 23 24 2 5 2 e 2174.

72-5

49.5 Figure 6.6: The magnetizing jig with the ferrite blocks, Figure 6.5: Ferrite magnets used in uncut, unmachined and ground. Mark II p.m. alternator. Figure 6.7: Rotor assembly of the Mark II p.m. alternator. r

(a) and (b): Layouts adopted for prototype.

r► •-~

Z9 dl J ciIliP di!

------1 L L (c) (d) Iif/if (c): Three alternative drive possibilities are indicated.

Figure 6.8: Standard shaft/bearing/drive/support arrangements with external rotor alternator. 289.

Figure 6.9: The lamination, the coil and its former of the Mark II p.m. alternator.

Figure 6.10: The complete Mark II p.m. alternator with the shroud removed. 290.

cooling air is circulated round the rotor "cup" through the ventilation

boles (19) fin the rotor.

Figure 6.7 shows the rotor assembly without the magnets and

the clamping aluminium rings. The boles for cooling and reduction of

rotor weight are shown. In Figure 6.3 the rotor "cup" was fixed in

position on the shaft ()-by means of a key (20) and an "Allan" screw (21).

A washer (22) was used to adjust the axial position of the magnets with

respect to the stack. The stack was double ended to facilite dynamometer

mounting in two supporting bearings (24) on a platform plate (23).

In production, many parts of the machine could be made of dural

castings. Figure 6.8(a), (b), (c) and (d) shows a number of possible

alternative bearing/drive/support arrangements. Figure 6.9 shows the

lamination with one of the coils of the armature and the coil former.

Figure 6.10 shows the machine with the shroud removed, and a tacbogenerator.

6.3 THEORY

This section presents a prediction theory for the performance

of the machine. Similar techniques and methods, were used for the

circumferential rotor machine.

6.3.1 Geometry of the Alternator

It is very important to classify the type of the machine.

Though the surface of the rotor of the machine (see Figure 6.2) is not smooth, the rotor structure, in particular the sequence of interpolar 291.

spaces, and low permeability (slope of Big characteristic) magnets are

equivalent in saliency terms to a cylindrical rotor uniform-gap machine. The

armature mmfs see a_large uniform effective airgap length (thickness of the magnets plus actual airgap).

Figure 6.1 shows the magnetic characteristic of the material

Magnadur 350 from which:

. o = Hr = /mar 272500 4.322.T .10-7 ✓ c

1.08/4

which is almost equal to the relative permeability of air, as in the

case of "Hera" magnets.

6.3.2 The Equivalent Circuit and Phasor Diagram of the Mark II P.M. Alternator connected to a Resistive Load

As was discussed in Section 5.5.2, the machine can be

represented in terms of an equivalent circuit as shown in Figure 5.13,

and a phasor diagram.

The flux produced by an mmf wave in the uniform-airgap machine

is independent of the spatial alignment of the wave with respect to the field poles. Therefore in this case the components of mmf, Fad and Faq,

produce proportional fluxes 0d and 0long q a their respective axes.

The factors of proportionality are equal for the two axes (Figure 5.12.

Assuming also that the radial rotor p.m. machine is connected to a resistive load, the armature current I is in phase with the terminal voltage V. The airgap voltage E is the same as in the circumferential rotor machine but the phasor diagram, as shown in Figure

6.11, is the same as for uniform-airgap machines, where the direct axis 292.

magnetizing reactance is equal to the quadrature-axis magnetizing

reactance (Xad = Xaq). In Figure 6.11 the phasoe Ēo (CG) represents

the field flux. The voltage induced by the direct-axis component of

flux is represented by GE and is equal to jXadĪd, and the voltage induced by the quadrature-axis component of flux represented by GH is equal to JXadĪq. CA is the phasor Ef representing the voltage which depends on the field flux, the direct-axis armature current Id and the quadrature-axis magnetizing reactance which is equal to Xad. Therefore

Ea = Ē. AJ represents the voltage induced by the component I, and can be considered as a reactive drop in the quadrature-axis magnetizing reactance. It leads the current by 90° and is equal to jXadl.

The voltage phasor diagram is completed by adding the resistance drop RaĪ and the leakage reactance drop jXiĪ to the internal voltage Vi.

The resultant is equal to the terminal voltage V, which makes an angle

S with the vertical-axis and the excitation voltage E.

A similar construction technique to the one used for the phasor diagram of the circumferential rotor machine was used but with X =X ad aq (see Figure 6.11 and Section 5.5.2).

6.3.3 Calculation of the Current I and Voltage V of the Alternator from its Phasor Diagram

As said before, the construction of the phasor diagram is similar to that for the circumferential rotor p.m. alternator. The technique used to define the current I and voltage V of the machine is hence exactly the same. Taking expression (5.4) and substituting into it: 293.

Figure 6.11: Phasor diagram of the uniform airgap radial rotor p.m. alternator.

294.

X = Xd or Xd = Xad + XQ

and Ef = Eo from Figure 6.11, then:

Id I = (6.1) o . Xd

From expression (5.5):

V = 1/Eo(Eo - XdId) - RsI (6.2)

and expression (5.8) becomes:

Eo = E + iXadld (6.3)

where Eo is the open-circuit emf,fi.e. the emf behind the direct-axis

magnetizing reactance Xad (see Figure 5.13) and E is the resultant

airgap emf after the direct-axis magnetizing reactance Xad. The values

of the machineos leakage reatance Xe and winding resistance Rs per phase

are calculated using the relations given in Sections 5.5.7 and 5.5.8,

respectively. The values of Eo and Xad are calculated from the magnetic

circuit of the machine, as shown later.

6.3.4 Magnetic Circuit of the Alternator on No-Load

As in the case of "Hera" magnets, the ferrite magnets have

their line of return along the main B-H characteristic, as shown in

Figure 6.1, line HcBr. Figure 6.12 shows the geometry of the magnets

on the rotor core. Though the distance W between the magnets is not m the same at the airgap as at the root of the magnet, for simplicity the shorter distance measured at the airgap was taken. The area of the magnet is: 295.

y

ROTOR IRON CORE

Figure 6.12: Geometry of the magnets.

MAGNET

Figure 6.13: Leakage paths of the magnets. 294.

m sc. a (6.4) and p ro = Br.(6.5)m and

Fo = H.1 (6.6)

As in the case of Hera, the ferrite magnet permeance is given by

expression (5.18). The airgap permeance across the half pole arc is

given by expression (5.19), and the effective airgap is given by

expression (5.20).

Figure 6.13 shoals a rough sketch of the three—dimensional

leakage flux path from the magnet. A formula for the calculation of the

leakage permeance, assuming elliptical paths, is given in [5.7] and is

thought to be sufficiently accurate:

2 W 2( m+ 1.1 P r1 + + X m~ + . (6. 7 ) J ° Ln L Wm ,~° 2Wm

where for this case

WT = (6.8)

Taking the path of 0 shown in Figure 6.2, the no—load

magnetic circuit for two half poles of the machine was drawn as shown in

Figure 6.14a. Because half of the area of each magnet is included in the circuit, the reluctance of the magnet in each branch is doubled.

The airgap permeance of the path is calculated as shown in Section 5.5.9.

Using Thevenin's theorem, the equivalent circuit in Figure 6.14b is obtained, in which: F .2R F R ° ~e _ ° ~e (6.9)( ) Fo - 2R + 2Ro - Rd + R° 297.

2R le 2Rte

Figure 6.14a: Equivalent magnetic circuit of one path of the magnet in the radial rotor p.m. alternator.

Figure 6.14b: The equivalent circuit after Thevenints theorem modification.

Fad —%

2R9+ 2R, 2 Fc

0

Figure 6.14c: Final stage of the equivalent circuit. •

298.

and 4RR 2RRDD o ° RI fe Ce Ro 2Ro + ZR RO+R~ (6.10)

The magnetic circuit can finally be drawn in the form shown in Figure

6.14c, from which:

2Rg + 2Rō + # = 2F' g o 2Ft 0 g 29'' + 29' (6.11)

but R = 2R' g g

and substituting expressions (6.9) and (6.10) into (6.11) gives FoR. 2 e RD.+R _ Le 4 °RQe Rg + Ro+R€ e

2FoR~ e (6.12) og R R +R R + 49 9 g ° g Qe o ~e Substituting from expression (5.32), expression (6.12) becomes:

2F o 1P~ 1 ~... 1 4 PgPO PgPr POPQ

2Fo 1Pe g P€ + Po + 4Pg (6.13) PoPgP~

Putting PI PO + P1 + 4Pg (6.14) into expression (6.13) gives the no—load flux of half a pole as: 299. P = 2 o og g (6.15) NL where from equation (5.18) P —~ (6.16) = 2 ~o Pt gNL

6.3.5 Calculation of the Resultant Flux in the Airgap of the Machine for On-Load Conditions

As in the case of the Mark I p.m. alternator, the demagnetising armature mmf Fad (see Section 5.5.13) can be introduced into the magnetic circuit of the machine as shown by the dashed lines in Figures 6.14(a),

(b) and (c). From Figure 6.14(c):

(211g 2R'),+ - 2F' + Fad 0 (6.17)

2F - O ad (6.18) g = 2Rg + 2Rō

Repeating the steps in a similar fashion to those in Section 6.3.4 gives:

P P (6.19) ~g = 2 0o Pt Fad Pt(P€ + Po) prg, the resultant flux in the airgap over half a pole for on-load conditions, can thus be expressed as:

(6.20) gNL ~gad where 0 is the demagnetizing flux in the airgap for a half pole. gad 300.

6.3.6 Calculation of the emfs in the Machine

The no—load enf Eo of the machine can be derived from expression (5.48) by substituting expression (6.16) into (5.48). The flux per pole:

#NL = 2# gNL P Oro Pt (6.21)

Hence: P Eo = 16.KB.T.Kw . f.yo' (6.22) Pt- :

The resultant emf in the airgap of the machine, E, which is shown in

Figure 6.11, can also be obtained from expression 5.58. From expression

(6.19) and (5.59), the resultant flux in the airgap per pole is:

P = 2 2 o P9 — F o) (6.23) C ~o ° ad P(P~ + P 1 The value of Fad is given in expression (5.57). From expressions (6.23), (6.22), (5.57) and (5.58) the resultant emf, E, is obtained in terms of the direct—axis current Id: (T.g )2 E = Eo — 48 T PP1 (Pe + Po),Id (6.24) P

Hence the direct—axis armature reactance of the radial external rotor p.m. alternator derived from its magnetic circuit, is:

Xad = 48 r (T.Kpw ) 2 P 2 .gd.KB.f.P(P~ + Po) (6.25)

The symbols in this relation correspond to those used for the circumferential rotor machine (Chapter 5). 301. 6.4 CALCULATION OF THE PERFORMANCE OF THE MACHINE

A computer program similar to the one for the Mark I machine was used. The parameters shown in the previous sections were introduced into the program. (See Appendix VI.1.) The formula given for the no—load losses in Section 5.6 (expression 5.69) for the calculation of the efficiency of the machine was used initially. However, when the machine was tested it was found that the measured efficiency was appreciably higher than calculated. This occurred because in expression (5.69) a grossly high value of coefficient KNL was assumed (actually that of the circumferential rotor generators of Chapter 5; KNL for the radial rotor machines is much lower due to lower rotor and stator iron losses). A new measured value of KNL for the radial type of machines was therefore introduced in expression (5.69) (KNL = 0.00354) and this resulted in fairly accurate overall performance predictions.

6.5 THEORETICAL AND EXPERIMENTAL RESULTS AND THEIR CORRELATION

Calculations were initially made using the manufacturerts magnetizing curve (see Figure 6.1, curve He Br). The predicted total demagnetizing reactance Xq or Xd was 18 Q at 1600 rev.min 1. The calculated per phase winding resistance was R = 1.1652 in comparison s. with the measured R = 1.12.C2. s

Figure 6.15(a) shows the regulation curves of the machine for— different rotational speeds with three three—phase resistive loads. The theoretical no—load voltage at low rotational speeds agrees well with the experimental points. Good agreement can also be seen between the experimental and theoretical regulation curves over a large range of load currents. At 1600 rev.min1 the difference between the two values of no—load voltage is only 2.5% (321 V theoretical to 313 V experimental). THEORETICAL EXPER:M::NTA'_ CURVES PO:I\:TS ' X 1500 rev min-' r ~ 0 1400 -' .. 3 C ~~OO - (,120~-~---~---r----r---~--~r---~--~----~ -~+---+--;-----il 4 A 'CCO - • ..- ~ V 800 -- X 6 • 600 - • lfl250 I ? • 400 - - ~100~-~---r---t---+~-t----~--__~--~-~ ~ .-r-__. ~6 .&200·" ~ ~ • 0::: eOI-----;-----I----t----i---;--__t---::-f----i-----! ~.200...--...-..::..== w <.9 o~ ~ 150~::::~==--~L::-- ~ 6.01----+---1----+----"".,:; ~ ~ 1001-----t--- ~ ~ 50~-=~--~-----~--~-=~~

°0~--~2~---4~--~6~--~e~-~'0~--~j2~~--'---~~ LOAD CURREN~AMPS (a)

,·2 ~---r----r---' 2·4 0::: 2 ~ 1·0~--+---+---;---t---+----t I 2·0 .. - I.lJ !J « 0·8 ~ '·6 w ! 0::: I Ir I. L ~f '·2 io' LL 0·6 (.!) 1 Z ~ -"

However, the agreement between the theoretical and experimental maximum

output powers is not so good. They differ by 21% (7.8 kW theoretical to

6.15 kW experimental). From 6.15(b) it can be seen that the theoretical

maximum power occurs at higher currents than occurs in practice. It is

interesting to notice that the correlation is good at low loads. When

the load currents exceeds 8 A, the power and voltage drop rapidly.

Saturation calculations indicated that under no—load conditions

the tooth flux density Bt is 1.26 T, lower than the saturation point of

Losil 450 (Brat = 1.4T). The stator core cross—section is large enough never to saturate and can withstand all range of fluxes passing it.

However, the demagnetizing mmf increases with load, which causes an

increase of flux density in some teeth. This is because the demagnetizing

mmf and the flux of the magnets coincide in an additive manner in one of

the teeth along the q—axis of the machine (see also Section 5.8).

The difference between the calculated and experimental short circuit current is 18.5% (17.8 A theoretical to 14.5 A experimental), and it is thought that tooth saturation at high current causes this.

As was mentioned in Section 6.4, the use of the circumferential rotor no—load loss formula for the calculation of the radial rotor no—load loss gives rather low efficiencies, e.g. at the full load and 1600 re.min 1 operating point the efficiency was only 83% compared to the experimental value of 90%. Therefore for the calculation of the radial

(see Figure rotor machine no—load loss, new experimental values of En 6.19) and active volume were used (SNL = 0.00354, 0.00324 m3). VMKII Vv°1=MHII See Section 5.6. Figure 6.15(c) shows the corrected efficiency curve and it can be seen that their correlation is quite good. 304.

Table 6.1: Data sheet of the Mark 11 p.m. alternator.

P.M. ALTERNATOR DESIGN I Mark 1I

S N la ~ 11. h, s JI ·1~oC~11- lr ~ Wm ::; @ Ls Y L9 -~ , 1 D!a ~±f Oro ~IWl h2 h3 ~ Lm - ---I • ..J ~ l . __ ._-- -

No. Of phases m - 3 Os';' 230 mm Ls - 78mm Lm = 197mm t wav -7 mm

No. of slots Z =- 36 Oso=296 mm 19= 0.4mm Wo= 4mm W1 =12.4mm

Naofpofes 2p= 12 La= 72-.5mm wm=13 mm w2=7.92mm h1=1.7 mm

NQ of turns/coil Tc = 32 Lr =22.4 y=60.2mm h2::' 2mm h3 =25.8 2 No. of Slot~ q = 1.0 con~uctor cross = 2. 02mm slot = 287rJ c =20.07 pole/phas s~ctlonal area area mm Type of magnek= Ferrite stack steel:. Losil 450 Type of . a~adur330 winding' Double-layer 500 Br 0.37Wb Ho -= 272·21 Bsat::. 1.4 T Hsat= -] Winding • = kATm ATm- connection' A R.P.M .• 1600' COS4)= 1.0 Kwd= 1.0 . Kp= 1.0 KSk= 0.955 Kz= 1, 0 ~L = I. 23mWl BNL = 0.41 T Bt= 1.26 T Htn= - Temperature rise = 75 Calculated Calculated Unsatur satur. Test \ Unsatur. Satur. Test

POUT 7.8 kW .-_ ..~ 6.15 kW Rs 1.16Q - 1.12.Q 6.76.Q V 214 V - 208 V Xad ,. - - Imax 12 A - 10 A Xaq 6.762 - -

VNL 321 A - 313 V X, 11.3Q - - Isc 17.8 A I, - 14.5 A Xd 18.0.Q - - 11 89% - 90% Xq 18.0Q - - 0 0 43 - - Overall weight: 50 k~ - 110 Ib 305.

Figure 6.15(d) shows the calculated load angle ō versus

load current. S = 43° at full load.

Predictions made using the low magnetization curve of the

magnets (shown in Figure 6.1) were pessimistic (i.e. theoretical perform-

ance much lower than the experimental). At 1600 rev.min 1 the no-load

voltage dropped to 278 V and the minimum power to 5.85 kW. This would

seem to indicate that the magnets' BH operating points lay on the

manufacturer's data sheet BH curve and that the magnetizing rig had

worked effectively. Table 6.1 shows the data sheet of the Mark II machine.

Time did not permit calculations to be done with a saturation factor

correction for the Mark II machine.

6.6 TESTS ON '1'l1F MARK II P.M. ALTERNATOR

The main tests carried out on the Mark II machine were very

similar to those carried out on the previous machines. However, some

additional tests were carried out.

As was mentioned in Section 6.2.1, the armature winding was divided into two halves to facilitate parallel and series connection.

(Figure 6.16 shows the connections of the winding terminals in the junction box mounted on the end plate of the machine; see photograph,

Figure 6.10.)

The machine was tested with the parallel connection on a.c. and d.c. loads and it was also tested with a leading power factor load

(capacitance and resistance). One of the objectives in undertaking the design and construction of this high efficiency, low starting torque 306.

B2 Bt N A2 C2 A'1 C1

A m mB C

Al . B1 C1 A2 B2 • C2

• Series connection of windings.

A2 82 C2 Al . 1E4 C1 N T

A BCb C • Ai B1 C1

Parallel connection of windings.

Figure 6.16: Connection of the terminals of the windings of the • Mark II p.m. alternator.

307.

machine was to facilitate the determination of efficiency characteristics

of windmill rotors. For this purpose a special half—controlled rectifier

bridge was built to cope with variable speed (frequency) and voltage

conditions and resistive loads [6.2D . The machine was tested with

constant resistive loads at different speeds using this rectifier bridge

A short circuit test was also carried out on the machine.

6.6.1 Test Rig

The test rig (Figures 6.17 and 6.18) is similar to the one used

for the Mark I machine. However, it was not necessary to use a step—down

transmission system. Figure 6.17-illustrates: (1) d.c. motor drive,

(2) flexible coupling, (3) two supporting bearings, (4) terminal box,

(5) spring balance, (6) p.m. alternator, (7) tachogenerator, and

(8) bedplate.

The power diagram used for the measurement was identical to

the one used for the "Rutherford" machine tests in the College

laboratory. See Figure 5.74.

6.6.2 Results and Discussion of Actual Performances of the Mark II p.m. alternator

As was explained in Section 6.2.1, during manufacture

precautions were taken to minimize the cogging torque. Measurements

indicated that the total starting torque (inertia and friction) was less

than 1 Nm. Figure 6.19 shows the no—load phase voltage and loss curves

versus rotational speed. It is important to mention that the no—load

losses were also found to be a function of n3 /2 as shown in Figure 6.19. 508.

7

_

Figure 6.17: Diagram of the test rig of the Mark II p.m. alternator.

Fizure 6.18: The Mark II p.m. alternator on its test rig. 309.

VP PNL Volts. Watts

No-load losses x Experimental o PL = KNL x 300 300 n312 • No-load voltage phase

2 00 200

• X

100 100

00 400 800 1200 1600 SHAFT SPEED, n, rev min-1

Figure 6.19: Series connection of windings. No—load phase voltage and no—load input power/speed. 310.

The machine was initially tested with series connection of

the armature winding.

Regulation output power and efficiency curves (experimental

points) are shown in Figures 6.15(a), (b), (c) and (d) for rotational

speeds of 200, 400, 600, 800, 1000, 1200, 1400 and 1600 rev.min-1. The

tests were carried out with three—phase resistive loads.

Figure 6.20 shows power output curves versus rotational speed

for different constant currents. Normally the power changes linearly

with the speed for constant currents. This is clear at load currents

of 2 A and 6 A. However, the curve does not change linearly with speed

near the maximum output power which occurs at 10 A. This is suspected

to be due to saturation effects at high load currents. Figure 6.21

shows the efficiency curves versus speed for these three constant load

currents. It is clearly seen that with higher load currents, higher

speeds are required to give E > IR for output power to be produced.

Figure 6.22 shows the power output of the machine versus speed

at different constant resistances. At the highest resistance of 45.2

it can be seen that power versus speed follows a square law curve.

However, this is not the case over a wide range of speed with a

resistance of 21.5 , the value at which the maximum power occurs. The

departure from square law behaviour becomes worse as the resistance is reduced further (to 17.5 SZ and 12.552).

Figure 6.23 shows the efficiency curves of the machine versos speed where it is clear that the efficiency does not change much with constant resistance over a very wide range of speeds. It also shows that it falls with decreasing resistance, i.e. with the increase of load. Pout kW 5 o I .10A X 1= 6A 1.0 s 1. 2A

4

1 '

sdo loco 1500 SHAFT SPEED, n, rev min''

Irr 500 1000 1500 SHAFT SPEED, n, rev min-1

Figure 6.20: Output power versus rotational Figure 6.21: Efficiency curves versus rotational speed for different constant load speed for different constant load currents for a three—phase currents for a three—phase resistive resistive load. load. 10

Pout kW oa Load resistance per phase • 12.5Q x 17552 o 21.5 S2 • R a12.50 o 45.20 x R ■ 17.5St 06 o Ra 21.552 • a R=45.252

4 04

02

400 800 1200 1600 400 600 1200 SHAFT SPEED, n, rev min-/ SHAFT' SPEED, n, rev mind

Figure 6.22: Series connection of windings. Figure 6.23: Series connection of windings. Output power/speed for different Efficiency%speed.for different resistances for an a.c. load. resistances of an a.c. load. - 313.

This is because when the armature resistance and load resistance are

near- to each other, the ratio of the copper losses to the power output

becomes comparable.

Figure 6.24 shows voltage waveforms for no-load (a) and 2 A

load (b). The speed is 200 rev.min 1 and the machine is connected

directly to a three-phase resistive load. It can be seen that the skewing

has eliminated the slot harmonics in the waveform of the mauhine and the

line voltage is a nearly pure sinusoidal waveform. Because the load is

so small, the effect of the demagnetizing reactance on the waveform of

the phase voltage cannot be seen. Figure 6.25 shows the no-load (a)

and the 3.9 A (b) voltage waveforms at 400 rev.min-1. Here the difference

of the armature reactance can be seen. Further increase of speed and load

increases the influence on the waveform. Figure 6.26 shows the no-load

(a) and the 5.5 A load (b) waveforms at 600 rev.min-1. As said before,

tests were also carried out using a d.c. resistive load through a diode

bridge.

Figure 6.27 shows the output power and voltage characteristics

versus load current'at constant speeds of 200, 400 and 600 rev.min

connected to a d.c. resistive load. Unfortunately the available rectifier bridge's reverse voltage limit was 500 V. Tests could therefore not be

carried out at higher speeds. The efficiency curves at the above- mentioned speeds are shown in Figure 6.28.

Comparing the maximum power output of the machine at 600 rev.min l for the two types of load (a.c. and d.c.) it can be seen that with a three-phase resistive load the machine gives a maximum power of 2063 W with an efficiency of 81.4%, whereas with a d.c. resistive load the maximum useful power in the load resistor is only 1932 W with a slightly 314.

(a)

1/1441:111EMkrd- I 'Wan Mr IMO III

(w)

Figure 6.24: Phase and line voltage waveforms of the Mark II p.m. alternator at a speed of 200 rev.min-1.

(a) No—load, P = 38.75 V, V1 = 67.1 V. (b) An a.c. on—load, I = 2 A, Vp = 36.2 V, VQ = 62.7 V 315.

(a) • I %AWN RE MN

Figure 6.25: Voltage waveforms at a speed of 400 rev.miā1 . (a) No—load, = 75.?5 V, V, = 131.2 V. P (b) On an a.c. load, I = 3.9 A, VI) = 68.75 V, V = 119.V. 316.

11 II topIAMB in

(a)

(b)

Figure 6.26: Voltage waveforms at a speed of 600 rev.min1 . (a) No—load, p = 115.75 V, V, = 200 V. (b) On an a.c. load, I = 5.5 A, P = 100 V, VV = 173 V. Pout Vdc 317. kW Volts

Rotational speed 0 600 rev mir x>400 • 200

2 Pout

Vdc

4 8 12 LOAD CURRENT, Idc ,Amps

Figure 6.27: Series connection of windings. Output power and voltage current for different speeds with a d.c. resistive load. 318.

11A

1.0

08 600 rev min-1

400 rev min-1

0.6

I200 rev min''

0.4

0 0 1 2 3 OUTPUT POWER, Pout, kW

Figure 6.28: Series connection of windings. Efficiency/output power for different speeds for a d.c. resistive load. 319.

higher efficiency of 82.4%. This is a drop of power of 6.3%. This is

a small figure, but there is clearly always some penalty with rectifier

loading, small compared with the Mark I case due partly to the 120°

conduction periods (as opposed to 180° with sine wave loads) in each

half cycle.

Figure 6.29 shows the d.c. power output curves versus speed

for constant resistances of 9.642, 17.8g2 and 36.5g2. Here it is also

clear that with higher load resistance the power curve obeys the square

law with speed.

Figure 6.30 shows efficiency curves for these resistances versus

speed. The lowest curve represents the resistance which gives the maximum

power output at 600 rev.min 1. The efficiency range of this curve is from

71% to 78% at a speed range of 100 to 600 rev.min 1. respectively.

Figure 6.31 shows the waveforms of d.c. and a.c. line voltages 1, at 300 rev.min (a) on no—load, with Vdc = 149 V and Ve = 110.42 V;

(b) on—load with a resistive load of 2 A and Vdc = 123 V, Ve = 97 V.

Figure 6.32 (a) and (b) show similar waveforms at a speed of

600.rev.min-1 at no-load (Vdc = 292 V, Ve = 216.5 V), Fig. 6.32 (a),

and on—load (I = 3 A, Vdc = 245 V, Ve = 194 V), Figure 6.32(b).

In both cases it can be seen that the pure waveform of the

machine gives a perfect rectified waveform with an absence of spikes

or extra harmonics. The line voltage waveforms show periods of zero

voltage during commutation, which increase in length as the frequency

and load of the machine increase, due to the increasing IX drops in the machine. Pout kW 2

Load resistance • 9.69 x 17.89 o 36.59 1) 10

08

06

04

O 200 400 SHAFT SPEED, n,rev min-1 SHAFT SPEED, n,rev min1

Figure 6.29: Series connection of windings. Figure 6.30: Series conn clion of windings. Output power/speed for different Efficiency/speed for different d.c. resistances. d.c. resistive loads. 321.

(a)

(b)

Figure 6.31: D.C. and line vontage waveforms of the Mark II p.m. alternator connected through a diode rectifier to a resistive load at a speed of 300 rev.min .

(a) No—load, Vdc = 149 V, V1 = 110.42 V.

(b) On—load, I = 2 A, Vdc = 123 V, VX = 97 V. 322.

(a)

(b)

Figure 6.32: D.C. and line voltage waveforms of the machine at 600 rev.min1 . (a) No-load, Vdc a 292 V, V1 = 216.5 V. (b) On-load, I = 3 A, Vdc = 245 V, Vp = 194 V. 323.

The winding of the Mark II p.m. alternator was then connected

in parallel as shown in Figure 6.16. The results were more or less

similar to those obtained previously and a second series of tests was

carried out. A check on the circulating currents in the branches of

the winding found that a maximum value of 4 mA existed, which shows that

a high degree of balance was present between the sections of the winding.

The zero sequence current:in the neutral was found to be no more than

2.75 A for any load or speed.

It was decided to connect the machine to a load with a leading

power factor. A bank of capacitors was connected in parallel with the

load resistance. The influence of the capacitors on the output power

of the machine is very obvious, as shown in Figure 6.33.

Figure 6.33 shows the output power and efficiency curves of

the machine versus speed for different values of capacitors but a constant

load resistance of 4.288. Power increase, as expected, with capacitance

value and with speed. At very low speeds (frequencies)a small increase

of capacitance (e.g. 60/4-F) changes the power output very little. At

a speed of 1500 rev.min 1 (150 Hz), however, the power increases by

16.4%. At 1500 rev.min—1 and with a capacitance of 80✓4.-F per phase the power in the resistive load was 7.05 kW where, as without the

capacitance, it was only 5.44 kW. It is also important to note that

the introduction of the capacitance does not reduce the efficiency of

the machine, as shown in Figure 6.33. The efficiency remains constant

at 88% for the whole speed range. This is an indication that the

machine is free from losses due to harmonics.

The Mark II alternator was also tested when connected to a

d.c. resistive load through a diode bridge with the windings connected

in parallel. The results were similar to those obtained in previous tests. 324.

Capacitance o C=OLIF Pout Ī O C=60pF R=4.28Q kW X C. 80uF 10 1• 0

TI

8 0.8

Pout

6 0.6

4 0.4

2 0.2

00 400 800 1200 1600 SHAFT SPEED, n, rev; min-1

Figure 6.33: Parallel connection of windings. Power output and efficiency for different capacitance and constant a.c. resistive load. Capacitance in parallel with resistance. 325.

Figure 6.34 shows the d.c. and the line voltage waveforms of

the machine on different loads at 1600 rev.min 1. Figure 6.34(a) shows

a load of 4.2 A, where Vdc = 333 V, V1 = 257.2 V and Figure 6.34(b) a

load of 26 A, where Vdc = 204 V and V1 = 175 V. The influence of the

commutation effect of the rectifier on the waveform of the machine is

very obvious with increase of load.

A series of beat run tests was performed on the machine with

a three-phase resistive load. It was found that:

(a) when the machine was run at 600 rev.min 1, with or without

the cowling, the temperature rise was not more than 72°C and 62.5°C,

respectively, at full load;

- (b) when the machine was run at a speed of 1600 rev.min 1 at its

full load, the temperature rise without the cowling was 74°C and with

the cowling 83°C.

It was clear at these high load conditions that insufficient

heat transfer to the air was occurring, and it was

decided to paint the machine black inside and outside (see Figure 6.18),

to raise beat radiation levels. Later tests proved that this technique

worked, the machine being able to run at full load and speed with lower

temperature rise of 75°C.

Unfortunately ferrite possesses a negative temperature characteristic (the flux decreases as temperature increases 20% per 100°C) and the machine's output power decreases with temperature. When the machine is warm (75° increase) it can only produve 4.4 kW. This is due partly to the drop in field flux and partly due to the increase in copper losses. Measures to increase cooling levels further would probably be worthwhile, perhaps including an abandonment of the "totally enclosed" ventilation system. 326.

(a)

Mir 11111....11OFV-nolpf

w w w w w w w w w

(b)

Figure 6.34: D.C. and line voltage waveform of the Mark II p.m. alternator with parallel connection of the winding on a d.c. resistive load through a diode bridge at a speed of 1600 rev.min1 . (a) On—load, I = 4.2 A, Vdc = 333 V, Ve = 257.2 V. (b) On—load, I =.26 A, Vdc = 204 V, VE = 175 V. 327.

Figure 6.35(a) shows the short circuit test circuit and

Figure 6.35(b) the short circuit current versus rotational speed. As can

be seen, the current reaches the maximum value of 14.5 A at a speed of

500 rev.min 1 ( f = 50 Hz) and then remains constant due to the increasing reactance of the machine, The currents in all three phases were roughly equal and at 500 rev.min 1 the machine required an intput power of about 900 W. Checks before and after the short circuit test indicated that no reduction in no—load voltage occurred,:.i.e.Ahe field had not been reduced. This means that the magnets can withstand the short circuit demagnetizing current. During the test no vibrations on the machine were noticed.

The final tests on the machine in the laboratory were with a d.c. load connected through a three—phase half—controlled rectifier bridge [6.2] . The tests were carried out with two constant resistances, 15.6S2 and 9.952, which gave maximum output power at 600 and 400 rev.min-1, respectively.

The bridge was designed to form a fast—acting controller for a complete wind generating system. Tests on the bridge showed that the bridge was unfortunately unable to commutate at zero firing angle (the condition at which maximum power output is obtainable) because the filter of the thyristor firing system possesses a phase shift which increases with frequency. Figure 7.11 (in Chapter 7) shows this very clearly.

Figure 6.36 shows that the power output versus load angle of the machine at two constant load resistances and variable firing angles.

It is seen that with either increase of speed and/or reduction of firing angle of the thyristors, the load power increases. The highest 328.

Figure 6.35a: Short circuit diagram. I S.C. A A

X X X 14 X

12

10

8

6 I I I 4 I I 1 I 2 I I I 00I 200 400 600 SHAFT SPEED, n, rev min'

Figure 6.35b: Short circuit test on the Mark II p.m. alternator. 329. out R1 -215.60 R, = 9.95I Wat x 600rev min'' Pout A a 400 rev min'' O 400 w ✓ 250 • • 200 • 100 •

1000

Pout

Figure 6.16

Outōut power versus current of the machine at constant RQ but variable firing angle a with half—controlled rectifier bridge.

500

2 4 6 . 8 10 12 LOAD CURRENT, 1<,Amps

500 • 1000 OUTPUT POWER, Pout ,Watts

Figure 6.37: Efficiency of the machine versus output power at variable speeds and firing angles p( but constant R. 330

power outputs correspond, as was expected, to minimum firing angles for

both cases (at 600 rev.min 1, ° and at 400 rev.min 1, in = 48 Din = 34°).

Figure 6.37 shows efficiency curves versus output where it is

noticed that with increase of speed and load the efficiency decreases.

For the two cases of 400 rev.min 1 it can be seen that, as before,

decrease of load resistance (i.e. increase of output power) reduces

the efficiency of the machine.

Figure 6.38(a) and (b) shows the line and d.c. voltage waveforms

of the machine loaded by the thyristor bridge at a constant speed of

300 rev.min-1 and a load resistance of 3052, with a = 90° corresponding

to a current of 1.8 A (a) and 0( = 45° corresponding to a current of 3 A (b).

The distortion of the waveforms due to the thyristors is very obvious.

At present, the alternator is mounted on the windmill rig at

the Silwood Park facility [6.2] . Figure 6.39 shows a photograph of

thr windmill rig with the Mark II machine mounted directly onto it.

The photograph was taken at the Energy Show 1979 in Birmingham.

Figure 6.40 shows the tower and the windmill at Silwood Park.

A 2.5 m diameter cambered plate blade rotor is mounted on it. This can 1 run at a maximum rotational speed of 400 rev.min with a wind speed of

about 7 m.sec-1 and a load of 1.5 kW r6.2, 6.3J . Tests at Silwood Park are currently being carried out to define the power coefficient

characteristic of the wind rotor. To calculate the experimental C P

curve of the windmill, the following procedure is followed (see also :6.23):

(a) The p.m. alternator is connected to a constant resistance of

9.9S2 through the half-controlled rectifier bridge.

(b) The firing angle is adjusted automatically such that it keeps

the rotational speed of the system constant. 331

(a)

(b)

Figure 6.38: D.C. and line voltage waveforms of the Mark II p.m. alternator through a half—controlled rectifier bridge at 300 rev.min-1 and R e 30 . (a) = 90°, I 1.8 A, Vdc = 53 V, Vac = 95.3 V. (b)IX = 45°, I. 3.0 A, Vdc = 92 V, Vac = 92.0 V. Figure 6.39: Windmill rig at the Energy Show 1979 in Birmingham.

Figure 6.40: Imperial College test tower at the Silwood Park with the windmill erected. Performance Characteristics of 2.44m dia. Arched Plate Rotor. Blade Root Angle 00=30° Theoretical --- -- Measured

U 0 • z° ' w 0 0 o 0 . U_ IL W N ..~ \b O A U %O Cr

0 C,._

UO 10 20 3 0 4.0 5.0 6.0 70 TIP SPEED RATIO Figure 6.41: C curve of the 2.5 m diameter cambered plate blade rotor. xperimer gl .1esults taken wing Mark II p.m. alternator. 3311 .

(C) Traces of windspeed, rotational speed and power output are

recorded on an ultra—violet recorder. These traces are analysed later.

(d) The traces are examined for periods (3 seconds and above)

of constant or near—constant windspeed and wind direction. The values

of alternator output (a.c. resistive load) power and rotational speed

are noted and the input power to the windmill calculated.using the

Figure 6.38 alternator' efficiency characteristic.

(e) Finally, the value of C is calculated using formula given in Chapter 3.

Figure 6.41 shows the C curve of the windmill takan from

[6.2] . During the tests the maximum output which was recorded was

about 500 W at a rotational speed of 206 rev.min 1 and a windspeed of

9.07 m.sec-1. The calculated C at this point was 0.281 at a tip speed ratio , = 2.93.

It is worth mentioning that windmill starting was very satisfactory. Starting occurred at a windspeed of about 2 m.sec-1 and stopping (on no—load) occurred at a windspeed of about 1 m.sec-1.

6.7 THE "WINDRIVE" P.M. ALTERNATOR

This section summarizes work on a small p.m. alternator similar in certain respects to the Mark II machine. The work was done as a co—operative project with a small local firm (Windrive).

The "Windrive" p.m. alternator is shown in Figure 6.8(c).

A solid steel tube, of external diameter of 81 mm and length 195 mm, acts as the rotor "core" and and as the casing. Two arched ferrite 335.

magnets of Magnadur 370 material were glued on the inside diameter of the

rotor tube. The stack was fixed on a shaft. The rotor was mounted on

the shaft on two bearings fixed to two dural end—plates. On the outside

periphery of the tube (rotor) a ring was welded on which the three

blades of the 1 m. diameter cambered plate blade rotor were attached, as

shown in Figure 6.42.

Figure 6.43 is a photograph of the alternator.

The two magnets of the machine were glued with "Araldite"

onto the rotor prior to magnetization, and magnetization was carried out by passing a d.c. current through the armature winding. A programme of testing and modification was carried out. Computed.. results for the final version of the machine were obtained using the computing program of Appendix VI.1. See Appendix VI.2. The 'low' line of return of the magnets was used (Br _ 0.2 T and He = 235 kATm 1).

Table 6.2 shows the parameters of. the "Windrive" machine.

Because the armature winding of the machine was tightly packed into the slots, the formula given in Section 5.5.8 gave an appreciably higher value than the measured one and the experimental value of R = s 1.222 per phase was used in the program.

Figure 6.44(a) shows the resultant theoretical regulation curves at speeds of 500, 1000, 1500, 2000, 2500 and 3000 rev.min1 , with their corresponding experimental points. The correlation between the two at low speeds and loads is reasonably gōod.With increases of load and speed the experimental points lie below the theoretical curves.

The difference between no—load voltages at 3000 rev.min 1 is 3.9%

(53.6 V theoretical to 51.5 V experimental). 336.

In Figure 6.44(b) the maximum power output at 300 rev.min 1 is 315 kW, in comparison to 440 W theoretical.

The efficiency curves in Figure 6.44(c) show also an increase in the difference between theory and experiment at higher loads and speeds. However, the maximum efficiency figure achieved is in the range of 83% for both cases.

Figuer 6.44(d) shows the theoretical load angle versus load current curve, the maximum power output occurring at ō = 420.

A check on the saturation of a tooth of the machine has shown that the flux density at no—load is 1.44 T, which means that the tooth saturates-.slightly. As already known, Losil 450 saturates at 1.4 T.

It is obvious that an increase of load (demagnetizing current) will increase the saturation level in the tooth. This is clearly seen in the regulation and power output curves in Figures 6.44(a) and (b). A current of 0.8 A or more is sufficient to give this increase of saturation.

Time did not permit any attempt to calculate the performance of the machine taking into account the saturation conditions on—load.

Heat problems which occurred with the Mark II machine also occurred with the "Windrive" machine. The temperature rise of the machine at 300 rev.min1 was higher than 75° and the reduction of output power and efficiency was 20% and 5% respectively.

Tests were carried out on the machine with a battery load connected through a rectifier bridge. WIND ROTOR BLADES

TE MINALS

MOUNTING RING OF THE BLADES FIXED SHAFT ON THE TOWER

ROTOR OF PM.ALTERNATOR

DURAL END PLATE OF THE ALTERNATOR

Figure 6.42: "Windrive" windmill p.m. alternator.

Figure 6.43: "Windrive" external radial rotor p.m. alternator.

THEcuRv9SAL EXP •NTSTAL 1 X 3000 rev min 48 2 0 2500 - • a)- 480 3 0 2000 - 4 A 15-00• - ā 40 5 V 1000 - - 400 0 5 • 500 • CC 32 320 ōa. _J 0 2 240 0 W ti < 1G O 160 I a J e • eo 6 00 . i I 0 8 1.6 2.4 3.2 4.0 4.8 5.6 6.4 72 0.8 1 6 2 4 3.2 4.0 4.8 5.6 64 LOAD CURRENT, AMPS LOAD CURRENT, AMPS (a) (b)

CC qir 12 1.2 W.1.0 J • 10

WO S p •= 08 0.6 W 0 006 >- Z0-4

C.) 0.2 W 0 r ~ a: 50 '00 150 200 250 300 350 400 TOTAL OUTPUT POWER, WATTS O.8 1.6 24 3 2 40 48 56 64 LOAD CURRENT, AMPS (C) • Figure 6.44: Performance curves of the "Windrive" p.m. alternator: (a) regulation curves, (b) power output, (c) efficiency, (d) load angle. 339.

Table 6.2: Parameters of the "Windrivelt machine.

P.M. ALTERNATOR DESIGN I "Windrive"

S N la ~ , \ IL ~II h1 S Ir ·1~oC~If- Wm @ ~ y t ls 19 ~~~ ~W Os 1 ~±f h2 Oro h3 Lm ~ - p .-j ~ \. . --- - No. of phases m - j Ds - 57.15mm ls -78 mm lm = 195 mm twav -j·2mm

No. of slots Z =- 15 050 = 81 mm Lg= 0.47mm Wo= 2.5 mm w1=7.jmm

No. of poles 2p= 2 la= 81.9mm wm=20.26t1l W2= 3.97 mm h1= 0.4mm

No of turnS/coil Tc = 32 lr= 7mm y= 89.8mm h2= 3.2 mm h3= 8 mm 2 11.97 No. of Slot~ q = 2.5 Conductor cross = 1 25 2 slot =51 mm c= pole/phas sectional area • mm area mm Type of . Type of magnet = Ferrite Stack steel = Losi1 450 winding' Double-layer M"","!!!tA1'I,..~'7r - 235 ;' 500 8 r 0.3 'I 1 Bsat= 1.4 T Winding • = Ho = kATm- H~t=ATm-1 connection· A R.P.M. - 3000 Costp= 1.0 Kwd= 0.957' Kp= 0.995 KSk= 1.0 Kz= 1.0

CPNL = 1. 59mWl BNL = 0.356T Bt =1;.44 T Htn= - Temperature rise = 85°C Calculated Calculated Unsatur Satur. Test Unsatur. Satur. Test

POUT 440 W \- 315 W 'RS -- 1.22

V 35 v - 30 v . Xad 6.77 - - Imax 4.2 A - 4A Xaq 6.77 - -

VNL 53.6v - 51.5V XL ~.72 - - Isc 6.2 - - Xd ~.49 - - 11 81% - 75% Xq ~.49 - - 0 42° - - Overall weight: 3 kg - 6~6 1b 3110

The machine was tested with the windmill rotor mounted on its

rig and run at wind speeds of about 5 m.sec-1 at rotational speeds up 1 to 1000 rev.minn with battery and resistance loads.

6.8 CONCLUDING REMARKS

This section has presented the results of an investigation into a novel p.m. alternator type which can be used in wind power systems.

Although a little further work is necessary on certain aspects of the alternator's design and operation, it would seem that its final cost, weight (50 kg for the Mark .II) and performance could compare well with those of existing types of alternator.

The estimated wholesale price of the Mark II p.m. alternator in small quantity production is about £400.

The machine has been shown to meet the requirements desirable for the testing of windmill rotors when load control or rectifier bridge control can be countenanced. It can be driven by direct drive at low power and speed or through a gear: box at higher powers and speeds.

Some of the advantages of the Mark II p.m. alternator over the Mark I p.m. alternator include:

(a) zero cogging torque,

(b) very low harmonic levels,.

(c) high power/weight ratio possible since operation at 1500

r.p.m. is feasible (no surface losses in rotor poles),

easily available and cheap magnetic material,

little use of expensive materuals such as dural. 3!41..

Some of the disadvantages of the Mark II type p.m. alternator

are:

(a) hard and brittle magnets which are difficult to machine to

shape;

(b) power to weight at low speeds (e.g. 300 r.p.m.) is low due

to the rather low field flux densities;

(c) cooling problems; further work is required under full load,

full speed conditions to prevent overheating;

(d) output falls with temperature rise due to the ferrite

temperature coefficient.

In the future, designs of such machines should take more care with the design of the machine to solve the cooling problem in a more efficient manner.

3112 , CHAPTER 7

ANNUAL ENERGY YIELD ASSESSMENT AND COMPARISON BETWEEN SMALL WIND—POWERED ELECTRIC GENERATING SYSTEMS

7.1 INTRODUCTION

Much attention has been paid over the years to the ways in which

possible sites should be assessed for WECS, and this work is continuing as

the need to obtain more reliable, more detailed and more comprehensive

wind and site data grows. Numerous. references can be found on this

topic, Golding [7.1, 7.2] giving a reasonably comprehensive account of

the standard assessment method and of the nature of the difference in

wind conditions between sites.

7.2 WIND CHARACTERISTICS

Figures 7.1 and 7.2 show Goldingos wind velocity and wind

duration curves for three sites. The reader is referred to Golding for

detailed information about these typesof characteristics, but briefly,

the velocity—duration curve shows, as ordinates, the range of wind

speed and, as abscissae, the number of hours in the year for which the

speed at a particular site equals or exceeds each particular value.

One way of characterising the annual duration of wind

speeds of different magnitude is the wind duration profile . A wind

duration profile (WDP) can have a general description. According to

Cbilcott [7.3] and Meel [7.4] the WDP may reasonably be approximated by

a Weibull distribution [7.12, 7.13] . 343 •

eoor------~------~------r_------_.--__T

600~--~---+------~------r------~---M 1---+LEICESTER

Cl) t.. 8 ~ 400~---+---+------~~------r------~----1 Z' o a::~ a200~~~-+~~--~------+-----~~--1

~-+-- RHOSSILI DOWN

80 90

Figure 7.1: Velocity frequency curves.

SO------~------r------~------~~__,

By Ljungstrom ByGolding o --..,;.. RHOSSILI DOWN A X ----5t:ANN·S HEAD B C -.- ~EICESTER C

00 2000 4000 6000 HOU~S IN THE YEAR Figure 7.2: Velocity duration curves. 344 .

A velocity-duration curve or a WDP of a Weibull form can be characterized by two parameters [7.4] :

w - the average wind speed, and - the Weibull exponent related to the kind of wind regime.

The Weibull WDP is described by the following formula, as given in [7.4] : k r t ( > w) -(VJCk) = e (7.1) total where: t () V w)is the duration of wind speeds higher than V w;

is the total observation time; k: is the Weibull exponent; and ttotal k r: C is a constant related to w by a gamma function of k V + 1/kr (7.2) Cw ) k

The definition and properties of gamma functions are given in Appendix VII.1 [7.5]

The Weibull exponent is correlated to wind regime in- the following way [7.3, 7.4] :

General Flow Type of Wind Regime Weibull exponent Character kr

Irregular Polar, wind shadow.. 1.0 Mediterranean, desert. 1.5 Isotropic Temperate maritime and continental. 2.0 Roaring fourties. 2.5 Constant Trade wind. 4.0

Rewriting expression (7.1), the WDP is now: V V k _( w r C ) k (7.3) V e 345,

when kr = 2.0, the expression (7.3) gives the Rayleigh distribution.

By differentiating expression (7.3) the frequency distribution

is obtained [7.43 :

V V k w w r 1 ( w)k ( ) d ( w) _ w Ok w r e (7.4) d ( w) w ~w w Ck V w LjungstrOm in his paper in 1976 [7.7] points out that analysis of a great number of WDPs for coastal, near coastal and_,inland sites in

Sweden has shown that for purposes of practical wind energy prospecting a simple normalized shape function (2) can be used as shown below:

Jw —(V ww) when 0.5 ~VV ¢(VW) ) = 2 w 4( 2.5 (7.5)

As LjungstrOm states: only one parameter, the exponent for Qw, is needed to characterize the shape of the WDP at a given average wind speed Vw, and for each wind site will be dependent on site location fi (coastal, near coastal, inland) and on wind fetch terrain properties.

This type of WDP—shape function is very convenient and useful in simplifying analysis of windmill performance and annual energy output.

LjungstrOm having studied the WDP of about 70 sites for ten years (1961-1970) came to the conclusion that the average values of were:

(a) for 8 inland sites: fi = 1.76.

(b) for 5 near coastal sites: ft = 2.0.

(c) for 8 coastal sites: 9 = 2.19. ...111 w 346 .

Figure 7.2 shows the calculated points of the velocity duration curves ':taken from expression (7.5) and also assuming that

V,Vw .0.5 and V./V>2.5. Results show a good correlation between the two types of curves. For the purpose of this study equation (7.5) and the above assumptions are accepted as valid approximations for

~(V ~. As can be seen from the points in Figure 7.2, formula (7.5) w matches reasonably well the three velocity duration curves given by

Golding [7.1] . This is very encouraging because the formula with its simplicity enables easy computation of the energy yield per year for different windmill electrical generating systems. Figure 7.3 shows the

WDP of the site at St. Ann's Head taken with expression (7.5).

In a similar way to the power—duration curves, the power— duration profiles (PDP) can be obtained, by cubing the ordinates which are proportional to the power in the wind for a given swept area.

Fig. 7.5 shows the PDP at St. Ann's Head taken from Figure 7.4.

It is realized that the area E under the curve is proportional to the annual average power in the wind. Multiplying this average power by the number of hours in the year, 8760, the annual amount of energy in the wind is obtained. This also corresponds to area D in Figure 7.3.

As in the case of the Weibull distribution curve, expression

(7.5) can be differentiated to obtain frequency distribution profile:

ß.ln2 9 dO(V~ _i = V exp( dV w w_ pp w -(Vw' 'w w VP►~ w 347 .

4.0 ST. ANN'S HEAD VW-VAV-7.242 m see 0:219 32 ,

2.4

1.6

08

0 0 0.2 0.4 0 6 08 1.0 WIND DURATION PROFILE, ON)

Figure 7.3: • WDP of the site at St. Ann's Head. 3~8 •

C'J..... 80------~------r_------~--~ ~L :::J .E --- RHOSSlLI DOWN A ~ ------ST. ANN'S HEAD B -'E 50 1',;--4---+------. LEICESTER C --+---1

20~~~~_+--~~--~------+------~--~

Figure 7.4: Power duration curves.

Vw (m sec-1)3

10000 ------~------~------~~------,_------~

aooo~------_+------~------r------~------1

I 5000~------~------4------~~~----~------~

5000~------+------~------~r------~------~

2000~~~--~------~-----~------;----~

0·2 0'4 o·a '·0

Figure 7.5: Power duration profile at st. Ann's Head from Ljungstr3m exponent.

3'49 .

7.3 CALCULATION OF THE ANNUAL AVERAGE POWER IN THE WIND AND ANNUAL ENERGY YIELD FOR DIFFERENT WIND—POWERED SYSTEMS

Figure 7.6 illustrates the various power'losses in a WECS,

starting with the power flow in the wind itself to the power in output

load, the useful extracted power. It is convenient to express all the

parameters involved in terms of the wind speed. Therefore the useful

power extracted from the wind will be:

P p(v geII(v POUT(v = a(V)w .C w). 7gb(v w) .// ) (7.7) w W or

P0-( (7.8) ) Pa (w) • 77s (w) where

s Cp( wt) . 7/ gb(w)' r/gen (w) (7.9) (w)

where Cp( ) ) and / 7/gen( ) are the power coefficient, the gear V , gb( box efficiency, and the generating system efficiency, respectively, all

expressed in terms of the wind speed.

From the PDP of Figure 7.4 and from expressions (7.8) and (3.3), the contribution to the average output power production of windspeeds ranging from Vw1 to V will be: w2

V w2 POUT1,2 = ā PA v J s(v)w3 11 d!~(w) (7.10) m l w

Expression (7.10) is obtained from the formula for an area of a curvilinear trapezoid if the curve is given in the parametric: form x = y(t), y =JO (t), t1 < t ‘t2 [7.5] : ~gen(Vw)

CP(Vw)

Electrical generating system losses

Mechanical transmission losses

Aerodynamic losses

Figure 7.6: Distribution of power losses in a wind-powered generating system t2 Area (t) Tt(t)dt t JJ 1 where in this case:

= Area; POUT . t = W; x = 0(v)'3 y = POUT(V ) 1,2 w An expression similar in form to (7.10) is used by Sarre [7.8]

( 7/ taken simply as equal to C), and a similar technique using the expression (7.11) for calculation of the annual wind energy yield is adopted by Joyadev and Smith [7.9, 7.10] (constant generator and gearbox efficiency assumed). Substituting expression (7.6) into (7.10) gives:

W2 VPw+2 P i .a w UT P A w w w exp( —a~V )dV J O (12 ) fl w V j1 s (V ) wl w (7.12) where ln 2 aw = (7.13) V W

The overall system efficiency 1given by the general form (7.9)-- 7 s (V ) is also a function of the wind speed. If is such that P Ls(V ) OUT(W ) stays constant from V v2 to V J3 (by pitch control' or stalling), then [7.8]

] (7.14) POUT(2,3) POUT(v~:)~()Vw2 °(W3 2 As was said before, the overall annual energy extracted from the wind between V Jl and V J3 will be:

.8760 (7. POUT 15) EOUT(1,3) (1 3) where: P OUT(1,3) 0UT(1,2) + P OUT(2,3) 352

It is generally accepted that the V J1 is the cut—in windspeed

(Vw ) which is set by the no—load (or load) and inertial loss c characteristics of the windmill in relation to the wind power sufficient

to overcome them. V is the rated wind speed (Vw ) at which the w2 R windmill produces its rated electrical output and incremental wind power

is spilled by the control system. is the furling wind speed at which w 3 the wind power reaches a level which would irreparably overload the

windmill; automatic cut—out is therefore provided at this point to

protect the system.

In [7.6] from calculations and meterological data, it is

concluded that the best relationship between "rated wind speed" V and wR "cut—in wind speed" V is given by: w c (7.16) w ti 2Vw R e

and the relationship between optimum rated wind speed and annual average

wind speed of the site is given by:

2.3 w (7.17) wR =

However, in [7.110 : V w 1.2< R <2.5 (7.18) V w and: V 2.0< R <3.0 (7.19) Vw c Later on, these relations will be checked for their validity.

In [7.9, 7.10, 7.12 and 7.13] the power output of WECS is

calculated for different types [7.12] : (1) ideal, (2) with mechanical

transmission losses, (3) with fixed pitch and constant speed. However, 353 .

a simple loss variation is assumed, but with a constant percentage of

power. This might be a good approximation for large windmill systems

connected to the grid and running at a constant rotational speed and

variable aerodynamic and generator efficiency at lower output powers than the rated. In the case of small windmill systems, however, the rotational speed of the system is variable. Under constant conditions

(maximum power extraction) the overall efficiency is therefore very likely to be a function not only of output power but also a function of other factors such as rotational'speed or wind speed.

7.3.1 Mechanical Transmission Losses

In the previous chapters it was shown that a mechanical transmission system tends to be used for most windmills for the generation of electricity for low generator size and weight. The Step—up transmission system can be of the belt pulley type or a gearbox. The spur—gear gearbox is the most common type of gearbox and the losses in this type of gearbox were looked into.

The overall efficiency of most gearbox types is dependent on three separate and distinct types of loss, known as [7.l4] :

(a) windage and churning. losses,

(b) bearing losses, and

(c) gear—mesh losses.

The windage losses of a gearbox are very difficult to measure or calculate (see Chapter 3). Investigations have been carried out on this subject, but very little good information has been published. In 354 . general terms, windage-loss determination is still pretty much based on individual experience of the gear designer and experimental measurements on the specific type of gearbox in question. The windage losses for a given gear design depend on many things, such as diameter of the rotating elements, length of the rotating elements, speed of rotation, the web or gear-blank design, overall casing design, type of oil-feed system (if atiy),. and the operating temperature and viscosity of the oil and the pressurization level in the casing.

A relation has been formulated that gives a fair approximation to the windage losses of small-diameter gears (up to approximately

0.508 m in diameter with a lib ratio of approximately 0.5):

n3D5L0.7 P (7.20)

100.1015 where n is the rotational speed, D is the diameter of the rotating element, and L is the length.

- It is extremely difficult to calculate bearing losses and have them coincide exactly with measured bearing losses. There are many sound reasons why variations between actual and predicted bearing losses exist. Some of these reasons are:

1. Bearing misalignment.

2. Difference between actual and assumed viscosity-temperature behaviour of the lubricating oil.

3. Presence of phenomena such as oil turbulence or recirculation.

4. Difference between actual and assumed operating variables such as shaft speed and bearing loads. 355

The losses of rolling-contact bearings depend to a large

degree on the type and quantity of lubricant used in a given application.

Exact predictions of these losses are also extremely difficult. However, the literature reports a considerable amount of experimental work has been done, together with empirically derived relations.

If the torque loss is calculable, then the power loss can be calculated as:

Tr.Qbearinen (7.21) Pbearing - 30 where is the bearing loss and is the torque loss per Pbearing Qbearing bearing.

The torque loss can sometimes be assumed to be Qbearing given by:

D1 (7.22) Qbearing - fbearing 2 wbearing where is a constant coefficient of friction for the particular fbearing type of bearing 7.14] , D1 is the bore diameter of the bearing, and

is the load on the bearing in kg. wbearing

This approach offers a.fast and reasonable approximation based upon normal operating loads and speeds with favourable conditions.

A short-cut method has been developed to analyze standard spur-gear trains which is quite helpful. The power loss of a given set of gears is a function of the coefficients of friction of the gear mesh and the so-called mechanical advantage of the gear mesh:

f. • 100 (7.23) mesh - M 356 .

where is Pmesh the per cent power loss, f is the coefficient of friction taken from [7.14] and M is the mechanical advantage of the mesh.

The mechanical advantage, M, can be plotted for various

combinations of number of gear and pinion teeth, as well as the friction

coefficient D.143 .

Because of the difficulties of predicting losses, even when

design details are available, it was decided to adopt a simplified basis

in which the total gearbox loss was taken to comprise:

(i) mesh loss, assumed to be proportional to power throughout only,

(ii) friction loss due to seals, bearings, etc. assumed proportional

to speed only (i.e. constant friction torque).

The friction torque, Qgb' can be measured with a spring balance on the

low speed shaft of the gearbox. Therefore the gearbox losses are

assumed to be given by:

_ w.m esh Pgb - 100 + Qgb.nw (7.24)

where nw is the windmill shaft rotational speed.

Substituting expression (3.34) into . (7.24), it becomes:

P _ w.pmesh n Pgb - 100 + Qgb kg (7.25)

7.3.2 Definition of the Starting Rotational Speed (Cut-in' Wind Speed) of the Windmill with a Load Control for Cubic Loading

In Figure 3.1 of Section 3.2.1 it can be seen that at wind speeds near the cut-in wind speed the windmill can work with a lower C p than C without stall until `~ .2Q and C - C . Amax J` Q 'max 357,

Figure 7.7(a) shows a family of torque characteristics versus

of a fixed pitch windmill at different wind speeds. A typical load

torque characteristic versus is given by the dotted line. From

Figure 7.7(a) it is clear that the system will not start rotating until

the wind speed reaches the value of w4 where at point D the windmill

starting torque is just higher than the(' local starting torque F. The windmill will then accelerate to pointa (assuming an unchanged V w) where load and windmill torques are equal. If an optimum —seeking control system is switched on, then the operating point will be pulled to poine A for that particular wind speed, where ;1= ; o and therefore C = C Pmax

The control system, ideally, will ensure that the operating point remains on the vertical line O(—i as wind speed varies. The windmill of course could run at lower C until the value of Vw , where 0 the system finally stalls, and it is worth bearing this in mind when designing a controller.

Figure 7.7(b) shows the family torque curves of the Imperial

College cambered plate blade windmill rotor with the no—load torque curve of the Mark II p.m. alternator. As can be seen, the windmill starts rotating with a wind speed of 2 msec-1 but it stalls when the wind speed is only 0.9 m.sec-1.

The starting wind speed hence does not represent the lowest wind speed at which the system can run, and a decision is necessary on which wind speed should be treated as the cut—in or starting wind speed for computational purposes. In what follows it is assumed that the starting wind speed of the system is that at which the control system cannot maintain cubic loading, providing also that at this wind speed Load torqu.ewith Q contrOl system for 18 cubing loading

I 1.6

1.4

1.2 vws

A 1.0 Load torque without system E / for cubing loading E b as Vw3 D F ■ 0.6 Vw2 C -0 vw, 0.4 C B No-load curve of the Mark Q B P.M.AItemator A I 0.2 Vwo 1 • A I 2 m sec-1 I ` I 1 E5 1'S 1175 f , 20 40 60 EO 100 120 ĀQ Xop T3 ■ A ' SHAFT SPEED n rev min' Figure 7.7a: Torque curves of a windmill at Figure 7.7b: Torque curves of the wind rotor versus different wind speeds versus shaft speed with the no—load curve of the Mark II p.m. alternator. L.J 359 the system can somehow start rotating (i.e. with variable pitch, or starting devices) (i.e. VJ on Figure 7.7(a)). 0

This approximation is reckoned to involve little error when calculating energy yields from systems because annual yields at these low wind speeds are small. Figure 7.7(b) also shows that there is no great difference between wind speeds at points 0 andC(.

In the case of resistance load control the cut-in and stall wind speed will hence be that at which the machine can supply load current whilst operating at optimum power coefficient. This is for the case of a fixed pitch windmill. In the case of a variable pitch windmill, it is the rated wind speed (at which feathering commences) at which

at n For higher wind speeds operation occurs at constant I - Imax max' power and system efficiency, until the furling wind speed where the system is shut down.

7.3.3 Operation of a Wind-powered Permament Magnet (P.M.) Alternator running at a Variable Rotational Speed at andC =C . °p p Amax

From expression (3.38), the input power to the p.m. alternator shaft, with Pf = 0, can be expressed as:

P~ = P +P+ (7.26) NL + POUT

As was shown in Chapter 5, the no-load losses of the p.m. alternator are given by expression (5.68):

n3/2 PNL

The armature losses in the alternator are given by: 360

PA = 312R (7.27) where the winding connection is in star and I and Rs are the current and resistance per phase respectively.

The output power from the alternator connected to a three-phase resistive load will be:

RI 28) OUT 312 (7.

It is assumed that the winding and load resistances remain constant with temperature. Therefore the input power to the alternator becomes:

(7.29) PIN = Kn3 + 312Rs + 312R€

If the alternator is coupled to a windmill rotor through a mechanical transmission system (gearbox), then the windmill's output power will be:

Pw Pgb + P IN (7.30)

As was said before, the maximum extracted power from the wind is obtained at a variable shaft speed of the windmill at and C °p • pmax

Substituting equations (3.35), (7.25) and (7.29) into expression (7.30) for maximum extraction of power from the wind, gives:

kg n3.P g n3 n 3/2 + 312115 kw 100 + Qgb'kg + 312R1 (7.31) where for a horizontal-axis windmill, 4R 5 g in TC w w a 3 •kg (7.32) 3)? Cpmax op 361

Expression (7.31) means that the windmill can run at op and C when the load resistance R on the current I can be controlled Amax 'e such that expression (7.31) is true when, from (3.31):

30. 2op V .kg. w n = (7.33) 1t . w

Rewriting expression (7.31) gives:

(1 - Pmesh)kg n3 - n3/2 - k•n - 312(R +R.) 100 w NL Q = 0 (7.34) g

7.3.4 Control with Variable Load Resistance

As was said in Section 3.3.3, (see Figure 3.86), one of the methods of control of a wind-powered system is load control. A suitable form for Re as a function of speed to achieve operation at op may be:

-5/2 + a RQ = aln3 + a2a3~2n 3n1 + a4 (7.35) where Nils a solution of expression (7.34). Assuming that the current varies as:

I = a5n2 (7.36)

a52n4 or I2 = (7.37) the coefficients al,...,a5 can be found by substituting expressions

(7.35) and (7.37) into (7.34):

mesb)kg n3-$ n3/2- Q (1 — -fn_3a52R5n4_3a1a52n_3a2ah/23 a52n3/'2_ 100 w NL g

-3a3a52n3-3a4a52n4 = 0 (7.38) the equation (7.38) is obeyed when: 362.

3a52Rs + 3a4a52 = 0 (7.39)

(1 - mesh)gk - 3a a 2 0 (7.40) -100 w 3 5 2 + 3a a 0 (7.41) KNL 2 3 a55 = @ + 3a1a52 = 0 (7.42)

From equation (7.39):

a4 = -Rs (7.43)

From (7.41):

•K a2 - 3a5 NL2a5 2 (7.44) 3 From (7.40):

(1 mesh)kg. 100 w 3 - (7.45) 3a52 and from (7.42):

6) a1 3a52 (7.4

The value of the coefficient a5 can be defined from the maximum values of current and speed at which the alternator should

operate. Therefore expressions (7.36) and (7.37) becomes:

2 (7. Imax = a5nmax 47)

= a 2 n4 (7.48) I2max 5 max 2 = n4 (7. a5 12ma rmax 49) 363 .

Substituting (7.49) into (7.45):

m eshkg _ (1 — 100 ) w 4 I2 nmax (7.50) 3I

Substituting (7.49) into (7.46):

al _ gb 4 (7.51) 3.k .1 nmax g max2 Substituting (7.49) and (7.50) into (7.44): 33/2.gg 13 a -NL max 2 (7.52) mesh g 5/2. 6 100 )kw J nmax All the coefficients of equations (7.35) and (7.36) can hence be defined from the windmill and alternator parameters.

7.3.4.1 Efficiency values

From expression (7.7) the efficiency values of different parts of the windmill system running at C max can be defined. The efficiency A of the system with C will be: max

POUT 113 (7.53) Tts(with C ) (w) w(w) max where P is given by expressions (7.35), (7.36) and (7.33)• OUT( w) P is given by expression (3.35). w ( wT) The gearbox efficiency will be:

P (7.54) 11 gb (w ) IN(w)1P w(11,) where P is given by expression (7.29) and by substituting to it IN(w ) expressions (7.35), (7.36) and (7.33). 364.

The generator efficiency will be:

gl gen ( ;) P0UT(v) w (7.55) `/IN(v )

The overall system efficiency, (7.53), can be expressed in

terms of the windmill, gearbox and generator parameters and can be written

in the form:

A + Bn 3/2 +Cn+Dn2 (7.56)

where:

Pmesh A = 1 100 (7.57)

B = — (7.58) kw 2 3 Imax R's (7.59) n4max k wg

D = — Qg" g = _ _gb (7.60) kg.kg and'n is given by expression (7.33).

The load resistance can also be expressed in terms of these parameters:

4 ( _ Pmesh 100 )kg _ _ R R nmax ( 1 w mak Q _ 2 (7.61) 31 n n 2 k n3) s max g

So the current will be:

Imax 2 I = (7.62) 2 n n max 365.

7.3.5 Control with Variable Load Current but Constant Load Resistance R

With an output regulator the load current from a p.m. alternator

can be varied so that expression (7.34) is solved when RQ = constant.

Solving expression (7.34) in terms of I2 gives:

_ mesh )kg 3/2 )Qkw 3 n — gb n 2 (1 100 (7.63) 3(Rs + RR) 'n 3(Rs+R~) kg(Rs+R~)

Therefore the output power will be:

_ g 3/2 R~(1 Pmesh 312R 100 )kN w n3 _ ReK Ln _ R2Qgbn POUT = R + RQ R~ (Rs+RQ)kg Rs+ (7.64)

The output load resistance can be defined from the windmill

and generator maximum parameters. Substituting into expression (7.34),

the maximum values of load current and rotational speed, the required

load resistance Rj is:

(1 _ Pmesh)kg K / Q 100 w ti3 _ NL 3 2 gb R _ Rs 2 max 3I2 max - 312 k nmax (7.65) 3 Imax max max g

The system can be controlled only when the current is greater than zero,

therefore this will determine the starting rotational speed, i.e. cut-in

wind speed.

7.3.5.1 Overall Efficiency of the System

This can be calculated for constanq working (at ? op) as

before from expression (7.53). Substituting expressions (7.64) and

(3.35) into (7.53), the overall efficiency of the system, in terms of the windmill and generator parameters, is: 366 •

= Al + Bln 3/2 + D1n 2 (7.66) s V ( w where:

Al = E.A (7.67)

B1 = -E.B (7.68) Dl = -E.D (7.69)

where: R,e E Rs + RQ (7.60)

A, B and D are given by expressions (7.57), (7.58) and (7.60), respectively.

7.3.6 Operation of a Wind-powered Wound Field Alternator running at a Variable Rotational Speed at a it op and C = C P Pmax

It is assumed here that the wound field alternator is self- excited through an ideal field control system as shown in Figure 4.14c.

The controller is assumed loss-free (which is not the case) and tbuild-upl problems are neglected, i.e. as soon as the alternator begins to rotate the residual magnetism is enough to build-up the system immediately.

Rewriting expression (7.30) for a wound field alternator which provides its own field power:

Pw = Pgb + PNL + PA + Pf + PO (7.61) where Pf is the loss in the field winding. The no-load losses of the alternator will be:

PNL - f.w. + Piron 367.

where the windage and friction losses from experimental results were

found to follow the law:

P = K n3/2 w.f w.f (7.63) where the windage and friction coefficient Kw.f is taken from measurements. The iron losses were also obtained through experimental

observations and seem to vary approximately as:

(7.64) Piron = K'iron i.e. a function of the field current and the rotational speed. The iron loss coefficient K. is also taken from experimental results. iron

The armature winding losses are:

PA = 312Rs (7.65) where from Figure (4.41c):

I II + I (7.66)

IL is the a.c. current to the field control system and I the load current. The, field losses are:

2 (7.6 Pf = If Rf 7)

The field current in terms of the a.c. current, commutation losses neglected [7.15], is:

3f.V Vf = p h . cos a (7.68) . where 0( is the firing angle for continuous conduction and 0 <0(.TC/3.

The phase voltage is: 368,

ph = (7.69)

and the field current:

If Vf f`_ (7.70)

can be rewritten in terms of I by substituting (7.69) into (7.68) and

then into (7.70):

I - R RQ I = It (7.71)

where If is a function of angle0(. For convenience the influence of a

is neglected, and from expression (7.66): 3 fl R.? I~ = I(1 + R ) R (7.72) T

Assuming temporarily that

PO = k' n3 UT (7.73) with constant Rk and Rf, then from

3 ph 4 POUT - Rx (7.7 )

Vp must vary as k.n3/2, since from expression (4.8):

Vph = kv JŌ n (7.75) and (4.12):

Ā. = k„f•n2

For the case when *xi from expression (4.17):

0 = kf If therefore: 369 kd 1 If = kf n2 (7.76)

or:

If = f..n2 (7.77)

where: k k0 (7.78) _ kf

Substituting expression (7.77) into (7.67):

2 Pf = ( f) Rf n (7.79)

Substituting in expression (7.61) the generator and windmill parameters become:

/ kg n3 = kg pmesh 3 n .n + K n3 2 K ktn3/2 w w 100 gb •kg w.f iron f 31/6R d + 312(1 + R p)2Rs + ( f)2Rfn + 312R. (7.80)

Solving equation (7.80) in terms of I2, equation (7.81) is obtained:

(1— mesh)kgn3—(K +K. k0)n312_ rat +(1 Y 2R ] n 100 w w.f iron f k fl

3 (1 + 3 R' Re] (7.81) R / 2R s C f From Ohm's law:

(7.82) Āh = I2 Ri but also from expressions (7.75) And (4.17):

Vph = kv.kf.I1.n or

Vph = k1.If.n (7.83) 370 •

where:

kv kv.kf (7.84)

From expression (7.83):

Vprkvn (7.85)

but from expression (7.82):

Vph = I2 (7.86)

Substituting (7.81) into (7.86) and then into (7.85) gives:

i (l n_( +. re +(k)2Rf] n-1 j P100b)kg w.f R ron"f)n-2- J If = g 3 tRQ )2 3 (Rk~v . )2 [(1 Tr Rf Q~ (7.87)

Expression (7.87) gives. field current to satisfy expression

(7.61) when the armature, field and load resistances are constant.

7.3.6.1 Efficiency of the System

The efficiency of the system given by:

) POUT(VP )

Iso Amax w(vw) is again expressed in terms of the windmill and generator parameters.

Putting 7/ in the form: s

s = F(A2 + B2n3 /2 + D2n 2) (7.88)

(Cpmax9 where n is given by expression (7.33), giving:

-

371 .

mesh A2 = 1 - 100 (7.89)

V g B2 = - (Ew.f + giron"f k!] (7.90)

k .. D -- - + (k )- R /k 2 = L f] (7.91) g R~ (7.92) [ 3 ~ RQ (1 + R ) 2Rs + R,] f Expressions (7.88) and (7.66) have similarity of form, and comparing the parameters of the two expressions, it can be concluded that if

both systems are working with the same values of kW°, Qg 1kg and Pmesh/100 then it is clear that from:

E F and

A = A2 but

D GD2 even when B and B2 are taken as equal.

Hence the efficiency given by expression (7.88) should be less than the efficiency given by expression (7.66), and hence a wind-powered system with a p.m. alternator should be more efficient than the one with a wound field generator, given the assumptions of the analysis.

The coefficients given in expressions (7.89) to (7.91) can be defined from the maximum parameters of the generator (0(= 00), i.e. the P From expression (7.64): , Piron , ' If f max and Rf. max max max max I P. iron max iron (7.93) If 'nmax max 372.

from expression (7.77):

k0 = 1.maxIf • (7.94) n2 max

the maximum field voltage is given by:

Vf = If .Rf (7.95) max max

therefore from expression (7.68) the maximum phase voltage will be:

V • Īt f max V b - (7.96) P max 31/6:ieosd

where from (7.83):

V f pmax kv (7.97) If max max

and also the load resistance will be: V R ph max = I (7.98) max

7.3.7 Computer Program for the Calculation of the Energy Yield for Different Wind-Powered Electrical Systems and their Comparison

Appendix VII.2 gives the program used to calculate the

efficiency values of the three types of system. The formula given by

LjungstrOm to calculate the annual average power and energy yield for

a given location are incorporated in the program.

Calculations were performed with parameters corresponding to

the Mark II alternator described in Chapter 6 and a standard alternator 373 .

in the laboratory (detailed in Chapter 4) were used. Equal alternator

input powers were assumed in order to give a common basis for the

comparison between the types of electrical system (three in number.).

The computer program allows all three systems to be calculated

together for a given location. Because of the difference between the

losses in the systems, the cut—in wind speeds differ slightly, but

the:feathering and furling wind speeds are taken to be the same. The

feathering or rated wind speed was taken from expression (7.19) which

in the case of St. Ann1s Head location is 11.174 m.sec-1 for w R 1.54 V. The windmill maximum C was taken as 0.35 and maximum

rotational speed was 160 rev.min 1. All the other windmill parameters were determined by the input power to the generators (PIN).

The gearbox losses are taken to be the same, though the gearbox ratio of the p.m. alternator system is slightly different from the gearbox ratio of the wound field generator system, in order that the windmill rotor should have the same aerodynamic characteristics for all three cases. The gearbox mesh loss was taken as 0.02 and the loss torque 2.5 Nm.

Figure 7.8a shows the load resistance change with wind speed required in order that the windmill—p.m. alternator system should extract the maximum power from the wind. It is seen that the cut—in wind speed

V = 3.114 m.sec-1 where V = 3.6V . This means that the expressions we wR we (7.16) and (7.19) are not quite correct for this wind—powered system where the system runs for a wider range of wind speeds.

Figure 7.9a shows the efficiency of the system versus wind speed. In the case of the system with constant resistance load and p.m. alternator, the change of load current versus wind speed is shown 33

29 12

N E25

0 21 zŪ

17 ūl W 13 0 0

30 40 5.0 60 70 BO 90 100 11•0 12.0 03.0 40 5.0 6.0 70 80 9.0 100 11.0 120 WIND SPEED, m sec'' WIND SPEED, m sec'' Figure 7.8a: Load resistance versus wind speed of the Mark Figure 7.8b: The change of load versus speed of the II p.m. alternator running by a windmill with Mark II when running at variable resistance constant and C load and with 9 and C op constant. Amax Amax 1.2 12

1.0 to 0 0 N E d E 6 ▪ 08 Q h z• z 6 W 06 W

V O4 0 4 0 J 0 u Q i., 0 2 0 2

0 03.0 47 55 63 71 79 87 95 103 114 30 40 50 60 70 80 90 100 11.0 12.0 WIND SPEED, m sec' WIND SPEED, msec' Fig[ire 7.8c: Field current versus wind speed of the 6 kW, 'Figure 7.8d: Load current versus wind speed of•the Mark II• 1500 rev.min"'I would field generator with p.m. alternator with constant load resistance running by a windmill with ) o and C constant load resistance and running by a • 375.

V 1.2 UJ Ū U. 1-0 UJ • 08

J 0-6 J' 0= UJ 0 4 O 0.2 d

4 0 5 0 5.0 70 8 0 9 0 10.0 110 120 WIND SPEED, m sec' Figure 7.9a: Overall system efficiency of the Mark II p.m. alternator with variable load resistance on a windmill with `) op and C '! Amax -

U U tC} 1 .0

U- UJ 18

UI 18 }N E t!i -J J c h4

. U Ō~ • a 0 9 47 5.5 63 71 79 87 9.5 10.3 WIND SPEED, m sec'1 Figure 7.9b: Overall system efficiency of the wound field *alternator with field control system with constant load resistance and and C 0.97 °p pmax

0 87

>- 0 77 U W U 0,87 U-w X 0.57 J 0 0-47 UJ v 6. 0.37 a

0 27 20 40 GO 80 100 120 140 160 180 200 GENERATOR SPEED, rev miff' x 101 Figure 7.9c: Gearbox efficiency curve versus generator shaft speed with the Mark II p.m. alternator and with a op and C pmax 376-.

in Figure 7.8b. The cut—in speed is the same as in the previous case.

The overall efficiency of this system is very nearly the same as the

previous one shown in Figure 7.9a.

In the case of the wound field generator with constant load resistance and variable field current, the cut—in wind speed was found

to be Vw = 3.985 m.sec-1, which is nearer to expression (7.19), = 2.8Vw .. The change of field current versus generator rotational wc c speed is shown in Figure 7.8c. The efficiency of the system is lower than in the two previous systems, as is shown in Figure 7.9b. Figure 7.9c shows the gearbox efficiency of the systems versus the generator rotational speed.

Table 7.1 shows estimates of annual kWh for the two geared systems with: A) the Mark II p.m. alternator with a regulsted resistive -1 load, and B) the 6kW, 1500 rev.min wound field generator with a field regulator and fixed resistive load. Both regulators were assumed loss free. Constant operation was assumed up to the rated wind speed of 2 11.174 m.sec-1 and constant power operation assumed for wind speeds between

11.174 and shut—down at 15.643 m.sec-1 for the high—furling—speed system. -1 The V J os 7.242 m.sec and of 2.19 which were taken correspond to the site parameters at St. Ann's Head.

Table 7.2 shows estimates of annual kWh for a direct drive and a gearbox system. The same site was used as before with the same wind speed ranges but the maximum rotational speed of the windmill was taken to be 150 rev.min1 to match the maximum rotātional speed of the

Rutherford p.m. alternator (generator A). Generator B was taken to be the same as in Table 7.1. The Rutherford machine has an input power of

6870 W at 150 rev.min1 with a current of 7.6 A. 377.

Table 7.1: Annual energy yields for two geared systems.

Wind speeds Annual mean powers* into Annual Alternator msec-T Gear Output ratio cut-in furling turbine gearbox generator load energy MWh • A 3.114 11.174 10 2.5 0.875 0.76 0.69 11.7 3.114 15.643 10 2.86 1.0 0.87 0.78 13.37 B 4.000 11.174 9.4 2.58 0.9 0.79 0.61 10.4 4.000 15.643 9.4 2.95 1.03. 0.91 0.70 11.92

Per unit figures, where 1 p.u. = 1.943 kW.

** Annual mean power in wind for operating wind conditions only. (Total annual mean power in wind = 5.9 p.u. for A and 6.15 for B).

Table 7.2: Annual energy yields for geared (A) and ungeared (B) systems.

Wind speeds Annual mean powers* into Annual Alternator, msec ratio energy cut-in furling turbine gearbox generator load

1.6 11.174 A 1.0 2.5 0.87 0.87'7 0.78 12.3, 1.6 , 15.643 1.0 , 2.86. 1.00 1.00 0.89 14.1 B 4.0 11.174 10.0 2.76 0.97 0.86 0.66 10.4 4.0 15.643 10.0 3.16 1.11 0.98 0.75 11.97

Per unit figures, where 1 p.u. = 1.81 kW.

* Annual mean power in wind for operating wind conditions only. (Total annual mean power in wind = 5.88 p.u. for A and,6.6 for B.)

Comparing Tables 7.1 and 7.2, it can be seen that for alternator B the output energy is the same, as would be expected. For generator A, however, there is an increase of 5% when using an ungeared system.

Alternator A, ungeared, gives a 15% increase in energy over Alternator B

(geared). 37S.

7.4 CALCULATION OF TUT ENERGY YIELD OF DIFFERENT WIND-POWERED ELECTRICAL GENERATING SYSTEMS WITH KNOWN CURVES OF EFFICIENCY-- VERSUS SPEED UNDER CUBIC LOADING CONDITIONS

There are some cases where it is not possible to formulate

algebraic expressions for generator efficiency (e.g. expression (7.61)).

However, it is possible to obtain efficiency characteristics in graphical

form either from measurements: or from standard prediction methods.

In this section a method of obtaining these experimental efficiency curves

for the case of cubic loading with speed is presented together with

typical results. Systems with: (a) variable a.c. load resistance with

p.m. alternator, (b) systems with d.c. thyristor control system with a

p.m. alternator, (c) wound field generator with variable field current, and (d) variable capacitor-excited induction generator, are examined.

Figure 7.10 shows one of the methods of obtaining the efficiency curve of the generator when the system is controlled so that the input power to the generator (output from the windmill) varies cubically with speed.. A p.m. alternator controlled by a variable resistive load is taken.

In the case of direct drive:

PIN = Pw kwn3 (7.99)

The same expression is used when the mechanical transmission losses are neglected for convenience To start with, the experimental family of curves of intput and output power versus load current for different rotational speeds are drawn. The rated input power and rotational speed are selected and the coefficient kw is calculated from expression (7.99).

Knowing the coefficient kw, the input powers to the generator are calculated for different speeds with cubic loading. Given the input powers, the output powers of the generator at the corresponding 379,

PN6

PIN

n3

PN4

PN3

1 PN2 -}- ---- 0 I6 ni n2 n3 n4 n5 n6 Load current, I Shaft speed, n PUT3

F UT4

Figure 7.10 Calculation of the efficiency of a p.m. alternator with cubic loading from experimental input and output,powers versus load PUTb n4 current. 380.

rotational speeds and at the same current can be defined and hence the

efficiency values, too.

Figure 7.11 shows the method of calculating the efficiency

from experimental' input and output powers, for constant load resistance

versus firing angle when the machine is connected through a half-

controlled rectifier bridge. Given here are the results of the tests

taken on the Mark II p.m. alternator as explained in Chapter 6. Because

of the reasons given in Chapter 6, the system could not be controlled down

to zero firing angles as shown by the dotted lines.

Using the same technique given for the a.c. load, the efficiency

of the system can be defined as shown in Figure 7.11. The test was

carried out with a constant load resistance of 15.6SĪ.

Figure 7.12 shows the method of defining the efficiency curve

of a self-excited wound field alternator or a capacitor-excited induction

generator connected to an a.c. constant resistive load. The input and

output powers are given in terms of field current for the wound field

alternator (or capacitance in the case of the induction generator).

The technique used for the definition of efficiency is the same as before.

Figure 7.15 shows the (1) efficiency curve of the Mark II p.m.

alternator with variable a.c. resistance load obtained as shown in.

Figure 7.10, where (2) is the efficiency curve of the same alternator with

a thyristorised bridge rectifier and a constant resistor load. In Figure

'7.13 the way in which the firing angle 0( changes with speed as as to

maintain an input power proportional to n3 is shown. For both cases, the •

alternator rotational speed was 0 to 600 rev.min1 . Measured efficiency--

curves are also shown for a typical wound field lorry alternator (4)

(0 to 1500 rev.min 1 speed range) and for a typical capacitor-excited PIN • 381 • Watts 600 rev min' x 500 " o 400 O 300 A 200 " 2400

PiN5 44 2000 44

1600 1 4 4 - PN 4 ` ------1200 x •' ` ♦I

800

PN3

4 00 PN2 RN1 0 EuTt 100 200 300 400 500 600 Shaft speed, n, rev min-1 Url 400 eUT3

8001- i'l i i 172414.44, i 1200

16001- / Figure 7.11: Calculated efficiency of the Mark II p.m. / alternator connected to a d.c. load through / a thyristor—rectifier bridge.

/ Pour5 2000

POUT Watts

382, PN P 11 A

IN6 n~ - - - PN. - - - -

1

4

—4------!>`--- n3

PoUT6

n2 1N4 1N4 -- - — - I IPUTS n, I I 1 PN 3 1Pa 41 / I1 1 I -4-n, FiN2 -1- —► rt - - - -i - y~ r 0 —0- O iX P5ur2I ~T3 I i Ī I 1 PUT2 Field current, If I n2 n4 n6 Ō UT3 xciIātion capacitance, C Shaft speed, n n,

Y

OUT

n4

ns Figure 7.12 Calculated efficiency curve of a wound field alternator or an induction generator when they are self-excited ---4---- n6 and connected to an a.c. resistive load.

POUT 383.

I I a,°FtRING ANGLE t fo1af'1( D' P.M.A1ternator, •.c. resistance lOad. 2. Mark I[ PM Alternator, thyristor bridge plus d.c. resistor load. ~ 1·2 3. induction generator. variable C plus Z a.c. resistance load. lLI 4 Lorry alternator, LC. resistance Ioid. ~ 1·0 IJ.. W 1 ~ 2_ ~ O'S "".- ~ W V - J- ~V ~ ell ~ ~ ~ 0-6 ~;o( ~ V ~ ...... f. ~. -I V -I "')Y...... ~0'4 ~o ~ !/V 1'- ...... ~ .... ~ o ()2 / -( .... " :j' L V ...... - 1' ...... C1...... 11/ V ~ ...... 00-1 0'2 0·3 0'4 0·5 06 0·7 0·8' 0·9 H) GENERATOR SPEED rev min-1

Figure 7.13: Efficiency versus shaft speed curves with "cubic loading".

240 - I PowerI In Wind'[ ----, Powe,. from windmill rotor 200 ....en I +J ·Ifi\ (I) '3'8~ MWh ~1GO I I 0::' V ,I W 120 \ I I I ) ~ (i\) 4'8~ MWh Cl.. V / WR I~ zeo I « 30-2 MWO w ,,~\VJ ;y j / I 1'. VWF . ~ 40 V / .1 '\ I / I" I \ ,," Co2sta~stan~ l~ :0 i power ~ 4 8 12 16 20 24 26 32 36 WIND SPEED m sec-1

,- ...... " Figure 7.14: Annual mean power in wind and from windmill rotor. Locatipn ~St~·A.mi:l.s~ .. .Head, from 0.5 m. sec-1 increment's of wind speed.

!So . en +J +Jns 3:40 0::' W ~30 0 Cl.. Z 20 L5 ~ 10

00 2 18

Figure 7.15: Annual mean powers from 0.5 m.sec-l increments of wind speed for four different generating systems. 384

three—phase, 8 pole induction generator (3) (0 to 750 rev.min1 speed range). See also Chapter 3.

Using expressions (7.12), (7.14) and (7.15) for energy yield

assessment and the experimental efficiency curve given in terms of a

function of rotational speed and therefore wind speed:

s(v) = f(Vw ) (7.100)

The method of interpolation was used to obtain the required

relation (7.100). Appendix VII.3 shows the computer program used to

obtain the energy yield of the four generating systems from their

experimental efficiency curves, neglecting gearbox losses.

Figures 7.14 and 7.15 relate to a 2.2 kW three—bladed arched

plate, horizontal—axis windmill of 3.14 m diameter. Site conditions and

rated and furling wind speeds were assumed to be the same as for the

systems given in Table 7.1. Figure 7.14 shows the contribution to the

total annual mean power made by winds of each speed (actually of each -1 0.5 m.sec speed band), (i) passing through and, (ii) converted by the

windmill. Figure 7.15 shows similar curves of electrical output. power

for each of the electrical systems detailed in Figure 7.13. Estimated annual MI figures (annual MWh = annual mean mW.10-3.8760) have been

marked in and indicate the gains to be had from high efficiency

mechanical to electrical conversion. Gearbox losses are neglected for

the geared lorry alternator and induction generator systems.

7.4.1 Economic Comparison of Small Wind—Powered Generating Systems

From [7.15] a guess on the cost of the previously examined horizontal—axis windmill of 3.14 m diameter can be obtained. These costs 385 •

represent the purchase of materials and manufactured articles for the

construction of one windmill, but using the four different generating

systems given above.

Table 7.3 shows the approximate retail prices of the four

windmill systems where the materials are multiplied by a factor to take

into account labour and overheads (k40 = 2.5)., the purchased articles

by a factor to allow for handling k = 1.15) and allowance is made y g ( hand. ) for manufacturer's and agent's profits (kman. 1.15, 1.2). kagent =

From Table 7.3 the approximate retail prices of the four

electric generating systems mounted on the same windmill will be:

(1) (672. x 2.5 + 1.15 x 380) x 1.15 x 1.2 = £2920. (2) (672 x 2.5 + 1.15 x 355) x 1.15 x 1.2 = £2880.

(3) -(562 x 2.5 + 1.15 x 650) x 1.15 x 1.2 = £2970. (4) (562 x 2.5'+ 1.15 x 505) x 1.15 x 1.2 = 02740.

In order to define the most profitable and realistic system

they have to be compared applying the cost benefit analysis given in [7.15] ,

which is based on the assumptions given there. The numbers in [7.15]

are not changed because for this comparison their real value today is

irrelevant. Taking as:

Celan = plan capital cost (E)

Eou = annual energy produced by plant (kWh) t = cost per kWh of fuel replaced (p/kWh) Fcost

Standard capital budgeting techniques [7.16.] give the total cash

outflow Co during the life of the plant given by [7.15] as:

= 1.399 C (7.101) Co plan 386.

Table 7.3: A guess cost of small wind-powered electric systems.

Purbbased Materials Item Articles £ E

Windmill: a) blades plus bub 90 15 b) bead assembly and 80 80 centrifugal brake c) yawing system 72 135 d) tower plus framework 220 100 e) wind, sensing transducers -

Windmill total 462 330

Generating system: 1) Mark II p.m. alternator, a.c. resistance load: a gearbox - - b alternator 110 c power electronics 100 50

Total (1) 380 . _ 672

2) Mark II p.m. alternator, d.c. resistance load: a gearbox - . b alternator 110 c power electronics 100 25

Total (2) 672 355

3) Induction generator: a gearbox - 100 b generator - 120 c } power electronics 100 100

Total (3) 562 650

4) Lorry alternator: a gearbox - 100 b generator - 50 c power electronics 100 25

Total (4) 562 505 387-

Applying the same technique to determine the discounted cash saving

Cs on conventional energy from [7.15J :

Cs = 0.329 E annual.Fcost (7.102)

The breakeven condition occurs when Co = Cs. .Therefore from expressions

(7.101) and (7.102), the fuel cost will be:

1 • .399•Cplan _ Celan Fcost — 0.329.E (7.103) annual 4.25 Eannual

From expression (7.103) and Figure 7.15 the equivalent fuel cost for the

four systems given above will be:

2920 (1) F = 4.25 —_ 2.86 p/kWh cost — 4.34 x 103 2880 (2) F _ 4.25 = 3.22 p/kWh cost 3.8 x 103

F 4,.25 2970 = (3) cost = 3.78 p/kWh 3.35 x 103

(4) F = 4.25 2740 — . 4.14.1 p/kWh cost 2.84 x 103.

The above fuel cost figures give a picture of the situation

between the four systems. The systems'with a more expensive but more

efficient generator with a higher annual energy yield give lower

breakeven fuel costs than the others with lower capital costs.

7.5 CONCLUDING REMARKS

An energy yield assessment method has been evolved to aid comparisons between the performance of different wind energy conversion systems. The method has only been applied to a small number of specific cases. It clearly has considerable potential for wider and more general use in the assessment of small wind power plants. 38E3 •

As reference [7.173 states, generator capital costs usually

form only a small part of the total cost of a system. If minimum

capital cost per rated kW is the primary criterion for equipment

selection, low cost generators may be chosen, even though they may

convert energy relatively inefficiently. Where minimum total cost per

kWh is the primary criterion, the use of generators of the highest

efficiency and reliability is normally justified and permanent magnet

generators have a useful role tos playin small wind plants feeding

isolated loads and there is no requirement for close frequency or

voltage control.

The assessment methods described in this chapter are powerful tools for system studies of wind generator plants, and it is unfortunate that time did not permit more than the single comparative study detailed above to be looked at. This study looked, in an exact but fairly broad manner, at the relative merits of specific examples of different generator types in terms of energy yield and overall costs. Further comparative studied will be extremely useful and now not too difficult to carry out. Particular studies that one might suggest here could help to determine, for example:

1) the best choice of generator (cost versus efficiency)

of a particular type and rating for minimum overall cost;

2) the best choice of generator rating and hence 9ratedt

windspeed) for a particular windmill. This matter has been

explored by others e.g. references [7.3, 7.8] ) but only with

extremely simplified versions of the generator efficiency

characteristics. 3š8a.

The crux of the choice is whether the adoption of a relatively large generator, and hence a rated wind speed near the windmill's cut- out speed, and a relatively high energy yield result in a lower or a higher net energy cost than the adoption of a smaller and cheaper generator and a lower rated wind speed. Energy yield is usually lower in the latter case, since wind is spilled above rated wind speed, and knowledge of the nature of generator's efficiency characteristic over the entire working range is obviously important. 3S9 . CHAPTER 8

CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK

This thesis has reported investigations relating to the

design, testing and selection of electric generators and systems for

small—scale wind power application. In this final chapter, the thesis

as a whole is reviewed on a chapter by chapter basis and the most

significant contributions and shortcomings, in the authors view, are

indicated.

The contribution of wind power to individual consumers in

small-scale applications is discussed in Chapter Two. It is concluded

that the contribution could be significant and economically viable,

given the increasing cost of fossil fuels and electricity.

Chapter Three discusses and examines a number of different

electric generators and systems applicable to small scale wind power

generation. It is hoped that this goes some way towards making good

the scarcity in the literature of papers dealing with the electrical

aspects of small wind plants. The induction generator which was

experimentally investigated showed that, for small—scale applications

involving isolated loads,'.this scheme is likely to be a good one to

choose when a simple capacitor excitation system is used (one or two

capacitor sections per phase) and when low generator coat and

availability rather than high efficiency is desired. The arguments

for induction generators are, of course, quite strong when grid

connection is involved, and the VAR requirement can be met from the

grid. This chapter and the thesis as a whole did not give consideration to large scale wind power generation, but some aspects of small—scale 390.

generating systems are of course relevant to larger systems. In

general, small wind power plants have been treated in the thesis as

variable speed systems in which maximum power from the wind is extracted

by operating at optimum tip speed ratio. It was shown how the

variation of rotational speed and load affects efficiency.

In Chapter Four, a novel wind power system is described. It is believed that the idea for the "self matching" of small wound field generators with resistance loads to windmills, and the theoretical treatment are original. It was shown that a fairly good natural match can be obtained between power/speed characteristics of generator and windmill with configuration, particularly when the magnetic circuit of the generator goes fairly hard into saturation at higher speeds and field currents. Test results indicated that an external d.c. source would often be necessary to initiate "build—up" in a practical system.

The need for fairly high magnetic saturation levels at rated conditions may require high field ampere—turn levels. This may tend to give rise to poor rated efficiency. Stability problems may also occur with windmills having a peaky C versus characteristic. However, the scheme involves no control system and is therefore simple and cheap.

The chapter does not include any results from field tests. These tests are suggested for future work on the existing windmill rig at

Silwood Park.

Chapter Five presents an account of the design and theoretical analysis of some special p.m. alternators of the "circumferential rotor" type. The pros and cons of the application of such machines for small wind power systems are given in Section 5.15. The computer programs given in Appendices V.1 and V.2 are reckoned to be useful for further 391 . design work on this type of machine. The effects of saturation are not allowed for in the programs, but the. use of a saturation factor is detailed in Sections 5.8 and 5.11.4. The circumferential rotor machines constructed possessed good performance and high efficiency, but were rather expensive, partly due to the expensive magnetic material used. Solutions were suggested to some of the problems mentioned in this chapter (cogging torque, harmonics and saturation).

Time and priority factors meant that no attempt was made to develop a theoretical analysis of the rectifier loaded p.m. alternator or to use a modified version of one of the analyses developed for rectifier loaded wound field alternators. However, the experimental results obtained during the work are presented and discussed. An analysis of the behaviour of this type of system could perhaps be formulated in a future programme of work. The reduction in maximum alternator output power due to rectifier loading has not been deeply examined and a theoretical analysis of the alternator—rectifier behaviour could explain this. The theory developed to predict alternator performance of the alternators assumes steady state, unity power factor load conditions. An extension of this theory to cope with leading or lagging power factor conditions should not be too difficult.

Chapter Six examines a second type of p.m. alternator using a radial permanent magnet layout. Ferrite—based excitation systems were looked at and the resulting designs seemed to be a good compromise between the needs for low cost, low rotational speed and low weight/power ratio. Slight overheating occurred under worst case conditions with this type of design but further work is likely to eliminate this. The use of cooling systems incorporating cooling fins or external cooling "radiators" could play a part here. 392,

The work reported in Chapter Seven suggested that:

(a) In the zero to 10 kW size range output per size and

weight for modern p.m. alternators can be competitive with that

from wound field generators if comparisons are made at equal

speeds and powers.

(b) P.M. alternators are generally somewhat more efficient

than wound field generators, but the margin with respect to the

more efficient examples of the latter type of machine is fairly

small.

(c) Output control circuits with p.m. alternators generally

have to handle an appreciable fraction of the rated output and

may be more costly than the field control circuits of wound

field generators. However, p.m. alternators need no field

circuit or slip rings and are free from "build-up" and "loss of

field" problems.

(d) The energy yield assessment methods which have been

evolved to aid comparisons between the performance of different

wind energy conversion systems have shown that it is not only

the efficiency generator level of the load combination that is

important for maximum energy extraction but also the efficiency

level of the generator control system.

(e) The absence of a step-up transmission system eliminates

certain problems, worries and losses and can sometimes be justified

through the use of a direct drive low speed alternator (purpose-

built or derated standard type) but is likely to involve- higher

capital costs.

(f ) As stated in E7.173 , generator capital costs usually

form only a small part of the total cost of a system. If

minimum capital cost per rated kW is the primary criterion for

equipment selection, low cost generators may be chosen even

though they may convert energy relatively inefficiently. Where

minimum total cost per kWh is the primary criterion, the use of

generators of the highest efficiency and reliability is normally

justified and p.m. alternators have a useful role to play in

small wind plants feeding isolated loads where there is no

requirement for stringent frequency or voltage control. The

methods given for energy yield assessment can, with some modific-

ations, be applied to large scale wind plants where different

types of generators, wind regimes and locations can be considered

and compared.

In this thesis, certain electrical aspects of small wind- generating systems have been examined. It has not been found possible to make strong recommendations about the correct selection of wind generator system for small wind plants because of the early complex issues involved and the lack of a clearly defined winner amongst the numerous generator and control system types. It is not clained that the thesis contains a comprehensive account of generator selection and application for small wind-powered plants. Future work can look at this matter, in particular examining the relative merits of the generator types listed in Table 3.1, and make more detailed analysis of different generator control systems. It will be appreciated that the thrust of the thesis, as that of the project, has been towards the design and performance of P.M. alternators, for the reasons given in Section 2.2 and that consideration of many important aspects, for instance of 393a. windmill and generator operation and rating, have not been examined.

The complexity of many of these matters means that it has probably been wise not to attempt superficial discussion of them and it is hoped that future work on the electrical aspects of small wind plants will fill some of the gaps.

•• ▪

. Cage induction motor-6'- 394 . C1OB12a APPENDIX III . 1 Degrees of protection IP44

. . Cooling form IC0141 . 50Hz 3 phase. Class B insulation, Temperature rise not greater than 80K by' resistance

• Rated Frame! Performance at rated output Torque Ratios Locked 1 Rotor pax j Motor :, Mean ' Mean output size I rotor moment locked 1 mass 1 sound I. 50,111t Lo,.td C011(9111 El I i,...icncY Powto Pull Pull I Locked rotor current ratios of !rotor j j pressure j por.e factor iiit up • inertia time r\jFilt:171 'il tevet ! level • at at DOL Star DOL Star no' 1 0;11(101,A I :-;80V 415V I 110Ita I delta I 0. I ' kW _L. I 1/0110 rNhn. A A • 1111- x 1;/101 x rated coriciu s , kg ;I 1,11'"''!::‘1"" 1 J 7 I r.._ 4 5 6 7 aa 1. n j 12 14 Ir. 113 I 1 / I la 1 19 .. . " 2 Pole '141 cue 63 -7 7600 r 9610 051 .I 0.46 65.0 0.83 1.1 4,1 i 67 ..... 0 053 2,1 1A .._ ....20 - 45 - 0000363 . 1! 51 0,37 71 I. 71 45- ! - 7- 0.0005 t.1 1 8 5,1 i - .1-i;. .. • I 2800 1 1.75 0.96 0.E18 69 0 0.85 1.4 1 --- 2.0 -IT. - 56 • . . obi."' 1 71 1 2900 '**■ 1.1:8*. 1.213 1 127 .... 71.0 085 , 24 15 22.0...4 i. ____- . _..45 ...... - 0.000533 1 _ 8 ', 7 1 5:, 1 66 770 SI.) - 0.0009110 1 .14 10 9 ; 6: - ' . io •. . . 0.75 1 80 .4 _ ..300 (.... 756 . 156 ....1 1,70 _6.32f-j-14 1.7 --,. _.. 1.1 ( 80 _ 2800 L 3,75 . . 2.60..1_735 . . 76.0 0,65 1 2,6 1,7 . 71 - 5,2 _ .... __:- 0 00114 i .14 10,9 . b2 _I ....._ 26 :'' - • 1-i-- ) li.15 - 7820 1 5'.06 3.35 ' 3 16 11,0 0 68 1 70 1,7 2,5 6.0 I_ 7,-3 1 000,..0600:1,:61_ i . _11 _ . i 1164.5.3 ..11 4 ' • _ __.;_. __ _Oil i___ /7: 2.2. I 90L I 2820 • 7,45 -1.85 . 4A5 ! 78,0 7.513 L 2,6 1--,7 2.5 . - -- - 6 - 3 r ;10,i1,1 . ..,820 i 102 .1. 65. _ 1 59 79.0 0 •89 ..... 1 20 1,7 2.4 0.60 6 0 - - - - 11 ' -- 25 4 .-/--. --lb. - $ 1 1 , 73 • 4,0 1 i i 20 • 2020 ■ 13.6 8.4 1 7,7 .. _81,0 0.69 _ 1 2.6 ... r..... 1 7 2 4 0,60 6.0 2.0 1 0.00735_ 20.1 0.0165 85, • 1328 ___I...... 2970 . . , +43 ...... 11,4... _ 1 10,5 825 0,89 ] 75 1 7 2 4 0.60 6.0 20 I • 75 , i . . 0,44 1 2,6 7.7 2.4 I 0,60- 65 - i 1 170 1 1,...p.4 • 7700 i 35,2 I-21,0 I 19.5 800 089 75 1,7 2 4 055 65 2,3 I 04u..1 , is 80.3 • 6, I so " - , . 15,0 , 160M 1 2930 I"- 404 29,5 i 27.0 890 087 2 1,7 2.4 055 6,5i. 2,3 I 0.0463 ','5 1 60 3 10 - ' - 90 126 . 1601. 2310 1 Gull,365 ! 330 885 0,87 _ 25 .. 1... 1.7 _75 11_0:.6 5 6,8 23 005231 25 ' •.,M,3 81 , I 90 :k . . _ .. 1 1600 2'J)0 , 72.0 890 088 1 35 20 . 0 . 11 -TO 1 -24 .--; 00506 , Iii ' I ' iciz.b- : - 81 ' ; - 40 ...... 225 _. . . r 475 1 395 • 4 _ .. 10,171 '....; -t ---;95- .?.(A,3 i 700L 4. 2950 . 07.0 675 i 57.0 1395 ciii 25 1 4 ---3.0.1--- 0,50. 0--- Ts S:5 . 200.1.I ■ 37.0 2001. :950 I l'-20.0 ma 1 70.0 ' 89.0 0,83 20 1,4 - -2.0 ' .--0.50 6.0 1.8 . 0.187 35 200 ■./ .;.■ ; 103 450 4.7750 .1_ 2055 . 146.0 89.0 ...1 .131.0 _ .. 90.5 .. 0.85 _... . 20 3.4 1..... 2,0 ...-..0.50 .. .. 60 ...... 10 r. 0204,.. . .. j ..-35 . i . 270.0 .94 .. _ 104 '• t . 1 ... 4 Pole • - : -ii,i3 63 r 1 0 820 0 47 60 0 0 65 2.8 1 5 2 1 4 0 000013,', ,0 .4 4,) 1 SS 1600 .1 0 43 - - - ' - 50 1 0)11 1 b3 1 1400 I 1,23. .. .. 052 057 . 640 059 28 75 2,1 40 - , 0.000365 :-.0 . 4.1 .. ,..1 56 • . - -Oil- .1.• 7i -1 1400 1 1,71 • 083 1 076 66.0 009 i Zn 1.5 21 45 - I .0,00054.: : 14 t 6,• ; " ,,0 5 8 . -- - 0717 • 71 • .-1400 : 7,57 1 1,15 I_. 105690 0,7) 2,6- 1,5 '..... 2.1 -- 4.5 - _1 0000543 1 14 tI 5,7 SO . .58 0.55 80 1 400 3,75 , 1,57 [... 1,44 10.0 0,76 7,5 1 4 . - 4.5 -. . .0,001,1 12 „ . inn 4 52 , 60 0.75 , 00 1403 5 10 1 2,10 1,90 72. 0 0,76 7,6 1,5 2,5 5.0 1-7 - .,.0,00)66 .4 •4 12 • 10,J , 52 . ' 60 • ' 1,1 NI,s. ' 1410 ' 7.45 • 2.75 1 2,5 75.0 0,81 2,5 1,5 2,1 5,5 -- 0.00343 ' 8 1 14 5 ' 54 1 62 .. ,. ., . 1,5 ' 30L ! 1426 10.1 • 3.15 ; 3.45 75o 0,81 7,5 I I,5 2,1 , _ 0.07393 1 163 53 62 . .- , , 1 1:4 _. I 27 0482 5,1 1 4,70 --. 600. 052 27 1A 21 - ' 66 06 7 i 0.00080 • 9 14 25,4 t,.4 : 6-2 . . r- _I___.... - •. 30 TOOL 6.8 '- 6,2 six) 0,83 2.7 1.4 .L 2,0 0.65 6,0 2,0 - I Q0115 ',. ' 9 , -',.4 * '54 T ---42 . •, 4.0 '(170 1420 - 71,0 I 8.8 8,1 83,0 0.133 2.0 4,7 -2.4 0.65 6.5 ,',2 • 0,0175 'I , _ 30,1 54. .._ 62 • _ 1.i.-- 1323 --1----I440 -.., 7 36.4 t -- 115 10,9 85.0 - 0,83 -- 2.5 15 - - 2.7 ) 050 -6.0 2,0 1 05310 14 44.5 . 64 . 12 ' ---• 7.5 1327.1 1 1440 ' 1 49-5--f--16,1-- 14,8- - -86.6 `-' .. iia3 - -2.5-- -1.6--.--2,2-1 - 050 --. _--6,61--_-:- in 0,03311 14 r 40,13 : t;': 1 -72 .1 : 11:6--htfiar:11 1.440 12,9 2:2,5 ._;. 20,9* .--- 58,0 i- 0,85-- -2,4 - 1,6 - ' 2.6 - 0,65 6,2 2.0 ' 0,0718 ' 18 ' 60...■ ' . 67 1 . 75 , • 15,0 • 1601 1 1459 : 000 305 1 .280 138,0 08i- 2.4 15 2,5 t 0,65 C3 _1. 20 . Q0853 , 10 : 94,:3 6- . 75 ' . . : • 18,5 , 11100 - 1460 . .i 21 375 - • 34,5. _ .. ' . .. 8/0.._. __.0,84 __ 2,6 --. ...._15 ....-2.7 - 1 --0,id __....ii '_ 2,3 --1 0,0083 . 12 , .107.0 71 . .. _ _...10 z:n .. 1801_ 1460 , 144 44,5 410 In 0,152 20 1455 4... II _ I _79 ..... 895 Q84 .1. 2 3 1,4 7,0 0 50 1. nn 30,0 , 2001_ 1 1465 1 196 59,5 545 30,5 0,85 73 1,9 202,1 0.55 6,0 , 1,8 : 0,188 ' 150.0 75 ! 81 375 1 225S : 14/0 240 ..- 110 650 920 L 086 7,3 1,7 1.: 25 _ 0513 6,5 1 20 4 0343 211 219e . 75 1 85 225M. ,..... 1470 ! 792 L86.0 _79,0 _. 02,0_ 0,06J2.3 _ 1.4....1..... 7.2.. 0.45 .5 2,0 1 0,3713 1 20 239,0 ' 80 - I 90 6 Pole .- - ' 0.3/ . art 1 1,15 66 ,0 058 2.1 IA - I - 7,9 - .40 ... j-.. -. 1 000)61 1 75 .1 10 4....5... _ . ow 1 3.89 1 78 T .... . _ - 055 BO 920 1 612 150 156 67,0 069 2.1 1,4 1,0 '' - 40 1 - • Q00161 25 10.9 ' 50 58 I O I - 930 . 4 5 - 1 0 03340 I -7, ' 14.. 1 * 55- * - • 63 ---1;1 ----I 901. 930 , - 11.3 115 2.90 730 ---1- 0. -72 3.2 1.4 - - 20 -4.5 • - I 0 00358 I 75 , 16.3 55 ! 63 ---iA . mat_ I - - 030 . 154 3.15 JA5 • 780 078 7.3 1.5 71 - 5.5-- 1 - - -1 Q0116 10 , 2..A ■ 58 -:.------66 Z2 1120 1 930 , :•:16 5.4 450 i_ 79,0 ' Q78 2.3 1,5 2,1 • 5.5_ - _.1. _00138 ' 6 _ 20.1 58 66 _ 7.2 6.6 83.0 0,76 7.3 1,5 _1. 2,1 0,50 55 1,8 00335 It, 44.5 58 66 . . ._. I - ▪ 476.-11.1.. t3.9.1 1 8,7 0,55 5,5 1,9 1 00340 , 151 45,0 52 66 '350. ., 49.3. 9.5 83,0 0,77 2.3 1.5 1 2 1 . . .- - 85 1320 I - 1 00415 . 15 40.e 54 66 0'.9 , 55 3 179 _. 115 840 077 •2 3 1,5 . 2,1 055 1. G.O 1 zn ... •. -,.-- -75 - i tra/r.1. I 1/,4 160 0.1.5 CO , 2,0 1 0.102 • 15 . 110,2 97 /1 ...,,,,, I. 71:.2.._ - . . 96.0 _ .07G . .. 2,3 1,5 2.1 • 11,0 ; irot. '1 000 2.1 000 6.0 7 0 1 0.120 15 0.1,) . 67 , /1 __. . 1 1e3 256 23,5 €6 .0 ....0,76 2.3 15 ' . _ .. 1 0,199 145.0 '. 61 76 15.0 . 180L 005 1 148 375 . 2/5 _ .....68.0 0.80 2.3 1.5 2,3 0.50 6.O ' 2,0 .11 . _. . . - 18 5 200L 9/0 1 184 795 35.0 090 0,60 73 15 ' 2,3 051J 60 ' 20 0249 . 1 75 . the.0 611 74 (lb0 . • 1,5 6,0 2,0 0,359 25 ' 700,0 ; sr : ---58 -- 22.0 2001. [ . . . . . 2.3 . I 313,0 - -r 725M .- 960 1 291_ _. .. 625 .. _ 55 5 ....._....'.. 01 6 --. 081.. _ .._ - -.,1 2,3.. 1.5 2.3 050 6.0 i 29 1. ()An .15 279 0 11 : 91 i . 8 Pole - -- T 2.0J" - 4 0 1 14,5 1 47 55 . 0.37-- ' 1- 90-5 ' 7 - ill) 5.05 ' - 7.77 1.16 .6.70. ---1 060. 21lA • 0.00740 I .5/ 1 7.50 1.13 67.0 1,4 2.0 0.00388 . 30 1 7(3 1 4! i 0.55 - 0011 ' '100 ' - 1.00 0.66 2.2 _ . . . _ 1,4 _._... _ _ 45 _ . 0.0116 20 I 10 69 0.75 1 Ian_ I _750 . 10.2 7.30 I_ 2.10 71.0 0.70 ... 22 _ .20 25.4 I -171 1001 I. - 100 - 3.30 . 3- 05 - 71.0 031 ' 2,2 60 : 99 r i3.0, -_ - --.. . - 1,4 2.0 4,5 - 1 033176 ! it) I 26.4 ' * 1,5 11701 ... • Thu : 70,4 4,40 4.00 - 77,0 - 0,72 2.2 1,4 . . _. 2,o .1_-.._. -1. 4,5 ._.- - 1.. 0.0138. _ 1 15 30 1 C0 ' 69 72 ins , iici i 26.6--- 61 ST' -000m 057- -- 22 1.4 20 50 I 00335 . 30 44.5 '. 60 64 i . . _ 2.0 _ 13713 , 710 • 1.4 1,6' 0,0415 , JO . 490 1 60 69 3.0 8 2 ._ 7 5 800 0 CO 2.2 _ . . 5.0 I, I ' . 45 . 1600 1-- 7)0 si.a ---10.5 - 9,6-- 670 053- - 2.1 1,4 70 0.40 5.0 1.6 1 0.102 35 ' BO 3 '''fl ----I - ---7.;- -- 2 1,4 15 i 0,102 ' 35 80.3 I 64 1 73 r 5.5 1600 I 770 74,0 146 13,4 83.0 0,69 . . _ 2O 0A0 5.0._ . . _ f 2.5 1GOL 710 101 195 18.2. -83.0 - - 051- -- 2,2 1,4 i 2,0 0:41; 6,0 1 6 0,120 , 30 : 9$.3 1 64 73 1. _ ... _ .. . . 4,5._.. _ • i 20 1 145,0 1,5 i 1. • 11.0 1801. 720 148 27,5 2-5.0 - ----86.5- 0;70 - 2,0 1,2 1.0 0.45 ... 4.51.5 I 0,199 7t1 15,0 2001. 725 197 315 3451 870 0,70 1,8 1,4 7,0 0,45 4.5 1,5 0.249 1 40 I 15011 I 66 76 F., 6,3 - - r • - - • • 1135 2253 4_ 131) 244 46.0 42,0 88.0 0,70 .2.0- . 1.2 ---70- - ---1045-- 4.33 - 1,3 0.416 I 40 4 7 .331 i 76 22,0 225M - 730 793 "--. 040 49.5 ... 885 0.70 20 12 0 0A5 45 1 3 OA 71 , 40 2395 1 7,1 ..... L. . tit? •ro .___ . ... . _ ..t.

• r:. . 395

TENDER REF: K/11/S/0684 8 SEP J978

kW lip Poles Frame Price kW Hp _ Poles Frame Price 4.00 5.5 2 0112M 74.36 0.18 0.25 4 D63 24.40 4 D112M 70.29 6 D'30.1 103.60 0.25 0.33 2 • D63 24.40 8 D1601.1 169.83

0.37 0.50 4 071 26.15 5.5 7.50 2 D132S 89.00 6 080 33.80 4 D132S ,91.45 8 D9OS 43.26 6 D132M 114.65 8 D160M 180.00 0132S 98.50 0.55 0.75 2 D71 27.50 7.50 10.00 2 112.00 4 080 ' 33.80 4 0132M 173.40 6 080 35.28 6 D160M 8 D90L 50.80 8 D160L 226.11 D160M 0.75 1.00 2 080 35.70 11.0 15.0 2 166.15 ' 4 D80 34.80 4 D160M 171.60 6 090S 39.80 6 0160L 217.60 8 D100L 59.80 8 D180L 341.20

1,10 1.50 2 080 38.20 15.0 20.0 2 Di60M 188.31 n ' D90S 33.85 4 0160L 205.00 6 D90L 47.25 r D180L 310.15 8 D100L 61.20 D200L 400.15 242.76 2.00 2 DOGS 42.00 18.5 25.0 2 01601- 1.50 258.00 4 D9UL 47.25 4 D1'80M 400.15 6 D100L 57.12 6 D200L 8 D112M 75.60 (8 D225S 510.15 0130m 302.24 2.20 3.00 2 090.L 49.50 22.0 30.0 2 4 D100L 53.40 4 111801. 307.25 6 0112M 71.13 6 D200L 404.95 a D132S 102.69 8 D225M 628.90

2 0200L 382.60 3.00 4.00 2 WOOL 60.20 30.0 40.0 4 D100L 56.80 4 D200L 382.60 6 D225M 6 D132S 98.07 640.20 8 D132M 120.75 37.0 50.0 2 D200L 420.85 4 D225S 517.75 45.0 60.0 2 D225?,1 787.70 4 D225M 634.20

EXTRAS Foot Mtg. C Face up to Oil Seal Slide Rails Frame D63/71 Frame ' Shaft Down D160LCand D Flange

D Flange 2.75 000/90 0.90 - 4.40 1.50 5.20 C Face 0100/132 .1.12 6.25 1.65 8.90 Foot C ) 0160/180 1.75 16.50 2.00 16.00 3.10 D200 2.35 18.90 4.35 29.15 or U 0225 3.50 24.10 4.50 29.1'5 . 396.

APPENDIX IV.1

The expression

vNl, k3 ►%_ nNL

allows the coefficient k to be determined. Taking logarithms, the expression becomes:

log(VNL/nNL) = log k + * log If

This is of the form:

Y = b + mX (IV.2) where,

Y = log(V NL/nNL); b = log k; m = *; X = log If (Iv.3)

The method of least squares gives:

b = Y — mX (IV.4) where,

X = average X value = (IV.5)

Y.1 Y = average Y value = i=1 N (Iv.6)

Hence using the experimental points (of a finite number N) and the expressions (N.1) to (IV.6), k can be found. 397 APPENDIX V.1

PROGRAM CRPMA(OUTPUT,TAPE62,TAPE6=OUTPUT, INPUT, TAPES=INPUT)

C)trt :tct: PERFORMANCE OF THE CIRCUMFERENTIAL ROTOR PERMANENT MAGNET C ALTERNATORS

C)t%c+ct, V. C . N ICODEMOU APRIL 1979

C%t= * PERFORMANCE OF THE MARK1 EXPERIMENTAL ALTERNATOR

C=A: MAIN PROGRAM

DIMENSION RPM (15) 9A (50) !DEL 1 (50,15) , CUR1 (50,15) , VOL 1 (50,15) , 2RR1 <50,15) , POW1 (50,15) , POWI1 (50, 15) , EFF1 (50,15) C1 (15) , NUM (15) 3X (800) . Y :600) K S1 (15) COMMON I,J , RPM, A ,PPN, P ,2C, HI ,HII,HIII,WD,WbWII,G1,DS,SL,TW,AL,RL, 2FL,BO,2P,HO, QI ,T,F, PP ,SC,BG , WK ,WLK,WE,SP,SLP,SKL,WKS,WW,SK,WKL,WM, 3GG,GK,G,AJ,AC,EWL,AVL, COL , RS , AM,FFO,FO,XL,PO,PG,WT,PL,CL,CLL,DKD, 4DK, AI ,CLF, C ,R,FG , TT ,AQ, DL ,BL, AD,D,Q,CUR,VOL,DE!,POW,RR,S,POWI,EFF, 5BP,BT, DELI ,CUR1 ,VOL1, RR.1,POWII,POW1,LFF1,C1IS1,TW1,TW2, SW, XK 6,FK,QE,BQ,CO,DO,TM GIVEN VALUES FOR ROTATIONAL SPEED RPM(J)=ROTATIONAL SPEED L =NUMBER (;F CURVES/GRAF L=6 DO 1 J=1,L RPM (J) =FLOAT (.:) )1'50 . GIVEN VALUES FOR DIRECT-AXIS CURRENT A(I)=DIRECT-AXIS CURRENT 00 2 I=1,15 A (I) =0.0193)t,FLOAT (I) CALL FUNCT CONTINUE DO 3 I=16,50 A (I) =0.29+0.516*FLOAT (I-15) CALL FUNCT CONTINUE CONTINUE

C)K**)I= WHRITE RESULTS 1000 FORMAT (1X, I4,12 (F10.2) ) 1001 FORMAT (1X, I4, 12 (E10.3) ) 1002 FORMAT (95HOJ RPM NL FLUX. NL VOLTAGE NL LOSSES) 1003 FORMAT (85H0I D--AXIS CUR CURRENT VOLTAGE POWER IN POWER 2 OUT EFFICIENC LOAD ANG LOAD RES ) 1004 FORMAT (125HOCURV SLOT AREA CON CSA WIN RES POLE PITCH POLE ARC 2.SLOT PITCH TOOTH WID SKEW. COEF WIN COEF D-A REACL D-A REACM 0-A 3REAC ) 1005 FORMAT (115HOCUR'/ W DIS FAC C-S FAC SL WID FLUXD POL FLU 2XD TE LEK REAC T D-A R T 0-A R .KX WI WII 3) 1006 FORMAT (85HOCURV POLE PAIR SLOTS SL/PO/PH 60 CO 2 DO TM FK ) WRITE (6,1004) WRITE (6,1001) L,AJ,AC,RS,PP,SC,SLP,TW,WKS,WW,DL,BL,AQ WRITE (6,1005) WRITE (6,1001) L,WK,WE,SW,BP,BT,CLL,D,Q,XK,WI+WII WRITE (6,1006) WRITE (6,1001) L.PPN,P.QI,sQ,CQ,DQITM,FK DO 5 J=1 ,L WRITE (6 ,1002) WRITE (6,1001) JI RPM (J) ,CLFICI (J) ,S1 (J) WRITE (6,1003) DO 5 I=1,50 WRITE (6,1000) I,A (I) ,CUR1 (I,J) , VOL1 (I,J) ,POWI1 (I,J) ,POW1 (I,J) 398

2EFF1 (I,J) ,DEL1 (I,J) ,RR1 (I,J) 5 CONTINUE C**' PLOT CURVES CALL START (2) DO 4 K=1,L NUM (K) =50 4 CONTINUE AA=9.7 BB=6.965 DO 6 J=1,L DO 6 I=1,50 N=I+(J-1) "50 X(N) =CUR1 (I,J) Y (N) =VOL 1 (I , J ) 6 CONTINUE . CALL GRAF(X,Y,NUM,L,0117HLOAD CURRENT AMPS,171 219HPHASE VOLTAGE 1+i3LTS , 19 , AA , BB) DO 7 J=1,L DO 7 I=1,50 N=I+(J-1) %K50 X(N) =CUR1 (I,J) Y

SUBROUTINE FUNCT DIMENSION RPM(15) , A (50) , DEL 1 (50,15) , CUR1 (50,15) , VOL 1 (50I 15) 2RR1 <50,15) , POW1 (50,15) , POWI1 (50, 15) , EFF1 (50,15) , C1 (15) , NUM (15) , 3X (800) , Y (800) , 51 (15) COMMON I,J,RPM,A,PPN,P,2C,HI,HII,HIII,WO,WI,WII,G1,DS,SL,TW,AL+RL+ 2FL,B0,2P,HO,QI,T,F,PP•SC,BG,WK,WLK,WE,SP,SLP,SKL,WKS,WW,SK,WKL,WM, 3GG,GK,G,AJ,AC,EWL,AVL,COL,RS,AM,FFO,FO,XL,PO,PG,WT,PL,CL,CLL,DKD, 4DK,AI,CLF.C,R,FG,TT,AO,DL,BL,AD,D,Q,CUR,VOL,DEL,POW,RR,S,POWI,EFF, 5BP,BT,DELI,CUR1,VOL1,RR1,POWII,POW1,EFF1,C1,S1,TW1,TW2,SW,XK 6,FK,QE,BQ,CQ,DQ,TM CM'II GIVEN DATA FOR THE ALTERNATOR C;r** ►s 2P =NUMBER OF PHASES aP=3. C%O,=i, PPN =NUMBER OF POLE PAIRS 399 ..

PPN=8.0 P =NUMBER OF SLOTS ON THE STATOR P=48. PC =NUMBER OF SLOTS/COIL PC=3. ZC =NUMBER OF CONDUCTORS/SLOT ZC=42.0 HI,HIIiHIII,W3IWI,WII=DIMENSIONS OF THE STATOR SLOT HI=0.0017 HII=0.002 HIII=0.0235 WO=0.003 WI=0.009 WII=0.0117 01 =AIRGAP LENGTH 01=0.000483 DS =STATOR DIAMETER DS=0.26599 SL =STATOR LENGTH 5L=0.057 AL =AXIAL LENGTH OF THE MAGNET AL=0.052 RL =RADIAL LENGTH OF THE MAGNET RL=0.046 FL =AXIAL LENGTH OF THE MAGNETIC FIELD FL=0.057 WM =WIDTH OF THE MAGNET WM=0.01 B0 =MAXIMIUM FLUX DENSITY OF THE MAGNET ON ITS LINE OF RETURN HO =STARTING POINT OF LINE OF RETURN OF THE MAGNET WHERE FLUX DENSITY EQUALS TO ZERO HIGH LINE OF RETURN B0=0.55 H0=400000. Clm;t::r: LOW LINE OF RETURN B0=0.48 H0=350000.0 RO =COPPER RESISTIVITY R0=0.1724/1.E7 PI=ARCOS (-1. ) OM =PERMEABILITY OF FREE SPACE OM=4.0%KPI/1. E7 BJ =PACKING COEFFICIENT OF THE WINDING BJ=0.4 AID =DIRECT AXIS CURRENT AID=A (I) REV =ROTATIONAL SPEED IN REVOLUTIONS/MINUTE REV=RPM (J) CALCULATED DATA FOR THE ALTERNATOR C:I"r.:I"K QI =NUMBER OF SLOTS/POLE/PHASE Q I=P/ (2 . %r'PPN%KZP), C%K%t"t"I: SLP =SLOT PITCH SLP=PIKDS/P C:r'.:rK T =NUMBER OF TURNS/PHASE T=ZC%KP/ (2 . *ZP) CX *Z* F =FREQUENCY F=REV%KPPN/60.0 C:r"I::t"K PP =POLE PITCH PP=DS-KP I/ (2 . -KPPN) 1100

C**:1,-r SC =POLE ARC SC=PP—WM SC=ABS (SC) C,=1',* BG =FORM FACTOR OF THE FIELD WAVE BG=P I/ (2 . (MORT (2.0) ) WHEN SATURATION IS CONSIDERED C:1=1:a; BG TAKES NEW VALUE

C-K%icic FK QE COEFFICIENTS FOR FRACTIONAL SLOT WINDING QE=QI C=K:i.* DEFINITION OF WHETHER QI IS INTEGER C%r*%K;r INTEGER VALUES OF 2P PPN P QI NZP=2P NPPN=PPN NP=P IQI=QI IIQ =2*NPPN*N2P JO I=MOD (NP IF (JO I . EQ . 0) GOTO 10 C:1:**%K DEFINITION OF THE MAXIMUM COMMON DIVIDER OF THE NUMERATOR AND C THE DENOMINATOR OF THE FRACTION OF 0I INP=NP—IQ1*IIQ DO 6 II=1 I INP/2+1 NA= INP/II MD=MOD (INP+ NA) +MOD (II0+NA) IF (MD.EQ.0) GOTO 7 6 CONTINUE 7 MQI=NA C%I*** DEFINITION OF QI=BQ+CQ/DQ BO= IQI CO= INP/MQI DQ=I IQ/MQ I Coc*** DEFINITION OF THE MAXIMUM COMON DIVIDER TM OF PPN AND P DO 8 II=1,NPPN/2+1 NA=NPPN/II MD=MOD (NP ,NA) +MOD (NPPN + NA) IF (MD.EQ.0) GOTO 9 8 CONTINUE , 9 TM=NA QE=BQ*DQ+CQ C*x%' WK =WINDING DISTRIBUTION FACTOR 10 WK=SIN (PI/(2.%►•'2P) ) / (WKS IN (PI/(2.)K2P*QE)) ) Ca:.r'Kx WLK =COIL SPAN WLK=PC*SLP BI=WLK/PP C*%IQIur WE =COIL—SPAN FACTOR WE=SIN CBI*PI/ (2.) ) C*N r SP =POLE ARC/POLE PITCH SP=SC/PP C**-+,-r TW =AVERAGE TOOTH WIDTH TW1= ( (DS/2. + (H I+H II) ) *2 —WI TW2= C (DS/2.+(HI+HII+H:II)) *2.*PI/P) —WII TW= (TW1+TW2) /2. C**** SW =AVERAGE SLOT WIDTH SW=(WI+WII) /2. C=c1cNt XK =SATURATION LINE KX XK=SW/C0.93*TW) C:K:c1t* SKL =SKEWING LENGTH SKL =SL P IF 'SKL . EQ .0 .) GOTO 1 C%r%r%rK WKS =SKEWING COEFFICIENT WKS= (SIN ( (SKL/PP) =r (PI.2.) ) ) / ( (SKL/PP) %K (PI/2.) ) 1101.

GOTO 4 1 WKS=1. C ICICK WW =WINDING FACTOR WW=WK%t WKS I LAE WW=ABS (WW) C2l tcICK 5K =COEFFICIENT OF THE END WINDING LEAKAGE SK= C3.0%KB I-1.0) 2.0 C;lCIClCK WKL =END WINDING LEAKAGE WKL=0.57*SK%tPP C*:trlCK GG =COEFFICIENT FOR CALCULATION OF CARTER COEFFICIENT GG= C (WO/G1) **2) /(5.0+WO/G1) C%'* GK =CARTER COEFFICIENT GK=SLP/(SLP—GG*G1) C**•*K G =EFFECTIVE AIRGAF G=GK*G1 c=icicK AJ =SLOT AREA AJ=0.5* (WI+WII) %KHIII+PI%K (WI I*•,2) /8.0 AC =CROSS SECTIONAL AREA OF A CONTACTOR AC=AJ%4BJ/ZC C;OZ:K* EWL =LENGTH OF THE END WINDING EWL=1.8:44LK AVL =AVERAGE LENGTH OF A HALF MEAN TURN AVL=SL+EWL C;SICK:K COL =CONDUCTOR LENGTH/PHASE COL=2.*T*AVL C=.^.K4: RS =WINDING RESISTANCE/PHASE RS=1.05%t•'RO*COL /AC C)I::1cK)K AM =CROSS SECTIONAL AREA OF THE MAGNET . AM=RL*AL C* 1.11.11: FFO =SHORT—CIRCUIT FLUX OF THE MAGNET FFO=AM%t,BO C:I:*** FO =OPEN—CIRCUIT MMF OF THE MAGNET FO=HO*WM C;t•h I t PO =PERMEANCE OF THE MAGNET PO=FFO/FO CNOICCK PG =AIRGAP PRMEANCE PG=OM* (FL*SC) / (4. G) CACIC:ICK XL =HALF POLE ARC XL=SC/2.0 C:trlr.t::t: WT =DISTANCE OF LEAKAGE AREAS OF THE MAGNET WT=AL+2.0*RL c**** PL =LEAKAGE PERMEANCE PL=OM* (WT/FI) *ALOG (1.0+2.0* (XL+SART (XL**2+XL*WhD) /WM) I- 1=PG+PO+PL CL =EQUIVALENT PERMEANCE OF THE SLOT LEAKAGES CL=0.623+ (2.0*HII I) / (3.0* (WI+WII)) +HI/WO C:ICK K CLL =INDUCTIVE LEAKAGE REACTANCE CLL=4.0*PI*F*OM*SL* CT%K2) * (CL+QI*WKL/SL) / (PPNKQI) CWK DKD =THE FORM FACTOR OF THE DIRECT—AXIS REACTION DKD= CSP*PI+SIN CSP*PI)) /PI C;t.%t.K DK =COEFFICIENT OF THE DIRECT—AXIS DEMAGNETIZING hlNF DK=6 . * CSQRT :2 .)) *DKD* 7 •KWW/ CP I*PPN) c**x K AI =COEFFICIENT OF THE RESULTANT EMF AI=4.0*8G*F*WW*T C`dr CLF =NO—LOAD FLUX/POLE CLF=2.*PG*FFO/PT C tcIc BP =NO—LOAD FLUX DENSITY/POLE BP=CLF/ C (2. /PI) *PP*SL) C:s :trt.^K BT =NO—LOAD FLUX DENSITY/TOOTH BT=BP*SLP/(0-93xT1.0 C%tQ.t.".K C =OPEN—CIRCUIT EFF C=CLF*AI C:t.^tc R =RADIUS OF THE AIRGAP R= CDS—G1) /2.0 402

C,ira=: FG =EFFECTIVE VALUE OF THE POLE DEPTH FG=RL+SP*WM/2.0+0.003.75 C=I QIci, TT =ANGLE TETA P I TT=ARCOS ((SIN (SP* (PI/2.0) ) ) / (SP* (P I/2.0) +PPN* (FG/ (WM/2.0)) (G/R)) ) C-I*%c ic AQ =QUADRATURE—AXIS REACTANCE AQ=48. O C C (T/ (2.0*PPN) ) N:WW) **2) -rR,t;F,ic (OM/G) *SL* (SP— (SIN (SP*PI) ) /PI) C*,i** WHEN SATURATION IS CONSIDERED C****** AQ IS DIVIDED BY THE SATURATION COEFFICIENT

Q=CLL+AQ C*3%1: DL =DIRECT—AXIS REACTANCE CALCULATED FROM LAWRENCE FORMULA DL=48.0* (C (T/ (2.0*PPP1) ` *WA) Nt3 2) RFKOM/G) *SL* (SP+ (SIN (SP*P I)) /P I) C* (1.0— (1.0+ (4. 0/P I-1.0) * (2.0%* (SP=3) —SP%ti*4)) *COS (TT) ) C t*%1: BL =DIRECT—AXIS REACTANCE CALCULATED FROM MAGNETIC CIRCUIT BL=2.0y, (PL+PO) %I'DK*AIKPG/PT C**-1= AD =AVERAGE DIRECT—AXIS REACTANCE AD= (DL+8L) /2.0 D=CLL+AD C*K1 CC =RESULTANT AIRGAP EMF CC=C— (0-0) a,A ID CU** CUR =TOTAL CURRENT/L INE CUR=O. IF (CC.LT.0.0) GOTO 2 CUR=SQRT (CC*AID/Q) IF (C.LE. AIM) GOTO 2 C*Q' VOL =TERMINAL VOLTAGE/PHASE VOL =SORT (CC* (CC—P:0 ID) ) —CUR%a,RS IF (VOL . LT . 0 . 0) GOTO 2 IF (AID . GT. CUR) GOTO 2 C%r*** RR =LOAD RESISTANCE/PHASE RR=VOL/CUR C%I*U DEL =LOAD ANGLE DEL=ARSIN (AID/CUR) DEL1 (I J) =DEL GOTO 3 2 VOL=0.0 DELI CI•J) =DELI (I-1,J) C**** POW =TOTAL OUTPUT POWER 3 POW=CUR*VOL *3.0 C%K01QKQK S =NO—LOAD LOSSES S= <0.0124* (REV:K*1.5)) (PI*SL* (R**2) /0.003158) CTX POW= INPUT POWER TO THE ALTERNATOR 2OWI=S+ (CUR%K*2) *'3 . *RS- POW C=PlccK EFF =EFFICIENC`' OF THE ALTERNATOR EFF=POW/POWI CUR1 (I . J) =CUR VOL 1 ( I , J) =VOL RR1 (I IJ) =RR POW1 (I , J) =POW 51 (J) =S POWI1 (I, J) =POWI EFF1 (I + J) =EFF Cl (J) =C RETURN END APPENDIX V.2 403

PROGRAM CRPMA (OUTPUT , `APE629TAPE6=OUTPUT, INPUT, TAPE5=INPUT)

C%=== PERFORMANCE OF THE CIRCUMFERENTIAL ROTOR PERMANENT MAGNET C ALTERNATORS

CII V.C. NICODEMOU APRIL :.979

C=:1 %tCK PERFORMANCE. OF THE RUTHERFORD PM ALTERNATOR

C%r-C=It MAIN PROGRAM

DIMENSION RPM (15) 9A (50) ,DEL 1 (50,15) , CUR1 (50,15) , VOL 1 (50,15) 2RR1 (50, 15) , POW1 (50 915) , POWI1 (50,15) , EFF1 (50,15) , C1 ( 15) , NUM (15) , 3X (800) , Y (800) , S1 (15) COMMON I,J,RPM,A,PPN,P,2C,HI,HII,HIII,WO,WI,WIIIGI,DS,BL,TW,AEIRL, 2FL,B0,ZP,HO,QI,T,F,JP,SC,BG,WK,WLK,WE,SP,SLP,SKL,WKS,WW,SK,WKL,WM, 3GGIGKIGIAJIAGIEWLIAVL,COL,RSIAMIEFO,F0IXL,P0,PG,WT,PL,CL,CLL,DKD, 40K,AI,CLF,C,R,FG,TT,AQ,DL,BL,AD,D,Q,CUR,VOL,DEL,POW,RR,S,POWI,EFF, 55PISTIDELlI CUR1,VOL1,RR1,POWI1,P0W1,EFE1,cl,Si,TW1,TW2,SW,XK 6,FK,QE,BQ,CQ,D0,TM C%crAcK GIVEN VALUES FOR ROTATIONAL SPEED C**** RPM (J) =ROTATIONAL SPEED C 1CIC$~ L =NUMBER OF CURVES/GRAF L=5 DO 1 J=1 ,L RPM (J) =FLOAT (J) )1.30 . Mt*** GIVEN VALUES FOR DIRECT—AXIS CURRENT C),=== A (I) =DIRECT—AXIS CURRE:NT . DO 2 I=1,15 A (I) =0.0193)KFLOAT (I) CALL FUNCT 2 CONTINUE DO 3 I=16,50 A (I) =0.29+0.732)isFLEAT (I-15) CALL FUNCT 3 CONTINUE 1 CONTINUE

C**** WHRITE RESULTS 1000 FORMAT (1X, I4, 12 (F10.2) ) 1001 FORMAT (1X, I4, 12 (E10.3) ) 1002 FORMAT (45H0J RPM NL FLUX NL VOLTAGE NL LOSSES)

1003 FORMAT <85H0I D--AXIS CUR CURRENT VOLTAGE POWER IN POWER 2 OUT EFFICIENC LOAD ANG LOAD RES ) 1004 FORMAT (125HOCURV SLOT AREA CON CSA WIN RES POLE PITCH POLE ARC 2 SLOT PITCH TOOTH WID SKEW COEF WIN COEF D—A REACL D—A REACM Q —A 3REAC ) 1005 FORMAT (115HOCURV W DIS FAC C—S FAC SL WID FLUXD POL FLU 2XD TE LEK REAC T D—A R T Q —A R KX WI WII 3) 1006 FORMAT (85HOCURV POLE PAIR SLOTS SL/PO/PH BO CO 2 DQ TM FK ) WRITE (6,1004) WRITE (6,1001) L,AJ,AC,RS,PP,SG,SLP,TW,WKS,WW,DL,BE,A0 WRITE (6,1005) WRITE (6,1001) L,WK,WE,SW,BP,BT,CLL,D,QIXK,WI,WII WRITE (6,1006) WRITE (6,1001) L,PPN,P,QI,BQ,CQ,DQ,TM,FK DO 5 J=1,L WRITE (6,1002) WRITE (6,1001) J, RPM (J) , CLF, C1 (J) , S1 (J) WRITE (6,1003) DO 5 I=1,50 WRITE (6,1000) IIA (I) ,CUR1 (I,J) ,VOL1 (I,J) ,POWI1 (I,J) ,POW1 (I,J) , 402,

2EFF1 (I,J) ,DEL1 (I,J) ,RR1 (I,J) 5 CONTINUE

C*A,L K PLOT CURVES CALL START(2). DO 4 K=1,L NUM (K) =50 4 CONTINUE AA=9.7 BB=6.965 DO 6 J=1,L DO 6 I=1,50 N=I+(J-1) X50 X(N)=CUR1 (I,J) Y(N) =VOL1 (I,J ) 6 CONTINUE CALL GRAF(X,r,NUM,L,0,17HLOAD CURRENT AMPS,17, 219HPHASE VOLTAGE VOLTS,19,AA,BB) DO 7 J=1,L DO 7 I=1,50 N= I+ (J-1) *50 X(N) =CUR1 (I,J) Y(N)=POW1 (I,J) 7 CONTINUE CALL GRAF(X,Y,NUM,L,0,17HLOAD CURRENT AMPS117, 224HTOTAL OUTPUT POWER WATTS,24,AA,BB) DO 8 J=1,L DO 8 I=1,50 N=I+CJ-1) %1450 X (N) =POW1 (I, J) Y(N) =EFF1 (I,J) 8 CONTINUE CALL GRAF(X,Y,NUM,L,0,24HTOTAL OUTPUT POWER WATTS,24, 228HEFFICIENCY OF THE ALTERNATOR,28,AA,BB) DO 9 J=1,L DO 9 I=1,50 N=I+(J-1) *50 X(N) =CUR1 (I,J) Y(M) =DEL 1 (I , J) 9 CONTINUE CALL GRAF(X,Y,NUM,L,0.17HLOAD CURRENT AMPS,17, 214HLOAD ANGLE RAD,I4,AA,BB) CALL ENPLOT STOP END

SUBROUTINE FUNCT DIMENSION RPM(15) , A (50) , DEL 1 (50 ,15) , CUR 1 (50 ,15) ,VOL 1 (50 ,15) , 2RR1 (50, 15) , POW1 (50,15) , POWI1 (50,15) , EFF1 (50,15) , C1 (15) , NtJM (15) , 3X(800) , Y (800) , S 1 (15) COMMON I,J,RPM,A,PPN,P,ZC,HI,HII,HIII,WO,WI,WII,G1,DS,SL,TW,AL,RL, 2FL,B0,2P,HO,QI,T,F,PP~SC,BG,WK,WLK,I,SP,SLP,SKL,WKS,WW,SK,WKL,WM, 3GG,GK,G,AJ,AC,EWL,AVL.COL,RS,AM,FFO,FO,XL,PO,PG,WT,PL,CL,CLL,DKD, 4DK,AI,CLF,C,R,FG,TT,A0,DL,BL,AD,D,Q,CUR,VOL,DEL,POW,RR,S,POWI,EFF, 5BP,BT,DELI,CUR1,VOL1,RR1,POWII,POW1,EFF1,C1,S1,TW1,TW2,SW,XK 6,FK,QE,BQ,CQ,DQ,TM C3v4CIur GIVEN DATA FOR THE ALTERNATOR C%+%+3I-%I ZP =NUMBER OF PHASES ZP=3. C%cntsr PPN =NUMBER OF POLE PAIRS 1105

PPN=24.0 P =NUMBER OF SLOTS ON THE STATOR P=132. PC =NUMBER OF SLOTS/COIL PC=3. 2C =NUMBER OF CONDUCTORS/SLOT 2C=36.0 HIeHII,HIII,NO, WIsWII=DIMENSIONS OF THE STATOR SLOT HI=0.0013 HII=0.0014 HIII=0.02427 W0=0.0039 WI=0.00843 WII=0.01046 Cu G1 =AIRGAP LENGTH G1=0.0004 C*'* DS =STATOR DIAMETER DS=0.78 C**01= SL =STATOR LENGTH SL=0.056 C=1= AL =AXIAL LENGTH OF THE MAGNET AL=0.048 RL =RADIAL LENGTH OF THE MAGNET RL=0.048 FL =AXIAL LENGTH OF THE MAGNETIC FIELD FL=0.056 C**** WM =WIDTH OF THE MAGNET W11 0.0123 C:10101 01: BO =MAXIMUM FLUX DENSITY OF THE MAGNET ON ITS LINE 9F RETURN HO =STARTING POINT OF LINE OF RETURN OF THE MAGNET C WHERE FLUX DENSITY EQUALS TO ZERO LOW LINE OF RETURN B0=0.48 H0=350000.0 RO =COPPER RESISTIVITY R0=0.1724/1.E7 P I=ARCOS (-1. ) OM =PERMEABILITY OF FREE: SPACE 0M=4. 0*PI/1. E7 BJ =PACKING COEFFICIENT OF THE WINDING BJ=0.4 HID =DIRECT AXIS CURRENT AID=A (I) REV =ROTATIONAL SPEED IN REVOLUTIONS/MINUTE REV=RPM (J) CNOICICK CALCULATED DATA FOR THE ALTERNATOR

C:4.^t:= QI =NUMBER OF SLOTS/POLE/PHASE QI=P/ C2."PPN ZP) SLP =SLOT PITCH SLP=PI*DS/P Cct* T =NUMBER OF TURNS/PHASE T=ZC*P/ (2 . *2P) C=CK F =FREQUENCY F=REVPN/60.0 Cl;t,!l PP =POLE PITCH PP=DS*PI/ (2 . *PPN) C;1=1:* SC =POLE ARC SC=PP—WM SC=ABS (SC) BG =FORM FACTOR OF THE FIELD WAVE 406 ,

BG=PI/ C2.0)rSQRT <2.0) ) C****I WHEN SATURATION IS CONSIDERED C)~^K* BG TAKES NEW VALUE C FK QE COEFFICIENTS FOR rRACTIONAL SLOT WINDING QE=QI CKK DEFINITION OF WHETHER QI IS INTEGER C**** INTEGER VALUES OF 2P PPN P Q I N.P=2P NPPN=PPN NP=P IQI=QI I IQ=2*NPPN*NZP JQI=MOD

WW=ABS (WW) SK =COEFFICIENT OF THE END WINDING LEAKAGE SK= (3.0%tB I-1.0) /2.0 WKL =END WINDING LEAKAGE WKL=0.57*SKk-'PP GG =COEFFICIENT FOR CALCULATION OF CARTER COEFFICIENT GG= ((WO/G1) **2) / (5.0+W0/G1) GK =CARTER COEFFICIENT GK=SLP/ (SLP-GG*G1) G =EFFECTIVE AIRGAP G=GK*G1 AJ =SLOT AREA AJ=0.5* (WI+WI I) *HI I I+PI* (WI I**2) /8.0 AC =CROSS SECTIONAL AREA OF A CONTACTOR AC=AJ-tBJ/ZC EWL =LENGTH OF THE ENDS WINDING EWL=1.5*WLK AVL =AVERAGE LENGTH OF is HALF MEAN TURN AVL=SL+EWL COL =CONDUCTOR LENGTH/PHASE COL=2.*T AVL RS =WINDING RESISTANCE/PHASE RS=1.05KRO%t,COL/AC AM =CROSS SECTIONAL AREA OF THE MAGNET AM=RL *AL FFO =SHORT-CIRCUIT FLUX OF THE MAGNET FFO=AM%t 6O FO =OPEN-CIRCUIT MMF OF THE MAGNET FO=HO;tUM PO =PERMEANCE OF THE MAGNET PO=FFO/FO PG =AIRGAP PRMEANCE PG=OM%t, (FL*SC) / (4. *G) XL =HALF POLE ARC XL=SC/2.0 WT =DISTANCE OF LEAKAGE AREAS OF THE MAGNET WT=AL+2.0*RL PL =LEAKAGE PERMEANCE PL=OM* CWT/PI) *ALOG 1.0+2.0* (XL+SART (XL**2+XL*WM)) /WM) PT=PG+PO+PL CL =EQUIVALENT PEREEANCE OF THE SLOT LEAKAGES CL=0.623+(2.0*HIII) / (:3.0* (WI+WII)) +HI/WO CLL =INDUCTIVE LEAKAGE REACTANCE CLL=4.0*PI%+ '*OM%t

C*)1 c= AQ =QUADRATURE-AXIS REACTANCE AQ=48.0)r (C (T/ (2.0)IPPN)) *WW) )r)r2) -rR*F-r (OM/G) *SL* (SP- (SIN (SP%i,PI)) /PI)

C'' 1 WHEN SATURATION IS CONSIDERED CU',ru'r AQ IS DIVIDED BY THE SATURATION COEFFICIENT

Q=CLL+AQ C**** DL =DIRECT-AXIS REACTANCE CALCULATED FROM LAWRENCE FORMULA DL=48.0)r ( C (T/ (2.0*'PPN)) %+'WW), 2) *RWK (OM/G) %rSL%r (SP+ (SIN (SP*PI) ) /PI) C)r (1.0- (1.0+ (4.0/P I-1. 0) )r (2.0* (SP)r)r3) -SP)r)r4) ) *COS (TT) ) Cu** BL =DIRECT-AXIS REACTANCE CALCULATED FROM MAGNETIC CIRCUIT BL =2.0* (PL+PO) )rDK)rAI*PG/PT CtI AD =AVERAGE DIRECT-AXIS REACTANCE AD= (DL+BL) /2.0 D=CLL+AD C)Ialt '* CC =RESULTANT AIRGAP EMF CC=C- (D-Q) )rA ID C*11:=t CUR =TOTAL CURRENT/L.INE CUR=O. IF (CC.LT.0.0) GOTO 2 CUR=SQRT (CCKAID/Q) IF (C.LE.AIDwD) GOTO a C:nopit VOL =TERMINAL VOLTAGE/PHASE VOL =SORT

PROGRAM RRPMA(OUTPUT+TAPE62+TAPE6=OUTPUT+ INPUT. TAPE5=INPUT)

Cara.i::u PERFORMANCE OF THE EXTERNAL RADIAL ROTOR PERMANENT MAGNET C ALTRNATORS

Cat*** V. C. NICODEMOU APRIL 1979

C=ti*%1Cr PERFORMANCE OF THE MARK2 AL TERNATOR

C,i *N K MAIN PROGRAM

DIMENSION RPM (15) + A (50) + DEL 1 (50 + 15) + CUR 1 (50,15) + VOL 1 (50 + 15) + . 2RR1 (50r 15) +POW1 <50115) +POWI1 '50+15) +EFF1 (50I 15) +C1 (15) + NUM (15) + 3X(800) 1Y (800) +S1 (15) COMMON I+J+RPM+A +PPN,P+ZCrHI+HII,HIII,WO +WI +WII+G1+DS +5L+TW+AL +RL, 2FL+BO+2P+HO+ QI rTrFrPF'►SC+ BG + WK ,WLK+WE+SP,SLP,SKL,WKS+WW,SK+WKL+WM, 3GG+ GK ,G+ AJ + AC +EWL.AVLICOL+RS,AM+FFO,FO+XL +PO +PGyWT+PL +CL,CLL+DKD+ 4DK+ AI+CLF+C+RrFGrTT+AG+DL+BLrADrD+Q+CUR +V0L+DECrPOWrRRsS.POWI +EFF+ 5BP+BT+DLL1+CUR1+VOL1+RR1+POWI1,POW1,EFFi+C1,S1,TW1,TW2,SW+XK 6+FKODE+BQ +CQ +DQ,TM CN=K GIVEN VALUES FOR kOTATIONAL SPEED CA=CK RPM (J) =ROTATIONAL SPEED C%g*** L =NUMBER OF CURVES/GRAF L=B DO 1 J=1+L RPM (J) =FLOAT (J) %Q00 . UK*** GIVEN VALUES FOR DIRECT—AXIS CURRENT Gt,*U A (I) =DIRECT—AXIS CURRENT DO 2 I=1+15 A (I) =0. 0193%1:FLOAT (I) CALL FUNCT 2 CONTINUE DO 3 I=16+50 A (I) =0:.29+0.500%I,FLOAT (I-15) CALL FUNCT 3 CONTINUE 1 CONTINUE

MO=%i,•=, WHRITE RESULTS 1000 FORMAT (1X+ I4+ 12 (F10.2) ) 1001 FORMAT (1X, I4s 12 (E10.3) ) 1002 FORMAT (45H0J RPM NL FLUX NL VOLTAGE NL LOSSES) 1003 FORMAT (85H0I 0—AXIS CUR CURRENT VOLTAGE POWER IN POWER 2 OUT EFFICIENC LOAD ANG LOAD RES ) 1004 FORMAT (125HOCURV SLOT AREA CON CSA WIN RES POLE PITCH POLE ARC 2 SLOT PITCH TOOTH WID SKEW COEF WIN COEF D—A REACL D—A REACM Q—A 3REAC ) 1005 FORMAT (115HOCURV W DIS FAC C—S FAC SL.WID FLUXD POL FLU 2XD TE LEK REAC T D—A R T 0—A R KX WI WII 3) 1006 FORMAT (85HOCURV POLE PAIR SLOTS SL/PO/PH BO CO 2 DQ TM FK ) WRITE (6+ 1004) WRITE (6+1001) L+AJ+AC+RSIPP,SCs5LPsTWIWKS+WW,OC+BC'AC WRITE (6+ 1005) WRITE (6+1001) D WKIWEISWrBP,BT+CLLrDsGsXK+WI+WII WRITE (6+ 1006) WRITE (6+1001) L+PPNrP+QI+BQ.CQ+DQ+TMrFK DO 5 J=1 WRITE (6 r 1002) WRITE (6+1001) J+ RPM (J) rCLFIC1 (J) ,51 (J) WRITE <611003) DO 5 I=1+50 WRITE (6+1000) IIA(I) +CUR1 (I+J) ,VOL1 (I ,J) +POWI1 (IrJ) +POW1 (I+J) r 410 .

2EFF1(I,J),DEL1(I,J),RR1(I,J) 5 CONTINUE C=1= PLOT CURVES CALL START (2) DO 4 K=1,L NUM(K)=50 4 CONTINUE AA=9.7 BB=6.965 DO 6 J=1,L DO 6 I=1,50 N=I+CJ-1) a,50 X(N)=CUR1 (I,J) Y (N) =VOL 1 (I , J ) 6 CONTINUE CALL GRAF(X,Y,NUM,L•C,17HLIAD CURRENT AMPS.17, 219HPHASE VOLTAGE V3LTS,19,AA,BB) DO 7 J=1,L DO 7 I=1,50 N=I+CJ-1) *50 X(N) =CUR1 (I,J) Y (N) =POW1 (I , J) 7 CONTINUE CALL GRAF(X,Y,NUM,L,C,17HLOAD CURRENT AMPS,17. 224HTOTAL OUTPUT POWER WATTS,24,AA,BB) DO 8 J=1,L DO 8 I=1,50 N= I+ (J-1) *50 X(N) =POW1 (I,J) Y(N) =EFF1 (I,J) 8 CONTINUE CALL GRAF(X,Y,NUM,L'O,24HTOTAL OUTPUT POWER WATTS024. 228HEFFICIENCY OF THE ALTERNATOR.28,AA,BB) DO 9 J=1,L DO 9 I=1,50 N= I+ (J-1) %i,50 X(N) =CUR1 (I,J) Y(N) =DEL 1 (I , J) 9 CONTINUE CALL GRAF(X,Y,NUM,L10,17HLOAD CURRENT AMPS,17, 214HLOAD ANGLE RAD,141AA,BB) CALL ENPLOT STOP END

SUBROUTINE FUNCT DIMENSION RPM(15) , A (50) , DE L 1 (50.15) , CUR1 (50,15) ,VGL 1 (50.15) , 2RR1 (50,15) , POW1 (50,15) , POWI1 (50,15) , EFF1 (50,15) , C1 (15) ,NUM (15) , 3X (800) , Y (800) , S 1 (15) COMMON I,J,RPM,A,PPN,P,2C,HI,HII,HIII,WO,WI,WIbG1+DS+SL,TW,AL,RL, 2FL,B0,2P.H0+QhT,F+PE+SC,BG,WK,WLK,WE+SP+SLP,SKL+WKS.WW.SK,WKL,WM, 3GG,GK,G,AJ,AC,EWL,AVL,COL,RS,AM,FFO,FO,XL,PO,PG,WT,PL,CL,CLL,DKD, 4DK,AI,CLF,C,R,FG,TT,RQ,DL,BL,AD,D,Q,CUR,VOL,DEL,POW,RR,S,POWI,EFF, 56P,BT,DELI,CURI,VOL1,RR1,POWII,POWI,EFFI,CI,SI,TW1,TW2,SW,XK 6,FK,QE,BQ,CO,DQPTM Com,* GIVEN DATA FOR THE ALTERNATOR C*% 2P =NUMBER OF PHASES 2P=3. C**Ncg PPN =NUMBER OF POLE PAIRS 411.

PPN=6.0 C**** P =NUMBER OF SLOTS ON THE STATOR P=36. C=4= PC =NUMBER OF SLOTS/COIL PC=3. C**** ZC =NUMBER OF CONDUCTORS/SLOT 2C=64. C**% HI,HII, Hill ,WO,WI,WI I=D IMENSIONS OF THE STATOR SLOT HI=0.0017 HII=0.002 HIII=0.0258 WO=0.004 C,u** TW =THICKNESS OF THE STATOR TOOTH TW=0.007 G**=1: G1 =AIRGAP LENGTH G1=0.0004 C=1::ICIC DS =STATOR DIAMETER DS=0.23 SL =STATOR LENGTH SL=0.078 C%K* AL =AXIAL LENGTH OF THE MAGNET AL =0.0725 C**** RL =RADIAL LENGTH OF THE MAGNET RL=0.0224 C=0= FL =AXIAL LENGTH OF THE MAGNETIC FIELD FL=0.075 C*+'** WM =WIDTH OF THE GAP BETUEEN MAGNETS WM=0.013 C**** BO =MAXIMUM FLUX DENSITY OF THE MAGNET ON ITS LINE OF RETURN C**-I HO =STARTING POINT OF LINE OF RETURN OF THE MAGNET C WHERE FLUX DENSITY EQUALS TO ZERO

C**** HIGH LINE OF RETURN B0=0.37 H0=272500.

C**** LOW LINE OF RETURN B0=0.3 H0=235000.

C%I,**%K RO =COPPER RESISTIVITY R0=0.1724/1.E7 P I=ARC05 (-1. ) C% Of : =PERMEABILITY OF FREE SPACE OM=4.0*P I/1. E7 CII%tip BJ =PACKING COEFFICIENT OF. THE WINDING BJ=0.45 C**** AID =DIRECT AXIS CURRENT AID=A (I) C****lCI REV =ROTATIONAL SPEED IN REVOLUTIONS/MINUTE REV=RPM (J)

C**** CALCULATED DATA FOR THE ALTERNATOR

WI= C (DS-2.0%* (HI+HII)) WI/P) -TW WI I= ( (DS-2.0* (HI+HII4HIII) ) WPI/P) -TW CU 't:* Q I =NUMBER OF SL OTS,POLE/PHASE QI=P/ (2 . *PPN*2P) C%; SLP =SLOT PITCH SL P=P I%I'DS/P C3== T =NUMBER OF TURNS/PHASE T=2C*P/ (2.7 ZP) C***** F =FREQUENCY F=REV-i,PPN/60.0 if ` •

Ca: I :r. PP =POLE P ITCH PP=DSW I/ (2 . %KPPN) C-ici"ICI, SC =POLE ARC SC=PP—WM SC=ABS (SC) C,Mri= n BG =FORM FACTOR OF THE FIELD WAVE BG=PI/ (2.0%ItSQRT (2.0) )

C%mitK FK QE COEFFICIENTS FAR FRACTIONAL SLOT WINDING QE=QI C**%1 %it DEFINITION OF WHETHER QI IS INTEGER MK*** INTEGER VALUES OF 2P PPN P QI NZP=2.P NPPN=PPN NP=P IQ I=0 I I IQ=2*NPPN%ti'NZP JQI=MOD (NP SI IQ) IF (JQI.EQ.0) GOTO 1C C=KM DEFINITION OF THE MAXIMUM COMMON DIVIDER OF THE NUMERATOR AND C THE DENOMINATOR OF TrE FRHCTION OF QI INP=NP—IQI%IIIQ DO 6 II=1,INP/2+1 NA= INP/II MD=MOD (INP , NA) +MOD (IIQ I NA) IF (MD.EQ.0) GOTO 7 6 CONTINUE 7 MQI=NA C**** DEF IN ITION OF Q I=BQ+CQ/DQ BQ=IQI CQ=INP/MQI DQ=I IQ/MQ I C%rJ,,%tci DEFINITION OF THE MAXIMUM COMON DIVIDER TM OF PPN AND P DO 8 II=1,NPPN/2+1 NA=NPPN/II MD=MOD (NP 9 NA) +MOD (NPPN • NA) IF (MD . EQ . U) GOTO 9 8 CONTINUE 9 TM=NA QE=BQ;I:DQ+CQ

C*%•:= WK =WINDING DISTRIBUTION FACTOR 10 WK=SIN (P I/ (2 . %+2P) ) / (QE*S 1N (P I/ (2. *ZP*QE)) ) C%c+ , K WLK =COIL SPAN WLK=PCNtSLP BI=WLK/PP C":.= WE =COIL—SPAN FACTOR WE=SIN (BPIP I/ (2 .) ) C%I ICK SP =POLE ARC/POLE PITCH SP=SC/PP C%ti%h%' %It SW =AVERAGE SLOT WICTH SW= (WI+WII) /2. XK =SATURATION LINE KX XK=SW/ (0.93% TW) C*N=K SKL =SKEWING LENGTH SKL =SL P IF (SKL . EQ . 0 .) GOTO 1 C%'' WKS =SKEWING COEFFICIENT WKS= (SIN ((SKL/PP) %+, (P I/2 •) ) ) / ( (SKL/PP) * (PI/2 •) ) GOTO 4 1 WKS=1. C**X* WW =WINDING FACTOR 4 WW=WK%I,WKS%I,WE WW=ABS (WW) C%I,-'%i,.0 SK =COEFFICIENT OF THE END WINDING LEAKAGE SK= (3.0= B I-1 .0) /2.0 C*Nr-K•r WKL =END WINDING LEAKAGE WKL =0.57%KSK*PP C.t1ZK GG =COEFFICIENT FOR CALCULATION OF CARTER COEFFICIENT GG= ( (WO/G1) NM2) / (5.0+WO/G1) C=+"r GK =CARTER COEFFICIENT GK=SLP/ (SLP—GG*G1) C**** G =EFFECTIVE AIRGAP G=GK*Gl C**='-'~; AJ =SLOT AREA AJ=0.5-r (WI+WI2) %~'HIII+PI J (WII%r-r2) /8.0 C.K*** AC =CROSS SECTIONAL AREA OF A CONTACTOR AC=AJ%"'BJ/ZC C%IA-r EWL =LENGTH OF THE END WINDING EWL=1 .244LK C^itr AVL =AVERAGE LENGTH OF A HALF MEAN TURN AVL=SLEWL Cl%r** COL =CONDUCTOR LE1iG1H/PHASE COL =2 . *T*AVL C.kt-i"r RS =WINDING RESISTANCE/PHASE RS=1.05 l RO%rCOL/AC RS=1.22 C%r%IK AM =CROSS SECTIONAL AREA OF THE MAGNET AM=SC*AL C%r%i,%r%r FF0 =SHORT—CIRCUIT FLUX OF THE MAGNET FFO=AM%rB0 C****K FO =OPEN—CIRCUIT MMF OF THE MAGNET FO=HO%rRL C%i,arK.K PO =PERMEANCE OF THE MAGNET PO=FFO/FO C%K%r%= PG =AIRGAP PRMEANCE PG=OM%i, (FL *SC) / (4. % G) C-iati•Kac XL =HALF POLE ARC XL=SC/2.0 C.r%K%i:.r WT. =DISTANCE OF LEAKAGE AREAS OF THE MAGNET WT=2.0%KRL CA01= PL =LEAKAGE PERMEANCE PL =0M* (VIA, I) %KALOG (1 .0+2.0 K (XL+SART 0(1.* r2+XL%rWM)) /WM) C+OM%rRL *AL / (2.0*WM) PT=PO+PL+4.0%*PG C%r%I*K CL =EQUIVALENT PERMEANCE OF THE SLOT LEAKAGES CL=0.623+ (2.0%*HIII) / (3.0* (WI+WII)) +HI/WO C'4•' 'e CLL =INDUCTIVE LEAKAGE REACTANCE CLL=4.0%rPI%uF%rOM4'SL* (T*K2) *(CL +0 I*WKL /SL) / (PPN;KGI) C:Pit*r DKD =THE FORM FACTOR OF THE DIRECT—AXIS REACTION DKD= (SPW'PI+SIN (SP*PI)) /PI CyCh'%K DK =COEFFICIENT OF THE DIRECT—AXIS DEMAGNETIZING MMF DK=6 .:K (SART (2 .)) 3;DKC01:71 WW/ (PI*PPN) 0= AI =COEFFICIENT OF THE RESULTANT EMF A I=4.0yBGyF*WW'-KT C: CLF =NO—LOAD FLUX/POLE CLF=4. y'PG%rFFO/PT C%ryri„K BP =NO—LOAD FLUX DENSITY/POLE BP=CLF/ ( (2 . /PI) 3:PP%rSL C=1:* BT =NO—LOAD FLUX DENSITY/TOOTH BT=BP%I SLP/ (0.93%+,TW) C%Icf:* r C =OPEN—CIRCUIT EMF C=CLFKAI C "K R =RADIUS OF THE A IRGAP R= (DS+G1) /2 . 0 C ..CK;K AD =DIRECT—AXIS REACTANCE CALCULATED FROM MAGNETIC CIRCUIT AD=2.O-K (PL+PO) y"DK%rA I I PG/PT D=CLL+AD AQ =QUADRATURE—AXIS REACTANCE AQ=AD Q=CLL+AQ CC =RESULTANT AIRGAP EMF CC=C— (D—Q) a,A ID CUR =TOTAL CURRENT/LINE CUR=O. IF (CC.LT.0.0) GOTO 2 CUR=SART (CC*A ID/Q) IF (C.LE.AID*D) GOTO 2 VOL =TERM.INAL VOLTAGF.'rW9SE VOL=SART (CC* (CC—Q%KAIC')) •-•CUR%tRS IF(VOL.LT.0.0) GOTO 2 IF (AID.GT.CUR) GOTO 2 RR =LOAD RESISTANCE/PHASE RR=VOL/CUR DEL =LOAD ANGLE DEL=ARSIN (AID/CUR) DEL 1 (I . J) =DEL GOTO 3 VOL=0.0 DELI (I . J) =DEL 1 (I-1. J) POW =TOTAL OUTPUT POWER POW=CUR)tNOL)t=3.0 S =N0—LOAD LOSSES 5= (0.00354)t, (REV)t:asl . 5)) )t< (P I)t,SL)K (R)ttt2) /0.00324) POWI=INPUT POWER TO THE ALTERNATOR POWI=S+ (CURU2) a'3.0)t,RS+POW EFF =EFFICIENCY OF TI-E ALTERNATOR EFF=POW/POWI CUR1 (I.J)=CUR VOL 1 (I . J) =VOL RR1 (I. J) =RR POW1 (I . J) =POW Sl(J)=S POWI1 (I . J) =POWI EFF1 (I. J) =EFF Cl(J)=C RETURN END APPENDIX VI.2 J •

PROGRAM RRPMA (OUTPUT ,TAPE62,TAPE6=OUTPUT, INPUTS TAPE5=INPUT) PERFORMANCE OF THE EXTERNAL RADIAL ROTOR PERMANENT MAGNET C ALTRNATORS Y.C. NICODEM0U APRIL 1979 PERFORMANCE OF THE WINDRIVE ALTERNATOR MAIN PROGRAM DIMENSION RPM(15) ,A(E0) ,DEL1 (50,15) ,CUR1 (50,15) ,VOL1 (50,15) 2RR1 (50,15) ,POW1 (50, 15) ,POWI1 (50, 15) ,EFF1 (50,15) ,C1 (15) ,NUM(15) , 3X(800) , Y (800) , S 1 (15) COMMON I,J,RPM,A,PPN,P,2C,HI,HII,HIIIIWO,WLWII,GI,DS,SLITW,ALIRL, 2FL,B0,2P,HO,QI,T,F,PF,SC,BG,WK,WLK,WE,SP,SLP,SKL,WKS,WW,SK,WKL,WM, 3GG,GK,G,AJ,AC,EWL,AVL,COL,RS,AM,FFO,FO,XL,PO,PG,WT,PL,GL,CLL,DKD, 40K,AI,CLF,C,R,FG,TTQ:DL,BL,AD,D,Q,CUR,VOL,DEL,POW,RR,S,POWI,EFF, 5BP,BT,DEL1,CUR1,VOLI,R U ,POWII,POW1,EFF1,C1,S1,TW1,TW2,SW,XK 6,FK,QE,BO,CQ,DQ,TM C%, =u GIVEN VALUES FOR ROTATIONAL SPEED C:=30u RPM(J)=ROTATIONAL SPEED C**** L =NUMBER OF CURVES/GRAF L=6 DO 1 J=1,L RPM(J)=FLOAT(J)=500. C:iru :u GIVEN VALUES FOR DIRECT-AXIS CURRENT Ca ul,:u A(I)=DIRECT-AXIS CURRENT DO 2 I=1,15 A (I) =0.00970"'FLOAT (I) CALL FUNCT 2 CONTINUE DO 3 I=16,50 A (I) =0.1460+0.221%uFLOAT (I-15) CALL FUNCT 3 CONTINUE 1 CONTINUE. C%PKU WHRITE RESULTS 1000 FORMAT (1X, I4,12 (F10.2) ) 1001 FORMAT (1X, I4,12 (E10.3) ) 1002 FORMAT (45H0J RPM NL FLUX NL VOLTAGE NL LOSSES) 1003 FORMAT (85H0I 0-AXIS CUR CURRENT VOLTAGE POWER IN POWER 2 OUT EFFICIENC LOAD ANG' LOAD RES ) 1004 FORMAT (125HOCURV SLOT AREA CON CSA WIN RES POLE PITCH POLE ARC 2 SLOT PITCH TOOTH WID SKEW COEF WIN COEF D-A REACL D-A REAGM Q-A 3REAC ) 1005 FORMAT (115HOCURV W DIS FAC C-S FAC SL WID FLUXD POL FLU 2XD TE LEK REAC T D-A R T Q-A R KX WI WII 3) 1006 FORMAT (85HOCURV POLE PAIR SLOTS SL/PO/PH BQ CO 2 DO TM FK ) WRITE (6,1004) WRITE (6,1001) L,AJ,AC,RS,PP,SC,SLP,TW,WKS,WW,DL,BL,AQ WRITE (6,1005) WRITE (6,1001) L,WKIWF'SW,RP,8T,GLL,D,Q,XK,WbWII .WRITE (6,1006) WRITE (6,1001) L,PPN,P,QI,BQ,CQ,DQ,TM,FK DO 5 J=1,L WRITE (6,1002) WRITE (6,1001) J, RPM (J) , CLF, C1 (J) , S1 (J) WRITE (5,1003) D'O 5 1=1,50 WRITE (6,1000) I,A(I) ,CUR1 (I,J) ,VOL1 (I,J) ,POWI1 (I,J) ,POW1 (I,J) , 416 .

2EFF1(I,J),DEL1(I,J),RR1(I,J) 5 CONTINUE C**** PLOT CURVES CALL START (2) DO 4 K=1,L NUM(K)=50 4 CONTINUE AA=9.7 BB=6.965 DO 6 J=1,L DO 6 I=1,50 N=I+(J-1) *'50 X(N) =CUR1 (I,J) Y(N)=VOL1 (I,J ) 6 CONTINUE CALL GRAF(X,Y,NUM,L,C,17HLOAD CURRENT AMPS,17, 219HPHASE VOLTAGE VOLM,19,AA,BB) DO 7 J=1,L DO 7 I=1,50 N=I+ (J-1) *50 X(N)=CUR1 (I,J) Y(N) =POW1 (I,J) 7 CONTINUE CALL GRAE(X,Y,NUH,C,0,17HLDAD CURRENT AMPS,17, 224HTOTAL OUTPUT POWER WATTS,24,AA,BB) DO 8 J=1,L DO 8 I=1,50 N=I+(J-1) *50 X(N) =POW1 ( I , J) Y(N) =EFF1 (I,J) 8 CONTINUE CALL GRAF(X,Y,NUM,L,0,24HTOTAL OUTPUT POWER WATTS,24, 228HEFFICIENCY OF THE ALTERNATOR, 28, AA, BB) DO 9 J=1,L DO 9 I=1,50 N=I+(J-1) x,50 X(N)=CUR1 (I,J) Y(N) =DEL1 (I,J) CONTINUE CALL GRAF(X,Y,NUM•L,0,17HLOAD CURRENT AMPS,17, 214HLOAD ANGLE RAD,14,AA,88) CALL ENPLOT STOP END

SUBROUTINE FUNCT DIMENSION RPM(15) , A (50) , DEL 1 (50 + 15) , CUR 1 (50 ,15) ,VOL 1 (50 , 15) , 2RR1 (50,15) ,POW1 (50,15) ,POW 1 (50,15) ,EFF1 (50,15) ,C1 (15) ,NUM(15) 3X(800) , Y (800) , S1 (15) COMMON I,J,RPM,A,PPN,P,2C,HI,HII,HIII,WO,WI,WII,GI,DS,SL,TW,AL,RL, 2FL,BO,2P,HO,QI,T,F,PF,SC,BG,WK,WLK,WE,SP,SLP,SKL,WKS,WW,SK,WKL,WM, 3GG,GK,G,AJ,AC,EWL,AVL,COL,RS,AM,FFO,FO,XL,PO,PG,WT,PL,CL,CLL,DKD, 4DK,AI,CLF,C,R,FG,TT,RQ,DL,BL,AD,D,O,CUR,VOL,DEL,POW,RR,S,POWI,EFF, 50P,BT,DEL1,CUR1,VOL1,RR1,POWII,P0W1,EFF1,C1,S1,TW1,TW2,SW,XK 6,FK,QE,BQ,CQ,DQ,TM C3=== GIVEN DATA FOR THE ALTERNATOR C 2P =NUMBER OF PHASES 2P=3. CN= PPN =NUMBER OF POLE FAIRS 417

PPN=1. C=OCICK P =NUMBER OF SLOTS ON THE STATOR P=15. C-tcic= PC =NUMBER OF SLOTS/COIL PC=7. CA= %K 2C =NUMBER OF CONDUCTORS/SLOT aC=64. C*%=It HI,HII, Hill ,WO,WI,WII=DIMENSIONS OF THE STATOR SLOT IiI=0.0004064 HiI=0.003175 HIII=0.007937 W0=0.0025146 C*c=ft TW =THICKNESS OF THE STATOR TOOTH TW=0.003175 CMT--= G1 =AIRGAP LENGTH G1=0.00047 C=Ci=K DS =STATOR DIAMETER DS=0.0571E C%=ate SL =STATOR LENGTH SL=0.078 C% AL =AXIAL LENGTH OF THE MAGNET AL =0.0819 C=CIC1 RL =RADIAL LENGTH OF THE MAGNET RL=0.007 C=1:3:K FL =AXIAL LENGTH OF THE MAGNETIC FIELD FL=0.084 C=310K WM =WIDTH OF THE GAP BETUEEN MAGNETS WM=0.02026 C**Nl=K, BO =MAXIMUM FLUX DENSITY OF THE MAGNET ON ITS L INE OF RETURN CNcic%:OK HO =STARTING POINT OF LINE OF RETURN OF THE MAGNET C WHERE FLUX DENSITY EQUALS TO ZERO

C** %1=3: HIGH L INE . OF RETURN 60=0.385 H0=350000.

C=1014 LOW L INE OF RETURN B0=0.3 H0=235000.

CACICICK RO =COPPER RESISTIVITY R0=0.1724/1 .E7 PI=ARCOS (-1. ) C CIPK* OM =PERMEABILITY OF FREE SPACE OM=4.0*PI/1.E7 C**** BJ =PACKING COEFFICIENT OF THE WINDING BJ=0.45 Cmc AID =DIRECT AXIS CURRENT AID=A (I) GG.":tcrwK REV =ROTATIONAL SPEED IN REVOLUTIONS/MINUTE REV=RPM (J)

C**** CALCULATED DATA FOR THE ALTERNATOR

WI= C (DS-2.0= (HI+H II) ) *PI/P) -TW WI I= C (DS-2 . CrK (HI+HII+HIII)) *PI/P) -114 CActorAc QI =NUMBER OF SLOTS/POLE/PHASE Q I=P/ (2. MPRIN P) C%'= SLP =SLOT PITCH SLP=PI*DS/P C%►cicr: T =NUMBER OF TURNS/PHASE T=ZCW/ (2 . %12P) CN"l%tcr F =FREQUENCY F=REV%r,PPN/60.0 418 .

C=I"*** PP =POLE P ITCH PP=DS*P I/ (2 . *PPN) C=c= SC =POLE ARC SC=PP—WM SC=ABS (SC) C)1= BG =FORM FACTOR OF THE FIELD WAVE BG=PI/ (2.0*SQRT (2.0) )

C**%mit FK QE COEFFICIENTS FOR FRACTIONAL SLOT WINDING QE=QI C)I 11, DEFINITION OF WHETHER Q I IS INTEGER CA =It* INTEGER VALUES OF 2P PPN P QI NZP=2P NPPN=PPN NP=P IQI=QI I IIB=2*'NPPNITIaP JO I=MOD (NP f I IQ) IF (JQI . FD . 0) GOTO 1C C**** DEFINITION 1W THE MAXIMUM COMMON DIVIDER OF THE NUMERATOR AND C THE DENOMINATOR OF THE FRACTION OF QI INP=NP—IQ IQ DO 6 I37=1•INP/2+1 NA=INP/II MD=MOD (INP • NA) +MOD (I IQ 9 NA) IF (MD . EQ . 0) GOTO 7 6 CONTINUE 7 MQI=NA C)10= DEFINITION OF QI=BQ+CQ/DQ BQ=IQI CG= INP/MQI DQ=I IQ/MQ I C)*Nolt DEFINITION OF THE MAXIMUM COMON DIVIDER TM OF PPN AND P DO 8 Ii=1•NPPN/2+1 NA=NPPN/II MD=MOD (NP 9 NA) +MOD (NPPN , NA) IF (MD .EQ . 0) GOTO 9 8 CONTINUE 9 TMNA QE=BQ*DQ+CQ

CA=;..' WK =WINDING DISTRIBUTION FACTOR 10 WK=SIN (PI/ (2. *2P)) / (QE*SIN (PI/ (2. *2P*QE)) ) C) WLK =COIL SPAN WLK=PC*SLP BI=WLK/PP C) WE =COIL—SPAN FACTOR WE=SIN (B I*P I/ (2 .) ) C 5P =POLE ARC/POLE PITCH SP=SC/PP Gam* SW =AVERAGE SLOT WIDTH SW= (WI+WII) /2. CU•** XK =SATURATION LINE KX XK=SW/ (0.933TW) C* SKL =SKEWING LENGTH SKL=O. IF (SKL . EQ .0 .) GOTO 1 C**** WKS =SKEWING COEFFICIENT WKS= (SIN ( (SKL/PP) * (PI/2.) ) ) / ( (SKL/PP) * (P I/2.) ) GOTO 4 1 WKS=1. Cy WW =WINDING FACTOR 4 WW=WK) JKS*WE 419 .

WW=ABS (WW) C:tr.K:t~K SK =COEFFICIENT OF THE END WINDING LEAKAGE SK= (3.0%1131-1.0) /2.0 Dolt** WKL =END WINDING LEAKAGE WKL =0.57*ti'SK)KPP D'Ilt GG =COEFFICIENT FOR CALCULATION OF CARTER COEFFICIENT GG= ( (WO/G1) )oK2) / (5.0+WO/G1) Dolt** GK =CARTER COEFFICIENT GK=SLP/ (SLP-GG%KG1) DoaoloK G =EFFECTIVE AIRGAP G=GIVIG1 Dolt= AJ =SLOT AREA AJ=O.5* (WI+WI I) )ti'HIII+P I* (WI T**2) /8.0 Dolt** AC =CROSS SECTIONAL AREA OF A CONTACTOR AC=AJ*BJ/ZC CA = EWL =LENGTH OF THE END WINDING EWL=1.2*WLK C "h'1 AVL =AVERAGE LENGTH OF A HALF MEAN TURN AVL=SL+E JL Doi= COL =CONGUC OR LENGTH/PHASE COL=2 . )KT*AVt Ct,cK* RS =WINDING RESISTANCE/PHASE RS=1.0E' KRO*COL/AC R5=1.22 Dolt** AM =CROSS SECTIONAL AREA OF THE MAGNET AM=SC*AL C*ol=loK FFO =SHORT-CIRCUIT FLUX OF THE MAGNET FFO=AM*BO C**** FO =OPEN-CIRCUIT MMF OF THE MAGNET FO=HO*RL C%DoK%K* PO =PERMEANCE OF THE MAGNET PO=FFO/FO C**NoK PG =A IRGAP PRMEANCE PG=OM* (FL*SC) / (4. )KG) C)r.%ii„K XL =HALF POLE ARC XL=SC/2.0 Doloh.K WT =DISTANCE OF LEAKAGE AREAS OF THE MAGNET WT=2.0%KRL C*%KU PL =LEAKAGE PERMEANCE PL=OM* (WT/PI) %KALOG (1.0+2.0* (XL+SQRT (XL**2+XL ;It WM) ) /WM) C+OM%KRL *AL/ (2.MUM) PT=PO+PL+4.0*PG C**** CL =EQUIVALENT PERMEANCE OF THE SLOT LEAKAGES CL=O.623t (2.0*rH I I I) / (3.0* (WI+WI I)) tH I/WO C)K)K CLL =INDUCTIVE LEAKAGE REACTANCE CLL=4.0*PI%KF*OM*SL* (T**2) %K (CL+QI*WKL/SL) / (PPN% QI) Don=CII DKD =THE FORM FACTOR OF THE DIRECT-AXIS REACTION DKD= (SP PI+SIN (SP*PI) ) /PI Com'** DK =COEFFICIENT OF THE DIRECT-AXIS DEMAGNETIZING MMF DK=6 . * (SART (2 .) ) *DKD*T*WW/ (P I IPPN) Com** AI =COEFFICIENT OF THE RESULTANT EMF A I=4.0*BG*F*WW%KT Colol =K CLF =N0-LOAD FLUX/POLE CLF=4.*PG*FFO/PT Do= BP =NO-LOAD FLUX DENSITY/POLE BP=CLF/ ((2 . /PI) *PP*SL) Dololott BT =N0-LOAD FLUX DENSITY/TOOTH BT=BP*SLP/ (0.93*TW) CoK** C =OPEN-CIRCUIT EMF C=CLF*AI Dot= R =RADIUS OF THE AIRGAP R= (DS+G1) /2.0 Dolt= AD =DIRECT-AXIS REACTANCE CALCULATED FROM MAGNETIC CIRCUIT AD=2.0* (PL+PO) *DK)KAI*PG/PT 420 •

D=CLL+AD VP= AQ =QUADRATURE-AXIS REACTANCE AQ=AD Q=CLL+AQ C -%' CC =RESULTANT AIRGAP EMF CC=C- (D-Q) *AID C**== CUR =TOTAL CURRENT/LINE CUR=0. IF (CC .LT.0.0) GOTO 2 CUR=SUR"; (C!'.'a,AIDA) IF (C.LE.AID*C) GOTO 2 DPI= VOL =TERMINAL VOLTAGE/PHASE VOL=SORT (CC* (CC-Q*AID) ) -CUR*RS IF (VOL . LT. 0 . 0) GOTO 2 IF (AID . GT. CUR) GOTO 2 C%IQ U RR =LOAD RESISTANCE/PHASE RR=VOL/CUR C%1'I"I DEL =LOAD ANGLE DEL=ARSIN (AID/CUR) DEL1 (I,J) =DEL GOTO 3 2 VOL =0.0 DEL 1 (I , J) =DEL 1 (I-1 , J) C%' POW =TOTAL OUTPUT POHER 3 POW=CUR%NOL*3.0 C%r%tC S =N0-LOAD LOSSES 5= (0. 00354* (REV==%r1.5)) 1 (PPI SL%K (R=2) /0. 00324) C=01= POWI=INPUT POWER TO THE ALTERNATOR POW1=S+ (CUR%*2) *3.0%KRS+POW C1%''U EFF =EFFICIENCY OF THE ALTERNATOR EFF=POW/POWI CUR 1 (IF J) =CUR VOL 1 ( I , J) =VOL RR1 (I ,J) =RR POW1 (I,J) =POW S1 (J) =5 POWI1 (I J) =POWI EFF1 ( I , J) =EFF Cl (J) =C RETURN END 421 •

APPENDIX VII.1

The notion of the factorial can be extended to arbitrary numbers x by means of the gamma function, I(x), defined as follows:

co -t x-1 f t dt (Euler's integral of the second 0 kind for x >0)

lim ri! rix-1 for arbitrary x. n-4œ x(x+l) (x+2) (x+n-1

Some of the main properties of the gamma function:

I(x+l) = x r(x); '(n) =1(n-1)! for integral positive n

In [7.5] is given a table for the values of the gamma function

r-(x) for x from 1 to 2.

The values of l(x)'for x<1 and x>. 2 can be computed from the formulae:

:. (x) _ ~x+1 and r() = r(x-1)-r(x-i) 422 . APPENDIX VII.2

PROGRAM ENER

DIMENSION V11 (60) , VAV1 (60) , VMH1 (60) , VP1 (60) , FW1 (60) , FWT1 (60) , 2NUM (5) , X (100) , Y (100) , RPM (60) S CURT (60) , FCUR (60) , PFLO (60) 3, C (60) , POW01 (60) , PWIND1 (60) °, FWT2 (60) , POWIW1 (60) , FWT3 (60) , EFF1 (60) , 4RLA (60) , CURA (60) , VOLP (60) , POWGA (60) , POWIA (60) , POWIM (60) , EFFG (60) , SEGB (60) , POWIO1 (60) , POWGB01 (60) , VC (10) , CPF (10) 6, V12 (60) , V13 (60) , POld02 (60) , POWGB02 (60) , POWI02 (60) , POWIW2 (60) , 7PWIND2 (60) COMMON BI,VAV,VM,N,I,V,V1,V2,DV,FW,FWT,VMH,VP,J,VII,VAVI,VMH1,VP1, 2FW1,FWT1,L,K+AA,RB,X,Y,FW2+TGB,RLA,RPM 3,RO,PI,CPM,RMW,RMM,GBE,YGB,PMI,CUR,CNL,RA,GB,T,VR,WK,R,WL,RM,WN,WI 4,A1,B1,C1,D1,VS,RL,A,VF,C,PWIND,FI,PWIND1,POWIW,POWIW1,FWT2,FWT3, 5EFF,EFF1,POWO,CURI,CURA,VOL,VOLP,POWA,POWGA,POWI,POWIA,POWIG,POWIM 6,EFFG,EFG,EGB,POWIO,POWI01,POWGBO,POWGB01,FIM,POWM,POWIOM,FOWGBOM, 7VC,CPF,POW01,POWIWM,ENERI,ENER2,ENER3,ENER4,ENER5,ENER6,ENER7,ENER 68 ENER9,EFL,EFWIN,EFGB,EFGN,EFSY1,EFSY2,EFSY3 -9,CWF,RAI,FC,RF,PIR,VOLM,T1,FK,CIR,CFV,RAK,B,CURW,CURT,FCU,FCUR,PFL 9,PFLO,V12,V13,POW02,POWGB02,POWI02,POWIW2,PWIND2,M C%* WIND CHARACTERISTIC OF LOCATION C*%1 NAME OF LOCATION C=== ST.ANNS HEAD C%ctc= GIVEN DATA Ct'K'a* BI =LJUNGSTROM EXPONENT BITA BI=2.19 014== VAV =ANNUAL AVERAGE WIND SPEED VAV=7.242 C%o VM =MAXIMUM WIND SPEED OF LOCATION VM=31 29 C**** RO =AIR DENSITY R0=1.23 A= CALOG (2.0)) / (VAV*%+.B-I) C**** GIVEN DATA FOR THE WINDMILL P I=ARCOS (-1. ) C**** CPM =MAXIMUM POWER COEFFICIENT OF THE WIND-ROTOR CPM=0.35 C RMW =MAXIMUM ALLOWED ROTATIONAL SPEED OF THE WIND-ROTOR SHAFT RMW# 160 . Ccc VR =RATED WIND SPEED OF THE WIND-ROTOR VR=11.174 C VF =FURLING WIND SPEED VF=15.643 C"K GIVEN DATA FOR THE GEARBOX C GBE =MESS LOSSES GBE=0.02 CK TGB =FRICTION TORQUE OF THE GEARBOX FROM WIND-ROTOR SIDE TGB=2.5 N=50 C=014 V =WIND SPEED IN MSEC C"K Vi,V2=WIND SPEED LIMITS OF THE INTEGRAL CX'K DV =INCREMENT OF WIND SPEED V1=0. V2=VM DV= (V2-V1) /FLOAT (N-1) CX*** CALCULATION OF WIND DURATION PROFILE DLS 1 I=1,N 423

V=V1+FLOAT (I-1) 4DV C'a*,.ICK FW =FUNCTION OF WIND DURATION PROFILE BY LJUNGSTROM FW=1./(2.*'K((V/VAV):K BI)) C%JC$* FWT =TIME OF WIND DURATION CURVE FWT=FW*8760. C:i."1.'14 VM-1 =WIND SPEED IN MILES/HOUR VMH=V/0.447 C=1= POWER DURATION CURVE AND PROFILE VP=Vh :u3 J=I V11(J)=V VAV1 (J) =V/VAV VM-11 (J) =VMH VP1 (J) =VP FW1 (J) =FW FWT1 (J) =FWT 1 CONTINUE AA=9.7 BB=6.965 CALL START (2). CALL CURVE1 C*% WRITE RESULTS C%1 ='' PLOT CURVES CALL WPMAR CNCrai.^.r. SUBROUTINE OF THE WINDMILL GENERATOR WITH A PM ALTERNATOR AND C WITH LOAD RESISTANCE CONTROL SYSTEM 1001 FORMAT (65HORESULTS OF THE PM ALTERNATOR WITH LOAD RESISTANCE CONT 1ROL SYSTEM) WRITE (6,1001) CALL CURVE2 C%PlaKAt WRITE RESULTS C1Q1CK=K PLOT CURVES CALL WPMAI MP= SUBROUTINE OF THE WINDMILL GENERATOR WITH A PM ALTERNATOR AND C WITH AC LOAD CURRENT CONTROL SYSTEM AND CONSTANT LOAD RESISTANCE 1002 FORMAT (91HORESULTS OF THE PM ALTERNATOR WITH LOAD CURRENT CONTRO 1L SYSTEM AND CONSTANT LOAD RESISTANCE) WRITE (6,1002) CALL CURVE2 CgcCicit WRITE RESULTS C=*4 PLOT CURVES CALL WWFAI CK SUBROUTINE OF THE WINDIMILL GENERATOR WITH A WOUND FIELD C ALTERNATOR WITH FIELD CONTROL SYSTEM C AND CONSTANT AC LOAD RESISTANCE 1003 FORMAT (101HORESULTS OF THE WOUND FIELD ALTERNATOR WITH FIELD CURR lENT CONTROL SYSTEM AND CONSTANT LOAD RESISTANCE) WRITE (6.1003) CALL CURVE2 C**Ncg PLOT CURVES CK%K WRITE RESULTS CALL ENPLOT STOP END

SUBROUTINE WPMAR C**** SUBROUTINE OF THE WINDMILL GENERATOR WITH A PM ALTERNATOR AND C WITH LOAD RESISTANCE CONTROL SYSTEM DIMENSION V11 (60) , VAV1 (60) , VMH1 (60) , VP1 (60) , FW1 (60) , FWT1 (60) , 2NUM (5) , X (100) Y (100) , RPM (60) , CURT (60) , FCUR (60) , P LO (60) 3 , C (60) , POW01 (60) , PWIND 1 (50) , FWT2 (60) , POWIWI (60) , FWT3 (60) , EFF1 (60) 4RLA (60) , CURA (60) , VOLP (60) , POWGA (60) , POWIA (60) , POWIM (60) , EFFG (60) , 424 .

5EGB (60) , POWIO 1 (60) , POWGBO 1 (60) , VC (10) ,CPF (10) 6, V12 (60) , V13 (60) , POW02 (60) , POWGBO2 (60) , POWI02 (60) , POWIW2 (60) , 7PWIND2 (60) COMMON BI,VAV,VM,N,I,V,V1,V2,DV,FW,FWT,VMH,VP,J,VII1VAVI,VMHI,VP1, 2FW1,FWT1,L,K,AA,BB,X,Y,FW2,TGB,RLA,RPM 3,RO,PI,CPM,RMW,RMM'GBE'YGB,PMI,CUR,CNL,RA,GB,T,VR,WK,R,WL,RM,WN,WI 4,A1,31,C1,D1,VS,RL,A,VF,C,PWIND,FI,PWINDI'POWIW'POWIWI,FWT2,FWT3, 5EFF,EFF1,POWO,CURI,CURA,VOL,VOLP,POWA,FOWGA,POWI+POWIA,POWIG+POWIM 6,EFFG,EFG,EGB,POWIO,P0WI01'POWGBO,POWGB01'FIM,POWM,POWIOM,POWGROM, 7VC,CPF,POW01,POWIWM,ENER1,ENER2,ENER3'ENER4,ENER5,ENER6,ENER7'ENER 88,ENER9'EFL,EFWIN,EFGB,EFGN,EFSY1,EFSY2'EFSY3 9,CWF,RA1,FC,RF,PIR,VOLM,T1,FK,CIR,CFV,RAK,B,CURW,CURT,ECU,FCUR,PFL 9,PFLO,V12,V13,POW02,POWG802,POWI02,POWIW2'PWIND2,N C=1== GIVEN DATA FOR THE GENERATOR C**** RMM =MAXIMUM ROTATIONAL SPEED OF GENERATOR SHAFT RMM=1600. C PMI =MAXIMUM INPUT POWER TO THE GENERATOR PMI=6780. C' CUR =MAXIMUM CURRENT OF THE GENERATOR CUR=10. C=== CNL =N0—LOAD LOSSES COEFFICIENT OF THE GENERATOR CNL=346.89532/1.E5 CU RA =WINDING RESISTANCE/PHASE RA=1.19 CK CALCULATED DATA C**** GB =GEARBOX RATIO GB=RMM/RMW CX =It T =FRICTION TORQUE OF THE GEARBOX FROM GENERATOR SIDE T=TGB/GB CPK CALCULATION OF CONSTANT COEFFICIENTS C%icii WK =COEFFICIENT OF THE WIND—ROTOR AT THE RATED WIND SPEED WK= CPMI+T*RMM) / ((1. —GBE) *VR**3) Ca ;%1K R =RADIUS OF THE WIND—ROTOR R=SART (WK/ (0.5*RO*P I*CPM) ) C**Nt = WL =OPTIMUM TIP SPEED RATIO WL= (PI/30..) *RMW*R/VR CK%: RM =TRANSFORMATION COEFFICIENT OF WIND—SPEED TO ROTATIONAL SPEED RM=30 . *WL *GB/(P I%KR) Cacr WN,WI=INPUT COEFFICIENTS WN=W(/RM:ICl 3 WI=WN* ( 1. —GBE) CI"K CALCULATION OF THE COEFFICIENTS OF THE OVERALL EFFICIENCY A1=WI/14i B1=—CNL/WN C1=-3. *CCR**2*RA/ (RMN**4*WN) D1=—T/WN C=301= CALCULATION OF THE CUT—IN WIND SPEED VS CK LET SAY VS=0.5 V1=VS V2=VR DV= (V2—V1) /FLOAT (N-1) DO 1 I=1'N V=V1+FLOAT(I-1) *DV C=01= RL =LOAD RESISTANCE/PHASE RL= (RM11K4/ (3 . *CUR**2)) * (WI/ (RMV) —CNL/ (RM*V) *:K (5 . /2.) —T/ CRM*V) 1=1)—RA IF CRL . GT. 0 .) GOTO 2 1 CONTINUE 2 VS=V V1=VS `/2=VR DV= CV2-V1) /FLOAT(N-1) i25

C*:r.:ic:!: CALCULATION OF THE ANUAL AVERAGE POWER POW0=0. POWGB0=0. DO 3 I=1.N Ca01= CALCULATION OF THE INTGRAL FROM THE FORMULA OF TRAPEZOIDS C(I)=0.5 IF((I .EQ .1) .OR. (I.EQ.N)) GOTO 4 C(I)=1. 4 J=I V=V1+FLOAT (I-1) *DV Vii (J) =V RL= (RFIIU4/ (3 . *CUR**2) ) * CWI/ (RMV) —CNL/ (RM.KV) ** (5 . /2 .) —T/ (RM*V) 1**3) —RA RLA (J) =RL C3=cg CURI=ARMATURE CURRENT CUR I= (CUR/RF11**2) *(RM*V) **2 CURA (J) =CURI FOUR (J) =0.' C-'3 VOL =VOLTAGE/PHASE VOL=CUR IRL VOLP (J) =VOL C 01c= GENERATOR SHAFT SPEED RPM (J) =V*RM C** POWA=OUTPUT POWER OF THE GENERATOR P3WA=3 . *CUR I%t312*RL POWGA (J) =POWA CU POWI=OUTPUT POWER FROM THE WIND—ROTOR POWI=14K=KV**3 POWIA (J) =POWI C*'K POWIG=OUTPUT POWER FROM THE GEARBOX POWIG=POWI* (1. —GBE) —T*RM*V POWIM (J) =POWIG C3=1cK EFG =EFFICIENCY OF THE GEARBOX EFG=POWIG/POWI EGB (J) =EFG C*3K** EFFG=EFFICIENCY OF THE GENERATOR EFFG (J) =POWA/POWIG C 01C EFF =EFFICIENCY OF THE SYSTEM EFF=AI+B1/ (RM*V) l 1. 5+C1%KRM'V+D1/ (RM%KV) -r*2 EFF1 (J) =EFF C**** AVERAGE OUTPUT POWER WHEN VF=VR FI=EXP (—A'A V**B I) POWO=POW0-(-WK;113I3ICA;IEFF'WV** (2.+BI) *FI*DV) *C (I) POW01 (J) =POWO P31402 (J) =WK*BI*A*EFF*V** (2.+5I) *FI*DV*C (I) CWK** AVERAGE POWER FROM THE GEARBOX POWGBO=POWGBO—(—WK*BI*A*EFG*V**(2.+BI) *'FIIDV) *C (I) POWGB01 (J) =POWGBO POWGB02 (J) =WK*BI r•A*EFG*V** (2. +6I) *FI*DV*C (I) 3 CONTINUE CALL COMPAR C=c CALCULATION OF COMMON PARAMETERS OF WIND—POWERED GENERATING C SYSTEMS RETURN END

SUBROUTINE WPMAI CKK* SUBROUTINE OF THE WINDMILL GENERATOR WITH A PM ALTERNATOR AND C WITH AC LOAD CURRENT CONTROL SYSTEM AND CONSTANT LOAD RESISTANCE DIMENSION V11 (60) , VAV1 (60) • VII-11 (60) • VP1 (60) , FW1 (60) • FWT1 (50) • 2NUM (5) • X (100) • Y (100) • RPM (60) + CURT (60) + FCUR (60) • PFLO (60) :3,C (60) • POWG 1 (60) • PW=ND1 (60) • FWT2 (60) • POWIWI (60) • F WT3 (60) , EFF1 (60) 4RLA (60) ,CURA (60) • VOLP (60) • POWGA (60) r POWIA (60) + POWIM (60) r EFFG (60) r 425

SFGB (60) , POWIO1 (60) , POWGB01 (60) , VC (10) ,CPF (10) 60/ 12 (60) , V13 (60) , POW02 (60) , POWGB02 (60) , POWI02 (60) , POWIW2 (60) , .7PWIND2 (60) COMMON BI,VAV,\41,N,I,V,V1,V2,DV,FW,FWT,VMH,VP,J,V11,VAV1,VMH1,VP1, 2FW1,FWT1,L,K,AA,BB,X,Y,FW2,TGB,RLAsRPM 3,RO,PI,CPM,RMW,RMM,GBE,YGB,PMI,CUR,CNL,RA,GB-T,VR,WK,R,WL,RM,WN,WI 4,A1,B1,C1,D1,VS,RL,A,VF,C,PWIND,FI,PWIND1,P01.IW,POWIW1,FWT2,FWT3, 5EFF,EFF1,POWO,CURI,CURA,VOL,VOLP,POWA,POWGA,POWI,POWIA,POWIG,PUWIM 6,EFFG,EFG,EGB,POWIO,POWIOI,POWGBO,POWGBO1,FIM,POWM,POWIOM,POWGBOM, 7VC,CPF,POWO1,POWIWM,ENER1,ENER2,ENER3,ENER4,ENER5,ENER6,ENER7,ENER 88,ENER9,EFL,EFWIN,EFGB,EFGN,EFSYI,EFSY2,EFSY3 9,CWF,RA1,FC,RF,PIR,VOLM,T1,FK,CIR,CFV,RAK,B,CURW,CURT,FCU,FCUR,PFL 9,PFLO,V12,V13,POW02,P0WGB029POWI029POWIW2,PWIND2,M N=50 C1 CALCULATED DATA WK= (PMI+T ZMM) / ((1. —GBE) *VR**'3) C*=K* RL =LOAD RESISTANCE/PHASE RL= (1. / (3 . *CUR**2)) * (WI*RMM**3—CNL' *RMM** (3 . /2.) —T*RMM) —RA C**** CALCULATION OF THE COEFFICIENTS OF THE OVERALL EFFICIENCY C**** B =COEFFICIENT FOR THE CALCULATION OF EFFICIENCY PARAMETERS B=RL/ (RA+RL) Al=A1*B B1=131313 C1=0. D1=D1*B C**=* CALCULATION OF THE CUT—IN WIND SPEED VS C**** LET SAY VS=0.5 DO 1 I=1,n V1=V5 V2=VR DV= (V2—V1) /FLOAT (N-1) V=V1+FLOAT (I-1) *DV C**** SQUARE OF THE CURRENT CURS= (B/ (3 . *RL)) * (WI* (RM- V) **3—CNL* CRM*V) K K (3 . /2.) —T*RM-KV) IF(CURS.GT.0.) GOTO 2 1 CONTINUE 2 VS=V C=K** CALCULATION OF THE ANtJAL AVERAGE POWER POW0=0. POWGBO=0. DO 3 I=1,N C**** CALCULATION OF THE INTGRAL FROM THE FORMULA OF TRAPEZOIDS C(I)=0.5 IF (CI.EQ.1) .OR. (I.EQ.N)) GOTO 4 C(I)=1. 4 J=I VT=VS V2=VR DV= (V2—V1) /FLOAT (N-1) V=V1+FLOAT (I-1) *DV V11(J)=V RLA (J) =RL Cx*** CURI=ARMATURE CURRENT CURI=SQRT C (B/ (3 . *RL)) * (WI* (RM*V) **3—CNL * (RM"KV) ** (3 . /2 .) —T*RM%KV) ) CURA (J) =CURI C= VOL =VOLTAGE/PHASE VOL=CURI*RL VOLP (J) =VOL 0101=1= GENERATOR SHAFT SPEED RPM (J) =V*RM C=J PUWA=OUTPUT POWER OF THE GENERATOR POLJA=3 . %K CUR Pc"'2%KRL POWGA (J) =POWA - 427 .

C= POWI=OUTPUT POWER FROM THE WIND—ROTOR POWI=WK*'V*•*3 POWIA (J) =POWI C%1CK'~CI POWIG=OUTPUT POWER FROM THE GEARBOX POWIG=POWI* (1. —GBE) —T''.'RM*V POWIM (J) =POWIG C%ICICl'* EFG =EFFICIENCY OF THE GEARBOX EFG=POWIG/POWI EGB (J) =EFG C**** EFFG=EFFICIENCY OF THE GENERATOR EFFG (J) =POWA/POWIG C**X* EFF =EFFICIENCY OF THE SYSTEM EFF=A1+81/ (RM*V)'11.5+C1*RM*V+01/ (RM*V) **2 EFF1 (J) =EFF C**** AVERAGE OUTPUT POWER WHEN VF=VR • FI=EXP C—A*VP'BI) POWO=POWO—(—WK*BI*A*EFF%+•'V** (2.+BI) *FI*DV) *C (I) POW01 (J) =POWO POW02 (..i) =WK*B I*A*EFF*V** (2. +B I) *FI*UV*C (I) CAcKN lc AVERAGE POWER FROM THE GEARBOX POWGBO=POWGBO— C—WK*BI*A*EFG*V** (2.+BI) *FI*DV) *C (I) POWGBO1 (J) =POWGBO POWGB02 (J) =WK*BI*A%ZEFG*V** (2.+BI) *FI*DV*C (I) 3 CONTINUE CALL COMPAR C**** CALCULATION OF COMMON PARAMETERS OF WIND-POWERED GENERATING C SYSTEMS RETURN END

SUBROUTINE WWFAI CK U SUBROUTINE OF THE WINDIMILL GENERATOR WITH A WOUND FIELD C ALTERNATOR WITH FIELD CONTROL SYSTEM C AND CONSTANT AC LOAD RESISTANCE DIMENSION Vii (60) , VAV1 (60) , VMH1 (60) , VP1 (60) , FW1 (60) , FWT1 (60) , 2NUM (5) , X (100) , Y (100) , RPM (60) ,CURT (60) , FCUR (60) , PFL O (60) 3, C (60) , POW01 (60) ,PWIND 1 (60) , FWT2 (60) , POWIW1 (60) , FWT3 (60) , EFF1 (60) , 4RLA (60) ,CURA (60) , VOLP (60) , POWGA (60) , POWĪA (60) , POWIM (60) , EFFG (60) , 5EGB (60) , POWI01 (50) , POWGB01 (60) , VC (10) ,CPF (10) 6, V12 (60) , V13 (60) , POW02 (60) , POWGB02 (60) , POWI02 (60) , POWIW2 (60) , 7PWIND2 (60) COMMON BI,VAV,V11,N,I,V,V1,V2,DV,FW,FWT,VMH,VP,J,V11,VAV1,VMH1,VP1, 2FWI,FWTI9L,K,AA,BB,X,Y,FW2,TGB,RLA,RPM 3,RO,PI,CPM,RMW,RMM,GBE,YGB,PMI,CUR,CNL,RA,GB,T,VR,WK,R,WL,RM,WN,WI 4,A1,B1,Cl,Di,VS,RL,A,VF,C,PWIND,FI,PWIND1,POWIW,POWIW1,FWT2,FWT3, 5EFF,EFFI,POWO,CURI,CURA,VOL,VOLP,POWA,POWGA,POWI,POWIA,POWIG,POWIM 6,EFFG,EFG,EGB,POWIO,POWI01,POWGBO,POWGBO1,FIM,POWM,POWIOM,POWGBOM, 7VC,CPF,POW01,POWIWM,ENER1,ENER2,ENER3 ENER4,ENER5,ENER5,ENER7pENER 88,ENER9IEFLPEFWINIEFGB,EFGN,EFSY1,EFSY2,EFSY3 9,CWF,RA1,FC,RF,PIR,VOLM,T1,FK,CIR,CFV,RAK,B,CURW,CURT,FCU,FCUR,PFL 9,PFLO,V12,V13,POW02,POWGB02,POWI021POWIW2,PWIND2,M N=50 C**** GIVEN DATA FOR THE GENERATOR C•• RMM =MAXIMUM ROTATIONAL SPEED OF GENERATOR SHAFT RM"=1500. C%K PMI =MAXIMUM INPUT POWER TO THE GENERATOR PMI=6780. C l CS CUR =MAXIMUM CURRENT OF THE GENERATOR CU2=8.1 C-I rAc1 WINDAGE AND FRICTION LOSSES COEFFICIENT C1=292.6/1.E5 C-IGKIcr, RA1 =WINDING RESISTANCE/PHASE RA1=1.255 1128

FC =MAXIMUM FIELD CURRENT FC=1. ca~K:K RF =FIELD RESISTANCE RF=301. PIR =MAXIMUM IRON LOSSES PIR=236. VOLM=MAXIMUM PHASE VOLTAGE VOL M240.

C3c CALCULATED DATA C= GB =GEARBOX RATIO GB=RMM/RMW C=Notc T1 =FRICTION TORQUE OF THE GEARBOX FROM GENERATOR SIDE T1=TGB/GB C=IcicK FK =FIELD COEFFICIENT FK=FC/RMM=K0.5 C=4= CIR =IRON LOSSES COEFFICIENT CIR=PIR/(FC=RMM) C''-K CNL =NO—LOAD LOSSES COEFFICIENT OF THE GENERATOR CNL=CWF+CIR%KFK CFV =VOLTAGE COEFFICIENT CFV=VOLM/(FCKRMM) Mg*** CALCULATION OF CONSTANT COEFFICIENTS C',K

C=K'..K CALCULATION OF THE ANUAL AVERAGE POWER POWO=O. POWGB0=0. D0 3 I=1.N C*'* CALCULATION OF THE INTGRAL FROM THE FORMULA OF TRAPEZOIDS C (I) =0.5 IF ((I.EQ.1) .OR. (I.EQ.N)) GOTO 4 C (I) =1. 4 J=I V1=V5 "2=VR DV= (V2—V1) /FLOAT (N-1) V=VI+FLOAT (I-1) *DV V11 (J) =V RLA (J) =RL Com** CURI=LOAD CURRENT CURI=SQRT ( (B/ (3. *RL)) * (WI* (RM*V) **3—CNL* (RM*V) = (3./2 . ) —T*RM*V) ) CURA (J) =CURI C CURW=ARMATURE CURRENT CURWCURI*RAK CURT (J) =CURW C VOL =VOLTAGE/PHASE VOL=CURI*RL VOLP (J) =VOL OPICTOK FCU =FIELD CURRENT FCU=VOL/(CFV*RM*V) FCUR (J) =FCU C***t: GENERATOR SHAFT SPEED RPM (J) =V*RM C3cicicK POWA=OUTPUT POWER OF THE GENERATOR POWA=3. *CUR I**2*RL POWGA (J) =POWA C**** POWI=OUTPUT POWER FROM THE WIND—ROTOR POWI=WK*'V3 3 POWIA (J) =POWI C*-3= POWIG=OUTPUT POWER FROM THE GEARBOX POWIG=POWI* (1. —GBE) —Tl*RM' V POWIM (J) =POWIG C3c1=1: EFG =EFFICIENCY OF THE GEARBOX EFG=POWIG/POWI EGB (J) =EFG C%' K PFL= FIELD LOSSES PFL=FCU*%K2xRF PFLO (J) =PFL C EFFG=EFFICIENCY OF THE GENERATOR EFFG (J) =P3WA/POWIG C%K** EFF =EFFICIENCY OF THE SYSTEM EFF=A1+81/ (RM*V) **1.5+C1*RM*V+01/ (RM'KV) **2 EFF1 (J) =EFF C= AVERAGE OUTPUT POWER WHEN VF=VR FI=EXP (—A*V KBI) POWO=POWO—(—WK*BI*A*EFF*V**(2.+BI) *FI*DV) *C (I) POW01 (J) =POWO POW02 (J) =WKx$I*A*EFF*V** (2.+BI) *FI*DV'-KC (I) C= AVERAGE POWER FROM THE GEARBOX POWGBO=POWGBO— (—WK%KB I*A*EFG*V** (2 . +B I) *FI*DV) *C (I) POWGB01 (J) =POWGBO PC!.JGBO2 (J) =WKNeI*A*EFG*V** (2. +B I) *FI*DV*C (I) 3 CONTINUE CALL COMPAR C,ic%1 K CALCULATION OF COMMON PARAMETERS OF WIND—POWERED GENERATING C SYSTEMS RETURN END 430 .

' SUBROUTINE COMPAR C4c= CALCULATION OF COMMON PARAMETERS OF WIND—POWERED GENERATING C SYSTEMS DIMENSION V11 (60) , VAV1 (60) , VMH 1 (50) , VP1 (60) , FW1 (60) , FWT1 (60) , 2NUM (5) , X (100) , Y (100) , RPM (60) , CURT (60) , FCUR (60) , PFLO (60) 3, C:(60) , POW01 (60) , PWIND1 (60) , FWT2 (60) , POWIW1 (60) , FWT3 (60) , EFF1 (60) , 4RLA (60) ,CURA (60) , VOLP (60) , POWGA (50) , POWIA (60) , POWIM (60) , EFFG (60) , SEGB (60) , POWI01 (60) , POWGB01 (60) , VC (10) ,CPF (10) 6, V12 (60) , V13 (60) , POW02 (60) , POWGB02 (60) , POWI02 (60) , POWIW2 (60) , 7PWIND2 (60) COMMON BI,VAV,VM,N,I,V,V1,V2,DV,FW,FWT,VMH,VP,J,V11,VAV1,VMH1,VP1, 2FW1,FWT1+L,K,AA,8B+X,Y,FW2,TGB,RLR,RPM 3,RO,PI,CPM,RMW,RMM,GBE,YGB,PMI,CUF:,CNL,RA,GB,T,VR,WK,R,WL,RM,WN,WI 4,A1.+B1,C1,D1,VS,RL,A,VF,C,PWIND,FI,PWINDI,POWIW,POWIW1,FWT2,FWT3, SEFT,EFFI,P0W0,CURI,CURA,VOL,VOLP,POWA,POWGA,POWI+POWIA,PQWIG,POWI 6,EFFG,EFG,EGB,POWIO,POWI01,P0WGBO,POWGB01,FIM,POWM,POWIOM,POWGBOM, 7VC,CPF, POW01,POWIWM,ENER1,ENER2,ENER3,ENER4,ENERS,ENER6,ENER7,ENER 88,ENER9,EFL,EFWIN,EFGB,EFGN,EFSY1,EFSY2,EFSY3 9,CWF,RAI,FC,RF,PIR,VOLM,T1,FK,CIR,CFV,RAK,B+CURW,CURT,FCU,FCUR,PFL 9,PFLO,V12,V13,POW02,POWGB02,POWI02,POWIW2,PWIND2,M N=50 POWI0=0. POWIW=0. PWIND=0. DO 3 I=1,N WK= (PMI+T.RMM) / ((1. —GBE) *VR**3) V1=VS V2=VR DV= (V2—V1) /FLOAT (N-1) C=I0K CALCULATION OF THE INTGRAL FROM THE FORMULA OF TRAPEZOIDS C(I)=0.5 IFC(I.EQ.1) .OR. (I.EQ.N)) GOTO 4 C(I)=1. 4 J=I V=V1+FLOAT (I-1) *DV V11(J)=V IF (I.EQ.1) GOTO 7 V12 (J) =V11 (J-1) +DV/2. GOTO8 7 V12(J)=DV/2. C* AVERAGE POWER FROM THE WIND—ROTOR. 8 FI=EXP C—A*VI) FW=1. / (2 . ** ((V/VAV) tB I) ) FW2=FW POWIO=POWIO—C—WKBP,A*v*'* (2.+BI) *FIIDV) 'C (I) POWI01 (J) =POWIO POWI02 (J) =WK*BI*A*VICK (2.+BI) *FI*DV*C (I) C3cIcIcK AVERAGE POWER IN THE LOCATION WHEN THE SYSTEM IS RUNNING WITH C VF=VR WK=WK/CPM PCWIW=POWIW—(—WK*BI*A*V** (2.+BI) *FI*DV) *C (I) F WT2 (J) =POWIW P0141142(J) =WK*BI*A*V= (2.+BI) *FI*DV*C (I) C AVERAGE POWER IN THE L CATION WITH ALL WIND SPEEDS V1=0. V2=VM DV= (V2—V1) /FLOAT (N-1) V=V1+FLOAT (I-1) *DV . FWT3 (J) =V IF (I.EQ.1) GOTO 9 V13 (J) =FWT3 (J-1) +DV/2. GOTO 10 431

9 V12 (J) =DV/2. 10 FI=EXP (—Aa V**BI) FW=1./ (2.*:u (CV/VAV) aut:BI) ) PWIND=PWIND— C—WK*B I%I:ANN** (2 . +8 I) *F I*DV) *C (I) PWIND1 (J) =PWIND PWIND2 (J) =WK*BI*A*V%W*(2.+BI) %ti'FI*DV%t:C (I) 3 CONTINUE C CALCULATION OF AVERAGE.POWER WHEN VF GREATER THAN VR AND WITH CP C VARIABLE AND EVERYTHING ELSE CONSTANT FW=FW2 FIM=1. / (2. ** C (VF/VAV) **B I) ) C**aCI: GENERATOR AVERAGE POWER OUTPUT POI41=POWO* (FW—FIM) +POWO C' WIND—ROTOR AVERAGE POWER OUTPUT POWIOM=POWIO*(FW—FIM)+POWIO C= GEARBOX AVERAGE POWER OUTPUT POWGBOM=POWG80*(FW—FIM)+POWGBO CI** LOCATION AVERAGE POWER POWIWM=POWIW* (FW—FIM) +POWIW C** CALCULATION OF CP WK= CPMI+T''RMM) / ( ( 1. —GBE) *VR**3) V1=VR V2=VF N=10 DV= (V2—V1) /FLOAT CN-1) DO 5 I=1.N L=I • V=V1+FLOAT (I-1) *DV VC(L)=V CPF (L) =CPF1 KPOWI/ C (VC (L) % 3) *WK) 5 CONTINUE

CK* ANNUAL ENERGY YIELD IN KWH CU CI FROM THE LOCATION FOR THE WHOLE RANGE OF WIND SPEEDS ENER1=PWIND*8.75 C** FROM THE LOCATION WHEN THE SYSTEM IS RUNNING UP TO V=VR ENER2=POWIW*8.76 C:H;rA.CK FROM THE WIND—ROTOR ENER3=POWIO%8.76 Caric:I :K FROM THE GEARBOX ENER4=POWGBO%r•8.76 C**** FROM THE GENERATOR ENER5=POWO*0.76 C=Nolor FROM THE LOCATION WHEN THE SYSTEM IS RUNNING WITH CP VARIABLE ENER6=POWIWM*8.76 C=oloc FROM THE WIND—ROTOR ENER7=POWIOM 8.76 C* FROM THE GEARBOX ENERB=POWGBOM*8.76 C%'** FROM THE GENERATOR ENER9=POWM*8.76 Dog= EFFICIENCY OF THE LOCATION WHEN THE SYSTEM IS RUNNING UPTO VR EFL=POWIW/PWIND C*K* EFFICIENCY OF THE WIND—ROTOR EFWIN=POWIO/POWIW Cc EFFICIENCY OF THE GEARBOX EFGB=POWGBO/POWIO C**** EFFICIENCY OF THE GENERATOR EFGN=POWO/POWGBO C SYSTEM OVERALL EFFICIENCIES CA:mx K FOR ALL WIND SPEED RANGE FROM THE LOCATION EFSY1=POWO/PWIND C=wirr. WHEN THE SYSTEM IS RUNNING UPTO VR C%IC1 lCK FROM THE LOCATION 1132 .

EFSY2=POWO/POWIW Ca=' ' FROM THE WIND—ROTOR EFSY3=POWO/POWIU RETURN END

SUBROUTINE CURVE1 DIMENSION V11 (60) , VAV1 (60) , VMH1 (60) , VP1 (60) , FW1 (50) , FWT1 (50) 2NUM (5) , X (100) 9Y (100) ,RPM (60) 'CURT (60) ,FCUR (60) , PFLO (60) 39C (60) , POW01 (60) ,PWIND 1 (60) , FWT2 (60) , POWIW1 (60) , FWT3 (60) , EFF1 (60) , 4RLA (60) ,CURA (60) , VOLP (60) , POWGA (60) , POWIA (60) , POWIM (60) , EFFG (60) 5EGB (60) , POWI01 (60) , POWGBO1 (50) , VC (10) , CPF (10) 6, V12 (60) , V13 (60) , POW02 (50) , POWGB02 (60) , POWI02 (60) , POWIW2 (60) 7PWIND2 (60) COMMON BI , VAV,V•11,N,I,V, V1 , V2 , DV ,FW,FWr,VMH,VP,J,VII,VAVI,VMH1,VP1, 2FW19FWT1,L,K,AA,BB,X,Y,FW2,TGB,RLA,RPM 3,RO , PI , CPM, RMW , RMMI, GBE , YGB ,PMI,CUR,CNL,RA,GB,T,VR,WK,R,WL,RM,WN,WI 4, Al , B1 , C1 ,D1,VS,RL,AhVF,C,PWIND, FI ,PWIND1,POWIW,POWIW1,FWT2,FWT3, 5EFFsEFF1,POWO,CURI,CURA, VOL ,VOLP,POWA, POWGA ,POWIhPOWIAhP0WIG,P0WIM 6,EFFG , EFG,EGB,POWIO , POWI0I,POWGBO,POWGB0I,FIM,POWM,POWIOM,POWGBOM, 7VC9CPF9POW01,POWIWM,ENER1,ENER2,ENER3,ENER4,ENER5,ENER69ENER7,ENER 68,ENER9,EFLhEFWINhEFGB,EFGN,EFSY1,EFSY2,EFSY3 9,CWF,RA1hFC ,RF, PIR , VOLM,T1,FK, CIR , CFV,RAK,B,CURW,CURT,FCU,FCUR,PFL 9,PFLO,V12,V13,POW02,POWGBO2,POWI02,POWIW2,PWIND2,M

C* 'X WRITE RESULTS 1000 FORMAT (1 X, I3 ,12 (F 10.3) ) 1002 FORMAT (64H0 -ti%:=ictiain.I='o*K*********RESULTS OF LOCATION-**%ti*x*****%K**

1001 FORMAT (64H0 J WS M/SEC WS MPH WS CUBE NORM.TIME TIME—YEAR 1 V/VAV) WRITE (6 91002) WRITE (691001) N=50 DO 2 J=1,N WRITE (5,1000) J, V11 (J) , VMH1 (J) , VP1 (J) , FW1 (J) , FWT1 (J) , VAV1 (J) 2 CONTINUE

C* K' PLOT CURVES CCK* L =NUMBER OF CURVES/GRAF L=1 DO 3 K=1,L NUM (K) =N 3 CONTINUE DO 4 J=1,N X (J) =FW1 (J) Y (J) =VAV1 (J) 4 CONTINUE CALL GRAF (X,Y,NUM,L,0,21HWIND DURATION PROFILE921, .15HV/VAV,5,AA,BB) DO 5 J=1,N X (J) =FW1 (J) Y(J)W1 (J) 5 CONTINUE CALL GRAF (XI Y, NUM, L,0 ,22HPOWER DURATION PROFILE •22• 215HV3 (M/SEC) X3,15, AA, BB) RETURN END

SUBROUTINE CURVE2 DIMENSION V11 (60) , VAV1 (60) , VMH1 (60) , VP1 (60) , FW1 (60) ,FWT1 (60) 2NUM (5) 9X (100) 1Y (100) ,RPM (60) 'CURT (60) ,FCUR (60) , PFLO (60) 433

3,C (60) , POWO1 (60),PWIND 1 (60) , FWT2(60) , POWIW1 (60) ,FWT3(60) , EFF1 (60), 4RLA (60) , CURA (60) , VO_P (60) , POWGA (60), POWIA (60) , POWIM (60), EFFG (60), SEGB (60), POWI01 (60), POWGB01 (60), VC (10) , CPF (10) 6, V12(60) , V13 (60), POW02(60) , POWGB02(60) , POWI02(60) , POWIW2(60) , 7PWIND2 (60) COMMON BI,VAV,VM,N,I,V,V1,V2,DV,FW,FWT,VMH,VP,J,V11,VAV1,VMH1,VP1, 2FWI,FWT1,L,K,AA,BB,X,Y,FW2,TGB,RLA,RPM 3,RO,PIICPM,RMW,RMM,GBE,YGB,PMI,CUR,CNL,RA,GB,T,VR,WK,R,WL,RM,WN,WI 4,A1,81,C1,D1,VS,RL,A,VF,CIPWIND,FI,PWINDI,POWIW,POWIW1,FWT2,FWT3, 5EFF,EFF1,POWO,CURI•CURAIVOL,VOLP•POWA,POWGA,POWI,POWIA,PGWIG,P0WIM 6,EFFG,EFGIEGB,POWIO,POWIO1,POWGBO,POWGBO1,FIM,POWM,POWIOM,POWGBOM, 7VC,CPF,POWO1,POWIWM,ENER1,ENER2,ENER3,ENER4,ENER5,ENER6,ENER7,ENER 881ENER91EFLIEFWIN,EFGB,EFGN,EFSY1,EFSY2,EFSY3 9,CWF,RA1,FC,RF,PIR,VOLM,T1,FK,CIR,CFV,RAK,B,CURW,CURT,FCU,FCUR,PFL 9,PFLO,V12,V13,POW02,POWGB02,POWI02,POWIW2,PWIND2,M

C=44= DITE RESULTS N=50 1000 FORMAT (1X, I3,12 (F10.3) ) 1009 FORMAT (33HOLOCATION AND WINDMILL PARAMETERS) 1010 FORMAT (94HO J MEAN WISP START WSP RATED WSP FURL WISP ROTOR RAD 1 CP MAX TIP SPRAT RPM MAX GB RATIO) 1011 FORMAT (114H0 J WINDSPEED RPM GENER EFF GRBOX EFF GENER EFF SYST. 1 POUT WMIL POUT GBOX POUT GENE LOAD RESI LOAD CURR FIELD CUR) 1012 FORMAT (46H0WHEN THE WINDMILL IS RUNNING WITH VARIABLE CP) 1013 FORMAT (24H0 L WS M/SEC PCOEFF CP) 1014 FORMAT (115HOENERGY YIELD WHEN VF=VR AND CP=CONST IN KWH 1 ENERGY YIELD WHEN V=VF AND CP VARIABLE--EFFICIENCY VALUES OF) 1015 FORMAT (124H0 J LOC ALLWS LOC VF=VR WINDMILL GEARBOX GENERATOR 1 LOC V=VF WINDMILL GEARBOX GENERATOR LOC V=VM LOC VF=VR WIND 2MILL) 1016 FORMAT (74H0 J VRW M/SEC APLOCV=VR APWINDMIL APGEARBOX APGENERAT ILOC VM WS LOCALLWSP) 1017 FORMAT (35HOANNUAL AVERAGE POWERS VERSUS SPEED) 1018 FORMAT (26HOTOTAL AVERAGE POWERS/YEAR) WRITE (6,1009) WRITE (6,1010) WRITE (6,1000) J,VAV,VS,VR,VF,R,CPM,WL,RMWIGB WRITE (6,1011) DO 3 J=1,N WRITE (6,1000) J, V11 (J) ,RPM (J) , EGB (J) , EFFG (J) , EFF1 (J) , POWIA (J) , POW 1 IM (J) , POWGA (J) ,RLA (J) ,CURA (J) , FCUR (J) 3 CONTINUE WRITE (6,1012) WRITE (6,1013) DO 2 L=1,10 WRITE . (6,1000) L, VC (L) , CPF (L) 2 CONTINUE WRITE (6,1017) WRITE (6,1016) DO 6 J=1,N WRITE (6,1000) J, V12 (J) , POWIW2 (J) , POWI02 (J) , POWGBO2 (J) , POW02 (J) , V1 13(J) I PWIND2 (J) 6 CONTINUE WRITE (6,1018) WRITE (6,1016) WRITE (6,1000) J, V11 (50) , POWIW, POWIO, POWGBO, POWO, FWT3 (50) ,PWIND WRITE (6,1014) WRITE (6,1015) WRITE (6,1000) J,ENER1,ENER2,ENER3,ENER4,ENER5,ENER6,ENER7,ENERB, 1ENER9,EFSY1,EFSY2,EFSY3 C=1= PLOT CURVES C;rrai„ic L =NUMBER OF CURVES/GRAF 434

L=1 DO 8 K=1,L NUM(K)=N 8 CONTINUE DO 9 J=1,N X(J)=V11(J) Y (J) =POWIA (J) 9 CONTINUE CALL GRAF (X,Y,NUM,Lr0116HWIND SPEED M/SEC,16, 117HINPUT POWER WATTS,17,AA,BB) DO 10 J=1,N X(J)=V11(J) Y (J) =POWGA (J) 10 CONTINUE CALL GRAF (X,Y,NUM,L,0,16HWIND SPEED M/SEC116, 118NOUTPUT POWER WATTS,18,AA,BB) DO 11 J=1,N X CJ) =RPM (J) Y CJ) =EGB (J) 11. CONTINUE CALL GRAF (X,Y,NUM,L10,19HGENERATOR SPEED RPM,19, 118HGEARBOX EFFICIENCY,18,AA,BB) DO 12 J=1,N X (J) =RPM (J) Y (J) =EFFG (J) 12 CONTINUE CALL GRAF (X,Y,NUM,L,0,19HGENERATOR SPEED RPM,19, 120HGENERATOR EFFICIENCY,20,AA,BB) DO 13 J=1,N Y (J) =CURA (J) X (J) =V11 :J) 13 CONTINUE CALL GRAF (X,Y,NUM,L,0,16HWIND SPEED M/SEC,16, 117HLOAD CURRENT AMPS,17,AA,BB) DO 14 J=1,N X(J)=V11(J) Y(J)RLA(J) 14 CONTINUE CALL GRAF (X,Y,NUM,L,0,16HWIND SPEED M/SEC,16, 12OHLOAD RESISTANCE OHMS,20,AA,BB) DO 5 J=1, N X(J)=V11(J) Y (J) =EFF1 (J) 5 CONTINUE CALL GRAF (X,Y,NUM,L,0,16HWIND SPEED M/SEC,16, 124HOVERALL SYSTEM EFFCIENCY,24,AA,BB) DO 4 J=1,N X(J)=V11(J) Y (J) =FCUR (J) 4 CONTINUE CALL GRAF (X,Y,NUM,L,0,16HWIND SPEED M/SEC,16, 118HFIELD CURRENT AMPS,18tAA,BB) RETURN END APPENDIX VII..3 435 .

PROGRAM ENEC(OUTPUT,TAPE62,TAPE6=OUTPUT,BILL5sTAPE7=BILL5 , INPUT , 1TAPE5=INPUT)

C**** CALCULATION OF THE ANNUAL ENERGY YIELD OF DIFFERENT WIND—POWERED C ELECTRICAL GENERATING SYSTEMS FROM THEIR EFFICIENCY CURVES C=1 V.C. NICODEMOU JUNE,1979

C=3= MAIN PROGRAM DIMENSION X (500) , Y (500) , X1 (500) , Y1 (500) , EFF1 (90) , C (90) , V11 (90) , 1POW01 (90) , POW02 (90) s V12 (90) , POWIO.1 (90) s POWI02 (90) , POWIW1 (90) , 2POWIW2 (90) , V13 (90) , V14 (90) ,PWIND 1 (90) , PWIND2 (90) s NUM (10) , WW (11) , 351(9) , R (50) , X2 (500) , Y2 (500) , RPM (50) , VC (50) , CPF (50) 4,X3(11) ,Y3(11) COMMON BI,VAV,VM,RO,A,PI,CPM,RMW,VR,VF,V.V1,V2,DV,NsX,Y,KI,I,WW , 1WK,GB,R,WL,RM,VS,X1,Y1,P,J,EFFI,POWO,POW0I,POW02,POWIO,POWI01, 2POWIO2,POWIW,POWIWI,POWIW2,PWIND,PWIND1,PWIND2,NUM,WN,SI,V11,V12, 3V13,V14,C,EFF,FI,FW,FW2,ENERI,ENER2,ENER3,ENER4,EFSYI,EFSY2,EFSY3 , 4X202,PMI,RMM,RPM,VC,CPF,POWIWII. OWM,POWIOM,ENER5,ENER6,ENER7 5,X3,Y31M1,M2

C**** WIND CHARACTERISTIC OF LOCATION C**** NAME OF LOCATION C*'**Nt ST.ANNS HEAD

C%OK* GIVEN DATA C**** BI =LJUNGSTROM EXPONENT BITA BI=2.19 C=4: VAV =ANNUAL AVERAGE WIND SPEED VAV=7.242 C*** VM =MAXIMUM WIND SPEED OF LOCATION VM=31.29 C**** RO =AIR DENSITY R0=1.23 A= ((SLOG (2.0)) / (VAVx=BI) C**** GIVEN DATA FOR THE WINDMILL P I=ARCOS (-1. ) G**** CPM =MAXIMUM POWER COEFFICIENT OF THE WIND—ROTOR CPM=0.35 G►•%e%T.%I RMW =MAXIMUM ALLOWED ROTATIONAL SPEED OF THE WIND—ROTOR SHAFT C**** VR =RATED WIND SPEED OF THE WIND—ROTOR VR=11.174 Do= VF =FURLING WIND SPEED VF=15.643 c***'* V =WIND SPEED IN M/SEC C V1,V2=WIND SPEED LIMITS OF THE INTEGRAL C**** DV =INCREMENT OF WIND SPEED RMW=600. PMI=2200. WK=PMI/VR**3 C%IPcC R =RADIUS OF THE WIND—ROTOR R=SART (WK/ (0.5*RO*P I*CPM) ) C**** WL =OPTIMUM TIP SPEED RATIO WL= (PI/30.) *RMW*R/VR CALL START (2) 1111 FORMAT (8F6.3) II:=10MK DATA OF THE LORRY ALTERNATOR EFFICIENCY WITH AC LOAD N=8 READ (5,1111) CX3 (I) , I=1, N) READ (5,1111) (Y3(I),I=1,N) RMM=1500. CALL EFC1 C3== CALCULATION OF EFFICIENCY CURVES N=M1 N9=N 35

DO 1 I=1•N M=I X(MG=X1(I) Y(M)=EFF1(I) 1 CONTINUE C=r-mot AVERAGE POWER PER YEAR N=M1+K1 N1=N DO 9 J=1.N MJ X2(M)=V11(J) Y2(MD=POW02:J) 9 CONTINUE C**x* DATA OF THE INDUCTION GENERATOR EFFICIENCY WITH AC LOAD N=8 READ (5.1111) (X3(1)11=1111) READ (5.1111) (r3(I),I=1,N) Rrt#750. CALL EFC1 C3=== CALCULATION OF EFFICIENCY CURVES N=M1 N10=N DO 6 I=1•N M=I+N9 X(M)=X1(I) Y(M)=EFF1(I) 6 CONTINUE Cm=== AVERAGE POWER PER YEAR N=M1+K1 N2=N DO 10 J=11N h#J+N1 X2(M)=V11(J) Y2 (M) =POW02 (J) 10 CONTINUE C**Ict: DATA OF THE PM ALTERNATOR EFFICIENCY WITH DC LOAD N=8 READ (5.1111) (X3(I),I=11N) READ (5.1111) (Y3(I),I=1,N) RMr'#600. CALL EFC1 C**** CALCULATION OF EFFICIENCY CURVES N=M1 1111=N DO 7 I=1•N :0=I+N9+N10 X(M)=X1(I; YMD=EFF1(I) 7 CONTINUE ==r= AVERAGE POWER PER YEAR N=M1+K1 N3=N 00 11 J=1N r•-•.J+N1+N2 X2 OD =V11 (J) Y2(M)=POW02(J) 11 CONTINUE C.1 = DATA OF THE PM ALTERNATOR EFFICIENCY WITH AC LOAD N=8 READ (5,1111) (X3(I),I=1,N) READ (5.1111) (Y3(I),I=1,N) 141600. CALL EFC1 CSI x* CALCULATION OF EFFICIENCY CURVES N=M1 N12=N DO 8 I=1 ,N 1"I-1-119+1`110+1`111 X CM) =X1 CI) Y C1"D =EFF1 CI) 8 CONTINUE )J AVERAGE POWER PER YEAR N=M1±K 1 N4=N DO 12 J=1,N MJ+1`11+N2+N3 X2 CM) =V11 (J) Y2 CM) =POW02 (J) 12 CONTINUE N=M1+K1 N.5=1.1 DO 13 J=1,N M=J+N1+N2+N3+N4 X2 CM) =V11 (J) Y2 (N) =POWIO2 (J) 13 CONTINUE N=M2 N8=N DO 14 J=1,N M=J+N1+N2+N3+N4+N5 X2 CM) =V13(J) Y2 CM) =PWIND2 CJ) 14 CONTINUE C*No t L =NUMBER OF CURVES/GRAF L=4 NUM (1) =N9 NUN (2) =N10 NUM (3) =N11 NUN (4) =N 12 AA=9.7 BB=6.965 CALL GRAF (X,Y,NUM,L,O,19HGENERATOR SPEED RPM,19, 1241-1OVERALL SYSTEM EFFCIENCY,24,AA ,BB: C)101 =I:I: AVERAGE POWER PER YEAR DO 2 M=1,N1+N2+N3+N4+N5 X CM) =X2 CM) Y CM) =Y2 (M) 2 CONTINUE C:lcrcicK L =NUMBER OF CURVES/GRAF L=5 NUM (1) =N1 NUM (2) =112 NL'°1 (3) =N3 NUM (4) =N4 NUM (5) =N5 CALL GRAF (X,Y,NUM,L,0,16HWIND SPEED M/SEC,16, 116HMEAN POWER WATTS:16,AA, 8B) N6=N1+N2+N3+N4+1 N7=N1+N2+N3+N4+N5+N8 DO 15 M=N6,N7 X CM) =X2 CM) Y(hD=Y2(1-D 15 CONTINUE C%== L =11013ER OF CURVES/GRAF L=2 NUMC1) =N5 NUM (2) =N8 CALL GRAF (X (N6) , Y (N6) , NUM, L , 0, 16HWIND SPEED M/SEC, 16 , 438 .

116HMEAN POWER WATTS,16,AA,BB) CALL ENPLOT STOP END

SUBROUTINE EFC1 C=Pi K CALCULATION OF EFFICIENCY CURVES DIMENSION X (500) , Y (500) , XI (500) , Y1 (500) , EFF1 (90) , C (90) , V11 (90) , 1POW01 (90) , POW02 (90) , V12 (90) , POWI01 (90) , POWI02 (90) , POWIW1 (90) 2POWIW2 (30) , V13 (90) , V14 (90) , PWIND1 (90) ,PWIND2 (90) . NUM (1 0) , WW (1 1) , 3SI (9) , P (50) , X2 (500) , Y2 (500) , RPM (50) , VC (50: ,CPF (50) 4,X3(11) ,Y3(11) COMMON BI,VAV,VM,R0,A,PI,CPM,RMW,VR,VF,V,V1,V2,DV,N,X,Y,Ki, I,WW, 1WK,GB,R,WL,RM,VS,X1,Y1,P,J,EFF1,POWO,POWO1,POW02,POWIO,POWI01 , 2POWI02,POWIW,POWIW1,POWIW2,PWIND , PW2NDl,PWIND2, NUM' WN,5I,V11,V12, 3113,V14,C,EFFBFI,FW,FW2,ENERI,ENER2,ENER3 9ENER4, EFSYI,EFSY2,EFSY3, 4X2,Y2,PMI,RMM, RPM, VC,CPF,POWIWM, POWs POWIOM,ENER5,ENER6,ENER7 5, X3, Y3, M1, M2 N=8 C3Ct= INCREMENT OF THE WIND SPEED DV=0.5 C 'K)K RM =TRANSFORMATION COEFFICIENT OF WIND—SPEED TO ROTATIONAL SPEED RM= (X3 (N) )ti'RMM) /VR V5= (X3 (1) *RMM) /RM V1=VS V2=VR C)K)K= PLOT OF EFFICIENCY CURVE BY INTERPOLATION M1=IFIX( (V2—V1) /DV) DO 5 J=1,M1 GK)K)' X1 =CALCULATED POINT OF PU ROTATIONAL SPEED C**** X3 =PU ROTATIONAL SPEED OF THE GENERATOR X1 (J) =X3 (1) + (X3 (N) —X3 (1) ) )KFLOAT (J-1) /FLOAT (M1-1) C)iaK)I V11 =CALCULATED WIND SPEED V11 (J) = (X1 (J) )KRMM) /RM IF (Xl (J) . EQ . X3 (1) ) GOTO 7 IF (X1 (J) . EQ . X3 (N)) GOTO 10 DO 9 I=2 ,N IF (X1 (J) .GT.X3 (I-1) . AND .X1 (J) .LT.X3 (I)) GOTO 8 9 CONTINUE Ci,.icK)J Y1 =EFFICIENCY OF THE GENERATOR CALCULATED FROM THE INTERPOLATION DV*** Y3 =EFFICIENCY OF THE GENERATOR PER UNIT 8 Y1 (J) =Y3 (I-1) +(Y3 (I) —Y3 (I-1)) )K (X1 (J) —X3 (I-1)) / (X3 (I) —X3 (I —1) ) GOTO 6 7 Yl (J) -Y3:1) 6 CONTINUE 10 Yl CJ) =Y3 :N) DO 5 I=1:111 EFF1 (I) =Y1 (I) 5 CONTINUE CALL AVPO C)K)K SUBROUTINE OF THE CALCULATION OF THE AVERAGE POWER RETURN END

SUBROUTINE AVPO C-' CK SUEPOUTINE OF THE CAL.CULATION OF THE AVERAGE POWER DIMENSION X (500) 9Y (500) , Xl (500) , Y1 (500) , EFF1 (90) , C (90) , V11 (90) , 1POW01 (90) , POW02 (90) , V12 (90) , POWIOi (90) , POWI02 (90) , POWIWI (90) 2POWIW2 (90) ,Via (:30) , V14 (90) , PWINDI (90) ,PWIND2 (90) , NUM (10) 914W (1 1) , 35I (9) , P (SAD , X2 (500) , Y2 (500) , RPM (50) , VC (50) ,CPF (50) 4,X3(11) ,Y3(11) COMMON BI,VAV,VM,R3,A,PI,CPM,RMW,VR,VF,V,V1,V2,DV,N,X,Y,KI,I,WW, 439 .

1WK,GB,R,WL,RM,VS,X1.Y1,P,J,EFF1,POWO,POW01,POWO2 , POWIO , POWI01 , 2POWI02,POWIW,POWIW1sPOWIW2,PWIND,PWIND1,PWIND2,NUM , WN , SI , V11 , V12 , 3V13,V14,C,EFF,FI,FW,FW2,ENER1,ENER2,ENER3,.ENER4.EFSYI,EFSY2,EFSY3 , 4X2,Y2,PMI,RMM,RPM,VC,CPF,POWIWM.P0WM.POWIOM,ENER5,ENER6,ENER7 5,X3,Y3,M1,M2 N=M1 C'=%= CALCULATION OF THE ANUAL AVERAGE POWER POW0=0. POWI0=0. POWIW-O . PWIND=O. DO 3 I=1,N WK=PMI/VR')K3 C= CALCULATION OF THE INTGRAL FROM THE FORMULA OF TRAPEZOIDS C (I) =0.5 IF((I.EQ.1) .OR. (I.EQ.N)) GOTO '4 C(I)=1. A J=I v=V11 (J) EFF=EFF1 (I) IF (I.EQ.N) GOTO 7 V12 (I) =V11 (I) +DV/2. GOTO 8 7 V12 (I) =V1. 1 (N) 8 FI=EXP (--A%KV)K:t:BI) CK•11:.=:K AVERAGE OUTPUT POWER WHEN VF=VR POWO=POWO—(—WK*BI)=A)KEFF)KV)K)=(2.+BI) )=FI>K)V) )KC (I) POWO1 (J) =POWO POW02 (J) =alK%KBPKAaEFF*V%K%K (2.4-BD %KFI*DV Cl.%K%K'.K AVERAGE POWER FROM THE WIND—ROTOR FW=1. / (2.3= ( (V/VAV) %=%=8I) ) FW2=FW POWIO=POWIO— (—WK-KBI%KA%KV%K%= (2 . +B I) %KFPKDV) %KC (I) POWI01 (J) =POWIO POWI02 (J) =WK;K8I;KA:KV:=;K (2.+BI) )KF I)KDV CAcitx)K AVERAGE POWER IN THE LOCATION WHEN THE SYSTEM IS RUNNING WITH C VF=VR WK=WK/CPM PDWIW=POWIW— (—WK%KBPKA:KVK%K (2 . +81) %KF I*DV) %KC (I) POWIW1 (J) =POWIW POWIW2 (J) =WK)KBI%KA=V** (2.+BI) )KFI)KDV 3 CONTINUE C)l,=ICK CALCULATION OF AVERAGE POWER WHEN VF GREATER THAN VR AND WITH CP C VARIABLE AND EVERYTHING ELSE CONSTANT FW=FW2 FIM=1. / (2. )k)K ( (VF/VAV) %CKBI) ) C= GENERATOR 4VERAGE POWER OUTPUT POWM=POWO* (FW—FIM) +POWO C%K%K 1 K WIND—ROTOR AVERAGE POWER OUTPUT POWIOM=POWIO)K (FW—FIM) +POWIO CK LOCATION AVERAGE POWER POWIWfl=POWIWK (FW—FIM) +POWIW C)I:K* CALCULATION OF CP V1=VR V2=VF K=IFIX r (V2—V1) /DV) +1 K1=K DO 5 L=1 ,K WK=PMI/VR%K' l 3 WK=WK/CPM I=N+L J=I V=V1+FLOAT (L) %KDV V11 U) =V EFF1 (J) =EFF VC(L)=V FI=EXP (—WI:W 8I) P0WIW2 (J) =14K :1=B I KA:LN:K:K (2 . +B I) :KF I:=DV CPF (L) =PMI/ (WO--NA: K3) WK=WKZCPF (L) POW02 (J) =WK:KB I:KA:R=FFNN:K:K (2. +8I) :KF I:KD V IF (! .E0 . K) GOTO 12 V12 (J) =V11 (J) +DV/2 GOTO 13 12 V12 (J) =V11 (N+K) —DV/2. 13 P0WI02 (J) =WK:1BI:Kf::v:K%K (2.+BI) ' FI:KDV 5 CONTINUE C3:'—k: AVERAGE POWER IN THE LOCATION WITH ALL WIND SPEEDS V1=0. V2=VM N=IFIX( (V2—V1) /DV) M2=N DO 1 I=1+N WK=PMIXVR:K:K3 WK=WK/CPM C(I)=0.5 IF<(I.EQ.1) .OR. (I.EQ.N)) GOTO 2 C

WRITE (6, 1000) J, V13 (J) , V14 (J) ,PWIND2 (J) , V11 (J) , V12(J) , POWIW2 (J) , 1POWI02 (J) , POW02 (J) , EFF 1 (J) 11 CONTINUE DO 15 L=1,K 'RITE (601000) L,VC(L) ,CPF(L) 15 CONTINUE RETURN END 4.42 . REFERENCES

Chapter 1 1.1 Wilson, C.L.: "Energy: Global Prospects 1985-2000", by the Workshop on Alternative Energy Strategies (McGraw—Hill, 1977).

1.2 Cheremisinoff, N.P.: "Fundamentals of Wind Energy", (Ann Arbor Science, 1978).

1.3 McVeigh, J.C.: "Sun Power, an Introduction to the Applications of Solar Energy", (Pergamon Press, 1977).

1.4 Harrah, B. and Harrah, D.: "Alternate Sources of Energy':: A Bibliography of Solar, Geothermal, Wind and Tidal Energy, and Environmental Architecture", (The Scarecrow Press, Inc., 1975). 1.5 Golding, E.W.: "The Generation of Electricity by Wind Power", (Conservation Tools and Technology Ltd., 1976).

1.6 Warne, D.F. and Calnan, P.G.: "Generation of Electricity from the Wind", Proc. IRE, 124 (11R), .IEE Review, pp. 963-985 (1977).

1.7 Haack, B.N.: "An Examination of Small Wind Electric Systems in Michigan", (Ann Arbor Science, 1977).

1.8 McGuigan, D: "Small Scale Wind Power", (Prison Press, 1978). 1.9 Buehring, I.K.: "Development, Control and Testing of an Aerogenerator", Ph.D. Thesis to be submitted, Elec. Eng. Dept., Imperial College, University of London (1979). 1.10 Webb, T.: "A Microprocessor—based Controller for an Aerogenerator", Thesis for the Diploma of Imperial College, to be submitted, Elec. Eng. Dept., Imperial College, London (1979).

Chapter 2 2.1 "Energy Conservation in the United Kingdom", A Report by the National Economic Development Office (H.M.S.O., 1974).

2.2 Smith, H.E.: "Storage Radiator Installation", Electrical Times, March 19, 1976. 2.3 "Energy Conservation: A Study of Energy Consumption in Buildings and Possible Means of Saving Energy in Housing", A BRE Working Party Report CP 5675, 1975.

443 .

2.4 McVeigh, J.C.: "Sun Power, An Introduction to the Applications of Solar Energy", (Pergamon Press, 1977).

2.5 Allen, J. and Bird, R.A.: "The Prospects for the Generation of Electricity from Wind Energy in the United Kingdom", Energy Paper No. 21, Department of Energy (1977).

2.6 Freris, L.L., Bolton, H.R., Buehring, I.K. and Nicodemou, V.C.: "A Low Cost Wind Energy Conversion System for Heating of Domestic Premises", IEE 1979 Conference Publication No. 171, pp. 282-285.

2.7 Sorensen, B.: "Direct and Indirect Economics of Wind Energy Systems relative to Fuel-based Systems", Symp. on Wind Energy Systems, Cambridge (1976). 2.8 Buehring, I.K.: "Development, Control and Testing of an Aerogenerator", Ph.D. Thesis to be submitted, University of London (1979).

2.9 Webb, T.: "A Microprocessor-based Controller for an Aerogenerator", Thesis for the Diploma of Imperial College, to be submitted, Electrical Engineering Department, Imperial College, 1979.

2.10 Ryle, M.: "Economics of Alternative Energy Sources", Nature, Vol. 267, 12 May 1977, pp. 111-117. 2.11 Cheremisinoff, N.P.: "Fundamentals of Wind Energy", (Ann Arbor Science, 1978).

Chapter 3 3.1 Shefter, Ya. I.: "Wind-powered Machines", (Mashinostroyeniye Press, 1972), (NASA Technical Translation, 1974).

3.2 Wilson, R.E. and Lissamon, P.S.S.: "Applied Aerodynamics of Wind Power Machines", (National Technical Information Service, U.S. Department of Commerce, 1974). 3.3 Golding, E.W.: "The Generation of Electricity by Wind Power", (Conservation Tools and Technology, Ltd., 1976).

3.4 Cheremisinoff, N.P.: "Fundamentals of Wind Energy", (Ann Arbor Science Publishers Inc., 1978).

3.5 Buehring, I.K.: "Development, Control and Testing of an Aerogenerator", Ph.D. Thesis to be submitted, University of London, 1979. I

3.6 McGuigan, D.: "Small-Scale Wind Power", (Prism Press, 1978).

3.7 Putnam, P.C.: "Power from the Wind", (Van Nostrand Reinhold Company, 1948).

3.8 Warne, D.F. and Calnan, P.G.: "Generation of Electricity from the Wind", Proc. IEE, 1977, 124 (11R), IEE Review, pp. 963-985. 3.9 Hwang, H.H. and Gilbert, L.J.: "Synchronisation of Wind Turbine Generators against an Infinite Bus under Gusting Wind Conditions", IEE Trans., 1978, PAS-97, (2), pp. 536-544.

3.10 Reddoch, T.W. and Klein, J.W.: "No Ill Winds for New Mexico Utility", IEEE Spectrum, 1979, 16(3), pp. 57-61.

3.11 Jorgensen, G.E., Lotker, M., Meier, R.C. and Brierley, D.: "Design, Economic and System Considerations of Large Wind- Driven Generators", IEEE Trans., 1976, PAS-95, (3), pp. 870-878. 3.12 Juul, J.: "Design of Wind Power Plants in Denmark", UNESCO Proceedings, 1956, 07, pp. 229-240.

3.13 Watson, G.R. and Bainbridge, G.R.: "The Design, Construction and Proving of a Low Cost 5 kW Wind-Powered Turbine for Isolated Applications", IEE Conf. Pubn., 1979, 171, pp. 277-281. 3.14 Littler, J.G.F. and Thomas, R.B.: "Wind Power for Domestic Use in the United Kingdom", IEE Conf. Pubn., 1979, 171, pp. 313-316.

3.15 Merriam, M.P.: "The Tvindmill", Rain, January 1978, pp. 13-14.

3.16 Nickols, W.R.: "The Design and Construction of the Aldborough Aerogenerator", IEE Conf. Pubn., 1979, 171, pp. 306-308.

3.17 Jayadev, T.S.: "Windmills Stage a Comeback", IEE, Spectrum, 1976, 13(1), pp. 44-49.. 3.18 Lam, W.C.: "Novel Induction Generation Scheme for Wind Power Generation, and Tests on Thermistor Protection of Induction Machines", M.Sc. Thesis,. University of London, 1978.

3.19 Kostenko, M.P.: "A.C. Commutator Generation with Frequency Regulation independent of Rotational Speed", Elektrichestro, (2), 1948. 4s5'

3.20 Hughes, Wm.L., Parker, J.D., Allison, H.J., Ramakumar, R.G. and Lingelbach, D.D.: "Survey of Oklahoma State University Work in Energy Storage, Variable-Speed Constant- Frequency Generators, and Wind Generation Systems", STU Investigation No. 52, 1976, pp. 5-3 to 5-62. 3.21 Zweygbergk, S.V.: "The Synchronous-Flux-Generator (SFG)", STU Investigation, No. 52, 1976, pp. 5-115 to 5-117. 3.22 S8dergard, B.: "D.C.-Generator%Thyristor Converter is a Good Alternative to A.C.-Synchronous for Large Wind-Electric Generators", STU Investigation No. 52, pp. 5-119.

3.23 Bolton, H.R. and Nicodemou, V.C.: "Permanent Magnet Alternators for Small Wind Systems", presented at the 1st BWEA Wind Energy Workshop, Cranfield Institute of Technology, Cranfield, April 1979. 3.24 Hitter, U.: "Review of Development in West Germany"; STU Investigation No. 52, 1976, pp. 1-51 to 1-72.

3.25 Sch8nball, W.: "The Noah Wind Energy Concept", STU Investigation No. 52, 1976, pp. 2-25 to 2-29. 3.26 "Wind Power Alternator Project", University of Manitoba, Dept. of Elec. Eng., private communication.

3.27 Basset, E.D. and Potter, F.M.: "Capacitive Excitation for Induction Generators", AIEE Trans. (Elec. Eng.), 1935, Vol. 54, pp. 540-544. 3.28 Wagner, C.F.: "Self-excitation of Induction Motors", AIEE Trans. (Elec. Eng.), 1939, Vol. 58, pp. 47-51. 3.29 Glazenap, M.S.: "Self-excited Asynchronous Generator with an Unbalanced Load", Elektrichestro, No. 3, 1952, pp. 37-38. 3.30 Barkle, J.E. and Ferguson, R.W.: "Induction Generator Theory and Application", AIEE Trans. (Elec. Eng.), 1954, Vol. 75, pp. 12-19. 3.31 Rechberger, H.: "Kondensatorerregle Asynchrongeneratoren in Kleinwasserkraftanlagen", E. and M., Vol. 71, 1957, PP. 379-385. 446 •

3.32 Eastham, J.F.: "Principles and Characteristics of Induction Generators", Electrical Review (G.B), 1960, Vol. 167, No. 20, pp. 809-819. 3.33 Hadley, H.K.: "Capacitor-Excited Induction Generator", Electrical Times, March 1964, 'pp. 398-399. 3.34 Bokhyan, S.K.: "An Induction-type Self-exciting High-frequency Generator with Stabilised Voltage", Elektrotechnika, 1965, 32(2), pp. 56-58. 3.35 Panda, P.C. and Ray, L.M.: "Self-excited Induction Generator", University of Roorke (India), Publ. Dept. of Elec. Eng., 1965-66, Vol. 1, pp. 209-228.

3.36 Sipaylov, G.A., Romanov, Yu. A. and Perezhirov, Yu. I.: "Capacitor Self-excitation of Asynchronous Generator", Elektrichestro, No. 4, 1972, pp. 43-47. 3.37 Chizhenko, I.M., Vydolob, Yu. F. and Golubtsov, V.N.: "Characteristics of a Bridge Rectifier Energised by an Independent Asynchronous Generator", Problemy Tekhnicheskoi - Elektrodinamiki, 1975, No. 50, pp. 50-53. 3.38 Novotny, D.W., Gritter, D.J. and Studtman, G.H.: "Self-excitation in Inverter-driven Induction Machines", IEEE Trans., 1977, PAS-96, 4, pp. 1117-1125. 3.39 Arrillaga, J. and Watson, D.B.: "Static Power Conversion from Self-excited Induction Generators", Proc. IEE, 1978, 125(8), pp. 743-746. 3.40 Moban, N. and Riaz, M.; "Wind-driven, Capacitor-excited Induction Generators for Residential Electric Heating", presented at IEEE PES Winter Meeting, New York, January 1978. 3.41 Debontridder, J., Vandenput, A., Marcelis, R., Geysen, W., De Keuster, C. and Fierens, E.: "The Combination Asynchronous. Generator-Vertical Axis Wind Turbine for Small Power Applications", presented at the Electrical Machines Conference, Brussels, 1978. 3.42 Ooi, B.T. and David, R.A.: "Induction-GeneratorfSynchronous- Condenser System for Wind-Turbine Power", Proc. IF E, 1979, 126(1), pp. 69-74.

4137

3.43 Johnson, G.L. and Walker, H.S.: "Three-phase Induction Motor Loads on a Variable Frequency Wind Electric Generator", Wind Engineering, 1977, 1(4), pp. 268-276. 3.44 Pontin, G.: "Electrical Machinery for Windmills", Electrical Review, 1978, 103(20), pp. 41-42.

3.45 University of Exeter, Wind Power Unit: "Present and Future Work at the Wind Power Unit", presented at the Workshop on Wind Energy Research and Development at the Cavendish Laboratory, Cambridge, January 1978.

3.46 Bolton, H.R. and Nicodemou, V.C.: "Development of Direct Drive Alternator for Wind Power Application", Internal Report, Elec. Eng. Dept., Imperial College, December 1977. Note: For references 3.47 and 3.48, see page 453. Chapter 4

4.1 Bolton, H.R. and Nicodemou, V.C.: "Operation of Self-excited Generators for Windmill Application", accepted paper, no, P3108, Proc. LEE, April 1979. 4.2 Preece, A.J.: "Conversion of a Lorry Alternator for Use in Wind Energy Conversion Plant", 3rd Year Project, E.ec. Eng. Dept., Imperial College, 1977. 4.3 Golding, E.W.: "The Generation of Electricity by Wind Power", (Conservation Tools and Technology,Ltd., 1976).

4.4 Juul, J.: "Design of Wind Power Plants in Denmark", Proc. U.N. Conf. on Wind Energy, Rome, 1962, pp. 229-240.

4.5 Johnson, G.L. and Walker, H.S.: "Three-phase Induction Motor Loads on a Variable Frequency Wind Electric Generator", Wind Engineering, 1977, Vol. 1, No. 4, pp. 268-277. 4.6 Law, W.C.: "Novel Induction Generation Scheme for Wind Power Generation, and Tests on Thermistor Protection of Induction Machines", M.Sc. Thesis, University of London, Imperial College, Elec. Eng. Dept., September 1978. 4.7 Debontridder, J., Vandenput, A., Marcelis, R., Geysen, W., De Keusler, C. and Fierens, E.: "The Combination Asynchronous Generator-Vertical Axis Wind Turbine for Small Power Applications", Proc. Int. Conf. on Elec. Mach., Brussels, September 1978. 448 .

4.8 Debontridder, J.: "Automatic Field Regulation for the Combination Darrieus Rotor/Generator", Proc. Int. Conf. on Elec. Mach., Paper G5/4, Brussels, September 1978.

4.9 Buehring, I.K.: "Development, Control and Testing of an Aerogenerator", Ph.D. Thesis to be submitted, University of London, Imperial College, Elec..Eng. Dept., 1979. 4.10 Bolton, H.R. and Nicodemou, V.C.: "Development of Wound Field Alternator for Wind Power Application", Internal Report, Elec. Eng. Dept., Imperial College, London, April 1978.

Chapter 5

5.1 Brainard, M.W.: "Synchronous Machines with Rotating Permanent- Magnet Fields, Part I: Characteristics and Mechanical Construction", AIEE Trans., Vol. 71, Part III, August 1952, pp. 67o-676. 5.2 Strauss, F.: "Synchronous Machines with Rotating Permanent-Magnet Fields, Part II: Magnetic and Electrical Design Considerations", AIEE Trans., Vol. 71, Part III, October 1952, pp. 887-893.

5.3 Goss, W.R.: "Evolution of Permanent-Magnet Fractional-Horsepower Size Motors and Generators", AIEE Trans., Vol. 72, Part III, April 1953, pp. 81-84. 5.4 Ginsberg, D. and Misenheimer, L.J.: "Design Calculations for Permanent-Magnet Generators", AIEE Trans., Vol. 72, Part III, April 1953, pp. 96-103.

5.5 Merrill, F.W.: "Permanent-Magnet-Excited Synchronous Motors", AIEE Trans., Vol. 73, Part III, February 1955, pp. 1754-1760.

5.6 Mole, C.J.: "Permanent-Magnet Generators", Electrical Times, December 1956, pp. 893-898. 5.7 Puder, A.T. and Strauss, F.: "Salient-Pole Permanent-Magnet Alternators for High-Speed Drive", AIEE Trans., Vol. 78, Part II, November 1957, pp. 333-338. 5.8 Hanrahan, D.J. and Toffolo, D.S.: "Permanent-Magnet Generators, Part I - Theory", AIEE Trans., Vol. 76, Part III, December 1957, pp. 1098-1103. 449 .

5.9 Hanraban, D.J. and Toffolo, D.S.: "Permanent-Magnet Generators, Part II - Optimum Design", AIEE Trans. Vol. 82', No. 65, April 1963, pp. 68-74. 5.10 Honsinger, V.B.: "Permanent-Magnet Motor", USA Patent 3, 126, 493,- (1976). 5.11 Gratzmuller, J.L.: "Improvements in and relating to Permanent Magnet Rotors", British Patent 1, 171, 858 (1969). 5.12 Siemens AG: "An Electric Machine having Permanent Magnets mounted in the Rotor between its Pole Segments", British Patent 1, 177, 247 (1970).

5.13 Westinghouse: "Permanent Magnet Rotor", British Patent 1, 147, 917 (1969). 5.14 Westinghouse: "Dynamoelectric Machine having Permanent Magnet Field Poles", British Patent 1 260 935 (1972). 5.15 Binns, K.J. and Barnard, W.R.: "Permanent-Magnet Rotor for, Synchronous Electric Machine", British Patent 1 324 147 (1973). 5.16 Binns, K.J.: "Permanent Magnetic Rotor for Synchronous Electric Machines", British Patent 1 359 548 (1974). 5.17 Rao, T.S.M. and Batra, V.P.: "Design Aspects and Reactances of Permanent Magnet Synchronous Generators", Electrical India, Vol. 13, July 1973, pp. 9-13. 5.18 Ahmad, H., Di Cenzo, C.D. and Sinha, N.K.: "Optimum Design of Permanent-Magnet Generators", presented at IEEE PES Summer Meeting, 1972.

5.19 Mullard Ltd.: "Magnadur Magnets for D.C. Motors", (Mullard, 1970).

5.20 Binns, K.J., Jabbar, M.A. and Barnard, W.R.: "Computation of the Magnetic Field of Permanent Magnets in Iron Cores", Proc. IEE, 1975, 122(12), pp. 1377-1381. 5.21 Lajoie-Mazenc, M., Carison, R., Hector, J. and Pesque, J.J.: "Characterisation of a New Machine with Ferrite Magnets by resolving the Partial Differential Equation for the Magnetic Field", Proc. IEE, 1977, 124(8), pp. 697-701. 450 .

5.22 Aliyu, A.: "Investigation into a Low Speed Permanent Magnet Alternator for Wind Power Application", M.sc. Thesis, University of London, 1976. . 5.23 Private communication: "Wind Power Alternator Project", University of. Manitoba., Dept. of Elec. Eng.

5.24• Kostenko, M.P. and Piotrovskiy, L.M.: "Electrical Machines", Part II (Energia, 1973). 5.25 Lawrenson, P.J. and Agu, L.A.: "Theory and.:. Performance of Polyphase Reluctance Machines", Proc. IEE, 1964, 111(8), pp. 1435-1445.

5.26 Tselikin, M.G. (main editor) et al: "Electrotechnical Handbook", Vol. I, Book I (Energia, 1971).

5.27 Parker, R.J. and Studders, R.J.: "Permanent Magnets and their Applications", (John Wiley and Sins, Inc., New York, 1962).

5.28 Say, M.G.: "The Performance and Design of Alternating Current Machines", (Pitman, 1974). 5.29 Say, M.G.: "Alternating Current Machines", (Pitman, 1977). 5.30 Fitzgerald, A.E., Kingsley, C. Jr. and Kusko, A.: "Electric Machinery", (McGraw—Hill, 1971).

5.31 Adkins,,B. and Harley, R.G.: "The General Theory of Alternating Current Machines", (Chapman and Hall, 1975)-

5.32 Hindmarsh, J.: "Electrical Machines and their Applications", (Pergamon Press, 1977). 5.33 Cahill, D.P.M.: "The Permanent Magnet Synchronous Motor", M.Sc. Thesis, Imperial College, London University, 1962.

5.34 Cahill, D.P.M. and Adkins, B.: "The Permanent Magnet Synchronous Motor", Proc. IEE, 1962, Vol. 109, Part A, No. 48. 5.35 Ford, A.W.: "Brushless Generators for Aircraft — A Review of Current Developments", Proc. IEE, 1962, Vol. 109, Part A.

5.36 Gould, J.E.: "Permanent. Magnets", Proc. IEE, 1978, Vol. 125, No. 11R. 5.37 Ashen, R.A.: "Some Aspects of High—torque, Low speed, Brudhless Electric Motors", Ph.D. Thesis, Imperial College, London University, 1977. 451

5.38 Ashen, R.A.: "Permanent-Magnet Behaviour under 'Open Circuit' Conditions", Proc. IEE, 1978, 125(12), pp. 1410-1414.

5.39 Ashen, R.A.: "Linear Scalar Potential Models for Permanent- Magnet Circuits", Proc. IEE, 1978, 125(12), p. 1403.

5.40 Bolton, H.R. and Nicodemou, V.C.: "Development of Direct Drive Alternator for Wind Power Application", Internal Report, Elec. Eng. Dept., Imperial College, December 1977.

5.41 Bolton, H.R. and Nicodemou, V.C.: "Design of a Low Speed Permanent Magnet Alternator for Wind Power Application: Rutherford Alternator 8 kW", Internal Report, Elec. Eng. Dept., Imperial College, April 1977.

Chapter 6

6.1 Mullard Ltd.: "Permanent Magnets Introductory Notes, Magnadur Data Sheet", (Mullard, 1975).

6.2 Buehring, I.K.: "Development Control and Testing of a Small Aerogenerator", Ph.D. Thesis to be submitted, University of London, 1979.

6.3 Freris, L.L., Bolton, H,R,, Buehring, I.K. and Nicodemou, V.C.: "A Low Cost Wind Energy Conversion System for heating of Domestic Premises", IEE Conf. Pub. No, 171, 1979, pp. 282-285.

Chapter 7

7.1. Golding,;E.W.: "The Generation of Electricity by Wind Power", (Conservation Tools and Technology Ltd., 1976).

7.2 Putnam, P.C.: "Power from the Wind", (Van Nostrand and Reinhold • Company, 1948).

7.3 Chilcott, R.E.: "Design Speeds for Wind Turbines", 5th Australian Conf. on Hydraulics and Fluid Mechanics, Christchurch, New Zealand, Dec. 1974, Proc. Vol. 1, pp. 35-41.

7.4 Meel, J.V.: "Weibull Distributions in Wind Energy Statistics", Rep. No. R-295-D, 1977, Wind Energie Groep, Vakgroep Transportpysika, afdeling Natuurkunde, Technische Hogeschool Eindhoven. 452-.

7.5 Bronshtein, I.N. and Semendyayev, K.A.: "A Guide Book to Mathematics", (Verlag Harri Deutsch, 1973).

7.6 Allen, J. and Bird, R.A.: "The Prospects for the Generation of Electricity from Wind Energy in the United Kingdom", (Department of Energy, HMSO, 1977), Energy Paper 21.

7.7 Ljungstrom, 0.: "Large Scale Wind Energy Conversion System (WECS) Design and Installation as affected by Site Wind Energy Characteristics, Grouping Arrangement and Social Acceptance", Wind Engineering, 1977, Vol, 1, No. 1, pp. 36-56.

7.8 Sarre, P.E.: "Year round Efficiency of a Wind Turbine as affected by Choice and Rating of Power Take-off System", Internal Report (WEP4, 1977), University of Exeter, Unit Energy Group. 7.9 Jayadev, T.S. and Smith, R.T.: "Wind-Powered Electric Utility Plants", presented at the Winter Annual Meeting, Houston, Texas, 1975, of the Am. Soc. of Mech. Engrs.

7.10 Smith, ROT. and Jaya Devaiah, T.S.: "Wind-Turbine Mechanical to Electrical Conversion Systems", STU Investigation No. 52, 1976, PP. 5-95 to 5-114. 7.11 Pontin, G.: "Electrical Machinery for Windmills", Electrical Review, 1978, 203(20, pp. 41-42.

7.12 Bossanyi, E.A., Whittle, G.E., Dunn, P.D., Lipman, N.H. and Musgrove, P.J.: "Wind Characteristics and the Output of Wind Turbines", presented at the 1st BWEA Wind Energy Workshop, Cranfield Institute of Technology, Cranfield, April 1979.

7.13 Johnson, G.L.: "Economic Design of Wind Electric Systems", IEEE Trans, PAS-97, (2), 1978, PP. 554-562. 7.14 Shipley, E.E.: "Loaded sears in Action",. "Gear Handbook", (Dudley, 1962), pp. 14-1 to 14-29. 7.15 Freris, L.L.: "Modes of Operation of Bridge-connected Converters. A Non-mathematical Discussion of Characteristics and Applications. Part 1", Electrical Times, 1 Oct. 1971, pp. 39-42. 453.

7.16 Nottingham, C.: "A Cost Benefit Analysis of Wind—Powered Generators", Accountance, June 1978, pp. 48-52.

7.17 Bolton, H.R. and Nicodemou, V.C.: "Permanent Magnet Alternators for Small Wind Systems", presented at the 1st BWEA Wind Energy Workshop, Cranfield Institute of Technology, Cranfield, April 1979.

Addition

3.47 Ott. R.R., Barber, R.J. and Roesel, J.F., Jr. : "The Roesel generator, a unique variable-speed, constant-frequency generator", IEEE No. 75CH0964-7MAG •

3.48 Walker, J.H.: "High-Frequency Alternators", Journal IEE, 1945, pp. 67-80. 454 .

PUBLICATIONS SUBMITTED IN SUPPORT OF THESIS C7.ty. Q P•3!6' P. ~d 1bp ( D

OPERATION OF SELF-EXCITED GENERATORS FOR WINDMILL APPLICATION OPERATION OF SELF-EXCITED GENERATORS FOR WINDMILL APPLICATION It is believed that the idea for the 'self matching' of small wound field generators with resistance loads to windmills, and the theoretical treatment are original. The material has not beeh S.R. Bolton, B.Sc., Ph.D., D.S.C. published by or submitted to any other journal. V.C. Nicodemou, M.Sc.(Eng.) It is believed that the paper falls into, the area dealt with by the P1 or SI groups.

.rl.J/ Z, H.R. Bolton

t Gm,04(. October 1970 V.C. Nicodemou

Department of Electrical Engineering, Imperial College of Science and Technology, London, SN7 2DT. 3.

List of symbols

windmill rotor power coefficient Indexing terms z Wind power, Electric generators. P I ▪ d.c. load current

If field current

K, p, KR, Kv, K + w generator constants Xg gearbox ratio Abstract Xn, Kw .coefficients for windmill power

The paper deals with the operation of self-controlled, n rotational speed rev.min l

• field loss wound-field generators for small-scale wind power application in pf P .which the output is connected to a constant resistance load and in + generator input power + the field is connected in plain shunt or series. It is shown pw power output from windmill

that a fairly good natural match can be obtained between power/ ✓ radius of windmill rotor

speed characteristics of gonerator and windmill with this R, RL . • load resistance

configuration particularly when the magnetic circuit of the Ra + armature resistance

generator goes fairly hard into saturation at higher speeds and Rf + field resistance

field currents. Test results are included and indicate that T torque

an external d.c. source would often be necessary to initiate V d.c. load terminal voltage

"build-up" in a practical system. Vf + field voltage

- r VNL no-load d.c. voltage Vp - r.m.s. phase voltage

+ w wind speed X armature reactance

fl - generator efficiency

~g - gearbox efficiency

a windmill rotor tip speed ratio

p + density of air

m + flux per pole

ul .rotational angular velocity 5.

1 Introduction 3. The thermal tine constant of the storage heaters is long

enough to smooth out the effects of short-term lulls in the wind. The increasing importance of fuel saving has been responsible for a revival of interest in so-called "alternative" sources of energy-and 4. a&.ttery costs are avoided. one of the most promising sources for the U.K. is wind. Work is

proceeding both on large scale wind generating systems1-4,whlch in The scheme is of course only appropriate for mains-connected

aggregate could perhaps supply up to 104 of the U.K. load,and smaller buildings and economic and environmental factors will probably only be

systems.5,6 There has been considerable effort since the war in satisfied for rural or cuter-suburban locations having annual mean wind 1 developing small, reliable wind generating systems for battery charging speeds of S m sec or mare, but it is thought to offer a means by which

at remote locations. Recently attempts have been made to develop small e fair number of individuals could harness a natural energy source for

systems for more general use either to help supply domestic or farm winter space heating in a reasonably economic manner.

premises or to feed low voltage power into the grid.7'0 The control of small wind power systems is complicated by the

The work reported in this paper was done within a project investi- variability of the energy source and by the need to-operate the wind-

gating the economic and technical feasibility of using 1-10 kW wind mill itself at variable speed if good wind energy conversion efficiency

power systems to aid the space heating of bulldings.5 When the project is to he obtained.g There are various lines of approach in a single

started, grid connection was ruled out on statutory grounds then in machine, isolated load system. One can control the windmill force and attention confined to systems incorporating "isolated" loads. (e.g. by changing blade pitch), the gearbox (the step-up ratio of i The principal system considered employs standard storage heaters. the transmission), the generator (e.g. by field control),

These are fed either from a wind generator or from the mains via an the generator output (e.g. by a thyristor bridge), or even the

automatically controlled switch. The advantages of the arrangement are load (e.g. by a load "dumping" or "ballast" scheme) or by any

several, combination of these. It is sometimes forgotten that a further

possibility exists. This is to leave the windmill, generator and load

1. The mains is used to eliminate the problem of wind without control means under normal conditions and design them so that

variability (put another way, the wind id used as a mains fuel saver). efficient operation occurs naturally. The design task is to • ensure that throughout normal operating range the windmill is loaded by V1 2. Since there is no connection between mains and wind the generator and load just enough to enable it to run at optimum • generator, there is no requirement for frequency and voltage matching. rotational cpocd (i.e. the speed at which the power extracted frcn the

wind at its current velocity is a maximum). briefly, this usually

means that the load torque on'the windmill be arranged to vary as the 6. 7.

square of the shaft rotational speed and that stable operating points 2 Theory be obtained where generator load torque and windmill drive torque equate. 2.1 Behaviour of windmill This can souetimes be achieved by careful choice of generator e.m.f./ speed, terminal voltage/load current or e.m.f./excitation current The power Pw developed by a windmill of blade radius r running characteristics and the advantages in terms of simplicity and reliability in a wind stream of velocity Vr is gererally given Ogg are obvious. P ' j p n r' Cp W' (1) Examples of "naturally" matched wind generator systems are found in the literature. Perhaps the most successful large windmill system where C is known as the power coefficient. For a given windmill C built so far - the Gedser windmill19 - employed a certain degree of turns out to be a function only of the ratio between the shaft speed and natural matching and incorporated a fixed pitch windmill and a simple the wind speed. Usually this speed ratio is dealt with as the "tip

induction generator connected to the mains. Systems incorporating speed ratio" A, given bys

uncontrolled induction generators have also been examined elsewhere.11-13 Wr/Vw A number of battery charging schemes14 used matched d.c. generator

systems. Schemes incorporating capacitor excited induction generators The C versus A curve (a family of curves when blade pitch is adjustable) with isolated resistance or induction motor loads and permanent magnet is one of the primary characteristics of a windmill rotor and together alternators with resistance or battery loads are also possible. It may with cqn. 1 and knowledge of load characteristics enables predictions to be noted that in most cases such windmill systems are not entirely free be made of the steady state behaviour of the wind power system. Fig. I of control means since special measures for starting and overspeed is a Cp/A curve for a typical, fixed pitch horizontal axis windmill and protection are often necessary. it can be seen that a single maximum in C occurs when the tip speed

ratio takes a particular value A'. Clearly the shaft speed should vary This paper examines systems using self-excited, wound-field as generators supplying resistive 3oads (e.g. heaters). It was found

possible with certain assumptions to draw up a theoretical basis for such W - A' vw /r

systems and the paper includes experimental results from a rig incorpora- if the windmill is to extract the maximum power from the wind. If the ting a wound-field vehicle alternator. windmill is run so as to maintain A at A', then the output power from

the windmill is

(y p n r' C ) V ' . (2) Pmax w 8. 9.

The expression in the brackets is now constant, and the output power e.g. air brakes or blade "feathering") in favour of low A operation in hence varies as the cubo of the windepeed i.e. order to avoid excessive windmill rotor speeds.

Kw Vw1 (3) Pw 2.2 Operation with generator where Kw Pare CPmax The behaviour in terms of speed of generators supplying resistive

loads is now examined. Consider first a separately excited d.c. Pw can alternatively be expressed in terms of w or ne generator feeding a load of constant resistance R. If armature Pw - Rr f r/y' )' W' resistance is negligible and the field current is held constant, V

varies directly with n and the power Pt. in the load is proportional to n' (4) Kn n'. This does not match the n' power curve for the windmill. However

if field excitation is now varied so that the field flux increases with r e 1 , where Kn w(F 30 Kg ) ' speed according to the relation

n is the generator rev.min1 and the ratio of the step-up • - Ka fn

gearbox, if used, is Kg (> 1). then V e Kv 4tn (5)

n~ . KV

and the power in the load is

W (Kv K6)' R R n (6) It may be noted that although the ideal of operation at constant X' is

assumed in thio eualynis and often brings tonnidorab3o benefits in terms If, for the time being, generator and gearbox lessee aro neglected, it is of wind energy conversion efficiency there aro often quite good reasons apparent that a windmill to generator match is now possible since Kv, Ko for adopting a modified operating policy. Typical examples are the or R can be chosen to givo a generator shaft power versus speed curve near constant shaft speed operation of windmills connected to grid- that is identical to the windmill shaft power curve. The question now connected induction generators, and the "mixed" policy adopted in many arises of how the correct flux versus speed relation can be achieved. battery charging windmills where a roughly constant A mode of operation Two self-excited arrangements will be considered: (a) plain shunt at low and medium wind sl::eds is abandoned at high wind speeds (using connection (b) plain series connection. 11.

If the field is connected in shunt across the armature and a as regards "build-up" capability but there is a fair chance that operation constant field resistance is assumed then the field current would be good enough for practical purposes. V If Rf If the field is connected in series with the armature and all losses 1 n_/ 2 (7) are again neglected, - Kv K0 He Kv Kt _/r v I - I - Since the flux must vary as K4, f , the appropriate magnetisation E R - R

characteristic and the magnetisation characteristic between @ and If to give the - tif f ) 4 required

must be 0

f (8) • - K Vi; relation is again:

where Kf is a constant. Substituting eqn. 7 gives $ - Kf f yK K Kf R . f K.

Substituting for If gives: as required, Km being given by

v K - K ,43 K (8) Q f Rf

K= Can a magnetisation characteristic corresponding to eqn. 8 be achieved K • f R (10) in practice? Fig. 7 shows n cube root curve of the type required and

it may be observed that it is remarkably similar to a normal magnetising It may be noted that if the magnetic circuit of the machine remains

curve, especially as regards the saturation region. However a real linear over the operating range, active field control is then required if a cubic power' versus speed curve is to be obtained. For the shunt magnetisation curve for a machine always possesses a straight line "air-

gap" portion corresponding to operation at low flux levels where the generator the field's effective resistance must vary according to

m.m.f. drop in the iron is negligible compared to that in the airgap, K' Rf - K K I V whereas the cubic curve has no straight line portion. Hence generator Īf - n/=

operation at low speed t,ul4 not be expected to be ideal, particularly 7 - Kv Kp n~= Kv n n

12. 13.

whore KĒ for the linear case is defined bys Since flux, voltage and armature current all decrease with speed (the

flux as ,, the others as n/=), both iron losses and armature losses $ . Kt If. decrease as power throughput falls. Hence the ratio of losses to power

A controller, perhaps of the car "regulator" typsiould normally be used input would be expected to remain reasonably constant for all but very to vary Rf but a non-linear resistor i•s the field circuit giving Rf low speed operation. Similarly armature resistance drop stays small at 1r varying as KRV low speeds in comparison to generated e.m.f. since at low speeds, armature

currents are small. Comprehensive efficiency data for step-up gearboxes where is very scarce but it is probable that like the iron losses in a generator, would also achieve this. a gearbox's friction losses stay in very rough proportion with power

throughput over much of the operating range when the speed varies as the

2.3 Effect of generator imperfections cube root of the power throughput.

It is possible to make allowances for some of the imperfections of The input power Pin to the machine is now no longer equal to the

a real generator, while still preserving an analytic rather than numerical load power Pt but is given by:

approach. The new assumptions ares " (P + Pf) Pin n' 1. Constant ratio between mechanical input and armature

output i.e. constant "armature efficiency". where Pf is the power dissipation in the field and n' is the ratio of armature electrical output to shaft mechanical input power. 2. Armature resistance and brush drops negligible compared

with generated e.m.f. Hence w (P. + Pf). 3. Constant field and load resistances Rf and R. n

4. Armature reaction and transient effects are negligible. where II, the overall efficiency of gearbox and generator, excluding

the effect of field losses, is given by 5. Magnetisation characteristic is again of the form given by, eqn. 8. n - ng.n' 6. Constant gearbox efficiency. and ng is the gearbox efficiency. T. "build-up" problems aro neglected.

Assumptions 1, 2 and 6 involve somewhat less error in the context The windmill output when running at is still given by expression 4. Cpmax of variable speed, cube-type loading than might at first sight be thought. For the shunt-excited machine, Pt + Pf is given by: 14. lb.

Pt + Pf - VI (R + RR) /Rf Rt it is possible to use relation 12 to obtain a quadratic equation for Rf (which includes the resistance of any field ballast resistor) in terms w Hence equating P from egns. 4 and 11: of load resistance Rt and other parameters. The real root of the

quadratic equation is: Kn n' - V (Rf + Rt) /r: Rf Rt K' + JKt + 4n K'K' RI Rf 2n Kn Rt Thus V must still vary as for cubic windmill loading. Writing V in teras of generator parameters and n gives; For the series-excited generator:

Kn - (Kv K)'(R f + Rt) / n Rf RL Pt + Pf I'R V' Ā Substituting eqn. 9 for K, then gives: Equating Pw as before: V2 Kn n' qR

24 7 ✓ must again vary as n and $ as Substituting for V as before

Kn K' (Rf + Re (12) gives: ) / n Rf, R fi. (K K0)' Ka nR where the new coefficient K is: Substituting eqn. 10 for K. then gives: K2 K Kv Kf (13) Kn /nR2 (14)

where K - K The expression 12 enables suitable values to be chosen for Rf and Rt in order to match a generator of known K and f1 to a windmill and gearbox The relation 14 again enables a value of R (which includes the field winding of known K or in order to help fix the design of a new generator in resistance) and K to be chosen for a windmill and gearbox of known K. which case K as well as Rf and Rt are under the control of the designer. Clearly

Since R

✓ - Kwt n 2.4 Ideal performance curves 2 a magnetisation characteristic of the type 4) - Kt f Fig. 2 shows curves of normalised •, V, I, PL, Vw, T, Pw and efficiency

is again required for cubic loading if field q versus speed for a typical 'ideal' system incorporating a shunt generator resistance is to be left unchanged. When K is fixed and q is known, having no - 0.75, Rf a 10 Rt. Gearbox efficiency ng is taken as 0.9. 16. 17.

The assumptions of section 2.3 are made. Superposed on Fig. 2 are four diode drop at low speeds, though for small alternators (say up to 10001.1) dotted lines indicating windmill torque versus shaft speed for two running at frequencies up to say 60 Hz, armature X/Ra is low and little constant windspeeds and two typical types of windmill. The way in error should be involved. which these lines cross the generator torque line indicates that the speed ste..ility of the system at constant wlndspeed will depend on the 2.6 Determination of coefficient K shape of the windmill characteristic. With some 'peaky' characteristics For prediction of system performance, knowledge of the coefficient X

(type 0) the steady-state operating point is not well defined and speed is required. The defining eqn. 13 gives K as: instability would be expected. However with the drooping characteristics of water-pumping type windmills or with characteristics (such as type A)

possessing any sort of plateau around the maximum torque point, speed

stability should be good.

2.5 Generation using a self-excited alternator Hence, ideally: V - K.n The advent of compact rectifiers has been largely responsible for Ē

the almost universal adoption for d.c. power generation of the polyphase It has been assumed that the terminal voltage V is negligibly different

alternator plus rectifier bridge in place of the d.c. generator. The from the open circuit voltage VHL (both measured beyond the rectifier

lower maintenance requirements of alternators are particularly advantageous for the case of an alternator. The coefficient can thus be obtained

in small wind generation schemes and a number of power circuit configura- from a calculated or measured magnetisation curve for the generator.

tions incorporating self-excited alternators are possible. The theory of This is done by using the method of least squares to fit a best

sections 2.lto 2.3 is generally applicable to these systems if allowance is V _ 3 HL K made for the difference between the d.c. voltage beyond the rectifier bridge 11141. f V and the alternator phase voltage V, e.g. for the Fig. 3 a system with a line to the magnetisation curve. The X corresponding to this best star connected, three phase alternator connected to the load via a full line is the required value (which can be obtained with the aid of log log diode bridge, _ 3 T V 1i VP graph paper). Often it is possible to sacrifice accuracy of fitting

over certain parts of the range of magnetisation for the sake of obtain- Assumption 2 of section 2.3 is of course made slightly more approximate ing good fitting and hence good power, matching elsewhere (e.g. in the mid since additional voltage drops now occur across the alternator's armature magnetisation and speed range). In this case, points over an appro- reactance and across the diodes. Commutation delay will also decrease priately restricted range can be fed in to the least squares method. V. Reactance effects will tend to be significant at high speeds, and 18. 19.

3 Experia.ntal measuremnts disconnect the battery when the d.c. load voltage exceeds the battery

Measurements were made on three systems, based in turn on voltage and the other to disconnect the battery from the load resistance.

(a) a 1.5 kW, 12 pole vehicle alternator with rewound armature and field when the battery voltage exceeds the d.c. load voltage. The speed for build-up was reduced by this means to 2000 rev.min connected in series, (b) a 1 kW, 12 pole vehicle alternator 1 (curve (iv) on with unmodified windings and connected in the Fig. 3 configuration, Fig. 4). There waaAortain amount of hysteresis in the power versus

(c) a 5 kW, 6 polo alternator of conventional salient pole construction speed characteristics, presumably due primarily to magnetic hysteresis connected in the Fig. 3 configuration. in the generator rotor particularly for system (b). Self-excitation was maintained during speed reductions for system (b) down to speeds of In all above systems the alternators were driven by a d.c. drive 1777 and 1500 rev.min 1 without and with the battery respectively. motor which simulated the windmill. In order to_achieve still lower build-up speeds, it is clearly Fig. 4 shows experimental curves of per unit shaft power versus per desirable to increase the field ampere-turns per output voltage (for unit speed for each system together with the ideal the shunt generator) or per output current (for the series generator).

To avoid excessive field heating at full load, a special P - K rewound w n . n' derated design would normally be needed, though it is possible that the curve. One per unit power and speed figures for the three systems area large air velocities available foi cooling at full load might enable 1.15 kW, 1500 rev.min 1 1 1.15 kW, 3000 rev.min 11 4.1 kW, 1000 rev.min 1 rewound versions of standard machines to be used without temperature 'respectively. rise limits being exceeded.

It may be observed that in general the shaft power varies with speed Fig. 6 shows a comparison between measured and predicted shaft in a manner which is not too far away from the required cubic law. power for system (a) as a function of speed, the predictions being nada During the tests, it was found that the ability of the generator to build using the approach outlined in section 2.3. The magnetisation curve up its flux from a residual value was in some cases rather poor. The for the system (a) alternator is shown in Fig. 7 together with an problem is of course made more severe by the presence of the permanently ideal connected load resistance and by the significant voltage drops across the V a K rectifier diodes even at quite small currents. Minimum speeds for build- i ill, up for the three systema were 500, 2750 and 500 rev.min 1 respectively. curve fitted over the range 0.7 < If < 3.0 Amp. The value of K, An investigation was made of the effect of using a 12V battery across the found using a measured magnetisation curve and the method of section 2.6,' field of the system (b) alternator to assist build-up. The circuit -1/3 was 0.139 Volts rev.min-1 Amp . The values of load and field layout, shown in Fig. S. includes two blocking diodes, one effectively to 21. resistance ware 21 and 89 0 respectively and the average efficiency n References determined from a number of standard load tests with separate excitation at a number of constant speeds was taken as 0.65. It can be seen that 1 WARNL', D.F., and CALNAN, P.G.t 'Generation of electricity from the agreement between prediction and measurement is fair except (in the wind', IEE Reviews, 1977, 124, (11R), pp.963-985 percentage terms) at speeds below the build-up speed. The maximum 2 JOHNSON, C.C., and SMITH, R.T.: 'Dynamics of wind generators of discrepancy in absolute terms (85 Watts at 700 rev.win 1) is reasonably electric utility networks', IEEE Trans. on Aerospace and Elnctronlc low. Systems, 1976, pp.403-493

3 ALLEN, J., and BIRD, R.A.t 'The prospects for the generation of

4 Conclusions electricity from wind energy in the United Kingdom', Energy Paper No.21, Dept. of Energy, 1977 An inherently self regulated class of resistance-load generation schemes suitable for windmill application has been examined. Measure- 4 JAYADER, P.S.t 'Windmills stage a comeback', IEEE Spectrum, menta show that, subject to certain criteria related to residual voltage Nov. 1976, pp.45-49 level and shape of magnetisation curve, generator input power can be 5 FRERIS, L.L., BOLTON, H., HUEIIRING, I.K., and•NICODEMOU, V.C.t made to vary with speed in a manner which should enable the windmill to 'A low cost wind energy conversion system for heating of domestic operate at near-optimum tip speed ratio over a wide range of wind speeds. premises', International Conference on 'Future Energy Concepts',

London, 30 Jan. - 1.Feb. 1979

S Acknowledgements 6 WALKER, J.G.t 'Utilization of random power with particular reference to small-scale wind power plants', Proc. of U.N. The authors wish to thank Dr. L.L. Freris, Mr. H.J. Prigmore and Conference on Wind Energy, Rome 1962, pp.370-374 Mr. I.K. Duehring of Imperial College and Mr. C. W-W. Pontin of Control

Technology Ltd for useful discussions. The work forms part of an 7 MOHAN, N., and RIA2, M.: 'Wind-driven, capacitor-excited induction

S.R.C. funded project and the authors are grateful to the SRC for its generators for residential electric heating', IEEE PES Winter support. Meeting, New York, NY, 29 Jan. - 3 Feb. 1970

8 Anon: 'Hydraulic drive for aerogonerator', IEE News, April 1978,

No.28, p.3 22.

9 GOLDING, E.H.: 'The generation of electricity by wind power' OPERATION OF SELF-EXCITED GENERATORS FOR WINDMILL APPLICATION (E. a P. Spon Ltd, London,1976), Chapter 3, pp.22-35 Lint of Figura Captions

10 JUUL, J.: 'Design of wind power plants in Denmark',,Proc. of Fig. 1 Typical power coefficient characteristic of a windmill U.N. Conference on Wind Energy, Rome, 1962, pp.229-240

Fig. 2 Normalised characteristics of an ideal self-excited windmill 11 JONN5011, C.L., and WALKER, U.S., 'Three-phase induction motor generator loads cn a variable frequency wind electric generator',

Wind Engineering, 1977, Vol.1, No.4, pp.268-277 Fig. 3 Self-excited alternator scheme with shunt field and d.c.

resistive load 12 LAN, W.C.: 'Novel induction generation scheme for wind power

generation, and tests on thermistor protection of induction Fig. 4 Input power versus speed characteristics : experimental machines', M.Sc. thesis, University of London, Imperial College, results

Elec. Eng. Dept., September 1978 I theoretical windpower Pw

II --X— rewound vehicle alternator 13 DEBO:1TRIDDER, J., VA.NDENPUT, A., MARCELIS, R., GEYSEN, W., III -ci- unmodified vehicle alternator with no battery DE KEUSLER, C., and FIERENS, E., 'The combination asynchronous Iv -®----unmodified vehicle alternator with battery generator-vertical axis wind turbine for small power applications', proc. V —p— salient pole alternator International Conference on Electrical Machines, Brussels,

September 1978 •Fig. 5 Circuit with auxiliary battery for initiating self-excitation

14 GOLDING, E.W.: 'The generation of electricity by wind power' Fig. 6 Power/speed characteristics of system with a series-excited (E.a F. Spon Ltd. London, 1976), Chapter 14, pp.226-245 alternator : comparison between predictions and measurements.

output power from windmill Pw - Kn.ns 15 DEBONTRIDDER, J.: 'Automatic field regulation for the cenhination Input power to alternator Darrieus'rotcr/generator', Proc. International Conference on power to resistive load Electrical Machines, Paper G5/4, Brussels, September 1978 efficiency of electrical system

Fig. 7 Magnetisation characteristic of alternator with fitted curve

experimental magnetisation curve • V fitted curve of the form: NL/nNL - K ' P

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PERMANENT MACE? ALTERNATORS FOR StelLL WIND SYSTEMS Basic Principles

H.R. Bolton and V.C. Nicodemou Power versus speed relations. A simplified equivalent circuit for an Department of Electrical Engineering alternator or d.c. generator is shown in fig. 1. A d.c.current If in the Imperial College of Science and Technology, London 'field' winding, (or a permanent magnet) sets up a field flux 0. When relative motion exists between the armature conductors and the field flux, an e.m.f. is produced. For a given generator. E a ki.0.W Abstract where E is the e.m.f. Induced in the armature winding, ki is a design con- The paper examines some of the basic technical factors relating to stant and w is the shaft speed in radians/sec. If the armature is connec- electrical generating systems for small wind turbines. The factors for ted to some load circuit, the voltage V at the armature terminals will and against the use of permanent magnet alternators are listed. Design differ from E due to the voltage drop I.Z across the armature impedance. and test data for some recently-developed P.M. alternators is presented, If the machine is a d.c. generator Z is merely the armature resistance Ra together with comeents and information about control schemes. Some recent and V a E - I.Ra . For small alternators (< 200W) working at moderate work on annual energy yield assessment is outlined. Preliminary results frequencies, Z is predominantly resistive. An assumption of Z a Ra will seem to show that although the use of a P.M. alternator increases energy be made for simplicity in what follows. If the generator is connected to yield by only 5-15% compared with that produced by a carefully-chosen wound a fixed load resistance RL, the power delivered to the load (neglecting field machine, and hence that correct choice of site, turbine, turbine losses in the output controller, if any) is: operating made, etc. are likely to be more crucial in maximising energy _ z R yield per total capital cost than the use of a P.M. alternator per se, PL ' V /RL RL (I Ra +RL ) other factors such as the P.M. machine's extra reliability and virtually zero maintenance needs, may often be deciding factors. The load on the wind turbine is Pin m E2/(Ra + RL) (neglecting iron and mechanical losses). If the machine is operated with fixed flux 0, as is a normally the case with P.M. generators, E k2w and both PL and in vary as Introduction W. At high speeds I must normally be limited, due to winding heating problems, to a limiting value Imax and and PL then vary linearly with The task of utilising alternative energy sources for electric power produc- in w. Output frequency f in the case of an alternator is given by the well- tion poses many novel problems, not least in the field of the design of the known relation f - l/4n . w . p where p is the number of field poles. electrical generating plant itself. In the case of wind power, the main problems stem from the variability of the power level over a wide range and If the generator is connected (via a rectifier in the case of an alternator) the high rates of change of power that occur, the fairly low ratio of mean to a battery load, the instantaneous output current i a re -(Vd + Vb)] / Ra power/rated power in comparison with most conventional generating systems, where a is the instantaneous e.m.f. and Vd and Vb aro the rectifier drop shaft speeds which though higher than those associated with wave power and battery voltage respectively. Clearly if the peak value Ē of e is devices cru still rather low especially for large wind power units, and the less than Vd+Vb, the rectifier remains blocked and i - 0. For a d.c. constraints on weight, size and type of enclosure posed by the frequent generator I is given by I a [E- (Vd+Vb)]/Ra (for I > 0). For a resis- need to locate the generator on the tower head. tance-dominated alternator it can bo shown that The choice of generator and electrical system configuration depends greatly 2

on the plant size, whether grid connection is intended and if not, what wan [coocos 112 I an Ra . ai - ( )1 type of electrical load is to be used. With small wind plants, a choice from a great variety of electric generator and system configurations must where ai a sin-I(Vb + Vd)/Ē and a2 a tt - a be made and table I lists a number of generator types which have been used i. The output power is Vb.Iman or uu99•uled for use with rnuul) wind plants. The tremendous Imvrnvenients and curves showing the variation of output powers for resistive and buttery loads are shown in fl). 2(a) sup.rletud on +. typical family of in permanent magnet materials over the last thirty years or so have meant turbine-output-power Pw'curves. It that steady improvements in the performance and cost of newly designed P.M. can be seen that with a resistive load, the generator will ptevcnt start up at low wind speeds, will tend to cause machines have occurred and table 2 lists a selection of commercially early stalling for decreasing wind speeds and that the windmill will tend available small windmill systems using P.M. alternators. to operate beyond Stn Cpmax point at high wind speeds. Since the genera- tor's power capability only increases as w2 A recent paper (11 described a current S.R.C.-supported project at Imperial at best, it is incapable of ab- sorbing the converted wind power (proportional to C College in which the electrical aspects of a small wind power system for p.w2) at high wind speeds. The starting situation is improved with battery loads space and water heating were examined. This paper presents test data for but opera- tion near some of the generators developed within the project and sketches, in some- Cpmax still occurs over a narrow range of wind speeds only. Fig. 2(b) shows the situation when the Cp versus A characteristic of the what simplified terms, the technical factors associated with the selection, turbine is very peaky. Clearly stalling can take place even after sudden operation and assessment of electrical systems for small wind plants increases in wind speed to levels which could give satisfactory steady supplying battery and resistance loads where close control of frequency and state operation. voltage are not required. One could opt to make do with this state of affairs and accept the reduced energy yield that would results with battery loads the reduction might be fairly small. However in most cases, particularly with resistance loads, mark:space ratio is varied to vary the rear, power. The high/low method is it is worth improving things by adding some form of control. used in the field circuits of most car d.c. generator systems. Method (c) can to some extent be regarded as a speeded up version of bang-bang or on/ Methods of control. At high wind speeds thorn are only three options; off methods. (i)use a large generator so that the maximum power capability of the e) other methods. For the sake of completeness, a number of other methods windmill at the maximum relevant wind speed lies within that of the should be mentioned. They involve the use of (i) fixed or controllable generator . reactances placed in the output circuit (ii) flux bucking and boosting (ii) allow the operation beyond the Come point even for the maximum wind windings on a P.H. machine's field poles, fed via slip rings (iii) toroidal speed. bias coils wound around the core of a P.M. alternator's stator fed with (iii)use aerodynamic means to redeem the converted wind power Pw. d.c. and used to saturate the stator core. Fig. 3(g) shows a typi- Option (i) may be costly and may lower energy yield due to increased mecha- cal circuit of the c(i) type. At low speeds and frequencies the shunt L nical losses. Option (ii) can be satisfactory with sub 100W and other acts as a short circuit and reduces output power. Fig. 5 shows output small systems where blade stresses even on run-away with high winds are characteristics for field-controlled, load-resistance-controlled and con- within reasonable limits, and can be adopted on larger systems where shut trolled rectifier systems. down by orientation out of the wind or the use of mechanical shaft brakes is possible. Cption (iii) is frequently adapted and a number of ways of minirdsing the added complexity and cost have b.+en found. Permanent Magnet Generators

At low wind speeds, the task is generally to reduce generator output (a) to Qualitative comparison. The pros and cons of P.M. generator usage are aid starting (b) to match the w2 ideal turbine characteristic. A number indicated in table 3. of methods are shown in fig. 3: Off-the-shelf machines. The opportunities for using 'as-purchased' or a) field current control. If the field flux is varied as Of k3,1 , out- modified versions cf existing P.M. machines are given in table 4. D.c. put volts and current into a fixed resistance load vary as w42 and power P.M. synchronous and induction motors can generally be run without modifi- as w1 . The method can also be applied to battery charging systems. The cation as generators, but often the opportunity arises of using a machine method is of course normally confined to wound-field machines. at rated speed or voltage conditions which differ from those on the name- b) load control. If the load re:durance R1, ie varied as R1, - k5/w - Re plate. In such cases the following ground rules apply: (i.e. R1, reducing as (a increases) then Pe and P in again vary as w° . This 1. E.m.f. (for fixed field flux) reduces proportionately.with speed. m:thea is often implemented by sectionalising the load and switching Hence if operated at a lower speed than rated, output voltage is reduced sections in and out using contactors to give a stepped-approximation to according to: V = Er . le/we - I.Ra (reactance etc. neglected)." At the required RL versus w characteristic. reasonably high speeds, where I.R4 is small, V varies approximately as c) regulator circuit in the output. D.c. to d.c. chopper circuits for Vr .w/we, so that if the load is adjusted to maintain current at a constant d.c. systems and thyristor regulators for a.c. systems are now widely used (say the rated) value, then output power Pt varies as: PL n Pr.w/wr. If for power control in industry. They can also be used for small generator therefore a machine is used at half speed, say, only half the output power control particularly when field control is difficult. Costs and losses can be expected even with a load adjusted to draw rated current. If the need not be high. The chief difficulty at present is that suitable machine is operated at too low speeds, I.Ra becomes significant. V sinks circuits are not available off-the-shelf. The a.c. regulators fall into badly with w and can. even disappear altogether particularly if one attempts two groups: (i) a.c. to a.c. phase-angle-controlled regulators to maintain I. Lower output currents than rated are inevitable and the (ii) a.c. to d.c. controlled rectifiers. ' machine rating decreases as 0a/w„)2. Their detailed behaviour is complex but in both, the thyristor switching 2. Output voltage can be raised by rewinding the armature with coils elements control the level of. power throughput by their ability to behave having more turns of thinner wire. If the new and old values of (wire as cpcn circuits until triggered by a pulse from an external source. The cross sectional area %: number of turns) are made equal, delay period a/2nf between the start of each period of normal conduction the rewound Lachine will operate aluust identically to the old except that V will be increased and the instant of triggering controls the mean throughput power. In the by the ratio: new turns per coil/old turns per coil and the output current case of a three phase controlled bridge rectifier (fig. 3(01, the through- correspondingly reduced. put power PL with a resistance load varies very approximately as: PL - PL(1 - a/u) where a is the delay angle and Pt is the throughput power 3. Rated output versus size is governed by the standard relation (for when a is zero and the bridge behaves as a diode rectifier. Hence if operatiOnTatt very low speeds): Pr a en/2. 13.3)D21.41„ where D and J are the Pe a k4ws is required and PL a k4.w2, then a must be controlled as mean values of field flux density and rated armature ampere-conductors per a a 5(1 -ma/Un) where we is the shaft speed at rated power. The thyristors metre of periphery and D and L are the rotor diameter and length (in metres) are 'phased back' for w < mr . Test results on a generator system using respectively. In practice the factor (s/2. D.J) varies between fairly such a regulator are included later. narrow limits, from about 0.003 for a small (sOW), low flux density machine to 0'02 for high flux density machines of several KW. The relation gives d) on/off or 'high/low' switching. Torque per inertia ratios in wind a guide to the D2Leirprodsct needed in a machine to obtain a given Pr, and plants are usually low enough to allow the use of two state load or field the influence of the relation on the feasibility of using 'direct drive' current switching systems using contactors, relays or thyristors. The generators for wind turbines is discussed later.

Losses and efficiency. It is important to be able to assess the extent to current is reduced. The aerated machine is large for its nominal maximum which the absence of field losses improves efficiency and energy yield of output power, as stated previously, but the improvement in energy yield may P.M. machines. The way in which the principal losses vary with speed in more than compensate. It is most important to note that derating may well 'equivalent' wound-field and P.M. generators when output is made to vary as lead to appreciable increases in a3 if carried ton far, particularly in w2 is shown in table 5. In drawing up this table it was assumed that both machines possessing significant brush and bearing-friction losses (which machines feed constant resistance loads and that the wound-field machine's reduce only as weer not as (a+/wr)n), so the derating route to high effi- field and the P.B. m.cmL•irmo's output are controlled by loss-free controllers. • ciency working is not invariably a good one to take. PC, Pf and PNL refer to the armature I2Ra winding loss, field 1201f winding loss and 'no-load' (iron plus mechanical) losses respectively. If the New developments. Table 6 gives details of four, recently developed ex- ratios at rate: apccd wr between the load power PL and each of the losses perimental P.M. alternators designed and built as part of, or in association with the S.R.C. project mentioned in the introduction. One of the reasons are given by: PL s Pw : Pf : PNL a 1 : al t 02 : a3 for undertaking the development was the virtual absence of off-the-shelf P.M. alternators of reaconabl.o cost, power output and rated speed. The then the total loss at any other speed (assuming PL rather than Pin varying experimental machines were all designed with three-phase windings to mini- mice torque pulsations and their rated powers ranged from 50%: to 0KW. The as w2) is approximately:. al W2 + a2 w + a3 w3h for the wound field machine rated speeds of the Mark I, '50W' and Rutherford alternators were chosen to enable than to operate as 'direct-drive' units (i.e. without step up trans- missions) with wind turbines of reasonably high tip. speed ratio. Output and a1 wt + a3 sash for the P.M. machine, control by thyristor controller or load resistance control was intended. The Mark II machine can be used as a direct drive 1IInJ machine or geared up where w = w/wr. The corresponding efficiencies nor and qpm are hence: (to 1600 r.p.m. nominal) as a 6KW machine. Test results have generally been encouraging (see below) and the developments have been valuable: (a) in verifying prediction methods and (b) assessing the viability of P.M. 1 and machines of reasonable power rating employing some of the more recently 1 + a1 + a2/11 + a3/w'h 1 + al + a3/a/w'3/ 2 developed P.M. materials.

respectively. Curves of n are shown in fig. 6 for machines having The pros and cons of direct drive are summarised in table 7. From what a ■ 0.2, a22 a 0.075 and a33 a 0'075 - typical figures for small machines. has been stated previously, it may be deduced that choice of a low rated Tiih s comparison allown for t e fact that, for cubic loading, field amps in speed (In comparison to 'standard' speeds for electrical plant: 1000 to 3000 the wound-field machine are turned down at speeds below rated, and hence r.p.m.) leads to a low power per generator D2L (i.e. size) and for very low that field winding losses reduce considerably when wind epecde are low. speeds can even lead to high u1 values. Wind turbine speeds fall with However it can be seen that the P.M. machine is still left with an effi- increasing power rating,and direct-drive hence involves an increasing D2L ciency advantage throunhout the speed range. • One should perhaps add in per output the larger the plant. Low-speed generator designers tend to fairness to the wound-field typo of machine that: minizdce the cost, weight and size penalties of high D7L designs by the a)in practice, 02 is low in large machines (a2 actually tends to fall as adoption of high D/L factors (i.e. high rotor aspect ratios). Water- rated KW per pole increases) so the P.M. machine's advantage is appreciable turi,ine-driven and cycle 'dynohub' generators for example usually have a only for machines whose rated i,owers'are less than 1 KW per pole or so. large rotor diameter to length aspect ratio. The rationale behind this is that although little can be done about total rotor and .stator volume levels, b) the assumption of zero controller loss is of course optimistic. The (rotor 'volume e w/4. 02L), the electrically active parts (windings, lamina- loss in an output controller of the thyristorised type used with a P.M. tions etc.) are essentially annular. The radial thicknesses of the stator machine will generally be a little greater than the loss in a field con- and rotor annuli remain roughly constant with D if the number of poles is troller of a wound-field machine. allowed to increase with D and hence the weight and cost of the active Comparative test data is given later. Clearly any machine used for wind parts increases only au D.L, not D2L. llulyht and coat Lier output increase power conversion should possess, if possible, low 01, a2 and a3 values. an DL.mr/D2L par a 1/D.wr. One can theoretically compensate for an ter, Low a2 and 03 (i.e. low per unit field and no-load loss figures at rated however low, by increasing D. In practice D is limited by irachenicall power and speed) are particularly important since the field, mechanical factors (cost and weight of support structures stiff enough to minimise and iron losses tend to increase in significance at low Lr. Many coin= ' variations in stator to rotor clearance, etc.) The highest D/L ratios mercially-available ma.:pines possess fairly high a values since this leads ever used were probably in early steam-engine driven generators and in the to low first cost and high power to weight, and it is perhaps true to say 'ring' generators of Honnef in the 1930s who located the rotor on the that the prospective increase in energy yield to be had by avoiding the blades of the wind turbine and used D values between 0.3 and 1'0 times the use of such machines in wind power systems may often be greater than the turbine diameter. The 8KW Rutherford P.H. alternator was designed for a increase resulting just from the elimination of field winding losses by rated speed of 120 r.p.m. and a D/L of 14:1 - probably fairly close to the the adoption of P.M. machines. A final. point is that for machines with upper practical limit. The 50W machine was given a much lower D/L since low mechanical losses, derating can often be used as a way of obtaining its rated speed is much higher. The overall economics of direct drive decreased a values. Per unit iron and fan losncs, and hence 03, often depend greatly on the cost, reliability, maintenance needs and efficiency fall if rated speed is reduced. as usually decreases if the nominal of the step-up transmission system that would be used with the comparison . rated field current is reduced; al reduces if the nominal rated armature standard-speed generator, and one cannot generalise here, since these factors vary eo much from system to system. The Mark I and the Rutherford machinca ueo a fairly costly but very high if the Ljungstrom/Weibull performanee P.M. material-polymer bonded rare earth/cobalt and this gives wind speed duration functions the alternators (m/2.B.J) factors (0.010 and 0.016 respectively) which 3 2 (V/vl compare very well with standard machines. Size and weight are low for 0 N) a the rated power and speed but cost per rated KW is high enough to make the is accepted as a true representation of the proportion m of the total hours economic case for their use a esarghm1 one unless Fairly high costs can be in a year for which the wind speed ata given site is less than V (and the mean allotted to the weight, bulk, losses and maintenance of the step-up trans- wind speedmV),then the contribution to the mean wind power production due mission that would otherwise be needed. Ferrite magnets are extremely to wind speedo between VI and V2, donned by cheap and though their remanent flus density in fairly low, they possess V2 a high coercivity and a low relative permeability - both useful propertie-. ° t2 0S J n(V).V3 .d4'(V) in machine applications. The SOW aad Mark II machines thus have lower P1,2 VI (11/2.11.3) factors (0.003 and 0.0015 respectively) and are bulkier for their is given by: V rated power and speed than the rare earth machtnc•s. However they are ex- 2 +B BPS f 2 n( -aV6 pected to be reasonably competitive with ether, commercially available F-% - v) .v a .dV generators in terms of cost and weight per KW. (tr/2.11.J) factors for VI vehicle alternators are 0.005 to 0.007 and for typical small stand-by where a o (log 2) /i713 : p is the density of the air, S is the effective alternators arc 0'005 to 0'02 and those figures 1..dicate that the weight wind turbine swept area, n is the efficiency of the wind energy converter and bulk of modern P.M. machines compare reasonably well with those of and B is a constant between 1.0 and 2.2 depending on the type of site. wound field machines at similar operating speeds. Sarrē used this relation to investigate the effects on energy yield of different rated wind speed/mean wind speed ratios, operating policies, etc. Both the 50W and the Mark II machine use an 'external rotor' layout in However it can also be used to compare the energy yields produced by dif- which the rotor, of annular shape, revolves around the outside of the ferent plants at the sane site. The overall efficiency 1) at a given wind stator. This arrangement enables a larger rotor airgap diameter D to be. speed is given by: used for a given overall diameter, clue to the radial thinness of the field 11(V) - magneto, and this increases output per overall volume and weight. In the Cp(i) •nGB' no.nc 5011 cathine, the rotor completely encloses the stator and the turbine where nGH, nG and n are the efficiencies of the gearbox, generator and blades can be attached directly to the rotor outer periphery. power controller respectively. Gearbox losses may be approximated by: + Tf.em Measured efficiency curves are shown in fig. 7. The curves are plotted PP CH kmesh • PW to a base of w and the input power is taken to vary as 60. This type of plot indicates in a dramatic way any efficiency fall off at low power since where k is the ratio: 'mash loss' at rated throughput pōwer/rated e.g. at 1/3 rated speed, input power is only 1/27 of rated. The efficiency throughput power, Tf is the "loss torque" (as;;umcd constant) caused by of the 50W machine is appreciably below that of the others but this is in- bearings, seals etc., and P4 is the shaft power from the windmill. The evitable with any small machine in the 0-1000 r.p.m. speed range and its generator losses are taken from measurements or are calculated for speci- perforcet:co may be regarded as 'good for its size'. no loads for all the fied control and load conditionn at each speed by ramming calculates] lenuan • testa consisted of three phase r:.eestats, controlled no as to maintain The annual mean power in the load is then calculated by numerical integra- tion of the FI, = Pr (w/ma rls. Per unit togging torques for tho Rutherford, 50W and Mark II 172,2 relation over tho appropriate range of wind speeds. machines were very low. Photographs of the Rutherford and Mark II machines Difficulties arise in determining start-up speeds because the presence of are chose in figs.' 8 and 9. The effect on measured efficiency (defined as postulated friction torques in the gearbox and generator cause the load power/shaft power so as to allow for converter losseu) of the addition 'starting' wind speed to be higher than the 'stopping' wind speed. In the of an output con: teller of the tlnyriutoriscd bridge rectifier type to the calculations performed so far, the 'stopping' wind speed is chosen for the Mark II alternator is shown in fig. 10. The curves relate to operation 'cut-in' condition and it is not thought that this should lead to much over-estimation of annual yield. with a constant resistance load (d.c.) and the way in which the firing anjle is changes with speed so. as to maintain an input power proportional to Figs. 11 and 12 relate 2.2KW, direct-drive system with a w' i:. steen. l:,':u:urvd vffita.'•y .•nrv.•n aro alae ;:hewn for a typical to a three bladed, ar elnm.l plat.:, her l son to t-axils to thine of 3.14 rm hila. t; ata r, mall wrurrl field lorry alternator (0 to ISOU r.p.m. speed range) and for a typird ticie, of 7.24 m/s capacitor-excited 3 phase, 8 pole induction generator (0 to 750 r.p.m. V = and B = 2.0 were assumed and the ratios Vrated/V and Vfurl/v were 1'5 and 2 respectively. speed range with capacitance varied to keep power in a three phase resis- It was also assumed that the system was controlled tive load proportional to speeds ). to give constant tip-speed-ratio working (C0 = 0'35) for V < Vr and to give constant power working for V > Vr. Fig. 11 shows the contri- bution to the total annual mean. power made by winds of each speed (actually Energy Yield Assessment of each 0.64 m/s speed band). (i) passing through and (ii) converted by the turbine. Fig. 12 shows similar curves of output electrical power for each 4- The variability of wind power with time etc. makes it impossible to reach of the electrical systems detailed in fig. 10. Iisticoted annual KWh figures (annual KWh - annual mean KW x 8700) have been marked in and indi- any sort of quantitative idea of the importance of generator efficiency mld and itn variation with speed and imwnr from just mho raw efficiency versus cate the gains to be had from high efficiency mechanical to electric con- version. Gearbox lonson arc neglected for the geared lorry alternator and • speed curves. Tn attempt has ).een nv,de to forran]ate an cnerey yield asseese nt method to oturcomo thiu uuag. Sarni (2) recently showed that induction generator systems. Table 0 shows estimates of annual KWh for a geared system for two alter- native alternators A and 0 and two alternative furling speeds VP1 and vf2 TABLE 1 Generator types (11.2 and 15.2 m/s►. The wind turbine in this case was a 3 bladed, 5.4 m did.,horI-ontdu axis type with a maximum C1, of 0.35 at l 4.1 and a rated r.p.m. of 160. The gearbox kocsl, was 0.05 and the loss torque 2.5 Nm. a, Approximate data for small machines Generator A was a 6.21:11, 1600 r.p.m. P.N. type with a regulated resistive Type of .4 load. ., Generator 0 was a CKW, 1500 r.p.m. wound field type with a field Type sliding Control eo regulator and fixed resistive load. Both regulators were assumed loss contacts Cost Efficiency at free. Constant a operation was assumed up to the rated wind speed of ti wt. full load a /KW P.u. 11.2 m/s and constant power opecath.a assumed for wind speeds between 11.2 ,n p.u. and shut down at 15.2 m/a for the high-furling-speed system. A V of 7.25 0-IKW 1-10KW and a 6 of 2.2 were taken as site parameters. D.c. 'dynamo' i) with wound Conclusions field commutator d.c.field ✓ 5 2 80 90 11► with permanent 2 90 1. Output per size and weight for nodern P.M. generators can be competi- magnets commutator various / 4 93 tive with those for wound field generators, if comparisons are made at equal speeds. Alternator 2. P.M. generators are generally somewhat more efficient than wound field i) with wound slip rings d.c.field / 3 1.3 80 90 generators but the margin with respect to the more efficient examples field of the latter. type of machine is fairl•, small. with permanent 1i) magnets none various / 3 1.3 '90 93 3. Output control circuits with P.M. generators generally have to handle an appreciable fraction of the rated output and may be more costly than Induction none/slip various / 1/1.5 1 85 90 the field control circuits of wound field generators. However P.M. machine rings generators need no field circuit or slip rings and are free from 'build Field modulated - up' and 'loss of field' problems. alternator slip rings a.c.field x - - - 4. An energy yield a::sessIa:nL r..ethod has been evolved to aid comparisons Roesel betue.m the 1;Aemrn ic.' of different wind energy coavoalou !I/steno. generator none a.c.field x 5? 1.5? - - Generator capital costs Usually form only a small part of the total cost of a system. If minimum capital cost per rated KW is the primary Commutator a.c. commutator a.c.field / 5? 1'3? - - criteria for equipment soleetlon, low cant generators may be chorion, generator even though they may convert energy relatively inefficiently. Where Inductor mirin:Md total cost per I:Wh in the prisrry criterion, the use of genera- generator none d.c.field x 5? 1.8? - - tors of the highest efficiency and reliability is normally justified and permanent magnet generators have a useful. role to play in small wind plants feeding isolated loads and there is no requirement for close frequency or volts control.

TABLE 2 Commercially available systems using P.M. generators References I. ereria, L.L., Bolton, H., Il ,hrtnq, I.K. and Nicodonou, V.C.: 'A low Rated generator Rated wind Manufacturer Turbine speed m/s cost wind energy conversion system for heating of domestic premises', KW r.p.m. Proc. of I.E.E.Conf.on Future Energy Concepts, January 1979, London. 7 2. SarrŌ, P.E.: 'Year round efficiency of a wind turbine as affected by Aerowatt H.A. up to 4.5 600? choice and rating of power take-off system', University of Exeter, 7 11 Department of Chemical Engineering report, WEP 4, December 1977. Dunlite/Pye H.A. 3 Elektro N.A. up to 5 800? 10 Acknowledgements .• Zephyr (U.S.) K.A. up to 15 300 - The authors wish to thank the S.R.C. for financial support and a large •V) nurber of individuals at Imperial College, Rutherford Laboratory, and Trimble H.A. 5 7 10 • elsewhere for their help, suggestions and opportunities for discussion. A.W.T. (U.S.) H.A. up to 3 4500 11

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0.6 --- — — 0 6

0 1 2 i z 3 a3 — t - 0.3 a) Field contra/ b) Lona res/stanae I Ip IS n/~ec R leacl-t 1O Ia R 10eat , Or baiter" vo/rale oink,/ 1 I .~. 0 30 60 0 J.20 r + s /sec O a F16-5 TYPICAL ALTERNATOR Powell r. SPEED CVRVES • BatFery 104 Shaft 110Cg ad►tery l oād SALF/' speed, FOR DIFFERP.VT MOPA', OF ANTRO/ (a) ro (b) a PG 4. POWER v. SPEED GVRVES FOR TOR616JE AND ALTp,'ATMR P I r I "`"jc* cud 1i "1~--(~i I I

a F1thL cor.Fral e(3i) 0v1-pvh rc vlahar (conhrllleaE reckFie r) r ---. r---1 I~ I e' 4—L7-11 Fl63., 1M9rTIIDDs 11 I I I "1 1 • i „ oft nriTROL L _ L __ . I a-120' b Load control e lleae?unce cent-rot r - -•--t r - - --~ I I 1 — ~ L- 1 I © 2 3 co O 02 0•4 0.6 OS 10 I Per voit wed se e..) rhy risfir ovl-pvt rc.1v/afor wll-4 f ixed boa F/6-. 6 EFFIPIv6Y tONP.IR/SON cti) Ov%ll+h rc9vl4F1r (a.c.) 3 !eaci'yuicc C0Hlml vs1.,3 WITH GVd/G/ LOAD/A/G- 1/ shv+lh tadvclers. TABLE 3 Comparison between wound field and P.M. alternators TABLE 5 Operation at variable speed and cubic loading

ADVANTAGES DISADVANTAGES W.F. machine P.M. machine Somewhat better efficiency. Smaller choice of already- 0 a.T z const. . No brushes, etc. .. almost no manufactured machines. maintenance and longer M.T.B.F. Normally not possible to E b.w'k f W control field. Always 'builds up'. V c.4.13/2 C.04* No field supply1 or control Control circuit, if required, normally has to handle output circuit required :. fewer slip I c.W*/RL c.&/RL a,b,c etc. are constants rings and wires on tower (B.A.). power. Armature winding faults (c2/RL)141 (C=/RL1.0 •r.m.s. load voltage assumed No risk of loss of field'. 1'load rather more troublesome. to be controlled by loss- PW - I'Ra cRawi cRawl less regulator in the output

Pf - If Rf d.W 0

PNL - kw$ e.012 e.w

TABLE 4 Commercially produced P.H. machines usable as wind generators TABLE 6 Data for .P.M. alternators Typical data Overall Rotor. Type of P.M. machine Rated: Rated speed size mm size mm No. Rated power Efficiency Weight Cost* r.p.m. at full power kg C of r.p.m. Dia. Lgth. Dia. Lgth. poles A) D.C. motors KW w•• Low voltage car or hcdgetrimmer motor 10-60 W 2-4000 40-65 Mark I 2.3 300 410 155 265 54 48 670 16 Servo motor 0-2 KW 0-4000 40-85 geared 6 1500 330 230 230 80 60 350 12 Disc servo motor 0-2 KW 2-4000 40-65 Mark II Philips washing ungeared 1.8 600 330 230 230 80 60 350 12 machine motor 75 W 000 z 60 Rutherford 120 • B) Alternators 8 930 265 780 56 220 2200 48

Exciter type (e.g.Newton- 50 watt 50 800 81 140 Pceby1 l;.:grmlmr 'NObrush.) 0„12 KW 3000 ? ' 57 81 3 30 2 Motor cycle alternator 100 W 6000 20-70 •Estimated 1978 workshop cost for small quantities, including labour. Dynohub cycle alternator 5-15 W 300 40? *• Volts and amps at rated speed levels set by turns per coil on winding. C) Machines rebuilt with Rated power figures assume 3 phase resistive load. Power figures would ferrite P.M. rotors be increased with capacitive load, decreased by about 12% with a Car alternator 140 W 1500 50? rectifier/resistance load and would decrease for inductive loads. Voltage droop from zero to rated load (at constant rated speed) is ',h.p. induction motor 76 W 1500 70? about 30-40%. TABLE 7 Use of direct drive generators -Power Ivied F1GS .i 1 AuP 12. ANNVAL MS'AN In Power frrm -- pew as FROM 0.64 r>/S ADVANTAGES DISADVANTAGES rvebin 57.5/ INC4EM°1/T5 OF w/ND VELOL/Ty, Meeip rwer 4Q•5 NN4 No step up transmission required. generator s✓sMt Lower speed. '300 Hence: Hence: Neat mechanical layout: no lubrica- Standard generator is derated, or tion or belt breakage problems; special generator required; I 200 cost, weight and bulk of step-up generator power/weight and power/ transmission avoided; no trans- cost is reduced. mission losses, .. higher K%h p.a. 00 >/aIC P.wer 0 4 10 v,IZ /4 V1 iG Eff;eienc4 Windt/180d re/3 0 9 0'ess P~rer 90 10 free: 1 vrbige 3 15 - (ii)MA I1, 4.c. rcif:Hic .12.3 8 u. (ii:) 11.4 0 MA If, the rif i'rr 0.2 0.4 0•i 0.8 1.0 10.2 70 br.(fe ~.c. 0)MkR P.M.AIrr.,0.c.res;#1.4 se rettsri/e ie.l Mk If PM. Aire, rl n>hr 00 (iv)fri vcki„ jenF, 60 Lri(9e plus cc.c•risisterJ121. verisble L Alvi (ili)LerrJ a1F- , a..c. resiSI446e revolie IOu. 50 Pr (Kw) Reret rt.N. 1044. (v)(errl1 Ov) Indvcken len; v4riable L ,lvs reliisll✓e 104C (i) I'lArk X .2 3 300 uay, reslihtlte las! 40 (ii, Nark lī 16 .O ! SOO ) SO U.S 600 ) FI& 10 EPPiciLNGY :! 30 t 5,141-.P, ED CiI?VE5 wir/I Ohl RV1helfOr' 1.0 120 CV$IG' L0401N6- 0 (;y) 50 wait 0.072 1000

10 _ /D / /4 yr /S Nlnl Spred n,/s • 0 02 0 4 °-6 0S 10 w%wr. TABLE 8 Annual energy yields for two systems F16:7 MEASURED EfFlei i/cY CVRVES FOR FkPT4 Wind speeds Annual mean powers* into: Annual ALTERA/ATOR5 WITH A.L. RES/STivF .COADSoc (Z) Gear Iv,. Alternator output ratio •m• cut in furling turbine** gearbox generator load Mh

3.2 11.2 10.1 2.51 0.08 0.76 0.60 11.6 A 3.2 15.2 10.1 4.87 1.0 0.87 0-78 13.3

4.1 11.2 9.4 2-51 0.9 0-73 0-61 10.4 B .1 4.1 15-2 9-4 4.87 1.0 0-81 0.68 11.8

* Per unit figures, where 1 p.u. - 1.95 KW F/4. S RvTHFRFORD' ALTERiATOR F/F. 9 'MARY re /1hrr'RNAraQ ** Annual mean power in wind for operating wind conditions only. (Total annual mean power in wind o 5.85 p.u.)