f* 3 ATkLL- -- A 31

LAPPEENRANNAN TEKNILLINEN KORKEAKOULU Energiatekniikan osasto

LAPPEENRANTA UNIVERSITY OF TECHNOLOGY Department of Energy Technology LTKK

RESEARCH REPORT EN A-33

DESIGN OF A SWITCHED RELUCTANCE GENERATOR

Thomas Heese Juha Pyrhonen

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FOREIGN SALES PROHIBITED

1996

ISBN 951-764-077-3 H ISSN 0785-823X DISTRIBUTION RESTRICTED TO U S. ONLY '» DISCLAIMER

Portions of this document may be illegible electronic image products. Images are produced from the best available original document. ABSTRACT LAPPEENRANTA UNIVERSITY OF TECHNOLOGY

Department of Energy Technology Section of Electric Power Engineering

Thomas Heese, researcher Juha Pyrhonen, associate professor, doctor of technology DESIGN OF A SWITCHED RELUCTANCE GENERATOR

LUT, Department of Energy Technology, September 1996, 105 pages, 61 pictures, 10 tables, 1 appendix

Research Report EN A-33

ISBN 951-764-077-3 ISSN 0785-823X UDK: 621.313

Key Words: Electrical Machines, Switched Reluctance Machines, Generators

This paper presents the design of a low voltage switched reluctance generator for variable speed applications showing the design of its construction and commutation unit. For the realisation of the control system the control strategy is presented. The principle and the theory of switched reluctance generators are described in this context. Also an overview of existing generator technology for these applications is given.

The results gained suggest that switched reluctance machines can also advantageously be used as generators if the generating operation is considered within the design process. Compared with the existing technology a higher output power and efficiency is reached over the whole speed range.

Lappeenranta, September 1996

Thomas Heese, Juha Pyrhonen

J 2

Contents

Preface ...... 1 Contents ...... 2 List of Symbols ...... 4 Tiivistelma ...... 9 1 Introduction ...... 10 2 Generators for Variable Speed Applications ...... 12 2.1 DC Generator ...... 13 2.2 Alternator ...... 15 2.3 Weak Spots of Existing Technology ...... 18 2.4 Supposed Improvements and Advantages of Switched Reluctance Technology21 3 Principle and Theory of Switched Reluctance Generators ...... 24 3.1 Construction ...... 24 3.1.1 Basic Characteristics ...... 25 3.1.2 Envelope and Internal Dimensions ...... 27 3.1.3 Pole Geometry ...... 30 3.1.4 Windings ...... 32 3.2 Working Principle...... 32 3.2.1 Rotor Position Dependency...... 33 3.2.2 Torque and Currents...... 37 3.2.3 Mathematical Description ...... 39 3.2.4 Energy Conversion ...... 41 3.3 Commutation Unit...... !...... 46 3.3.1 Classic Converter ...... 47 3.3.2 (»+l)-switch converter ...... :...... 48 3.3.3 Boost and Buck Converter ...... 49 3.3.4 Bifilar Winding Converter ...... 51 3.3.5 Other Converter Topologies ...... 52 3.4 Dynamic Operation ...... 52 3.4.1 Single-Pulse Operation ...... 53 3.4.2 Chopping ...... 55 3.5 Control System...... 55 3.5.1 Structure...... 56 3.5.2 Control Modes and Strategy ...... 56 3.5.3 Sensorless Control ...... 58 Contents 3

4 Generator Design ...... 59 4.1 Construction ...... 60 4.1.1 Basic Characteristics ...... 62 4.1.2 Envelope and Internal Dimensions ...... 63 4.1.3 Pole Size and Geometry ...... 66 4.1.4 Winding ...... 68 4.1.5 Further Estimations ...... 72 4.2 Commutation Unit...... 73 4.2.1 Topology ...... 75 4.2.2 Transistors ...... 76 4.2.3 Diodes ...... 78 4.2.4 Zener Diode ...... 79 4.3 Control System...... 80 4.3.1 Control Strategy ...... 80 4.3.2 Sensing ...... 82 5 Simulation Results...... 84 5.1 Input...... 85 5.2 Output...... 90 5.3 Phase Current...... 93 5.4 Efficiency...... 95 5.5 Losses ...... 97 6 Conclusion and Prospects ...... 101 7 References...... 102 Appendix A: Measuring Results of an Alternator ...... 106 Appendix B: True Scale Figures of the Generator ...... 118 Appendix C: Conclusion of Characteristic and Dimension Values ...... 120 Appendix D: Tables of the Simulation Results...... 121 List of Symbols

•'i comer comer area Acu winding copper area Acu+insul cross sectional winding area with insulation Acu wire nominal cross sectional copper area Ainsul insulation area Ar area of rotor cross section Aglotr rotor slot area AglotS stator slot area Aslotsnet net stator slot area A wire cross sectional wire area with insulation B magnetic flux density •Bio flux density at 10 kA/m B2.5 flux density at 2.5 kA/m B30 flux density at 30 kA/m d thickness of insulation layer dr rotor slot depth ds stator slot depth D duty cycle •DcUwire nominal copper diameter of a wire Dr rotor diameter Drm minor rotor diameter ' Ds stator lamination diameter Dsb stator slot bottom diameter DSh shaft diameter •Dwire maximum wire diameter with insulation E modulus of elasticity Er modulus of elasticity in rolling direction Et modulus of elasticity in transverse direction fstk lamination stacking factor H magnetic field strength He coercive force i phase current b diode current

zpeak peak current h transistor current I modulus of inertia b continuous drain current List of Symbols 5

Idc output current Idm peak of pulsed drain current fomean diode mean current ■fopeak diode peak current ^DRMS diode RMS current ■lexc excitation current fpRM repetitive peak forward current Io output current h phase current fppeak phase peak current /r reverse current ■^Tmean transistor mean current ■^Tpeak transistor peak current

/trms transistor RMS current J moment of inertia K20 nominal capacity L phase inductance U aligned inductance LaO unsaturated aligned phase inductance

Lds drain-source internal parasitic inductance u overall length Loh overhang length of winding Lratio inductance ratio Lstk stack length Lu unaligned inductance LuO unsaturated unaligned phase inductance m number of phases Np number of turns per pole Npalh number of parallel paths per phase Nr number of rotor poles Ns number of stator poles Nstrokes/rev number of strokes per revolution Mvp number of parallel wires per turn per pole P10 core losses at 1 T f lOmax maximum core losses at 1 T Pl5 core losses at 1.5 T P ISmax maximum core losses at 1.5 T fexc mean electrical excitation power

Pl power losses Plosses total power losses List of Symbols 6

Pmech mean mechanical input power •Pout mean electrical output power Pshaft shaft power Pjpeak peak of transistor leakage power r radius of comer at stator slot bottom R phase resistance P wiremax maximum wire resistance per length P wiremin minimum wire resistance per length Ro minor rotor radius Ri rotor radius Pi radius of stator slot bottom P3 stator outside radius T?DS(on) drain-source on-resistance PphDC direct-current phase resistance Psh shaft radius Pthjc thermal resistance Sfill slot fill factor ^fillinsul slot fill factor with consideration of insulation t time toif turn-off time ton turn-on time fP pulse duration tr rotor pole width ts stator pole width tstk layer thickness of the lamination stacking T temperature T torque PAV(in) average input torque Pcmax maximum permissible junction temperature Pexc excitation period Thigh period of high level Tj junction temperature Plow period of low level Toff non-conducting period Ton conducting period TpuRV torque per unit rotor volume Trev revolution period Tshaft shaft torque Tstroke stroke period Plot total period List of Symbols 7

u phase voltage U voltage Udis discharged voltage Uus drain-source voltage Uv forward voltage Ugas gassing voltage Ugs gate-source voltage Umax maximum charged voltage

C/n nominal voltage U o ut output voltage Ur continuous reverse voltage Ure f reference voltage Urest rest voltage U rrm repetitive peak reverse voltage US supply voltage V velocity

Vi first critical speed We total iron volume Wr°ss gross electromagnetic volume Wet net electromagnetic volume WFe volume of rotor iron Wpe volume of stator iron W* coenergy Wcu copper weight with insulation Wexc excitation energy Wf stored field energy Wpe total iron weight Wm mechanical energy IWi(in) total mechanical input energy Wm(inl) mechanical input energy while excitation period VW(in2) mechanical input energy while output period IWi(out) mechanical output energy Wr rotor iron weight Wiot total weight

X abbreviation for comer area calculation

Jr rotor yoke thickness % stator yoke thickness List of Symbols 8

a constant for calculation of temperature influence on resistivity abbreviation for comer area calculation Pr rotor pole arc Ardiff abbreviation for rotor slot area calculation Ps stator pole arc

Ps diff abbreviation for stator slot area calculation

Ps lot abbreviation for insulation area calculation

Pslotback abbreviation for insulation area calculation 8 air gap length e excitation penalty e stroke angle n efficiency Vgen generator efficiency P number of working poles per phase Pmax maximum relative permeability of iron

Pstart relative permeability of iron e rotor position angle e0 turn-on angle 0c turn-off angle 0D dwell angle 6q extinction angle 0S sensor position

P resistivity

PA absolute overlap ratio pc u resistivity of copper Pe effective overlap ratio PFe density of iron

PresFe resistivity of iron a mechanical stress ov yield point rotor pole pitch Ts stator pole pitch (0 angular velocity first critical angular velocity ■^riax maximum angular velocity phase flux linkage tyc maximum flux linkage at commutation AU voltage error Tiivistelma

Tutkimus esittelee pienjannitteisen molemminpuolin avonapaisen reluktanssigeneraat- torin suunnittelua. Kone on tarkoitettu ajoneuvogeneraattoriksi ja toimii siten vaihte- levalla nopeudella. Tyossa kehitetaan koneen konstraktio ja perehdytaan erityisesti kommutoinnin ajoitukseen optimaalisen tuloksen saavuttamiseksi.

Tyossa esitellaan aluksi molemminpuolin avonapaisen reluktanssigeneraattorin toimin- taperiaate ja tarkastellaan konetyyppiin liittyvaa teoriaa. Lisaksi tarkastellaan nykyisin kaytettyjen generaattorityyppien ominaisuuksia ja puutteita.

Tyossa saavutetut tulokset osoittavat, etta molemminpuolin avonapainen reluktanssi- kone voidaan haluttaessa suunnitella erityisesti generaattorikayttoon. Simulointitulos- ten perusteella talla konetyypilla on mahdollista saada nykyisia konetyyppeja suurempi lahtoteho samasta konetilavuudesta ja etenkin hyotysuhdetta voidaan kohottaa merkit- tavasti nykytekniikan tasosta. 10

1 Introduction

The history of low voltage generators for variable speed applications dates back to the beginning of this century. Since then the technologies used have changed. First the DC generator was used. Later it was not powerful enough anymore and replaced by the alternator. The demands are still increasing steadily and the limits of the alternator technology are almost reached nowadays. Thus innovative technologies have to be developed. The switched reluctance technology should be able to meet the new demands.

Switched reluctance motors are examined in the literature for recent years. Nowadays they have started to compete with inverter-fed induction motors. Whereas switched reluctance generators have been left almost unexplored. Only few machines for four-quadrant operation have been built [12]. Nevertheless it can be expected that switched reluctance generators will be as competitive and advantageous than the motors.

The advantages of the switched reluctance technology are

• high output power, • high efficiency, • no extra excitation winding, • no brushes, • simple and robust construction, • and fault tolerance.

As a main field of application the generator is considered to be used for the on-board power supply in motor vehicles. This requires that the generator is capable of supplying loads with direct current and has power reserves for charging the battery. A constant output voltage over the whole speed range is demanded. It should be as maintenance-free as possible and tolerate external loading, like vibrations, temperature changes, dirt and damp. Low weight, compact dimensions, low noise and long life are essential. Most important is that it is easy and inexpensive to produce in large quantities within mass-production. The task of this work is to design a generator which fulfils these requirements by using the advantages of the switched reluctance technology.

The work begins with an overview of the existing DC generator and alternator technologies. Their weak spots and on the other hand the supposed improvements Chapter 1: Introduction 11 and advantages of the switched reluctance technology are pointed out. Lots of effort has been put on working out the principle and theory of switched reluctance generators in general. All characteristics of the construction are presented and the working principle is described in detail. The usable converter topologies for the commutation are summarised. The dynamic operation and the control system are other contents. Based on this important knowledge the design of the generator is made. It is distinguished in the construction and commutation unit design. The control strategy and the sensing for the realisation of the control are also given. Simulation results are obtained and evaluated for input and output characteristics, efficiency, phase current and losses. Finally, a conclusion and prospects are given. 12

2 Generators for Variable Speed Applications

The major field of application for generators with variable speed and low output power is the electricity generation in motor vehicles. The electric systems of motor vehicles are working on DC current and the voltage is 12 V, or for bigger vehicles 24 V. All circuits contain a battery for energy storage, a generator for energy conversion and several loads with different demands on power and time characteristic.

The biggest load is the starting motor. It needs from 800 W to 3,000 W, but only for a very short period of time. The time characteristic of the loads can be categorised in continuous, prolonged and brief loads. Continuous loads are ignition, electric fuel pump and electric gasoline injection. The car radio, different lamps and the heater form the category of prolonged loads. Brief loads like electric window lifter, electric radiator fan, rear window heating etc. form the largest category. Table 2.1 shows the power requirement of the mentioned loads.

Table 2.1: Power requirement of the loads in motor vehicles

Starting motor 800... 3,000 W Ignition 20 W Fuel pump 50... 70 W Gasoline injection 70... 100 W Car radio 10... 15 W Lamps (altogether) approx. 200 W Heater 20... 60 W Window lifter 150 W Radiator fan 200 W Rear window heating 120 W

The task of the generator is to provide electric power for supplying the loads and for storage in battery. The first generator type used in variable speed applications was the DC generator. Later the DC generator was replaced by the alternator. Both generator types, the rectification and the control are described in the following. The weak spots of these generator types and the improvements and advantages of switched reluctance technology are pointed out afterwards. For a further overview on the electrical part of car technology see references [14],[17],[44],[45]. Chapter 2: Generators for Variable Speed Applications 13

2.1 DC Generator

Figure 2.1 shows the construction of a DC generator. The stationary stator frame (1) has pole shoes (7) and carries the excitation winding (8). The rotor core (2) is made of laminated iron and is fitted on the shaft. In the rotor core the armature winding is embedded. Because this winding is on the rotating part, brushes (9) are needed. They are made of carbon and are put on the commutator (4). Also the electric terminal (3), the commutator end shield (5) and the drive end shield (6) are shown in the figure.

2 3 5

The operating principle works the way that AC voltage is induced in the armature winding due to the magnetic field variations during rotation. It is rectified by the commutator and the resulting DC current is picked off at the commutator segments by the brushes. DC generators for these applications are shunt-wound machines. The armature winding and the excitation winding are connected in parallel. This has the effect that the necessary excitation current is produced by the machine itself. It is tapped from the armature current. This is the principle of self-excitation.

A voltage regulator is required for all DC generators to keep the generator voltage in a tolerance range over the entire speed range irrespective of the load. The regulation Chapter 2: Generators for Variable Speed Applications 14

principle consists of regulating the excitation current as a function of the generated voltage. The excitation current is regulated by a regulating contact which interrupts the excitation current when a voltage tolerance range is exceeded and is contacted again when a minimum set value is reached. This voltage regulator protects the electric loads against overvoltage and prevents the battery from being overcharged. It also takes the electro-chemical properties of the battery into account, like the temperature-depending charging voltage.

Besides a voltage regulator DC generators need an extra current regulator which protects the machine against overloading. To protect the battery from discharging at low speeds an independent electromagnetic relay is also required to interrupt the connection between the generator and the battery.

The speed versus generator current curve (see Figure 2.2) shows the characteristic behaviour of the generator in interaction with the regulation. At speeds close to the per unit idle speed of the internal combustion engine of motor vehicles, in many cases above it, the charging voltage is reached and the generator is connected to the battery through the automatic cut-out relay. At this point the generator starts to deliver power, though higher speed is needed until the maximum generator current is reached. When the maximum current is reached it is limited by the current regulator and kept constant. The maximum rotational speed is limited by the commutation because of the danger of overheating and heavy wear on the carbon brushes.

Engine idle speed range

Per unit speed Figure 2.2: Maximum output current characteristic curve of a DC generator Chapter 2: Generators for Variable Speed Applications 15

2.2 Alternator

The most common alternator type is the claw-pole alternator currently installed almost in every motor vehicle. Figure 2.3 shows the construction of a claw-pole alternator. In the laminated stator core (6) the three-phase stator winding is embedded in slots. The stator is clamped between the slip-ring end shield (1) and the drive end shield (10). The rotor (7) carries the poles and the DC excitation winding. This winding consists of a single circular coil enclosed by the claw-poles. To supply the excitation current, carbon brushes are put on slip rings which are mounted on the shaft. Also the fan (8) and the pulley (9) are mounted on the shaft.

Figure 2.3: Construction of an alternator [44]

Alternators need an electrical rectification because during rotation AC voltage is induced in the three-phase stator winding. This is done by a bridge circuit of six power diodes (3). For the conversion of the three-phase current to excitation current three exciter diodes (4) are needed. All these diodes are fixed on a diode plate (2) which fulfils the function of a heat sink at the same time.

The output voltage of alternators has to be regulated. It must be kept in a tolerance range over the whole speed range. Unlike DC generators alternators need only a voltage regulator which works the same way than the voltage regulators used for DC Chapter 2: Generators for Variable Speed Applications 16

generators. The excitation current is diminished, when the voltage tolerance range is exceeded and increased again after a minimum set value is reached. The regulator (5) is connected to the brush holders and, depending on the type, sometimes mounted straight on them like in figure 2.3.

Generally different types of regulators exist but the latest invented hybrid regulator is mostly used nowadays. Other regulator types are the conventional electromagnetic vibrating-type and the transistor regulator. The advantages of the hybrid regulator are compact construction, high reliability, small amount of components and connections. The main component of the hybrid regulator is an integrated circuit that combines all control functions. Basically the hybrid regulator is a further development of the transistor regulator.

The invention of the transistor regulator was a large progress in regulator technology because it has no mechanical contacts and moving parts anymore, thus it is maintenance free. It is also a lot smaller and lighter than the conventional electromagnetic vibrating-type regulator and insensitive to vibrations. These advantages allow the transistor regulator to be mounted directly on the alternator. Other positive features are short switching times, narrow regulation tolerances, allowance of high switching currents, spark-free switching and electronic temperature compensation. The conventional electromagnetic vibrating-type regulator is not used anymore because of the obvious advantages of the new regulator types.

Figure 2.4 shows the total connection diagram for an alternator with generation, rectification, pre-excitation, excitation and regulation. The interaction of the three generator circuits for pre-excitation, excitation and generation can be seen. The pre-excitation starts when the ignition is switched on and the excitation current supplied by the battery flows through the generator warning lamp to the excitation winding of the rotor. From there it flows through the regulator to ground. The pre-excitation is necessary because at low speeds the remanence in the iron core is not sufficient to build up a magnetic field just by a self-excitation strong enough to generate the desired minimum voltage for the excitation circuit. At least the generated voltage has to be higher than the voltage drop of the in series connected negative rectifier diode and excitation diode.

When the desired minimum voltage is reached, the excitation circuit starts to work and the excitation is taken straight from the generated current. No external power source is needed after that. The alternator excites itself. At the same time the Chapter 2: Generators for Variable Speed Applications 17

generator warning lamp goes out and signals that current is delivered by the generator. For the excitation some current of the phase windings is rectified by the excitation diodes and supplied to the excitation winding. Through the regulator and the negative rectifier diodes the path goes back to the phase windings. The excitation circuit has the task to produce the magnetic field which is necessary to induce the output voltage in the three-phase stator winding.

Generator warning lamp

Ignition Positive switch rectifier diodes Exciter diodes'

Battery

Negative rectifier Excitation winding diodes

Regulator

Figure 2.4: Alternator connection diagram with generation, rectification, pre-excitation, excitation and regulation

The generation circuit supplies the current for charging of the battery and for coincidence of the loads. Thus it is divided into load and battery current. Before it can be delivered, the AC current of the three-phase stator winding has to be rectified. This is done by the bridge circuit which consists of the positive and negative rectifier diodes.

A schematic diagram of the speed versus generator current curve is shown in figure 2.5. The figure shows the characteristic behaviour of alternators in interaction with the regulation. The schematic diagram has been verified by measurements that have been made within this work (see Appendix A and especially Figure A.4). In contrast Chapter 2: Generators for Variable Speed Applications 18

to DC generators alternators already deliver an output current at the per unit idle speed of the internal combustion engine of motor vehicles. This has the advantage that the battery can be kept in a good state of charge even in winter and while driving in town with frequent waiting times. The output current at idle speed reaches approximately one third of the absolute maximum output current.

Engine idle speedrange

Per unitspeed Figure 2.5: Maximum output current characteristic curve of an alternator

The maximum output current increases rapidly with an increase of the speed at low speeds. At high speeds it increases slightly with an increase of speed. It is not kept constant like for DC generators because alternators are not equipped with current regulation. Compared with DC generators the reached maximum output current is always higher. The maximum rotational speed is limited by centrifugal force and appearing vibrations.

2.3 Weak Spots of Existing Technology

As already mentioned, DC generators were used at first for low output power and variable speed applications but nowadays they are almost not used anymore. The main reason for this can be seen from the maximum output current characteristic curve which was already shown in figure 2.2. It can be seen that the speed range is severely restricted to a range not broad enough for modem variable speed applications. Especially for motor vehicles the output characteristic does not meet the demands because no energy is supplied at the per unit idle speed. This will cause a discharge of the battery while driving in town because of the high average proportion of waiting times in town driving. The development of the average proportion of Chapter 2: Generators for Variable Speed Applications 19 waiting times in town driving from 1950 to 1990 is illustrated in figure 2.6 and it can be observed that the situation has not become better.

Figure 2.6: Development of average proportion of waiting times in town driving from 1950 to 1990

Another disadvantage of DC generators is the need of maintenance due to the wear of the carbon commutator brushes. A high output power can be reached only with large dimensions and high weight. The advantage and the reason for former use is the simple, mechanical rectification by the commutator. Since semiconductor components are common and inexpensive, the mechanical rectification is not needed or advantageous anymore. Rectification can be better and easier made by bridge circuits of power diodes.

Nowadays the alternator is used for low output power and variable speed applications. It has some advantages compared with DC generators. Especially the maximum output current characteristic curve (already shown in figure 2.5) is more suitable. The alternator supplies energy over a broader speed range and even at the per unit idle speed of the combustion engine of motor vehicles. Also the output power is higher and that is important because the demand of output power has increased. Figure 2.7 shows the rapid increase of the required generator output for motor vehicles since 1950.

Another advantage of alternators is the electronic rectification of the three-phase current with diodes, because it makes the mechanical rectification by the commutator superfluous. This, together with the fact that the rotor winding is only for the excitation, decreases the wear of the brushes because the coal of the brushes will be Chapter 2: Generators for Variable Speed Applications 20

rubbed off more slowly and because the excitation current is a lot smaller than the output current. This guarantees a longer service life. Mostly the brushes or the bearings wear out first after around 100,000 km. The diodes perform also an automatic relay which cuts the alternator from the battery if the alternator voltage drops below the battery voltage. Alternators are also lighter than DC generators and they can better tolerate external influences like high temperatures, damp, dirt and vibrations. The disadvantage of alternators is their smaller efficiency.

1200 T

1000 --

800 --

Figure 2.7: Development of generator output from 1950 to 1990

As just pointed out alternators have some advantages compared with DC generators, but still they have their weak spots. One main disadvantage is that they provide only approximately one third of the maximum output power at idle speed (see Chapter 2.2). This can cause the discharging of the battery under unfavourable conditions, for example in winter time when many loads are switched on and long waiting times occur at the same time.

The other main disadvantage of alternators is the low efficiency. Especially at high speeds the efficiency decreases noticeably. This can be seen from the measurement results documented in the Appendix A. Figure A.5 shows the decrease of efficiency with increasing speed. In the same picture it can also be seen that the efficiency decreases with a decrease of the load. Alternators reach a reasonable efficiency only at nominal output power and not too high speed. The low alternator efficiency reacts, for example negatively on the fuel consumption of motor vehicles, as it is investigated in reference [25]. Chapter 2: Generators for Variable Speed Applications 21

The constantly increasing power demand and the changed traffic conditions led to such requirements that the DC generator was not capable of fulfilling them anymore. The alternator solved the problems that cropped up with the new demands. Nowadays the development is going still in the direction that higher and higher electric power is demanded. It can be noticed that the alternators are almost reaching their output power limits and new technology or different system suppositions, like a higher voltage level, are necessary to fulfil the requirements of modem car technology. Switched reluctance generators can exceed the alternator limits, and they have also other advantages.

2.4 Supposed Improvements and Advantages of Switched Reluctance Technology

Comparisons of switched reluctance machines with other machine types have been made and they are reported in literature [5],[15],[28],[35],[47]. Most of them are concentrating on motor applications and are quite general, but some of them also point out that the advantages of switched reluctance machines can be recognised in all four quadrants of operation (see Figure 3.1).

The first main advantage of switched reluctance generators is the high output power. A higher output power compared with other machine types is reached because more copper can be fitted in the large slot area. Over a broad speed range and especially at low speeds the output power is higher than for alternators. Only at very high speeds it is lower. The maximum output power is supplied over a broad range at medium speeds.

Figure 2.8 shows a schematic comparison of the maximum output current of the three generator types versus the per unit speed range of the internal combustion engine of a motor vehicle. It can be seen in the figure that compared with the alternator the maximum output current of switched reluctance generators is around three times higher at idle speed and still higher until the motor overspeed range is reached. In the overspeed range it is smaller, but this speed range is rarely used for driving. The output current behaviour is almost equal to the output power behaviour because of the nearly constant average voltage.

The other main benefit of switched reluctance generators is the high efficiency. Contrarily to alternators, it is almost constant over the whole speed range and nearly Chapter 2: Generators for Variable Speed Applications 22

independent from the load. This will react positively on the fuel consumption of motor vehicles, as investigated in reference [25].

Engine idle Switched reluctance Engine over­ speed range generator speed range

Alternator

DC generator

Per unit speed Figure 2.8: Maximum output current characteristic curve for the different generator types

The high efficiency is reached because the losses are low and this leads to a small temperature rise [22]. Because of this the additional fan losses are low, too. The fan is needed for the cooling of the heat produced by the other losses and can be less powerful if they are smaller. The fan losses are also positively effected by the lower absolute speed of switched reluctance generators compared with alternators, because the fan losses increase intensely with the speed. As pointed out in chapter 2.3 and verified in Appendix A, the fan losses are the major part of the losses of alternators, especially at high speeds. Thus the overall efficiency of switched reluctance generators is much higher than for alternators.

Another advantage is that no extra excitation winding is needed. This saves an additional excitation circuit and the necessity of slip rings and brushes. The simple construction which enables inexpensive mass production is also a positive aspect. The construction is compact as well, so the size is as small as the size of alternators in the same range.

The fault tolerance of switched reluctance machines together with the commutation should also be mentioned. The reason for this is the lack of excitation and the independence of the phases. An open circuit in a phase circuit does not produce any generated voltage and a short circuit condition does not produce any fault current, because there is no field winding or permanent magnet for excitation. If one phase is Chapter 2: Generators for Variable Speed Applications 23 faulted, the healthy ones can operate almost unaffected because of the independence of the phases. Commutation units of the form of the classic converter (see chapter 3.3.1) have no shoot-through path and thus the DC supply can be shorted only if the phase winding itself is short circuited. Additional information on the behaviour of switched reluctance machines under internal and external fault conditions is given in the references [1],[2],[26].

The disadvantages of switched reluctance generators are the high level of current ripple and the control dependent on rotor position, which requires a rotor position feedback. They are also known for producing higher acoustic noise [51]. The main advantages of high output power and high efficiency compensate these disadvantages. 24

3 Principle and Theory of Switched Reluctance Generators

Switched reluctance machines are widely used for motor applications and because of this most of the published theory is about motoring operation. Only a bit of information on switched reluctance generators can be extracted from the literature. On the other hand motoring and generating are operating states of one machine. This is the reason why motor theory and generator theory are connected. Figure 3.1 illustrates the four quadrant operation of a machine. The theory mentioned in this chapter refers to literature, if mentioned, or is verified by investigations with the simulation tool PC-SRD [30],[31]. This chapter gives an overview of the switched reluctance machine theory with special attention to the characteristics of generating operation.

Forward

r 0 v> 0 v > 0 Generating Motoring

0 Motoring Generating T< 0 T> 0 v<0 v< 0

Reverse i

Figure 3.1: Speed over torque diagram for four quadrant machine operation

3.1 Construction

The main construction characteristic of switched reluctance machines is that they have salient stator and rotor poles which differ in number. Basically the motion can be rotary or linear and the rotor interior or exterior, but interior rotors with rotary motion are most common. The way of motion and the arrangement of the rotor determine the cross section layout. Only the most commonly used construction is described here. Another basic characteristic is that only the stator poles are equipped with windings and the rotor carries no windings. Usually the windings of two opposite poles form one phase winding. Both the rotor and the stator are made of Chapter 3: Principle and Theory of Switched Reluctance Generators 25 laminated iron. Figure 3.2 shows the cross section of a three phase 6/4-switched reluctance machine to give a first impression of the construction.

Figure 3.2: Cross section of a three phase 6/4-switched reluctance machine

3.1.1 Basic Characteristics

Switched reluctance machines can be distinguished by the number of phases m, stator Nt and rotor poles Nt. Different combinations of these main design criteria enable a functional machine. It must be mentioned that the one and two phase machines need assistance for starting if they are used for motor applications. Table 3.1 shows different possible phase and pole combinations most commonly used in practice [27]. The combinations supported by the PC-SRD can be seen in reference [30].

All combinations included in the table are so called regular designs. A regular design means that the stator and rotor poles are symmetric about their centre lines and equally spaced around the rotor and stator respectively. Most of the practical switched reluctance machine designs are included in the table, but irregular machines are existing, too, as it can be seen in reference [27]. This reference also gives an overview of different motor designs. The stroke angle e = 360°/(mA/r) and the number of strokes per revolution Mtrokes/rev = rnNr can be calculated from the number of phases and rotor poles. These characteristic values are also included in the table. Chapter 3: Principle and Theory of Switched Reluctance Generators 26

Table 3.1: Phase and pole combinations

Number of Number of Number of Number of Stroke Angle Strokes per Phases m Stator Poles Rotor Poles Nt Working Poles £ Revolution Ns per Phase p N .strokes/rev 1 2 2 1 180.00 2 2 4 2 1 90.00 4 2 8 4 2 45.00 8 3 6 2 1 60.00 6 3 6 4 1 30.00 12 3 12 8 2 15.00 24 3 18 12 3 10.00 36 3 24 16 4 7.50 48 4 8 6 1 15.00 24 4 16 12 2 7.50 48 5 10 4 1 18.00 20 5 10 6 1 12.00 30 5 10 8 1 9.00 40 6 12 10 1 6.00 60 6 24 20 2 3.00 120 6 12 14 1 4.29 84 7 14 10 1 5.14 70 7 14 12 1 4.29 84

Other characteristics of a switched reluctance machine are the absolute and effective torque zones and the absolute and effective overlap ratios. The absolute torque zone is the angle through which one phase can produce a non-zero torque in motoring operation. For a regular motor it is maximally 180 °/Nt. In generating operation this is the maximum zone where a positive output current is available. In this operating mode a better name would be absolute current zone. The effective value of this dimension is comparable to the smaller pole arc of the overlapping rotor and stator poles and it gives the angle where useful torque or respectively useful output current can be produced.

The absolute overlap ratio is defined as the ratio of the absolute torque zone to the stroke angle. Its value is equal to mil. For a regular motor a value of at least one is necessary so that torque can be produced at all rotor positions, but a value of one is not sufficient because the nominal torque can never be provided throughout the whole absolute torque zone by only one phase. For a generator the same feature can be seen for the output current.

The effective overlap ratio is defined by the ratio of the effective torque zone and the stroke angle respectively. It is always smaller than the value of the absolute overlap ratio. The ratio is approximately equal to the stator pole arc divided by the Chapter 3: Principle and Theory of Switched Reluctance Generators 27 stroke angle if the stator pole arc is smaller than the rotor pole arc for a regular machine, which is normal in common conditions. A value of at least one is necessary to get a starting torque at every rotor position but not sufficient for avoiding torque ripple. In generating operation there is no need for a starting torque, because it is given by the driving machine. For a steady output current a value bigger than one of the effective overlap ratio is necessary.

3.1.2 Envelope and Internal Dimensions

The internal and envelope dimensions mainly determine the machine performance. The envelope dimensions are the stator lamination diameter A and the overall length Le which is measured over the end turn overhangs of the winding. These dimensions define the gross electromagnetic volume Vgross- The net electromagnetic volume Vnet is defined by the stack length Lstk and the stator lamination diameter. The stack length is an inner dimension and the overall length can be calculated from it by Le=Lstk+ 2 L0h with L0h as the overhang length of the winding. The overhang length is approximately equal to the stator pole width ts which is introduced later in this chapter. All these and some more inner dimensions (stator slot bottom diameter Ab, shaft diameter Ah, minor rotor diameter Am, rotor diameter A and air gap length 8) are illustrated in figure 3.3. The figure shows the longitudinal cross section of a machine and the main parts of the construction are named.

Some ratios of the above mentioned dimensions can be used for machine characterisation. One is the standard or split ratio which is defined by the rotor diameter divided by the stator diameter. Dc/Ds can vary between 0.4 and 0.7 but for most designs it is between 0.5 and 0.55 [27] and tends to be larger with a higher number of poles. According to the reference [10] a suitable value should be between 0.57 and 0.63. Another characterising ratio is the length per diameter ratio given ' exactly by the stack length and the rotor diameter. A typical value for Atk/A is 1.

From the net electromagnetic rotor volume and the torque T the torque per unit rotor volume rpURv can be estimated as

^puRV — (3.1) f D“4k

According to table 3.2 the Tpurv value enables a rough categorisation of the machine and shows the extent of machine utilisation which is mostly limited by the used Chapter 3: Principle and Theory of Switched Reluctance Generators 28 cooling method. Usually this value is used as a starting point for the first rough estimation of a new machine design.

Stator

Stator pole

Rotor

Rotor pole End turn Winding overhang Stator yoke

Figure 3.3: Longitudinal machine cross section (rotor in aligned position)

Other inner dimensions can be seen from the cross-section of a machine. Figure 3.4 shows the cross section of a three phase 6/4-machine, including the inner dimensions shaft radius Rsh, minor rotor radius Rq, rotor radius Ru radius of stator slot bottom R2. stator outside radius Rz, rotor pole arc /Jr, stator pole arc /5S, rotor pole width /, and stator pole width ts.

Table 3.2: Machine categorisation from the torque per unit rotor volume [ 27 j

Machine category T durv in kNm/m3 Small totally enclosed machines 2.5-7 Integral-kW industrial machines 7-30 High-performance servomotors 15-50 Aerospace machines 30-75 Large liquid-cooled machines 100 - 250

All important information of a machine construction is given with the mentioned basic dimensions and all other necessary values can be calculated from them, like the rotor tooth width Chapter 3: Principle and Theory of Switched Reluctance Generators 29

tt=2R x sin^L (3.2) the stator tooth width K -2(^i+<$)sin^-^ (3.3) the rotor pole pitch K Tr = 2ft, sin (3.4) and the stator pole pitch

ts = 2 (ft, +5 )sin (3.5)

Other important derivative values are the stator slot area Aio*-[%A Ri+sT]{y-Y

Psdiff D Pstiff + [ft, - (R, + 5)] ^jl - sin' ~ ft; COS (3.6)

2 with Chapter 3: Principle and Theory of Switched Reluctance Generators 30

where the winding is embedded, the stator iron volume v,„ = {* [*? - ft+S f ] ■- WA-} (3.7) and the rotor iron volume

(3.8) with Asiotr as the rotor slot area which is calculated in the same way than the stator slot area, but the values R2, (Ri+S), Ns and j3s have to be replaced by Ru Ro, Nr and jSr and the within used abbreviation f3sm then changed to /Wf respectively.

Also some derivative dimensions can be defined. Mainly the rotor slot depth dT = Rx-Rq, the stator slot depth ds = R2-(R\+S), the rotor yoke thickness yT = Ro-Rsh and the stator yoke thickness ys = R3-R2 are important to mention and they are especially used during the designing process because of their better clarity in connection to the electric and magnetic phenomena occurring in a machine.

3.1.3 Pole Geometry

Figure 3.4 has already shown the basic pole geometry, but variations especially for the stator poles are common and sometimes advantageous depending on the intention. Figure 3.5 shows some different possible modifications of the stator pole geometry. Modifications of the rotor pole geometry are not so common and, because of that, not mentioned here.

One very useful and advantageous modification of the standard pole geometry (Figure 3.5 (a)) is shown in figure 3.5 (b). The radius at the comers of the slot bottom increases the stiffness of the poles against lateral deflection and also stabilises the stator. This has a positive effect on acoustic noise reduction, but on the other hand the usable slot area for embedding of the winding is decreased. The comer area taken by the radius r is

A, comerasa.------COS (3.9) 'comer 2 2 1 with

and Chapter 3: Principle and Theory of Switched Reluctance Generators 31

^cornercomer = 2 arcs (3.10)

The stator slot area is recalculated Asiots (new) = Asi0ts(old) - 2 Acom er with Asi0ts(old) calculated by equation (3.6). The loss of usable slot area taken away by the radius is in practice not so significant because the round wires are not fitting exactly into the comer, so the area is partly unusable for the winding anyway.

(a) (b) (C) (d) Figure 3.5: Details of stator pole geometry

The slight taper in figure 3.5 (c) concentrates the saturation near the air gap and decreases the magnetic voltage drop over the pole. On the other hand, the slot area will be decreased and the required quantity of iron and thus the machine weight is increased.

Pole overhangs (Figure 3.5 (d)) have the advantage that the pole width can be extended almost without reducing the slot area. The negative consequence is that ready wound coils can only be used if the coil is made wide enough and pressed against the poles after it has been slipped over the pole overhangs. This method has the disadvantage of an extra end turn overhang and can only be used if the slot fill factor is small. Anyway, the production is more complicated and thus its costs are increased.

Basically a pole geometry with multiple teeth is possible but they are not very common. In reference [27] it is mentioned that their benefits are liable to be restricted Chapter 3: Principle and Theory of Switched Reluctance Generators 32

to low speeds and they have the same disadvantage concerning the winding than a pole geometry with overhangs as well.

3.1.4 Windings

The windings of switched reluctance machines are simpler than those of other machine types and an extra winding for excitation is not needed. Only one coil is wound on each stator pole and it is not necessary to make use of special winding patterns. Normally the windings of opposite poles comprise to one phase. They can be connected in series or in parallel.

Basically the winding can be defined by the slot fill factor Sen, the number of turns per pole Np and the number of parallel paths per phase /Vpat h. The theoretical maximum achievable slot fill factor is restricted to itlA because round wires can not be joined to each other without leaving some empty space in-between. In practice the theoretical slot fill factor can not be reached because of the area losses by the insulation, the distance that has to be kept from the air gap and the geometrical circumstances. A realistic maximum slot fill factor for an insulated slot area is between 0.6 and 0.7.

The slot fill factor also determines if pre-wound windings can be used. In that case the slot fill factor should be smaller than around 0.4. This value ensures that the ready wound winding can be slipped over the poles. It has to be also permissible by the pole geometry (see chapter 3.1.3).

3.2 Working Principle

The working principle of switched reluctance machines is based on the change of the magnetic reluctance depending on the rotor position. The rotor tries to adjust the position with the smallest magnetic reluctance and produces a torque. For a generator with a torque given by a driving machine, a voltage which will cause a current will be induced in the stator winding. Because the rotor poles are without a winding, the excitation and the output current must be taken from the same winding. Thus the current of each phase has to be switched depending on the rotor position. Chapter 3: Principle and Theory of Switched Reluctance Generators 33

3.2.1 Rotor Position Dependency

As already mentioned, the working principle is based on the rotor position. To describe this dependency it is easier and enough to concentrate just on the positions according to one phase. Then two positions and two zones can be distinguished. The positions are the aligned and the unaligned position.

The rotor is in the aligned position according to one phase when one pair of the rotor poles is exactly aligned with the stator poles on which the winding of this phase is wound. Figure 3.6 illustrates the aligned position on the phase in the horizontal axis for a 6/4-switched reluctance machine.

Figure 3.6: 6/4-switched reluctance machine in the aligned position on the phase which is marked

In this position the magnetic reluctance of the flux path is lowest because most of the reluctance is in the air gap and the gap is smallest in this position. Because the reluctance is at its minimum, the phase inductance is at its maximum. The reluctance in the iron is lower than in the air gap but can not be neglected, because the long path through the iron also absorbs a significant magneto motive force. The iron is also susceptible to saturation, especially in the stator and rotor yokes. Because of these reasons the aligned inductance will be reduced.

The aligned position is a stable position. A current in this phase can not produce a torque because the magnetic reluctance is already at its minimum. If the rotor is displaced to either side, a restoring torque tends to return the rotor towards the position of minimum reluctance - the aligned position. Chapter 3: Principle and Theory of Switched Reluctance Generators 34

The rotor is in the unaligned position according to one phase when the interpolar axis of the rotor is aligned with the stator poles on which the winding of this phase is wound. Figure 3.7 illustrates the unaligned position on the horizontal axis for the same 6/4-switched reluctance machine.

Figure 3.7: 6/4-switched reluctance machine in the unaligned position on the phase which is marked

In this position the magnetic reluctance is at its highest because of the large air gap. Because the reluctance is at its maximum, the phase inductance is at its minimum. The iron is unreceptive to saturation in this position because the current when saturation begins has to be much higher than in the aligned position. This is because the leakage flux is relatively much greater and the winding is laid out to avoid high saturation even in the aligned position.

If the phase is excited, the unaligned position is an unstable equilibrium. There is no torque in this position, but if the rotor is displaced to either side, a torque appears that tends to displace the rotor further until it is aligned with the next aligned position.

The intermediate positions can be summarised to two zones. The direction of forward motion is always set counterclockwise. Then the intermediate positions of the first zone are those that are taken while the rotor turns from the unaligned towards the aligned position. Respectively, when the rotor turns from the aligned towards the following unaligned position, the intermediate positions of the second zone are taken. Figure 3.8 shows these two zones for the same 6/4-switched reluctance machine. Chapter 3: Principle and Theory of Switched Reluctance Generators 35

In the first zone the magnetic reluctance decreases towards the aligned position, thus the inductance increases. Especially with the start of pole overlap the inductance changes rapidly because of the smaller air gap. Before overlap there is only a slight increase. In the second zone the inductance shows a contrary behaviour. It decreases with further rotation. With the start of pole overlap also the iron starts to be susceptible to saturation. Before the pole overlap there is only the possibility of local saturation of the pole comers.

direction of rotation unaligned

Zone 2

aligned

Zone 1

unaligned

Figure 3.8: 6/4-switched reluctance machine with the two zones of intermediate rotor positions

If the phase is excited in the first zone, the appearing torque assists the counterclockwise rotation towards the aligned position. Thus this zone is relevant for the motoring operation. In the second zone the appearing torque counteracts against the counterclockwise rotation and a driving torque is necessary to enable the movement towards the unaligned position. Thus this zone is relevant for generating operation.

The influence of the different rotor positions can be also described by the magnetisation and inductance curves. These figures give a closer survey and form the basis for the further mathematical description. Figure 3.9 shows a set of magnetisation curves. The flux linkage y/ versus the current i is presented for one phase. Chapter 3: Principle and Theory of Switched Reluctance Generators 36

This set of magnetisation curves is for the rotor in several positions between the unaligned and aligned positions. The aligned curve is the highest and the unaligned curve is the lowest. Before the start of pole overlap the curves do not vary a lot and rise almost linearly, but with the begin of overlap they rise sharply and their shape gets closer to that of the aligned curve. Just before alignment they change less again.

V

i

Figure 3.9: Set of magnetisation curves for one phase [27]

Figure 3.10 shows the shape of the phase inductance curves versus the rotor positions between the two zones for different phase currents. The curves are periodic with the rotor pole pitch which is equal to the width of the two zones, thus only this part of the curves is included in the figure. As already mentioned above, the inductance L is a function of the rotor position angle G. From the figure it can be seen that the inductance is not only a function of the rotor position but a function of the rotor position and the phase current as well. The phase current dependency is caused by the influence of saturation. With an increase of the current the inductance decreases.

The most used inductances in switched reluctance machine theory are the unsaturated unaligned inductance Lu0 and the unsaturated aligned inductance Lao which are included in the figure. For a good electrical behaviour and a high output power of the generator the unaligned inductance should be as low as possible and the unsaturated aligned inductance as high as possible. Typical motor designs have a ratio Lao /Luo around 10 [27]. Basically, the higher this ratio is the more output power can be delivered by a generator. The reason for this will be clear after the energy conversion diagram is introduced in chapter 3.2.4. Chapter 3: Principle and Theory of Switched Reluctance Generators 37

Zone 1 Zone 2

increasing /current

unaligned aligned unaligned Figure 3.10: Inductance versus rotor position angle with the effect of saturation as the current increases

3.2.2 Torque and Currents

When current flows in one phase, the appearing torque tends to move the rotor into a position where the magnetic reluctance will be minimised, which is equal to the maximisation of the inductance. Thus the rotor movement is always in the direction of increasing inductance. The direction of the phase current is insignificant for this behaviour. Therefore a positive torque can be produced only in zone 1 and the periodic equivalents in counterclockwise rotation. Respectively a negative torque will be produced in zone 2. For generating operation only this negative torque of zone 2 is useful. Because of this the phase current has to be switched during a revolution according to the operating state of the machine. Otherwise the efficiency will be decreased or, in the worst case, the machine will not operate. How this commutation of the phase current can be realised is the topic of chapter 3.3.

The total torque is assembled by the instantaneous torques of each phase. More phases are needed to produce an unidirectional torque at all rotor position. The torque waveform gets more constant with an increase of the number of phases. For switched reluctance motors torque ripple is usual and a lot of articles have been published about the research and progress on torque ripple reduction, like [48] and [50]. The negative torque used for generating has a ripple, too, and causes a rippled output current. Generators with a low number of phases do not usually produce a steady current. The current is pulsating instead and sometimes the peak of the pulse can be very high and sharp. These peaks have to be limited by a careful construction design Chapter 3: Principle and Theory of Switched Reluctance Generators 38

and by a suitable control strategy (see chapter 3.5). Otherwise the commutation devices might be destroyed.

Figure 3.11 shows the output current waveform for a 6/4-switched reluctance generator with 12 V supply voltage and 1.5 kW output power at a speed of 3,000 rpm computed by the simulation tool PC-SRD. It can be seen that the positive current peak is quite sharp. This is because the excitation is taken straight from the output current in the beginning and only later from the supply. The negative part of the waveform is wider and the peak is a lot higher, so a high output is reached.

PC Link curr» r>~ A x 1.0*2

Peter position x 1.0*1

Figure 3.11: DC link current versus rotor position for a 6/4-switched reluctance generator with 12 V supply voltage and 1.5 kW output power at a speed of 3,000 rpm

The necessary input torque for generation of the DC link current in figure 3.11 is shown in figure 3.12. This torque has to be provided by the driving machine. From the figure it can be seen that also the input torque has very high peaks like the generated output current.

Torque versus rotor position ie < Nm > x l.Oel

12.00 18.00 -0.25 - -0.50 - -0.75 -

-1.00- -1.25 - -1.50 -

Rotor position < deq ) x l.Oel

Figure 3.12: Torque versus rotor position for a 6/4-switched reluctance generator with 12 V supply voltage and 1.5 kW output power at 3,000 rpm Chapter 3: Principle and Theory of Switched Reluctance Generators 39

3.2.3 Mathematical Description

The mathematical description of the switched reluctance machine is based on the voltage equation and the energy balance. The equations are derived for an one-phase model with neglecting skin and hysteresis effects and magnetic coupling of the phases. The voltage equation of one phase is

u = Ri+M$. (3.11) at with the phase resistance R, the phase current i and the phase flux linkage iff. The flux linkage depends on the phase current and rotor position angle d which are changing with time. The power balance dif/ di . diff dd ui = Ri2 + i ■+i (3.12) di dt dd dt is got by multiplying the voltage equation with the phase current. The used energy

ui dt — R ?dt+i ^ di+i ^ dd — R i2 dt+dWt + dWm (3.13) consists of the change in mechanical work dWm,. stored field energy dW{ and resistance losses. The magnetical energy depends on the current and the rotor position and its change is given by dWf=^di+^-dd. (3.14) f di dd Thus the change of the mechanical energy is

(3.15 )

The energy stored in the magnetic field at a certain operative condition can be calculated by

W(=ji diff =iy/-j\]/di, (3.16) and its partial derivation regarding the current is

(3.17) di di l di di

Equation (3.15) has given the change of mechanical energy and it can be written easier by using equation (3.17). It equals then

(3.18)

The torque equals the derivation of the mechanical energy regarding the rotor position and it is Chapter 3: Principle and Theory of Switched Reluctance Generators 40

dWm ,d y dW{ (3.19) do de de This equation can be simplified more by replacing the stored field energy with the coenergy defined by / W‘=\\}fdi. (3.20) o The graphic definition of the coenergy is shown by figure 3.13. Also the graphic interpretation of the stored field energy is given in the figure. The knowledge of the different energy types is needed for understanding the energy conversion principle (Chapter 3.2.4).

The flux linkage for the coenergy calculation is y/ = j(Us-Ri)dt (3.21) with Us as the supply voltage.

From the figure can be seen straight that the sum of the stored field energy and coenergy is Wf+W*=z>. (3.22) The derivation of the coenergy regarding the rotor position is dW* = . dyr dW{ (3.23) dQ dG d6 By replacing this result in equation (3.19) the torque produced by one phase can be calculated from Chapter 3: Principle and Theory of Switched Reluctance Generators 41

rM)=M (3.24) i=const

The equations (3.20), (3.21) and (3.24) are the general expressions used for switched reluctance machine calculations. For the realisation of machine designs these equations have to be solved, but an analytical solution can be found only if the effects of saturation are neglected. With neglecting the saturation the magnetisation curves become linear and the instantaneous torque is then 1 .2 dL T (3.25) 2 dO

For a good machine design the effect of saturation can not be neglected and the equations (3.20), (3.21) and (3.24) have to be solved. This requires computer-based simulation because the torque is a function of phase current and rotor position and affected by saturation, especially intensely at the pole comers. Another reason is that the instantaneous torque and current vary with the rotor position. Thus the average torque can be determined only by integration over a period of rotation. Different computer-based simulation tools or models are reported in literature which are based on those equations. The already mentioned simulation tool PC-SRD is among them [6],[29],[31],[32],[33],[41].

3.2.4 Energy Conversion

The energy conversion principle can be best explained by using the energy conversion diagram which is also called i-yr diagram. An advantage of this diagram is that the average torque can be derived from the areas on the diagram. This method for deriving the average torque is used for computer based simulations, for example the simulation tool PC-SRD uses it [29]. Figure 3.14 shows a diagram like that computed by the PC-SRD.

Some suppositions have to be set so that the energy conversion diagram can be used. The machine must rotate at constant speed and a constant voltage has to be supplied to one phase. For the here described generating operation the voltage is supplied close before the rotor reaches the aligned position and the commutation takes place after the aligned position, but before the next unaligned position. The working principle is explained neglecting all losses for an easier understanding. Thus in the fundamental figures of the energy conversion diagram (Figure 3.15 to 3.17) which are used for explanation of the principle, the losses are neglected, too. Chapter 3: Principle and Theory of Switched Reluctance Generators 42

The energy conversion diagram can be separated into two periods. The first period is the excitation period. It starts with the supply of the voltage to the phase and ends with the commutation. Its necessity is justified because switched reluctance generators are singly excited machines and the excitation energy must be supplied every stroke. The second period is the output period after commutation during which the output current is provided to the power supply. This period stretches as far as the next unaligned position is reached.

Flux linkage versus current U-s x 1.0e-2

8.50-

1.00- 7.50-

5.50- 5.00-

4.00- 3.50- 3.00- 2.50- 2.00- 1.50- 1.00-

Figure 3.14: Energy conversion diagram computed by the PC-SRD

Figure 3.15 shows the part of the energy conversion diagram for the first period. During this period the excitation energy WeXC combines with the mechanical input energy W^mi; to build up the stored field energy Wf. No energy is supplied to the output during this period. It is all stored in the magnetic field.

The magnified part of figure 3.15 shows the mechanical output energy Wm(0Ut). It is a part of the energy supplied by the source but it is not stored in the magnetic field. Instead it is converted to mechanical work and produces a small positive torque. This is caused by the switch-on of the excitation before the aligned position is reached. It seems that the mechanical output energy is wasted in the generating operation, but the produced positive torque can be used by another phase depending on the number of phases, the position in which the excitation will be switched on and the moment of commutation. If these dependencies suit, the torque will be taken over straight from another phase and thus the necessary driving torque will be decreased. Chapter 3: Principle and Theory of Switched Reluctance Generators 43

Moment of commutation

m(out)

Figure 3.15: Energy conversion diagram: Excitation period

In the figure the area taken by the mechanical output energy is rather small compared with the others, but the area will increase with an switch-on of the excitation far before the aligned position. Thus it can not always be neglected. The production of mechanical output energy can only be avoided if the excitation is not switched on before the aligned position is reached. In this case the time for building up the stored field energy is very short and only a low flux linkage will be reached until the moment of commutation. This flattens the energy conversion loop and the output power will be low. Because of this the mechanical output energy can not be avoided if the machine is supposed to work at high capacity.

Figure 3.16 shows the part of the energy conversion loop for the second period. During this period the stored field energy Wf = Wexc + Wm(ini) is released as output energy. At the same time the mechanical input energy Wm(in2) is converted straight to output energy. When the unaligned position is reached, the stored field energy is completely exhausted and the flux linkage and the phase current reaches zero.

Figure 3.17 shows the complete energy conversion diagram. Both periods together form the energy conversion loop. The area inside the loop is the total mechanical input energy = Wm(i„i) + Wm(in2). The average torque taken from the driving machine can be calculated from it as Chapter 3: Principle and Theory of Switched Reluctance Generators 44

(3.26)

The mechanical input power equals the effective output energy if the excitation current is taken from the same source than the output current is provided to. Depending on the commutation circuit different sources for excitation and output are possible (see chapter 3.3.3). Then the excitation energy has to be added to the total mechanical input energy to get the total input energy. Also the total output energy is increased by the excitation energy.

0 i

Figure 3.16: Energy conversions diagram: Output period

The output capability of switched reluctance generators clearly depends on the available area of the i-y/ diagram. To achieve a high specific output, it is important to have a large inductance ratio and a high aligned saturation flux linkage. This ensures a large usable area for the energy conversion loop between the unaligned and aligned magnetisation curves.

The energy flow in a switched reluctance generator can be characterised by the excitation penalty

(3.27) with Pexc as the average electrical excitation power and Pout as the average electrical output power. Ideally the excitation penalty would be zero, but this is impossible Chapter 3: Principle and Theory of Switched Reluctance Generators 45 because it would require a zero air gap and non-saturable iron. Thus the excitation penalty should be as small as possible.

Figure 3.17: Complete energy conversion diagram

If the excitation and output sources are equal, the efficiency is

out 77 = - (3.28) 1 mech with Pmech as the mean mechanical input power. For different sources the efficiency is

V = (3.29) xP exc + 1p mech

3.3 Commutation Unit

Switched reluctance generators need essentially a commutation unit, because unipolar current pulses have to be supplied every stroke for excitation. The magnitude and amplitude of the excitation current pulses have to be controlled to fulfil the requirements of the output power control and of the commutation components. Also a reverse voltage has to be supplied for demagnetisation to get the output current. The commutation in the converter is a current commutation. This means that the current in one phase has to be reduced to zero and the current in the following phase build up from zero. Chapter 3: Principle and Theory of Switched Reluctance Generators 46

The commutation unit is required to raise the current in the on-going phase in the minimum time to get enough excitation and to minimise current disturbances. For this it needs a sufficiently high forcing voltage at each operation point, so that the current is injected quickly enough into the winding. This is critical at high speeds since the available time is decreased, because the time for excitation is inversely proportional to the rotation speed. At low speeds the current has to be limited because of appearing high current peaks which could destroy the commutation components. It also has to have a high demagnetising voltage to provide efficient energy extraction during the demagnetisation interval, which is important for a highly cyclical energy exchange between the converter and the generator, and it has to permit an extension of the excitation period.

Another requirement is to provide independent control of the phase currents for the possibility of an overlap, so that excitation can be supplied to one phase while extracting it simultaneously from the other phase. Obvious requirements are high efficiency, low switch to phase ratio and as low converter power rating as possible to save production costs, high reliability and robustness and low noise and current pulsation. The converter current rating is determined at low speeds, whereas the voltage rating is fixed by the maximum speed.

The converter topologies can be distinguished into groups by the voltages used for magnetisation and demagnetisation and their ability to provide independent phase control. Single-rail circuits are characterised by having the same voltage available for magnetisation and demagnetisation, whereas dual-rail circuits use different voltages. Single phase circuits allow an independent control of each phase, whereas multiple phase circuits can not cope with phase overlap. These are the key parameter that affect the inverter selection, and most important is whether the generator operates with or without an overlapping current through its speed range.

Lots of effort has been lately put on the task to develop new and cheap converter topologies for motoring operation, as it can be seen from the literature [4],[7],[13],[18], [19],[40]. The main attempt was to reduce the number of switches per phase, and many different converter circuits with a reduced amount of switches have been designed. Other publications concentrate on comparative evaluations like [49] and a basic general overview is given in references [27],[48]. Every converter circuit mentioned in the literature can not be used for generating operation because some of them do not allow to deliver energy to the source during the demagnetisation Chapter 3: Principle and Theory of Switched Reluctance Generators 47 interval. The usable converter topologies for generating operation are described in this chapter.

3.3.1 Classic Converter

The classic converter is the most popular converter topology, especially for four-quadrant operation. Sometimes it is also called standard or asymmetric bridge converter. The connection diagram of the classic converter for a three-phase machine is shown in figure 3.18. It consists of two active switches and two diodes for each phase. Thus the number of switches is twice the number of phases, which is the highest switch per phase ratio of a converter topology. The advantage of this high ratio is that the phases can be controlled independently of each other. Because of this the classic converter belongs to the group of single phase converters and, because it works only on one voltage level, it is also a single-rail converter.

S1\D1A

Figure 3.18: Classic converter topology for a three-phase machine

The classic converter enables three connecting states independent for each phase. The first connecting state is when the switches SI and S2 are connected. At that time the excitation current flows and builds up the magnetic field. This is the converter state during the excitation period of the generator. The other important state for generating operation is when both switches (SI and S2) are turned off. Then the demagnetisation takes place and the output current is delivered to the supply. This is the converter state during the output period. The third possible state is called freewheeling and only one of the switches (SI or S2) is connected. This state is necessary for soft chopping (see chapter 3.4.2) but not essentially necessary for generating operation, because chopping is not advantageous in generating operation. Chapter 3: Principle and Theory of Switched Reluctance Generators 48

The classic converter has many advantages. The most important is that the current overlap does not affect. Thus the phases can be controlled independently. The full supply voltage is applied to the winding in either direction of polarity and the components have a low voltage rating. It has also some disadvantages of which the most significant is the high total number of switches which equals a high switch to phase ratio. Others are the need of a DC link filter, the low demagnetisation voltage at high speeds and the high voltage drop across the converter switches which is a significant fraction of the supply voltage in low-voltage applications.

3.3.2 (n+l)-switch converter

The (n+l)-switch converter is named after the number of switches used. The number of switches is one higher than the number of phases. This is one switch more than the minimum possible number (for example compare chapters 3.3.3 and 3.3.4). Sometimes this converter is also called Miller or common switch converter. It is derived from the classic converter by substituting switches and diodes. The connection diagram of the (n+l)-switch converter for a three-phase machine is shown in figure 3.19. It consists of one common diode and active switch for all phases and another diode and active switch for each phase. The disadvantage of the low switch per phase ratio is that the phases can not be controlled independently of each other. The (n+l)-switch converter belongs to the group of multiple phase and single-rail converters.

Figure 3.19: (n+l)-switch converter for a three-phase machine

Like the classic converter, also the (n+l)-switch converter enables the three connecting states for excitation, output and freewheeling. The main limitation is that Chapter 3: Principle and Theory of Switched Reluctance Generators 49 the demagnetisation of any of the phases is impossible when the switch SI is turned on. Thus it does not tolerate phase overlapping and therefore its capability is very limited. This is the major disadvantage of the (n+1)-switch converter and limits its operational area to low speed applications. Its benefits are the reduced number of switches and the low converter power rating which reduces the production costs.

3.3.3 Boost and Buck Converter

Boost and buck converters (for their connection diagrams see Figure 3.20 and 3.21) are almost solely used for generating operation. One reason is that they do not allow the freewheeling state. Thus they enable soft chopping but it does not affect generating operation. Only two connecting states independent for each phase are allowed. The first connecting state is when the switch S is connected. This is during the excitation period. The other state is when the switch S is switched off and the output current is delivered through the diode D to the supply.

Figure 3.20: Boost converter topology for a three-phase generator

Boost and buck converters are dual-rail converters because the excitation circuit is separated from the output circuit and the voltage levels of both circuits have to be different. One advantage of these converter topologies is that each phase can be controlled independently. This is characteristic for single phase converters. Another advantage is that only one switch per phase is needed. This is the lowest possible switch per phase ratio. The major disadvantage is that two independent voltage sources are needed. Chapter 3: Principle and Theory of Switched Reluctance Generators 50

Characteristic for boost converters is that the output voltage has to exceed the input voltage. This leads to a problem at slow speeds because the high reverse voltage across the phase winding extinguishes the flux too quickly and the energy conversion is cut off with only a fraction of its maximum possible output. The boost converter is sometimes also called up converter

Figure 3.21: Buck converter topology for a three-phase generator

Buck converters are characterised by a lower output voltage than input voltage. This has the advantage that the problem of boost converters does not appear in buck converters. The lower output voltage leads to a longer output period with a slower extinction of the flux. A higher output can be reached because a fuller energy conversion loop is obtained. The buck converter is sometimes also called down converter.

3.3.4 Bifilar Winding Converter

The bifilar winding converter, like the boost and buck converters, uses the smallest possible number of power devices. Just one switch is required per phase and this leads to the lowest possible switch per phase ratio. Figure 3.22 shows the connection diagram of a bifilar winding converter for a three-phase machine. The converter allows two connecting states independent for each phase. At first, when the switch S is connected, the magnetic field for the excitation is build up. After the switch S is switched off, the output current is delivered through the diode D to the supply. These are the two possible states. The bifilar winding converter can not operate in the freewheeling state and thus soft chopping is enabled, which does not affect generating operation. Chapter 3: Principle and Theory of Switched Reluctance Generators 51

O-

Ad A A

s O' Figure 3.22: Bifilar winding converter for a three-phase machine

The advantages of the bifilar winding converter are the low switch per phase ratio and the full reverse voltage. A negative point is the need of an extra winding for each phase. This causes additional costs and reduces the efficiency, because additional copper losses are associated with the auxiliary winding. Also voltage spikes resulting from imperfect magnetic coupling can appear and necessitate the use of snubbers. A high voltage rating is necessary.

3.3.5 Other Converter Topologies

Several other converter topologies are developed but most of them are restricted to motoring operation. Only converters which can connect the reverse voltage to the phase winding through freewheeling diodes are useful for generating operation.

Common for motoring operation are, for example, C-dump or modified C-dump converters. They recover the stored energy by dumping it in a capacitor and the trapped energy is returned to the source by using a chopper. These converters need additional components and their control is complicated but they need only one active switch more than the minimum. For generating operation the chopper components and the dump capacitor have to be very large, even larger than for motoring operation, because the energy returned to the supply is a lot higher. Also the additional losses associated with the reactive elements enable their use for generating operation.

Other quite common converters for motoring operation are converters which use a resistor for suppression. The advantage of these converters is that they have low Chapter 3: Principle and Theory of Switched Reluctance Generators 52

production costs because they require just the minimum number of switches without an auxiliary bifilar winding. Because they dissipate the stored energy or at least parts of it in the resistor, they can not be used for generating operation.

3.4 Dynamic Operation

The dynamic operation of switched reluctance machines depends on the commutation unit and the control strategy. The operation modes are single-pulse operation and chopping. Both operation modes are described in this chapter. All commutation units allow single-pulse operation and hard chopping and most of them also allow soft chopping (compare chapter 3.3). The control strategy builds on these different operation modes depending on its task. Especially in motoring operation chopping is used very often to smooth the output torque and to control the current at low speeds.

3.4.1 Single-Pulse Operation

The single-pulse operation is the main operation mode because the flux in switched reluctance machines is not constant and has to be build up from zero every stroke. This is realised by switching the supply voltage on at the turn-on angle 6q and off at the turn-off angle 6c- The switching is made by the active switches of the commutation unit. The turn-off angle is often also called commutation angle, because at this rotor position the reverse voltage is supplied through the commutation diodes to the phase winding. Figure 3.23 shows the characteristic waveforms of the idealised inductance, voltage, flux linkage and phase current for single-pulse operation.

The waveforms are typical for generating operation at middle speeds. At low and high speeds the waveform shape can vary, but the general appearance is not very different. The inductance waveform is idealised between the aligned La and unaligned inductance L^. The other waveforms can be related to the rotor position from it. The supply voltage Us is switched on while the inductance is rising and before the aligned position is reached. The commutation takes place behind the aligned position but still far before the unaligned position so that the output period is long enough to deliver a sufficient output current. At the commutation angle the active switches are switched off and the reverse voltage is supplied through the diodes. The flux linkage reaches its maximum y/c at the moment of commutation, whereas the maximum current peak /peak is reached later. At the extinction angle 9q Chapter 3: Principle and Theory of Switched Reluctance Generators 53 the voltage, flux linkage and phase current are back to zero and the diodes are closed again.

Idealised inductance

Aligned

Unaligned

Voltage

Flux linkage

■ Phase current

Excitation period Figure 3.23: Single-pulse waveforms for generating operation

Ideally the switch-on angle should be close to the aligned position because otherwise a small positive torque is produced by the supply current of the battery. On the other hand, the excitation will not be sufficient if the period is too short. Especially at high speeds the disadvantage of positive torque production has to be accepted (compare chapter 3.2.4). The angle difference between the turn-off and the tum-on angle is called dwell angle It is the angle that stretches across the excitation period. The control of switched reluctance machines uses both the tum-on and the turn-off and thus also the dwell angle. In generating operation the output power and the height of the peak currents are depending on these angles. Chapter 3: Principle and Theory of Switched Reluctance Generators 54

3.4.2 Chopping

Chopping is necessary in motoring operation to control the current at low speeds and to smooth the output torque. It is realised by using the freewheeling or reversing state of the commutation unit which were already explained in chapter 3.3. The types of chopping are distinguished in voltage pulse-width modulation and current regulation. Both types of chopping can be realised by soft and hard chopping. In soft chopping the supply voltage is switched off by using the freewheeling state, whereas in hard chopping the voltage is reversed by using the reversing state of the commutation unit. The characteristic of voltage pulse-width modulation is that the state of the commutation unit is switched at high frequency with a fixed duty cycle during the dwell period. For current regulation the state is switched during the dwell period depending on the current being greater or smaller than a reference current. Thus the duty cycle is variable.

Chopping is not advantageous in generating operation because the peak of the output current appears during the output period and not during the excitation or dwell period (see chapter 3.4.1) when chopping is used. Thus chopping reduces only the excitation current but that is not desirable and has no direct influence on the peak of the output current. Other strategies have to be used to reduce the high peak of the output current, especially at slow speeds.

3.5 Control System

Switched reluctance machines need a control system because the current waveform shape and its magnitude must be controlled in relation to the variations of speed and load. This task is quite difficult to fulfil because the relationships between torque, current, speed and firing angles are highly non-linear and vary as a function of speed and load. The control strategy has to cope with these difficulties and sometimes it has to fulfil also the requirements of peak current regulation. Another difficulty is that switched reluctance machines have no axis transformation like AC motors and no field oriented control principle has been developed for them. Thus it is necessary to use high-speed real time controllers which operate with phase currents and voltages directly. Also the switching precision is critical in switched reluctance drives and a precision of 0.5° or even 0.25° is desirable, as it is pointed out in reference [27].

Motors are normally controlled by closed-loop speed and sometimes torque control, whereas generators are controlled by keeping the output voltage constant. The Chapter 3: Principle and Theory of Switched Reluctance Generators 55 parameters for the control are the turn-on and the turn-off angles. A rotor position feedback is necessary to synchronise the switching of the commutation devices depending on the firing angles with the rotor position. The rotor position can be obtained by direct or indirect sensing. The conventional way is to use direct position sensing and it is realised by using a slotted disk together with optical interrupters, Hall-effect or other type of sensors. The indirect rotor position sensing is a popular field for investigations and research and many articles have been published, like [8],[9],[16],[21],[23],[36],[37],[38]. It is described later in this chapter.

3.5.1 Structure

The structure of the control system for switched reluctance generators is shown in figure 3.24. The controller, commutation unit and switched reluctance generator are considered as a black box for the reason of simplicity. The system input value is a reference voltage UKfwhich is generally kept constant depending on the voltage level of the source and loads. The system output is the output voltage Uou t of the generator and varies with load and speed. It has to be kept constant and thus a voltage error AU is derived by comparison with the reference voltage after feedback. The voltage error together with the rotor position 6 and angular velocity (0 feedback is the input of the controller which has to estimate the firing angles 0O and 0c for the commutation unit. The commutation unit then switches the phase currents i\, i% and h of the generator. This all put together results in the structure of the control system.

AU Commutation Controller SR-Generator Unit

Figure 3.24: Control system structure for a three-phase generator

3.5.2 Control Modes and Strategy

Different control modes for switched reluctance motors are mentioned in the literature [3],[27]. The modes are normal, boost and long dwell and are distinguished according to the values of the firing angles and the resulting characteristics. The Chapter 3: Principle and Theory of Switched Reluctance Generators 56

references mention only one mode for generating or braking operation, but simulations with the PC-SRD have shown that the three modes can be observed also in generating operation. Figure 3.25 shows the current waveforms of the three control modes for generating operation.

Normal

Boost

Long dwell

Figure 3.25: Phase current waveforms for normal, boost and long dwell control modes

The normal mode is characterised by a short excitation period with the tum-on angle 6q close before and the turn-off angle 0c close behind the aligned position. Only a small negative torque is produced during excitation before the aligned position is reached. Because the excitation period is short, the output period is also short and thus the output power is small. A positive effect is that the current peak /peak is small, too. This control mode is most suitable at low speeds for restricting the current peak.

Compared with the normal mode the boost mode has a longer excitation period and thus also a longer output period. More output power is generated and the current peak is higher. The negative torque produced during excitation is still quite small. This Chapter 3: Principle and Theory of Switched Reluctance Generators 57 mode should be used at medium speeds. Because of the higher speed a longer excitation period is needed to reach the nominal output power.

The long dwell or also called the advanced mode has the longest excitation period with the turn-on angle far before and turn-off angle far after the aligned position. The first smaller current peak of the current waveform for the long dwell mode, which can be seen in the figure, produces a worth mentioning negative torque because of the turn-on of the excitation far before the aligned position. The output period is extended and thus a high output power is reached. A negative feature is the high output current peak. This mode is supposed to be used at high and very high speeds to reach a high output power. There is no clear distinction between the modes.

Basically the control strategy can be realised in two ways. The first and the easier possibility is to vary just the turn-on angle and to keep the turn-off angle constant at a sufficiently high value. This has the consequence that very high current peaks can appear at low speeds together with high load, which may not be tolerated by the commutation unit. At low load the ratio of peak current and RMS-current can be high, but these current peaks will not cause damage to the commutation, because their level is lower than in the other situation. This control strategy is mainly based on the long dwell mode with the turn-off angle far behind the aligned position.

The other possibility is to vary both firing angles. Then a smoother output current waveform is reached and the critical high current peaks are avoided. The reason for this is that all control modes are used in their suitable speed ranges. This control strategy is more sophisticated but has the mentioned major advantages.

3.5.3 Sensorless Control

The sensorless control can be distinguished into four schemes. The schemes are open-loop control, passive waveform detection, active probing and observers. In open-loop control the dwell period is controlled but the firing angles are not synchronised to the rotor position. These controllers are unstable and they have to be stabilised by using other external values, like torque or current, to recognise load or speed changes. They are not useful in generating operation because the firing angles have to be kept exactly in position to keep the output voltage constant and to avoid high current peaks. Chapter 3: Principle and Theory of Switched Reluctance Generators 58

The passive waveform detection mainly relies on characteristics in the phase current waveform, for example maximum or minimum. Phase current measurements are necessary to realise this scheme. Reference [23] illustrates the realisation of such a scheme that detects the change of current ripple and converts it to a rotor position signal, but it can provide the signal only at low speeds. References [36],[37],[38] describe a sensing technique that uses the current rise and fall times. Restrictions to low speeds are mentioned and the successful detection of the rotor position is related to chopping operation. Another method is to measure the mutual induced voltage in an unexcited phase as it is described in reference [16]. It is suitable for low speeds, low voltage and high current drives with single switch per phase converters. In generating operation passive waveform detection does not seem very suitable because the high current peaks appear at low speeds and thus switched reluctance generators should operate at higher speeds.

For sensing with active probing, a square-wave voltage is applied to an unexcited phase. The resulting current pulses vary with the phase inductance. The minimum and the maximum are reached with the aligned and unaligned positions. The rotor position can be detected from this. The references [8 ],[9],[21] describe the realisation of position sensing with active probing. Problems occur with a small number of phases because of phase overlap and the references mention that the realisation is most reliable for machines with at least three or preferably four phases.

The most demanding control scheme uses observers. A state observer is a mathematical simulation of the machine running on-line on a microcomputer in parallel with the drive. Measured currents and voltages are the input for a model which gives then the rotor position and speed. 59

4 Generator Design

Before the generator design can be made, some suppositions have to be defined. The main suppositions are supply voltage, speed-range and size. A common 12 V battery is chosen for the power supply, as it is used in motor vehicles. This is the cheapest and most reliable solution. It also opens the easiest possibility of using the generator in the most common field of applications - in motor vehicles. A detailed description of battery characteristics is given in the references [14] and [17].

Table 4.1 includes the main battery characteristics. It can be seen that different characteristic voltages are necessary to describe the battery behaviour because the voltage depends on the state of charge. Besides the conventional nominal voltage also rest, discharged, maximum charged and gassing voltages are introduced. Also the nominal capacity is included. This capacity is defined by the amount of current which can be delivered during 20 hours of discharging at 27° C with a constant current.

Table 4.1: Main battery characteristics

Nominal voltage C/N= 12 V Rest voltage U rest = 12.72 V Discharged voltage t/dis= 11.76... 11.88 V Maximum charged voltage Umax = 15.6 ... 16.2 V Gassing voltage UR as = 14.4 V Nominal capacity K 20 = 84 Ah

The voltage drops down to the rest voltage after charging of the battery and it will be held. If the battery is partly discharged, the rest voltage will be reached after a few seconds of charging. The lowest possible voltage is reached when the battery is discharged. Analogously the maximum voltage is reached when the battery is fully charged but before reaching that level the battery water will start to decompose at the gassing voltage. Thus the gassing voltage should not be exceeded. Figure 4.1 illustrates this voltage behaviour versus time for charging and discharging.

The voltage behaviour of batteries is also depending on the temperature. The above mentioned values of the voltage levels are applied to 20° C and they decrease in colder surroundings. Thus a voltage of 14 V has been chosen as operating voltage of the generator to surely avoid the decomposition of the battery water at the gassing voltage of 14.4 V. It also provides some clearance for the control system. Chapter 4: Generator Design 60

UN 14.4 t

13.8 "

13.2 -- — Charging —Discharging

12.0 --

11.4 --

0123456789 10

Figure 4.1: Battery voltage versus time for charging and discharging

The speed range of the generator is chosen according to the speed range of the internal combustion engine of motor vehicles to provide the best output characteristic for this main application. A speed range multiplied by a constant ratio factor is also suitable. This can be realised by the variation of the pulley size. It can be suited in the same way for other applications with a different speed range. The speed range of combustion engines spans from the idling speed 800 rpm up to 8,000 rpm. At a speed of 6,000 rpm the overspeed range begins, so this range is rarely used for driving. Speeds around 3,000 to 4,000 rpm are used mostly.

The size of the switched reluctance generator should be around the size of large alternators for 12 V applications. Then the new generator with its supposed higher output power would be advantageous in this point. The outer stator diameter of these alternators is around 150 mm, the outer length is usually a bit smaller than the diameter and the weight is around 7 kg.

4.1 Construction

Before geometrical details of the construction can be designed the magnetic material has to be chosen because it has a major influence on the machine performance. Its typical magnetic values, magnetisation curve, core losses and mechanical properties have to be known before a design can be made. The material has to fulfil the special demands of switched reluctance machines, like high commutation frequency, high Chapter 4: Generator Design 61

harmonics of the flux density waveform and high saturation, especially of the pole comers. Thin lamination is desirable, and Silicon steels are preferred [27].

Here is chosen a cold rolled, non-oriented electrical steel of grade DK-66 which contains 1.3 per cent of Silicon. The layer thickness of the lamination stacking rstk is selected to 0.5 mm. For the lamination stacking factor fs± is chosen the value 0.97. The important magnetic and mechanical properties of this steel are summarised in table 4.2.

Table 4.2: Properties of DK-66

Resistivity P resFE = 2.8* 10'3 £2/m

Relative permeability at 2*10 4 T and 50 Hz P start — 290 Maximum relative permeability at 50 Hz P max = 5000 Flux density at 2.5* 103 A/m DC B 25= 1.65 T Flux density at 10* 103 A/m DC B io= 1.83 T Flux density at 30* 103 A/m DC B 30 = 2.06 T Coercive force at DC Hc = 90 A/m

Guaranteed maximum core losses at 1.0 T and 50 Hz P 10max = 2.6 w/kg

Guaranteed maximum core losses at 1.5 T and 50 Hz P 15 max = 6.0 w/kg Core losses at 1.0 T f 10 = 2.4 W/kg Core losses at 1.5 T P15 = 5.4 W/kg Density Pfe = 7740 kg/m 3 Modulus of elasticity in rolling direction £r=1.8443*10 nkg/(ms 2) Modulus of elasticity in transverse direction £, = 2.119*10n kg/(ms 2) Yield point C7y=2.845*10 8 N/m2

Even though this material is non-oriented it should be mentioned that the property values are different in the rolling and traverse direction, for example the permeability is higher and the core losses are lower in rolling direction. Table 4.2 includes average or worst case values so that they can be used safely for further calculations.

This steel is a common material in many AC machines and especially in high-efficiency applications because the Silicon reduces the core losses. The major advantage of this material is the high saturation flux density as can be seen from the magnetisation curve in figure 4.2. This fact is decisive for the use in switched reluctance machines to reach a good output power. Chapter 4: Generator Design 62

2.00 •

1.80 ■

1.00-

0.40 •

0.20*

0.60 2.00 2.60 3.00 Ax* x 1.0*4

Figure 4.2: Magnetisation curve of DK-66 as integrated into the PC-SRD

4.1.1 Basic Characteristics

In order to get a competitive machine the number of phases should be as low as possible. This guarantees low production costs because of the easy construction and a commutation unit with a small amount of switches. A one-phase generator has the minimum number of phases but it has only an absolute current output zone of one half. This means that output current can be produced maximum over only one half of each revolution. The other half of the revolution is over a blank zone and can not be used for current generation. This is definitely too low utilisation of a machine. To get output current almost over a full revolution the absolute current zone has to be at least one. This together with the already mentioned demand fulfils a two-phase generator. Thus a two-phase generator is chosen.

Table 3.1 shows two different possible rotor and stator pole combinations for two-phase machines. In reference [20] the influence of the number of poles per phase in switched reluctance motors has been researched. It concludes that both single- and multiple-pole-pair-per-phase motors have their advantages depending on the application. Because of this an analysis of two-phase generators with single- and multiple-pole-pairs-per-phase has been made with the PC-SRD in this work to examine the influence for generator applications. The results show that the generator with eight stator poles and four rotor poles has only disadvantages compared with the other one. The peak currents are higher, a more precise controller is needed and the geometry is more complicated. Thus the number of stator poles is chosen to 4 and the Chapter 4: Generator Design 63

number of rotor poles to 2 respectively. Then the stroke angle is 90° and the number of strokes per revolution is 4.

4.1.2 Envelope and Internal Dimensions

For the design of the geometrical dimensions a starting point has to be found to enable simulations with the PC-SRD. This can be done by solving equation (3.1) for typical values. An average torque of around 10 Nm is necessary to reach the output power of 1.5 kW at slow speeds. From table 3.2 the value for the torque per unit rotor volume can be chosen to 35 kNm/m3 to get a good performing and utilised machine.

Equation (3.1) can be solved by using these values together with a common stack length per rotor diameter ratio of 1. Then the stack length and rotor diameter are calculated to around 72 mm. For a rotor diameter per stator lamination diameter ratio of 0.5 which is typical for machines with a small number of poles, the stator lamination diameter is 144 mm. This fulfils the supposition for the approximated generator size and with a stack length of 72 mm the overall length will be also less than 150 mm.

A large shaft diameter is desirable to maximise the lateral stiffness of the rotor. It raises the first critical resonance speed and reduces the acoustic noise. Thus the shaft diameter is chosen quite large to 20 mm. The rotor yoke has to be sufficient to carry the rotor flux, which means, that it should be at least half the rotor pole width, because the flux divides into two equal parts when it leaves the rotor poles. For a rotor yoke of half the rotor pole width the minor rotor diameter can be calculated by

Am = Ah+ tT with tT given by equation (3.2). For a typical rotor pole arc of 45° the result is 47.5 mm (for the pole arc selection and optimisation see chapter 4.1.3).

The air gap length is initially chosen to 0.5 mm. This is larger than the minimum limit of 0.2 mm which is caused by the very difficult production situation under this limit. The last missing parameter value is the stator slot bottom diameter. The facts for the stator yoke are equal to those for the rotor yoke except that the stator yoke thickness has in addition a major influence on the acoustic noise of the generator. Thus the stator yoke should be chosen thicker than ts /2 to increase the stiffness and thus to reduce acoustic noise. A suitable value is 2/3 ts. The stator slot bottom diameter can be calculated by Dsb = DS- 4/3 ts with ts given by equation (3.3). With a typical stator pole arc of 45° it equals to 106.5 mm. Chapter 4: Generator Design 64

Now the corresponding radiuses can be calculated from the diameter values. The shaft radius is 10 mm, the minor rotor radius 23.75 mm, the rotor radius 36 mm, the stator slot bottom radius 53.25 mm and the stator radius is 72 mm.

After the starting point for the simulations with the PC-SRD has been found, the geometrical dimensions are varied and the effect on certain characteristic values is examined. The geometrical dimensions are varied over a range around their starting value. The observed characteristics are the inductance ratio L^o, shaft torque Tshaft, shaft power fshaft, efficiency t}, total power losses P\0sses, diode peak current /Dpeak, transistor peak current /rpeak and the output current /Dc. The values of the shaft torque, shaft power and output current are negative in generating operation and thus the absolute value is taken. The results of these variations of the geometrical dimensions are summarised in table 4.3.

Table 4.3: Effect of an increase of the geometrical dimensions on characteristic values; the symbols are standing for: 0 / almost no changes, + / increase, - / decrease, (+) or (-) / slight increase or decrease

R sh Ro Ri Ri R 3 8 •t-stk 1* ratio 0 - + - 0 - 0 abs(7 shaft) + - + 0 (-) - - abs(P shaft) ■ + - + 0 (-) - -

77 - + - + (+) - + P Losses + - + - - + - I Dpeak + - + 0 0 0 - f Tpeak ■ + - 0 + - + - abs(/Dc) + - + + (-) - -

In the table it can be seen that a large shaft radius results besides the higher lateral stiffness of the rotor in an increase of the output power. Decrease of the efficiency and increase of the peak currents of the commutation devices come along with the higher output power. Thus the shaft radius should not be made larger than it already is.

The variation of the minor rotor radius shows that it has a significant influence on the output power. To get a high output power this radius should be small but, as already mentioned, the rotor yoke has to be wide enough to carry the rotor flux. Thus it should not be made smaller to avoid high saturation of the rotor iron and it is finally chosen to 24 mm. Chapter 4: Generator Design 65

The rotor radius is the best parameter to be changed to reach a high output power because an increase of this dimension increases the output power significantly. This is quite surprising because the slot area is decreased and thus less copper can be fitted in, but still the output power rises. This can be explained from the energy conversion diagram (see chapter 3.2.4). Because of the higher inductance ratio the area between the unaligned and the aligned magnetisation curves will be enlarged and thus the energy conversion loop will be bigger. Very positive is also the fact that the critical transistor peak current does not rise with an increase of the output power.

The rotor radius is chosen to its highest value that can be used with the chosen minor rotor radius and this is 37.5 mm. A higher value would cause very high saturation of the rotor iron and the rotor yoke would have to be enlarged. Then the larger minor rotor radius would decrease the output power. Changes of the minor rotor radius and the rotor radius effect contrary on the characteristics and mainly the difference between these dimensions (rotor tooth length) determines the inductance ratio and thus the output power. This is confirmed by reference [43].

The influence of the stator slot bottom radius is rather small. It mainly effects the slot area and with a larger radius more copper can be fitted in. This will slightly increase the output power. It is positive that the generator will become more efficient at the same time. Thus the stator slot bottom radius is enlarged to 56 mm. The disadvantages are that the transistor peak current is raised and the stiffness of the stator yoke is reduced, but they can be compensated by the right choice of the stator radius.

The stator radius has only a slight effect on most of the characteristics for the designing process. Thus the main criterion for its choice is the stator stiffness to reduce the acoustic noise. Positive, but not significant, is the reduction of the transistor peak current with a larger radius. To compensate the yoke thickness reduction from the enlargement of the stator slot bottom radius, the stator radius is chosen to 74 mm.

Highly significant is the influence of the air gap length as it is pointed out in reference [34]. A small air gap effects positively on all characteristics without exception and thus it should be as small as possible. The absolute minimum given by the production possibilities is 0.2 mm [27]. The air gap length is finally chosen a bit wider to 0.3 mm to keep some clearance to the limit to ensure the production. Chapter 4: Generator Design 66

An increase of the stack length gives lower peak currents and the efficiency will be higher, but on the other hand the output power will be decreased. Thus a good compromise between these characteristics has to be found. Because the influence on the peak currents is more sufficient the stack length is chosen to 75 mm. A small stack length also enlarges the influence of end effects. The effect of end core flux on the machine performance is presented in reference [24].

The optimum choice of the values of all dimensions had been verified for different speeds and load conditions. From these finally settled dimensions the longitudinal generator cross section can be drawn. It is shown scaled down in figure 4.3 and truly scaled in figure B.2 in Appendix B.

Figure 4.3: Longitudinal cross section of the generator

4.1.3 Pole Size and Geometry

The stator and the rotor poles have to be designed. The pole sizes are determined mainly by the stator and rotor pole arcs. The other dimensions effecting on the pole sizes are already fixed in the previous chapter. A good starting point for the rotor and stator pole arc is 45°. This value equals to half of the stroke angle and is the most common choice because it enables output current to be produced almost during a whole revolution and enough clearance between the rotor and stator poles. Chapter 4: Generator Design 67

In most applications the stator and rotor pole arcs have approximately the same size because otherwise the dead zone, where no torque or output current is produced, would be extended. Basically the increase of one pole arc decreases the output current. This is a disadvantage but, on the other hand, the peak currents will be decreased, too. If both pole arcs are enlarged in the same way the current ripple will get lower for the same output current, but to reach the same output power with a larger stator pole arc a higher slot fill factor of the winding is necessary, because with an increase of the stator pole arc the slot area for the winding decreases. Thus the stator pole arc of 45° is not changed to keep the size of the slot area and the rotor pole arc is enlarged to 47.5° to reduce the peak currents. Enlarging both pole arcs does not reduce current ripple significantly because a two-phase machine with an effective overlap ratio less than 1 always produces a pulsating output current.

The most suitable pole geometry is the modification (b) introduced in figure 3.5. It is chosen because it increases the stiffness of the poles and stabilises the stator yoke which affects on noise reduction. Also it does not decrease the usable slot area significantly and it is quite easy to produce compared with other modifications. The radius of the comer area is chosen quite high to 5 mm to reduce acoustic noise. Now all the required information for drawing the cross section of the generator is given and it is shown scaled down in figure 4.4 and truly scaled in figure B.l in Appendix B.

Figure 4.4: Cross section of the generator

Modification (d) in figure 3.5 could have been another solution but the pole overhangs are not necessary because the stator pole arc is not enlarged and thus the Chapter 4: Generator Design 68

slot area is large enough to fit in the winding. Different pole profiles for motoring operation are discussed in the reference [34]. For generating operation it can not be said if some of this profiles would be advantageous and a more complicated profile would increase the production costs. Thus the traditional profile used with the pole geometry in figure 3.5 is not changed.

4.1.4 Winding

The winding has a major influence on the machine performance. It determines mainly the phase current behaviour, especially the peak current and the output power. Because of that the winding design has to be carefully and well suited.

First, the slot fill factor has to be chosen. Because of its influence on the electrical behaviour it should be as high as possible because with an increase of the slot fill factor the output power and efficiency will be increased. Another advantage is that the copper losses will be decreased, but the slot fill factor is limited by the geometry of the slot and the essential insulation. The only disadvantage of a high slot fill factor is that pre-wound windings can not be used.

Afterwards the number of turns per pole has to be chosen. Generally with an increase in the number of turns per pole the output power and the peak current will be decreased. A good compromise according to these two criteria has to be found and especially at low speeds the peak currents have to be limited. Otherwise suitable commutation devices can not be found.

The windings of opposite poles can be connected in series or parallel. Simulations with the PC-SRD have shown that the basic machine performance does not differ between serial and parallel connected windings if the number of turns per pole is chosen respectively. For parallel connected windings the number of turns per pole would have to be double compared to serial ones. Generally, serial connected windings have a better behaviour according to the influence of harmonics. Thus serial windings have been chosen here. The number of parallel paths per phase is then 1.

Various simulations with the PC-SRD have shown that the optimum fixed number of turns per pole for the serial connected winding over the whole speed range is 12. This value provides the desired output power of 1.5 kW over a broad speed range and it limits the peak currents at low speeds so that a good but not the desired output power Chapter 4: Generator Design 69 can be reached at these speeds, too. Limitations of the output power at low and very high speeds have to be made anyway if a fixed number of turns per pole is used, and the number of turns per poles has to be fixed to realise an easy and cheap winding.

With Np that equals to 12 and %u around 0.6 the wire diameters will be very high and with the phase current waveform high eddy current losses will be caused. A solution for this is to use smaller wire diameters and to connect them in parallel. This has also the advantage that a higher slot fill factor can be reached because smaller wires can be better fitted into the given slot area geometiy. A suitable wire diameter is 1 mm.

For the above estimated generator geometry the slot area can be calculated with equation (3.6) and it is 805 mm2. The usable slot area will be decreased by the area of the pole comers that is taken away by the radius r because of the chosen pole geometry (see chapter 4.1.3). ACOmer equals to 9.56 mm2 and is calculated from equation (3.9) with the geometric dimensions mentioned in the previous chapters, thus the real slot area is 786 mm2. The windings have to be insulated from the stator core iron and the two windings in the slot from each other. This will reduce the usable slot area, too. The area taken away by an insulation layer of the thickness d around the slot and of the thickness 2d between the windings is

= 2 d (2^-2/?,-3d-25-r)+[(/?, +S+df-(R1 +S)2]^l

(4.1) + -(#2- J)2j^'°'back T ^corner _ (r~df] with

A>iot -4r(27r~NsPs)’

'slotback \7Z-N, arcsin 5, 12 M and /Corner already given by equation (3.10). The net stator slot area can then be calculated as

Alotsnet Alois 2Acomer Ansul • (4.2) For sufficient insulation the insulation layer thickness should be at least 0.2 mm and the net slot area then equals to 755.5 mm2.

A very suitable and common wire for all small electrical machine windings and for many other applications is the enamelled round copper wire with DFV quality and grade 2 insulation thickness. The wire insulation is a THEIC-modified polyester imide enamel according to EEC 317-8 standard which has good chemical and Chapter 4: Generator Design 70

electrical properties. Because of its hard surface it can resist mechanical stresses. The enamel insulation belongs to the temperature class H, which guarantees that it can tolerate temperatures up to 180° C. It can also tolerate quite high temperature changes without any damage. If the wires are prepared with paraffin before coiling, machines can be used for the winding process, which will decrease the production costs. All these characteristics seem very likely for this type of wire. The technical specifications for the wire with 1 mm nominal copper diameter for a temperature of 20° C are shown in table 4.4.

Table 4.4: Wire specifications

Nominal diameter of copper D CUwire — 1 Him Nominal cross sectional copper area A cuwire = 0.7854 mm2

Minimum resistance per length R' wiremin = 0.02115 D/m

Maximum resistance per length R' wiremax = 0.02240 D/m Average resistivity Pcu= 1.7102*10-8 Dm Maximum diameter with insulation D wire = 1.0930 mm Cross sectional area with insulation A wire = 0.9383 mm2 Wire density with insulation P wire = 7613 kg/m 3

Finally, the number of parallel wires per turn per pole jVwp has to be estimated. From the cross sectional area of the winding with insulation Acu+insui = Np Nwp Awm the slot fill factor with consideration of the insulation can be calculated as

SfiUinsui = 2 Acu+insui/Asiotsnet with Asi0tsnet given by equation (4.2). This factor should be smaller than 0.75 to be sure that the windings will fit into the net stator slot area. From these equations the number of parallel wires per turn per pole can be calculated to 24. This gives a slot fill factor with consideration of the insulation of 0.715 and the

copper area Acu = 7/pMvpAwirecu equals then to 226.2 mm2. The slot fill factor

without the consideration of the insulation is then Sfm = 2 Acu/Asiots = 0.576. This high slot fill factor makes it impossible to use pre-wound windings, but concerning the electrical behaviour a slot fill factor lower than 0.4 is not suitable because the output power will be decreased for slow and high speeds and the efficiency decreased over the whole speed range. Figure 4.5 shows a possible arrangement of the wires in the slot area and it confirms that the wires can be fitted.

The winding properties are completely defined now and the direct-current resistance of one phase can be approximated as

(4.3) Chapter 4: Generator Design 71

and for a temperature of 20° C it equals to 6.3 m£l For higher temperatures the resistivity of the copper rises and thus the phase resistance will be increased. The temperature-depending resistivity is p(T) = p(20° C) [1 + a (7-20° C)] (4.4) with a that equals to 0.0038 for copper. Machines are usually reaching a stable temperature of around 80° C while operation. Depending on the characteristics of the surroundings the temperatures can rise even higher. For the following calculations a temperature of 90° C has been scheduled to ensure that the generator will work properly in the warm surrounding of the internal combustion engine of motor vehicles. The resistivity of the copper equals then to 2.1651*10' 8 Qm. This means an increase of around 25 %. The direct-current phase resistance rises to 8 mfl.

The phase resistance for non-direct currents is basically higher than for direct currents because of the influence of the skin effect. Here the influence of the skin effect can be neglected because of the small diameter of the used wires. Thus the direct-current phase resistance can be used as an approximation for the phase resistance. Chapter 4: Generator Design 72

4.1.5 Further Estimations

After all the basic geometrical dimensions have been set, some other interesting values can be estimated, like the length, weight and moment of inertia. The overall length Le can be approximated to 133.5 mm from Le = Lstk+2L0h with L„h almost equal to the stator pole width ts. For the total length of the generator the width of the shields with the bearings and the fan must be added to the overall length, but all this together still fulfils the previously made suppositions for the generator size.

The weight of the generator Wto t can be approximated from the weight of the used iron and copper. The total iron weight Wpe equals to Wr? = ppe We with ppe given in table 4.2 and We as the total iron volume which can be calculated by adding the rotor and stator iron volume given by the equations (3.7) and (3.8). Its value is 6.7 kg. The copper weight with insulation Wcu is given approximately by (4.5) with the already mentioned dimensions and pwire and Awire from table 4.4. The copper weight equals then to 2.4 kg. All together the weight is then 9.1 kg. This value will be increased by the weight of shaft, shields, bearings, fan and armature. Compared with alternators the weight is higher, but this is thoroughly justified by the higher output.

For the calculation of the moment of inertia J the geometry of the rotor pole teeth is assumed to be a rectangular parallelepiped with the side lengths Lstk, tx and (R\ - Rq) for simplification. Then it can be calculated from

2 (4.6) + Ptehlk{Rl-Ro)tr +

with the previous set dimensions and ppe given in table 4.2. The result is 7.94* 10"4 kgm 2.

Further, it has to be checked that the mechanical properties of the generator are satisfactory. The maximum operating speed has to be lower than the first critical speed. Two approaches are used for calculating the first critical speed. The first approach is introduced in reference [42] and based mainly on the mechanical characteristics of the iron material. The first critical angular velocity Q\ can be calculated from Chapter 4: Generator Design 73

n £7 Qx = (4.7) ■^stkl3 PpeA- with £ as the modulus of elasticity, 7 as the modulus of inertia and Ar as the area of the rotor cross section. Table 4.2 includes two values for the modulus of elasticity. For this calculation is taken the lower value in rolling direction £r to estimate the worst case. The modulus of inertia can be calculated from the moment of inertia given by equation (4.6) with

7 = (4.8)

The area of the rotor cross section is Ar= VrFe/£stk with VrFe given by equation (3.8). The result for the first critical speed calculated with this approach is very high, so that definitely no danger appears.

The second approach is introduced in reference [27] and based on the shaft quantities. An equation for the first critical speed Vi is given, and converted to Si-units it is

Vj =9.236*10 •^slk V^tk^r" (4.9) where 7?Sh is the shaft radius in m, Lstk the stack length in m and WT the rotor weight in kg. The unit of the result is rpm. The first critical speed is calculated to around 41,500 rpm. This is clearly above the maximum speed of the generator.

The rotor has to tolerate the centrifugal force at maximum rotational speed. If the rotor is assumed to be cylindrical, the mechanical stress cr is calculated according to reference [42] by = Ppe^l ^max (4.10) with Qmzx as the maximum angular velocity. For a maximum speed of 12,000 rpm the stress is 1.72*10 7 Pa. Compared with the yield point of the iron given in table 4.2 the safety factor is 16.5, which is sufficient.

4.2 Commutation Unit

The commutation unit has to fulfil the demands given by the generator. The devices are mainly determined by the current they have to commutate. Current peak and waveform are important criteria for the device selection. Mainly it is enough to concentrate on the worst case currents for the transistors and diodes to ensure their Chapter 4: Generator Design 74 proper operation. Attention has to be paid also on the commutation losses. For sure they should be as small as possible to maximise the efficiency, and their influence is huge because they are a major part of the total losses. Because of the low voltage and the high current the voltage drop across the diodes and the transistor resistance has to be small. In the selection of the converter topology one has to consider the phase overlap at high speeds and output power.

The worst case transistor current waveform is shown in figure 4.6. It is characterised by a slight linear increase after the transistor is switched on and after around 5 ms it starts to rise rapidly up to the peak Apeak = 255 A. At this moment after the conducting period Ton = 6.5 ms the transistor is switched off and the current drops to zero. After the non-conducting period T0ff= 18.5 ms the transistor is switched on again and the same current waveform is following. Thus the whole period Ttot is

25 ms. The mean value of the transistor current Amean equals to 11.3 A and the RMS value Arms is 35.1 A.

VA

240 -

160 -

120 -

Figure 4.6: Transistor current (worst case for commutation)

Figure 4.7 shows the waveform of the worst case of the diode current. After the transistors have been switched off the current commutates through the diodes and rises immediately up to around 260 A. Then it rises slightly up to the peak Apeak = 340 in the next 2.7 ms. From there it drops almost linearly down to zero. This takes 4.1 ms and thus the diode is conducting for the conducting period Ton =6.8 ms altogether. After the non-conducting period T0ff= 14.6 ms the diode is conducted again and the same waveform follows. Thus the whole period Act is 21.4 ms. The Chapter 4: Generator Design 75

mean value of the diode current /Dmean equals to 65.3 A and the RMS value /drms is 135.6 A.

VA

240-

200-

Figure 4.7: Diode current (worst case for commutation)

4.2.1 Topology

The classic converter topology is chosen which was introduced in chapter 3.3.1. The most important reason for this choice is that the phases can be controlled independent from each other. This is necessary because of the phase overlap at high speeds and output power. From the other converter topologies mentioned in chapter 3.3.1 the boost and buck converters are able to cope with phase overlap but they need two independent voltage sources, which is not allowed here. Also the bifilar winding converter could be used, but the need of the second winding stays in contrast to the supposition made to enable good efficiency and easy and inexpensive production. The disadvantage of the classic converter is the high number of switches, which causes high commutation losses. Thus special attention has to be paid on loss reduction when selecting the devices.

Figure 4.8 shows the topology of the commutation unit. The commutation of phase one Phi is made by the transistors T1 and T2 together with the diodes D1 and D2 corresponding to the classic converter topology. Phase two Ph2 is commutated by the transistors T3 and T4 together with the diodes D3 and D4. The zener diode Z is to Chapter 4: Generator Design 76

protect against voltage peaks which can appear by sudden changes of the load or during the switch-off time of transistors because of parasitic inductances.

T1 i T3 i

Figure 4.8: Commutation unit topology

Generally, commutation units of switched reluctance machines need a capacitor filter to smooth the low-frequency link current. This can be done by using a large capacitor, but it can be renounced here because the battery U has a huge capacity itself.

4.2.2 Transistors

Power MOSFETs are most suitable for this commutation unit because they can switch the high currents. Another reason is the low driving power because they are voltage controlled and thus only a small current is needed for the control. Also the frequency range and the switching times fulfil the demands. The chosen transistor type is the SEMITRANS M power MOSFET module SKM 101 AR which is produced by SEMIKRON. It is an N-channel enhancement mode MOSFET. The data sheet is included in reference [46] and the most important absolute maximum ratings and characteristic values are summarised in table 4.5. In context with the table it should be mentioned that the given switching times can be used for rough Chapter 4: Generator Design 77

orientation. Exact values can only be measured in the practical circuit because they depend on the base and collector current waveform.

Table 4.5: Maximum ratings and characteristics of SEMITRANS M power MOSFET module SKM 101 AR

Maximum drain-source voltage U DS = 50 V

Maximum continuous drain current 7d = 200 A

Peak value of pulsed drain current /dm = 600 A

Maximum gate-source voltage t/ gs = 20 V Drain-source on-resistance R DS(on) — 3 m£2

Internal parasitic inductance L ds = 20 nH Turn-on time ron = 540 ns

Turn-off time t off =960 ns Maximum junction temperature Tj=150°C

It can not be seen in the table if the MOSFET is capable of tolerating the current waveform shown in figure 4.6 because the peak current is higher than the maximum continuous drain current. On the other hand, it is lower than the maximum peak value of a pulsed drain current, but the current of 600 A is allowed to flow for only the maximum time of 1 ms and that non-repetitive. The most important limiting value concerning the permissible current rating of a power MOSFET is the maximum permissible junction temperature Tcmax- Hence, if the maximum permissible junction temperature is not exceeded, the transistor will operate properly. It can be calculated by Amax = A ~ Apeak Ahjc (4.11) with the maximum junction temperature 7j given in table 4.5, Prpeak as the peak of the transistor leakage power and Pthjc as the thermal resistance under pulse conditions. The peak of the leakage power equals to

Apeak = Apeak % A>S(on) ’ (412) because for a MOSFET in the fully conducting state the voltage is proportional to the current and thus it behaves like an ohmic resistance. This is described by the on-resistance Pcston) which increases with the junction temperature. This is taken into account by the factor of 2 in the equation, because at a junction temperature close to 150 °C its value is almost double compared to the case temperature of 25 °C. The thermal resistance under pulse conditions is a function of the pulse duration rp and can be taken from Fig. 52 on page B6-6 of reference [46]. It equals to 0.015 °C/W for the pulse duration of 1.5 ms and a duty cycle D of 0.06. Then the peak leakage power Chapter 4: Generator Design 78

is 390 W, and the maximum permissible junction temperature is 144 °C. Thus the current can be tolerated if the junction temperature is kept below this limit.

The peak voltage which will arise from the current drop during turn-off of the transistor has to be observed, as well. Its maximum value is not allowed to exceed the maximum drain-source voltage Uus- Thus the inequation us+L^ (4.14) uDS~us and its value is around 145 ns. Compared with the turn-off time of 960 ns of the transistor given in table 4.5 this value is much lower and thus it is insured that the voltage peak caused by the internal parasitic inductance will not exceed the maximum drain-source voltage. It should be mentioned that the parasitic inductances of the connecting wires were neglected in this calculation. In addition the zener diode is responsible for ensuring the safety of the transistors and diodes towards . high frequency voltage peaks.

Concerning the commutation losses it is important that the transistor has a very low on-resistance because it determines the losses. This is given by the chosen type, because an on-resistance of 3 m£2 is very low for a MOSFET. Finally, it can be concluded that the chosen MOSFET type fulfils the set demands.

4.2.3 Diodes

Schottky diodes are most suitable here because they can tolerate the high currents and compared with other diodes they have a lower forward voltage drop, which effects significantly on the commutation losses. Other reasons are the low capacitance, absence of stored charge, zero switching losses and the fact that they can withstand reverse voltage transients. The chosen diode type is the PBYR40045CT which is produced by PHILIPS. It is a schottky barrier double rectifier diode. The data sheet is included in reference [39] and the most important absolute maximum ratings and characteristic values are summarised in table 4.6. Chapter 4: Generator Design 79

Table 4.6: Maximum ratings and characteristics of PHILIPS schottky diode PBYR40045CT

Maximum continuous reverse voltage C7r = 45 V

Maximum repetitive peak reverse voltage U rrm = 45 V Maximum output current Io — 400 A Maximum repetitive peak forward current per diode 7 FRM = 3000 A Maximum forward voltage (200 A, 25 °C) UF = 0.69 V Typical forward voltage (200 A, 125 °C) UF = 0.58 V Maximum forward voltage (200 A, 150 °C) UF = 0.63 V Typical forward voltage (400 A, 125 °C) I/F = 0.75 V Maximum reverse current (25 °C) 7 R = 4mA

Maximum reverse current (125 °C) 7r = 400 mA Maximum junction temperature T, = 150 °C

The table shows that this diode can tolerate the high current whose waveform was shown in figure 4.7 because its peak is even lower than the maximum continuous output current. The low forward voltage has a very positive effect on the losses because it causes the main part of the commutation loses. It is only 0.75 V at high current and decreases with a lower current.

4.2.4 Zener Diode

The zener diode is to protect the commutation unit from voltage peaks which can appear because of sudden changes of the load or during the switch-off time of the transistors because of parasitic inductances. It is a semiconductor P-N junction diode that has a controlled reverse-bias breakdown voltage and thus it can be used to clamp the voltage of the commutation unit and the supply circuit.

The zener diode type chosen is BZY91C18 and is produced by SEMTTRON (see also reference [11]). It is recommended for transient suppression because of the very short conducting time of around 5 ns. This is much quicker than the turn-off time of the transistor and thus it is able to protect against the quick voltage peaks arising with the transistor switch-off. It also has a high continuous power dissipation of 75 W which is necessary to protect against the voltage peaks arising with sudden changes of the load. These voltage peaks are slower but, on the other hand, more powerful than the peaks arising during the transistor switch-off. A power dissipation of 75 W for the zener diode should be enough, and higher values are hard to find. For example, if the generator output is for a short while higher than the demand of the loads, most of the power is dissipated in the battery because of its very small inner resistance. The diode Chapter 4: Generator Design 80

has to tolerate only the fast transients. This diode type has a break-down voltage of 18 V. This is a bit higher than the nominal output voltage of the generator of 14 V but it is usual for transient suppression applications.

4.3 Control System

The control system has to keep the output voltage of the generator constant. The voltage varies with changes of speed and load. Most suitable is a constant voltage of 14 V. This ensures charging of the battery and provides clearance to its gassing voltage. The control system can be realised according to the structure shown in figure 3.24. The controller needs voltage and rotor position feedbacks.as input. It derives the firing angles for the commutation from the voltage error and the speed according to the control strategy. '

The optimum speed range of the generator is between 1,200 rpm and 12,000 rpm which is 1.5 times the speed of internal combustion engines of motor vehicles. At speeds under 1,200 rpm the transistor peak currents are becoming tremendous. Thus the speed range has to be restricted to this minimum limit. Only small maximum output power is supplied at speeds over 12,000 rpm but basically the generator is able to operate above this limit.

The control strategy has to be chosen in a way that the transistor peak currents are restricted to 250 A. This is necessary at low speeds. It will ensure the safe operation of the commutation unit. Good efficiency and high maximum output power are also demanding the choice of the control strategy. In addition the control strategy should be as simple as possible to make the controller as inexpensive as possible. The sensing should enable fast reaction and provide sufficient precision.

4.3.1 Control Strategy

The control strategy has to be chosen in the way that both firing angles are controlled. This is necessary because otherwise the transistor peak currents at low speeds can not be kept under 250 A. The dwell period has to be enlarged with an increase of speed or load by changing the control modes. Because of the variation of both firing angles the control modes can be used in their suitable speed range. This will affect positively on the efficiency. Chapter 4: Generator Design 81

The control strategy chosen builds on three discrete load levels over different speed ranges. The load levels are no, medium and maximum output power. The speed ranges are determined by the maximum output power. They mainly cover 1,000 rpm ranges except at low and high speeds. Smaller ranges are necessary at low speeds because the influence of firing angle variations is high. At speeds over 8,000 rpm the turn-on angle is at its minimum and the turn-off angle at its maximum. Table 4.7 summarises the firing angles for the different load levels over the speed ranges. The angles in the table are given in mechanical degrees according to the aligned position of the first phase at 180°. The second phase will be aligned at 270° and thus an angle of 90° degrees has to be added to the firing angle values in the table for the second phase. Then the first phase is aligned again at 0° and the second one at 90°.

Table 4.7: Discrete firing angles of the controller for the load levels over the speed ranges

0O / 0c in ° for 0o / 0c in ° for 0o / 0c in ° for v/rpm no output power medium output power maximum output 1200-1500 180/180 160/210 157/210 1500-2000 it " 149/210 ii 2000-3000 150/210 142/210 3000-4000 ii 140/215 4000-5000 u 145/215 139 / 220 5000-6000 ii 137/225 n 6000-7000 130/225 7000-8000 n 135/220 121/225 8000-9000 n 115/227 >9000 ii 135/225

The angles at the maximum output power for each speed range are chosen so that they are optimum for the lowest speed in the range. This will ensure that the peak currents are limited because they decrease with an increase of the speed. The disadvantage is that the maximum output power is decreased a bit at the higher speeds in the range. The angles at medium load are chosen that they provide an output power between 1.0 kW and 0.5 kW. It decreases with an increase of the speed. At no output power the turn-on and turn-off angle are identical and thus the dwell angle is zero, so that no output power is supplied.

The controller has to change the firing angles according to the voltage error and the speed. The fastest change can be after one stroke if the sensing enables it because this control strategy can not influence the turn-off angle after the excitation has started. If the. voltage error AU is between -0.1 V and 0.1 V the output power chosen can be Chapter 4: Generator Design 82 kept and no change is necessary. Between -0.3 V and -0.1 V the controller has to change to a higher output level, so that the output voltage will rise. If the voltage error is between 0.1 V and 0.3 V the output power level has to be decreased to decrease the output voltage. If the voltage error is less than -0.3 V maximum output power has to be chosen to protect the battery from becoming discharged. Over a voltage error of 0.3 V the generator has to be switched off by changing to the no output power level to ensure that the gassing voltage of the battery is not exceeded. The changes of the speed have to be done by the controller according to the table. This strategy will enable in the average all load conditions and keep the output voltage almost constant. It should be also mentioned that too high output power can be taken over by the battery for a short while. The battery can also supply a part of the output power if it is too low.

The precision of the firing angles can be 1° or even less because of the low number of phases the pole arcs are large compared with other machines. A precision of 0.5° or 0.25°, as it was mentioned in chapter 3.5, is here not necessary. The tolerance can be enlarged by choosing the turn-off angle for the maximum output power level at the lowest speed range one or two degrees in advance than mentioned in the table but with the disadvantage of a decreased maximum output power at these speeds.

4.3.2 Sensing

Direct position sensing is chosen. Indirect sensing with active probing can not be used because of the low number of phases. State observers demand an expensive microcomputer and a model of the generator which is not known. It is enough to use one sensor and obtain the signal from the rotor poles while rotation. The sensor signal of the shaft position feedback obtained in such way is shown in figure 4.9. The high level is made by the rotor poles.

■ stroke £ ■ low

— zhigh

Figure 4.9: Sensor signal of the shaft position feedback

The period of one revolution is Chapter 4: Generator Design 83

60 T = (4.15) the period of the high level is

(4.16) the period of the low level is

(4.17) and the excitation period is 60 9c-90 (4.18) exc v 2tc with v as the speed in rpm. The unit of the results is seconds. From equation (4.15) the period of one stroke can be calculated by

= ■T‘stroke (4.19) N.strokes/rev

Table 4.8 shows the periods of time for different speeds. It can be seen that the stroke period is shorter than the low level period. This has the disadvantage that the sensing is too slow to enable the controller to react after each stroke. The delay will be utmost two strokes. At speeds between 1,200 rpm and 1,500 rpm a delay of one stroke can be realised if the sensor is placed in the right position because of the short excitation period. The position for the sensor can be calculated by 0S = 2^1 - —j - 0O • (4.20) and it is equal to 70.5°. A good position for the sensor then is 65° to provide some clearance to the limit. This enables fast control after one stroke at the smallest speed range, where it is most necessary, because of the high transistor peak currents and the long period of one stroke. This should be fast enough for motor vehicle applications because speed changes of the driving engine are quite small within the delay time of the sensing because of the high inertia.

Table 4.8: The periods of time for different speeds

v/rpm 1200 1500 3000 6000 9000 12000 T tot / ms 50 40 20 10 6.66 5 T high / HIS 6.6 5.28 2.64 1.32 0.88 0.66 T low / ms 18.4 14.72 7.36 3.68 2.45 1.84 T stroke / mS 12.5 10 5 2.5 1.665 1.25 T exc / ms 7.36 6.78 4.167 2.638 2.074 1.556 84

5 Simulation Results

The simulation results are obtained by simulations with the PC-SRD. They describe the performance of the whole system including generator, commutation and control. The results are put together in a way that shows the system behaviour versus the speed range and different load conditions. The speed range spans from 1,200 rpm to 12.000 rpm and the output power is varied in the four steps of 0.1 kW, 0.5 kW, 1.0 kW and the maximum output power. The maximum output power versus speed is shown in figure 5.1. It is important to mention that the nominal output power of 1.5 kW is not reached at low and high speeds because it influences other characteristic values and will be noticed in the following figures.

1600 T

1400 --

1200 --

1000 --

800 - •

600 - -

400 - -

200--

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Figure 5.1: Maximum output power versus speed

The output power is kept constant or at its maximum to imitate the influence of the controller. This is done by varying the firing angles. The turn-off angle is varied throughout its range in 5° steps and the turn-on angle in 1° steps to reduce the simulation effort with the PC-SRD. Otherwise many simulation runs have to be made until the desired output power is obtained and different solutions are possible. At low speeds and under maximum output power the turn-on angle is exceptionally varied in 0.5° steps, because the reaction of the generator on the control of the angles is more sensible. The summary of the results is distinguished into input, output and inner characteristics, efficiency and losses. The figures are derived from the tables included in Appendix D. Also the waveforms of some dimensions are presented for different speeds. The speeds are chosen to 1,200 rpm, 4,500 rpm and 9,000 rpm to cover the whole range. Chapter 5: Simulation Results 85

5.1 Input

The generator input consists of mechanical and electrical input. Mechanical input is the shaft torque provided by the driving machine. The shaft power corresponds with it. Electrical input is the excitation current supplied by the battery. It builds up the magnetic field.

The average shaft torque versus speed is shown in figure 5.2 for the four load conditions. It can be seen that it decreases significantly with the speed and depends also on the load. Less output power has to be provided with lower load and thus the mechanical input decreases, because only the mechanical input is converted to output power. The shaft torque decreasing with the speed can be explained by the equation

7'shaft CO = f shaft together with figure 5.4. As the figure shows, the shaft power is almost constant over the speed range and thus the shaft torque indirectly proportional to the angular velocity. This explains the curve shape in figure 5.2.

T Shaft/Nm 14.0 T 13.0- 12.0" —max (1.5 kW) 11.0 - —1.0 kW 10.0- —0.5 kW 9.0- — 0.1 kW

7.0--

6.0 - - 5.0- 4.0 - - 3.0- 2.0-

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Figure 5.2: Average shaft torque versus speed for different load conditions

The shaft torque at the maximum load is partly influenced by the maximum output power decreased at low and high speed. At low speeds it rises with the speed until the nominal output power is supplied. At this point the shaft torque is at its maximum. Also at high speeds it is lower than expected for the same reason. The curve differs a bit from the ideal shape at low speeds because of the sensitivity of the generator related to the control. The firing angles are not chosen accurately enough because otherwise, as already mentioned, the simulation effort would be tremendous. This can Chapter 5: Simulation Results 86

be, and sometimes even better, noticed from the other figures included in this chapter.

Besides the average shaft torque, the waveform of the torque is of interest. It is shown in figure 5.3 for three speeds at the maximum output power. Actually, the total torque of both phases and the torque of just one phase is included, but in parts (a) and (b) it can not be noticed because they overlap totally. This can be explained by the total independence of the phases at these speeds. Thus the waveforms of single phases are just added to the total waveform. They do not affect each other. The difference can be seen only in part (c) of the figure. The torque of single phases intersects and thus the total waveform does not overlap.

The figure shows that the torque is pulsating and has quite high peaks. With an increase of the speed the peak is getting sharper but its maximum value is decreasing. The comparison of the peak value with the average torque shows that their ratio is increasing with the speed from around 2.5 up to 9.5. Compared with the. output torque produced by the internal combustion engine of a motor vehicle for driving, the average torque and the peak torque are small. Thus the pulsating torque will cause just a small ripple and is not a problem in this kind of application.

The peak is also a bit postponed because of the postponed turn-off angle. The turn-off angles for the different speeds are (a) 210°, (b) 220° and (c) 227°. It can be seen that the torque is taken over already before the turn-off angle. It is stored in the field energy at first because it can not be delivered to the supply before the turn-off of the transistors. At 9,000 rpm the waveform for a single phase shows a positive torque which is produced by the supply current because of the turn-on angle far before the aligned position caused by the long dwell control mode. This positive torque overlaps with the negative torque of the other phase. It is taken straight over by it and thus it is not wasted.

The average shaft power is shown in figure 5.4. It is constant over the speed range for a constant output. At the maximum output power it is not constant because of the not always reached nominal output power. The waveform has almost the same shape than the waveform of maximum output power. This quite similar behaviour of input and output points towards almost constant total losses versus speed and load. Chapter 5: Simulation Results 87

(a) Torque versus rotor position < Nm ) x l.Uel

1. 10 1.60 3.60 -0.40- -0.80- -1.20- -1.40- -2.00- -2.40- -2.80- -3.20- Rotor position ( dea ) x 1.0e2

(b)

Torque versus rotor position < Nm > x l.Oel

1. !0 2 ------2"80 -0.40-

-0.80-

-1.20-

-1.40-

-2.00-

-2.40- Rotor position < dea > x 1.0e2

(C)

Torque versus rotor position < Nm > x l.Oel

0. 10 1.00—2.00 3.20 -0.25- -0.50- -0.75- -1.00- -1.26- -1.60- -1.75- Rotor position ( deq > x 1.0e2

Figure 5.3: Shaft torque versus rotor position for (a) 1200 rpm, (b) 4500 rpm and (c) 9000 rpm at the maximum output power

Electrical input is necessary to build up the magnetic field. This is done by the excitation current provided by the supply. The excitation current versus speed for the different load conditions is shown in figure 5.5. The figure shows that the excitation current is high at low speeds. This is caused by the small back-EMF which enables an increase of the excitation current forced by the almost full supply voltage. The reason for this small back-EMF is that the excitation takes part around the aligned position at low speeds. Close to the aligned position the inductance remains nearly Chapter 5: Simulation Results 88 constant and only a changing inductance generates a sufficient back-EMF which consumes part of the supply voltage.

P shaft/W — max (1.5 kW) 2000 T 1.0 kW 1800-- 0.5 kW 0.1 kW 1600 - -

1400 --

1200 - -

1000--

800 -

600 -

400 - -

200--

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Figure 5.4: Average shaft power versus speed for different load conditions

—max (1.5 kW) —1.0 kW —0.5 kW — 0.1 kW

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Figure 5.5: Excitation current versus speed for different load conditions

At medium speeds the excitation current is at its minimum, because the back-EMF is bigger because of the advanced beginning of the excitation. Another main influence on the excitation current besides the back-EMF is the control mode, and the normal control mode is still used at medium speeds. The advantage of the normal control mode is that only a very small positive torque is produced and its influence on the Chapter 5: Simulation Results 89

excitation current can not be noticed. For low output power the excitation current stays at its minimum also at high speeds because the normal control mode can be used over the whole speed range.

At higher speeds the control mode changes to boost mode and the positive torque can not be neglected any longer. The produced positive torque is quite small and thus the excitation current increases only slightly. At high speeds the control mode changes to long dwell mode and a noticeable positive torque is produced. Thus the excitation current rises. For maximum output the excitation current decreases even in long dwell mode at speeds over 8000 rpm because of the not reached nominal output.

The disadvantage of the small back-EMF at low speeds can be noticed also from the peak of the excitation current. It is shown in figure 5.6, and very high peak currents appear at slow speeds. The ratio of peak current to average current is around 11 for output power higher than 500 W. It should be mentioned that already lots of effort were taken to reduce these current peaks during construction and controller design. These high peak currents are very critical because they almost exceed the limits of available transistors. Also high voltage peaks can appear during switch-off of the transistors because of the parasitic inductances (compare chapter 4.2.2). The behaviour of peak current at higher speeds is similar to the mean current behaviour for the same reasons. The increase of the peak currents at high speeds and high output power is again caused by the change of the control modes as it was already explained for the mean current.

/rpeak/A

250 -- —max (1.5 —1.0 kW 225 - —0.5 kW 200- — 0.1 kW 175 -

150--

125 --

100-

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Figure 5.6: Transistor peak current versus speed for different load conditions Chapter 5: Simulation Results 90

5.2 Output

Output is provided by the DC link current. The current is directly proportional to the output power according to equation Pcu = kc U because of the constant controlled voltage. Thus it is not shown here because its behaviour versus speed and load is equal to the output power behaviour which is shown in figure 5.7. Of interest are mainly just the nominal output current of 107 A and the waveforms shown later.

PoutAV —max (1.5 kW) 1600 T 1.0 kW 0.5 kW 1400 -- — 0.1 kW

1200 - -

1000--

800 - ■

600 - -

400 - ■

200--

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Figure 5.7: Output power versus speed for different load conditions

The output power is kept constant according to the demands of the load. Above the power of 1 kW it can not be kept constant over the whole speed range because for some speeds the maximum output power is then reached. From the curve of maximum output power it can be seen that the nominal output power can not be reached over the whole speed range. At low speeds up to 1,400 rpm it has to be reduced for limiting the excitation peak current. At speeds over 8,000 rpm the output power is decreasing because the excitation period is too short to enable a sufficient excitation and it can not be extended above the already reached maximum. In these cases the battery has to provide the power if an output higher than the maximum is demanded.

For the use in motor vehicles it is not momentous that the maximum output power is lower than the nominal output power at these speeds. An output power of 1.25 kW at the speed of 1,200 is already quite high and at least higher than for alternators. If the battery gets partly discharged while the combustion engine is at idling speed, it can be charged again at a higher speeds during driving. The reduced output power at high Chapter 5: Simulation Results 91

speeds does not have a major influence because these speeds are rarely reached. At the speed of 9,000 rpm the overspeed range of the internal combustion engine starts (the ratio of 1.5 from generator to engine speed has to be taken into account). It can be concluded that the generator shows good performance over the speed range and it is particularly suitable for motor vehicle applications.

Concerning the DC link current the waveform is of interest. Figure 5.8 shows the DC link current at the speed of 1,200 rpm for the maximum output power. The DC link current is composed by the transistor and diode currents of both phases. At the speed of 1,200 rpm almost no phase overlap can be noticed. Thus the positive parts of the current are almost equivalent to the transistor currents and the negative parts to the diode currents. The periods of the positive and negative parts are almost the same. Also it can be seen well in the figure that the current is pulsating and high peaks appear. The positive peak is 250 A and the negative one is 315 A. On the average the negative part predominates. Thus the generator delivers output power.

DC Link current

2.00-

1.20- 0.80-

1. >0 2.00 2.40 2.80 -0.40- -0.80-

-2.00-

Rotor position x 1.0*2

Figure 5.8: DC link current versus rotor position for 1200 rpm at the maximum output power

Figure 5.9 shows the DC link current at the speed of 4,500 rpm for maximum output power. At this speed a phase overlap can be noticed. The negative output current pulse is extended and overlaps with the positive excitation current pulse of the next phase. The excitation current is straight supplied by the output current pulse of the previous phase. The peaks are decreased to 85 A and 245 A. Chapter 5: Simulation Results 92

DC Link current fT x 1.0e2

0.40-

1. >0 2.40 2.80 3.20

-0.40-

-0.80-

-1.20-

-2.00-

-2.20-

Rotor position x 1.0o2

Figure 5.9: DC link current versus rotor position for 4500 rpm at the maximum output power

Figure 5.10 shows the DC link current at a speed of 9,000 rpm for maximum output power. At this speed the phase currents overlap completely. The turn-on of the second phase is at an angle of 115° and the first phase is turned off later at an angle of 137°. The positive current pulse is very short now because the negative output current pulse is still more extended and supplies straight the excitation of the other phase. The positive peak is increased again up to 135 A because of the change of the control mode to long dwell mode. The negative peak is more decreased down to 195 A.

DC Link current A x 1.01

1.40- 1.20- 1.00- 0.80-

0.40- 0.20-

1.20 2.00 2.40 2.80 3.20

-0.40-

-1.00- -1.20-

-1.80-

Potor positi' 1.0o2

Figure 5.10: DC link current versus rotor position for 9000 rpm at the maximum output power Chapter 5: Simulation Results 93

From the comparison of the figures of the DC link current waveforms it can be concluded that the pulse of the negative output current is extended with the speed. Also its peak value decreases and the peak appears earlier after commutation. Respectively the positive pulse is shortened at higher speeds. Its peak value is at the maximum at low speeds, medium at medium speeds and increases again at high speeds. The rising time of the current up to the peak increases with higher speeds.

5.3 Phase Current

Figure 5.11 presents the average phase current. It is almost constant versus speed at not maximum output power. This shows that the losses are almost constant versus speed because the output current is constant, too. At 1 kW output power the phase current increases a bit at high speeds. This is caused by the higher excitation current because of the changed control mode. The phase current at maximum output power is influenced by the not always reached maximum output power. Thus it decreases at high speeds and is also not at its maximum at low speeds. The increase at speeds from 5,000 rpm to 8,000 rpm is caused by the higher excitation current for the same reason than at the lower output power. The phase current is higher at low speeds for all load conditions because of the very high excitation current.

—max (1.5 kW) —1.0 kW —0.5 kW — 0.1 kW

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Figure 5.11: Phase current versus speed for different load conditions

The phase peak current is shown in figure 5.12. It equals the peak of the diode current. The equality with the diode peak current is obvious because the diode peak current is much higher than the transistor peak current. The phase peak current has Chapter 5: Simulation Results 94

also almost the same height as the output current. The excitation current of the other phase overlaps only with the diode current and at the time when the diode current peak appears is the excitation current still small. Thus the peak value of the output current is decreased only slightly.

350 T —max (1.5 kW)

325 -- 1.0 kW 300 - 0.5 kW

275 -- 0.1 kW 250 --

225 --

200-- ■

175 -- 150 - -

125 --

100-

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Figure 5.12: Phase peak current versus speed for different load conditions

The figure shows that the peak value decreases with higher speeds and smaller loads. The ratio of peak to mean value of the phase current is at low speeds between 4.5 and 7.5. It rises with a decrease of the load and is lower at high speeds. The ratio is lower for the output current because of the higher mean value of the output current resulting from the two phases. These current peaks are not so problematic than the transistor current peaks because the diode can easily tolerate them and the diode current is not switched off at its peak, like the transistor current. The diode current falls steadily and unforced down to zero after a while.

Figure 5.13 shows the phase current waveform for different speeds. The influence of the different control modes can be seen clearly by comparison with figure 3.25. The excitation and output periods increase with higher speeds. At 9,000 rpm the first peak of the excitation current comes from the produced positive output torque (see also chapter 3.5.2). Chapter 5: Simulation Results 95

(a) Current versus rotor position Phase ips ) x 1.0e2 3.20-] 2.80- 2.40- 2.00-

1.20- 0.80-

2.80 Rotor position < deg > x 1.0e2 (b) Current versus rotor position Phase current < amps > x 1.0e2 2.80-1

2.00-

1.20-

0.80-

2.80 3.20 Rotor position < deg > x 1.0e2 (c) Current versus rotor position Phase current ( amps ) x 1.0e2 2.00-1

1.50- 1.25- 1.00- 0.76-

0.26-

0.80 2.00 2.40 2.80____ 3.20 Rotor position ( deg > • t. 0e2

Figure 5.13: Phase current versus rotor position for (a) 1200 rpm, (b) 4500 rpm and (c) 9000 rpm at the maximum output power

5.4 Efficiency

Besides the output power, the efficiency shows the superiority of the switched reluctance generator. Figure 5.14 presents the efficiency of the pure switched reluctance generator without consideration of the commutation and fan losses. It can be seen that the generator has a very high efficiency. It reaches for middle output power 90 % and even sometimes a bit more. At maximum output power it is worst over most of the speed range but still over 80 % and at high speeds it also reaches 90 %. For low output power the efficiency is high at low speeds but it drops down to Chapter 5: Simulation Results 96 around 80 % at high speeds. The current-depending copper losses are the reason for the reduced efficiency at high output power. At low output power the windage losses which increase squared with the speed are becoming significant at high speeds and thus the efficiency decreases.

h gen in 100 T

—max (1.5 kW) —1.0 kW —0.5 kW - 0.1 kW

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Figure 5.14: Generator efficiency versus speed for different load conditions

Unfortunately, values for the efficiency of a pure alternator were not found and the measurement results reported in Appendix A are obtained with the influence of the controller and fan. The fan losses are estimated from the measurements, but the effort to measure the commutation losses would be too high. Thus the switched reluctance generator efficiency can not be compared with the efficiency of a pure alternator.

Figure 5.15 shows the generator efficiency with consideration of the commutation losses. As expected, this efficiency is lower than the efficiency of the pure generator shown in figure 5.14. It can be seen that this efficiency is still quite high. It reaches a maximum of 85 % and is always above 75 %. Its behaviour versus speed and load is almost equal to the pure generator efficiency. The influence of the load is a bit stronger because the commutation losses are current dependent.

Compared with the efficiency of an alternator with consideration of the same losses, which is estimated in Appendix A and shown in figure A.7, the switched reluctance generator efficiency is a lot higher. The alternator efficiency is around 50 % whereas the switched reluctance generator efficiency is around 75 %. Chapter 5: Simulation Results 97

77 in % 100 T

—max (1.5 kW) —1.0 kW —0.5 kW — 0.1 kW

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Figure 5.15: Generator efficiency versus speed for different load conditions with consideration of the commutation losses

The switched reluctance generator efficiency without consideration of the fan losses varies only slightly with speed and load. If fan losses are considered the efficiency will be lower and it will decrease with an increase of the speed. Also it will decrease with a decrease of the load because the fan losses will become dominant. The efficiency of the alternator with consideration of the fan losses varies significantly with speed and load as it can be seen from figure A.5 in Appendix A. It goes down to very low values under unfavourable conditions. It can be expected that this will not happen for the switched reluctance generator because its efficiency without consideration of the fan losses is much higher and the fan losses will be also lower than for an alternator as it is pointed out in the following chapter.

5.5 Losses

The total losses of the switched reluctance generator can be mainly distinguished into copper, iron, windage, commutation and fan losses. Simulation results are obtained by the PC-SRD except for the fan losses and thus the figures in this chapter do not include the fan losses. About the fan losses of the switched reluctance generator it can be said that they are lower than those of an alternator. The total losses of the switched reluctance generator are smaller because of the better efficiency. Thus the heat produced by the losses will be smaller and a less powerful fan can be used. Hence, the fan itself will produce fewer losses. The fan losses are also positively affected by the lower absolute speed of switched reluctance generators compared Chapter 5: Simulation Results 98

with alternators, because the fan losses increase intensely with the speed. The switched reluctance generator operates at a speed of 1.5 times the speed of an internal combustion engine of a motor vehicle, whereas alternators operate usually at 2 times the engine speed.

Figure 5.16 shows the losses versus speed for maximum output power. At this load condition the copper losses are the major part of the total losses because they are proportional to the square value of the current. Thus the behaviour of the total losses is mainly influenced by copper losses. They are very high at low speeds because of the high excitation current. They are also influenced by the not reached nominal output power and thus they decrease at high speeds. The commutation losses are the other main fraction of the total losses in this load condition. They are also current dependent but only partly proportional to the square value. Their main part is linear proportional to the current. Versus the speed they are almost constant and at high speeds they decrease because of the not reduced output power. The iron and windage losses can be almost neglected at the maximum output power because they are much lower than copper and commutation losses.

P l/w —total 500 T — copper —commutation 450- — iron 400 * • — windage 350 - ■

300 -

250 - -

200--

150-

100-

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Figure 5.16: Losses versus speed for maximum output power

The losses for an output power of 1 kW are shown in figure 5.17. The copper and commutation losses still determine the total losses. They are almost in the same range. Only at low speeds the copper losses exceed the commutation losses because of the high excitation current. The iron and windage losses are still a small fraction. Only at high speeds the influence of the windage losses can be noticed by a slight increase of the total losses. Chapter 5: Simulation Results 99

PJW —total 275 T —copper 250 - —commutation — iron 225 -- — windage 200-

175 -

150 -

125 -

100 -

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Figure 5.17: Losses versus speed for 1.0 kW output power

Figure 5.18 shows the losses versus speed for an output power of 0.5 kW. The commutation losses are the biggest fraction of the total losses. They are almost constant over the speed range. The copper losses are smaller and only as high as the commutation losses at low speeds because of the influence of the high excitation current. They decrease with an increase of the speed because less excitation current is supplied because of the rising back-EMF. Also the control mode is not changed at this load condition and thus does not cause an increase of the excitation current at high speeds.

PlAV —total 125 T —copper —commutation —iron 100 - —windage

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Figure 5.18: Losses versus speed for 0.5 kW output power Chapter 5: Simulation Results 100

Iron and windage losses are still smaller than the commutation and the copper losses but they are giving a noticeable contribution to the total losses at this load condition. The iron losses are almost constant over the speed range whereas the windage losses increase with higher speeds. The windage losses are dependent on the speed and not on the current. They increase proportionally to the square value of the speed. This time the windage losses do not cause a visible increase of the total losses at high speeds because the copper losses decrease simultaneously.

The losses for the output power of 0.1 kW are shown in figure 5.19. Because of the small output power, the current is small and thus the current-depending losses are small, too. The lowest losses are the copper losses. The commutation losses are highest at low and medium speeds whereas the windage losses are dominating at high speeds. The behaviour of the total losses is determined by the windage losses already at middle speeds and significant at high speeds. At low speeds the influence of the high excitation current can still be noticed.

•Pl/W —total — copper —commutation — iron — windage 22--

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000

Figure 5.19: Losses versus speed for 0.1 kW output power 101

6 Conclusion and Prospects

The task of this work has been to design a low voltage switched reluctance generator for variable speed applications. As appropriate and main field of application the generator is considered to be used for the on-board power supply in motor vehicles.

As basis for the designing process the principle and theory of switched reluctance generators have been worked out. The construction and the commutation unit are designed in detail. The strategy for the realisation of the control system is given. The performance of the whole system is presented by the obtained simulation results. An overview, of the existing technology for variable speed applications has been presented to complete the expositions of the topic.

The switched reluctance generator, which has been designed in this work, fulfils the required demands, like high output power and efficiency. It is capable of supplying a nominal output power of 1.5 kW and the efficiency is above 75 %. These values are reached almost over the whole speed range and the efficiency varies only slightly over the output power range. The performance of the generator exceeds the characteristics of the nowadays alternator technology used. The better efficiency will affect positively on the fuel consumption of motor vehicles.

Prospective work could be to complete the design of the control system based on the recommended strategy. The next step then would be to build and investigate a prototype generator. 102

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[27] Miller, T.J.E.: Switched Reluctance Motors and Their Control. Magna Physiscs Publishing and Clarendon Press, Oxford, 1993.

[28] Miller, T.J.E.; et al.: “Design of a Synchronous Reluctance Motor Drive”. IEEE Transactions on Industry Applications, Vol. 27, No. 4, 1991, pp. 741-749.

[29] Miller, T.J.E.; McGilp, M.: “Nonlinear Theory of the Switched Reluctance Motor for Rapid Computer-Aided Design ”. IEE Proceedings-B, Vol. 137, No. 6, 1990, pp. 337-347.

[30] Miller, T.J.E.; McGilp, M.: PC-SRD4: User’s Manual. SPEED Consortium, University of Galsgow, 1991.

[31] Miller, T.J.E.; McGilp, M.: “PC CAD for Switched Reluctance Drives”. Electric Machines and Drives Conference, London, 1987, IEE Conference Publication, No. 282, pp. 360-366.

[32] Moallem, M.; Ong, C.M.: “Predicting the Steady-State Performance of a Switched Reluctance Machine ”. IEEE Transactions on Industry Applications, Vol. 27, No. 6,1991, pp. 1087-1097.

[33] Moallem, M.; Ong, C.M.: “Predicting the Torque of a Switched Reluctance Machine from its Finite Element Field Solution ”. IEEE Transactions on Energy Conversion, Vol. 5, No. 4,1990, pp. 733-739.

[34] Moallem, M.; Ong, C.M.; Unnewehr, L.E.: “Effect of Rotor Profiles on the Torque of a Switched-Reluctance Motor ”. IEEE Transactions on Industry Applications, Vol. 28, No. 2,1992, pp. 364-369.

[35] Moghbelli, H.; Adams, G.E.; Hoft, R.G.: “Performance of a 10-Hp Switched Reluctance Motor and Comparison with Induction Motors ”. IEEE Transactions on Industry Applications, Vol. 27, No. 3,1991, pp. 531-538.

[36] Panda, S.K.; Amaratunga, G.A.J.: “Analysis of the Waveform-Detection Technique for Indirect Rotor-Position Sensing of Switched Reluctance Motor Drives”. IEEE Transactions on Energy Conversion, Vol. 6, No. 3, 1991, pp. 476-483.

[37] Panda, S.K.; Amaratunga, G.A.J.: “Waveform Detection Technique for Indirect Rotor-Position Sensing of Switched-Reluctance Motor Drives: Part 1: Analysis ”. IEE Proceedings-B, Vol. 140, No. 1, 1993, pp. 80-88.

[38] Panda, S.K.; Amaratunga, G.A.J.: “Waveform Detection Technique for Indirect Rotor-Position Sensing of Switched-Reluctance Motor Drives: Part 2: Experimental Results”. IEE Proceedings-B, Vol. 140, No. 1, 1993, pp. 89-96. Chapter 7: References 105

[39] Philips (Publ.): Data Handbook: Power Devices. 1990.

[40] Pollock, C.; Williams, B.W.: “Power Converter Circuits for Switched Reluctance Motors with the Minimum Number of Switches”. IFF, Proceedings-B, Vol. 137, No. 6,1990, pp. 373-384.

[41] Pulle, D.W.J.: “New Data Base for Switched Reluctance Drive Simulation”. IEE Proceedings-B, Vol. 138, No. 6,1991, pp. 331-337.

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[50] Wallace, R.S.; Taylor, D.G.: “A Balanced Commutator for Switched Reluctance Motors to Reduce Torque Ripple”. IEEE Transactions on Power Electronics, Vol. 7, No. 4,1992, pp. 617-626.

[51] Wu, C.Y.; Pollock, C.: “Analysis and Reduction of Vibration and Acoustic Noise in the Switched Reluctance Drive”. IEEE Transactions on Industry Applications, Vol. 31, No. 1,1995, pp. 91-98. 106

Appendix A: Measuring Results of an Alternator

A commonly used claw-pole alternator with a nominal output power of 770 W has been examined. Over a speed range from 1,340 to 10,400 rpm the root-mean-square of the output voltage, the torque, the mechanical input power and the root-mean-square of the output current have been measured under different load conditions. The generator was first driven by a solid rotor high-speed induction motor, but to examine a broader speed range another induction motor was used as driving machine at slow speeds. A 12 V battery was used as excitation power supply. The measurement set-up was made according to Figure 2.4.

With the solid rotor high-speed induction motor as driving machine, the lowest measurable speed was 3,000 rpm because the induction motor was not able to produce the necessary torque and stopped when the load was switched on. Thus another series of measurements was made with the driving motor for low speeds. The low speed limit was then caused by the generator because it was not capable of producing the necessary output for the excitation. At speeds over 10,000 rpm the vibrations of the test rack were getting so high that it would have been dangerous to continue to increase the speed.

Four different load conditions have been measured. At first the measurements were made without any extra load - just the battery and the excitation. The measured values and the derived results for the output power and efficiency are included in the tables A.1 and A.2. The tables show that the output current for the high speed measurements was higher, because the battery was less charged. The results would be more comparable if the output current had the same value, but to get a general impression of the generator performance the results are useful.

Starting from this “no extra load ”-condition the load was increased in three steps until the nominal output current was generated. The results for the “load 1’’-condition are shown in the tables A.3 and A.4. The results for the “load 2”-condition can be seen in the tables A.5 and A.6. The most convincing results were reached at the nominal output and they are included in the tables A.7 and A.8. For an actual comparison of the different load conditions it should be mentioned that the output voltage is decreased a bit with higher load and higher output current respectively. This is caused by the higher voltage drop of the rectifying diodes at higher currents.

The tables mentioned already include all the necessary information but for a better understanding and overview the important values are concluded in figures A.1, A.2, Appendix A: Measuring Results of an Alternator 107

A.3 and A.5. Figure A.l shows the absolute value of the torque versus speed for the different load conditions. It can be seen that the input torque shows a different behaviour according to the load condition. At low loads the torque increases mainly with the increase of the angular velocity but at high loads the torque decreases with the velocity. The effect at low load is caused by the increase of losses, especially the fan losses (see below). At high load the influence of the losses can not be seen this straight from the torque behaviour because the high output power dominates the behaviour and less torque is generally needed at higher speeds.

abs(7)/Nm 5.0 T —no extra load 4.5 -- — load 1 —load 2 4.0" —loads 3.5 -

3.0--

2.5--

2.0-

1.0--

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000

Figure A.1: Absolute value of torque versus speed for the different load conditions

Figure A.2 shows the absolute value of the mechanical input power versus speed for the different load conditions. This figure illustrates the influence of the losses better than the previous one because the contrary influence of the angular velocity is not affecting the mechanical input power. It can be seen that the mechanical input power increases for all load conditions with the increase of speed. This is caused by the speed-depending increase of the losses.

Figure A.3 concludes the output power versus speed for the different load conditions. It can be seen that the output power is held almost constant over a very broad speed range and only at slow speeds some problems occur for high loads. At low loads the generator is able to deliver the necessary output through the whole speed range but at “load 2”-condition the generator is not able to produce the output power at speeds under 2,000 rpm and at “load 3”-condition at speeds under 2,500 rpm. Thus only the maximum reachable output current was measured for the “load 3”-condition under Appendix A: Measuring Results of an Alternator 108

2,500 rpm (see Table A.8). It is impossible to get other values, because the load is overtaken by the battery and thus it is quickly discharged. With the discharge of the battery the voltage drops quickly and useful results can not be measured anymore.

abs(f mech)/W 2500 T

2000 --

1500 --

1000-- — no extra load — load 1 500 - —load 2 — load3

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000

Figure A.2: Absolute value of mechanical input power versus speed for the different load conditions

P outAV 900 T

800 - -

700 --

600 -

500-- —no extra load 400 - - — load 1 300 - - —load 2 —load 3 200--

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000

Figure A.3: Output power versus speed for the different load conditions

Figure A.4 shows the maximum output current versus speed. The current curve has the same behaviour than expected in the theory (compare Figure 2.5). Especially remarkable is that the nominal current can only be reached at speeds higher than Appendix A: Measuring Results of an Alternator 109

3,000 rpm. Under this speed the maximum output current decreases rapidly with a decrease of the speed. This behaviour explains the low maximum output power of alternators at low speeds.

I max/A

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000

Figure A.4: Maximum current versus speed

Most convincing is figure A.5. It illustrates the efficiency versus speed for different load conditions^ It can be seen that the efficiency goes down with the increase of the speed independently of the load condition. The low efficiency for the “no extra load"-condition is not very convincing because almost no output power is supplied. Only the battery is slightly charged. Almost all the mechanical input power is needed straight to cover the losses, especially at high speeds. At low speeds quite a good efficiency is reached for all load conditions but at high speeds the efficiency is rather poor. The maximum efficiency reached is 65 %. This is quite good, but the maximum efficiency at nominal output is only 50 %.

The large decrease of the efficiency with an increase of the angular velocity indicates that some of the losses are highly speed-depending. The fan losses are the most reasonable explanation because the air resistance is highly speed-depending. To estimate the fan losses two more measurement series were made with the driving machine for high speeds. The first series was with the excitation turned off and for the second series also the fan was taken away. The results are included in the tables A.9 and A. 10. From these results the fan losses can be estimated and they are included in table Aril. Appendix A: Measuring Results of an Alternator 110

77 in % 70.0 T — no extra load — load 1 60.0 - - — load 2 — load 3 50.0 - -

40.0 - -

30.0 - -

20.0 - -

10.0-

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000

Figure A.5: Efficiency versus speed for the different load conditions

Figure A.6 illustrates the measurement results and the derived fan losses. It can be seen that the fan losses are the major part of the losses. Especially at high speeds they rise very high up to 680 W at 8,000 rpm and at higher speeds even more. The curve for the measurement results without excitation and fan shows the height of the rest of the losses but it is difficult to distinguish them. They are mainly frictional losses in the bearings and particularly the speed-depending part of the losses seems to be from the air resistance of the clutches between the alternator and the driving machine.

abs(Pmcch)/W 1200 T

1000 -- — estimated fan losses —no excitation — no excitation and no fan 800 --

600 --

400 --

200 --

4 v/rpm

Figure A.6: Absolute value of mechanical input power versus speed for the not excited generator with and without fan and estimated fan losses Appendix A: Measuring Results of an Alternator 111

Finally, after estimation of the fan losses the alternator efficiency without consideration of the fan losses can be estimated. It is shown in figure A.7 for nominal output. Its value is around 50 % and decreases slightly with the speed.

77 in %

Figure A.7: Estimated efficiency versus speed at nominal output power without fan losses

The tables of the measuring results are following on the next pages. Appendix A: Measuring Results of an Alternator 112

Table A. 1: Measuring results of the alternator without extra load at high speeds

v/rpm TfNm f rms/A C/rms/V P mech/W P out/W 77 in % 3043 -0.736 6.8 14.10 -234.6 95.9 40.9 3498 -0.802 8.8 14.15 -293.8 124.5 42.4 4010 -0.766 8.2 14.12 -321.7 115.8 36.0 4507 -0.714 7.7 14.11 -337.0 108.6 32.2 5002 -0.722 7.6 14.11 -378.2 107.2 28.4 5502 -0.718 7.0 14.11 -413.7 98.8 23.9 5980 -0.760 6.9 14.10 -475.9 97.3 20.4 6519 -0.814 6.4 14.10 -555.7 90.2 16.2 6969 -0.854 6.2 14.11 -623.2 87.5 14.0 7399 -0.948 6.1 14.10 -734.6 86.0 11.7 8075 -1.124 5.6 14.10 -950.4 79.0 8.3 8836 -1.180 4.9 14.13 -1013.7 69.2 6.8 9177 -1.328 5.5 14.11 -1158.1 77.6 6.7 9691 -1.228 5.2 14.11 -1064.4 73.4 6.9 10391 -1.382 5.4 14.11 -1290.1 76.2 5.9

Table A.2: Measuring results of the alternator without extra load at low speeds

v/rpm r/Nm / rms/A C/ms/V f mech/W P out/W 77 in % 1340 -0.83 2.9 14.22 -116.5 41.2 35.4 1500 -0.65 2.8 14.20 -102.1 39.8 38.9 2000 -0.42 2.5 14.19 -88.0 35.5 40.3 2500 -0.35 2.9 14.18 -91.6 41.1 44.9 3000 -0.29 2.5 14.19 -91.1 35.5 38.9 3500 -0.28 2.7 14.20 -102.6 38.3 37.4 4000 -0.30 3.3 14.18 -125.7 46.8 37.2 Appendix A: Measuring Results of an Alternator 113

Table A.3: Measuring results of the alternator for load 1 at high speeds

v/rpm 7YNm ■^rms/A t/rms/V P mech/W Pout/W 77 in % 3008 -1.236 13.5 14.08 -389.3 190.1 48.8 3500 -1.188 14.9 14.10 -435.4 210.1 48.3 4012 -1.102 14.3 14.06 -463.0 201.1 43.4 4505 -1.012 13.5 14.07 -477.4 189.9 39.8 5001 -0.990 13.7 14.07 -518.5 192.8 37.2 5508 -0.966 13.3 14.06 -557.1 187.0 33.6 6016 -0.980 13.0 14.06 -617.4 182.8 29.6 6515 -1.008 12.7 14.07 -687.7 178.7 26.0 7008 -1.048 12.6 14.08 -769.1 177.4 23.1 7550 -1.140 12.5 14.08 -901.3 176.0 19.5 8010 -1.336 12.0 14.07 -1120.7 168.8 15.1 8824 -1.334 11.5 14.10 -1138.8 162.2 14.2 9166 -1.500 12.0 14.07 -1305.8 168.8 12.9 9681 -1.378 11.9 14.06 -1199.9 167.3 13.9 10379 -1.494 12.0 14.06 -1330.8 168.7 12.7

Table A.4: Measuring results of the alternator for load 1 at low speeds

v/rpm r/Nm ^rms/A t/rms/V P mech/W P out/W rj in % 1340 -1.81 8.0 13.90 -254.0 111.2 43.8 1500 -1.65 10.0 14.11 -259.2 141.1 54.4 2000 -1.09 10.3 14.06 -228.3 144.8 63.4 2500 -0.85 10.3 14.07 -222.5 144.9 65.1 3000 -0.72 10.0 14.05 -226.2 140.5 62.1 3500 -0.66 10.1 14.05 -241.9 141.9 58.7 4000 -0.61 10.5 14.06 -255.5 147.6 57.8 Appendix A: Measuring Results of an Alternator 114

Table A.5: Measuring results of the alternator for load 2 at high speeds

v/rpm 77Nm ■^rms/A C/rms/V P mech/W P out/W Tj in % 3000 -2.974 34.5 13.98 -934.3 482.3 51.6 4009 -2.498 35.8 14.01 -1048.7 501.6 47.8 4503 -2.286 35.5 14.03 -1078.0 498.1 46.2 5008 -2.132 35.1 13.99 -1118.0 491.0 43.9 5505 -2.016 35.0 13.99 -1162.1 489.7 42.1 6001 -1.906 34.7 13.99 -1197.7 485.5 40.5 6495 -1.864 34.1 14.00 -1267.7 477.4 37.7 6996 -1.858 34.5 14.01 -1361.2 483.3 35.5 7557 -1.892 34.2 14.00 -1497.4 478.8 32.0 8063 -2.010 33.5 13.99 -1697.1 468.7 27.6 8770 -1.970 33.5 14.00 -1673.1 469.0 28.0 9110 -2.168 33.8 13.99 -1864.1 472.9 25.4 9627 -1.990 33.4 13.96 -1721.8 466.3 27.1 10326 -2.046 33.5 13.96 -1817.8 467.7 25.7

Table A.6: Measuring results of the alternator for load 2 at low speeds

v/rpm r/Nm •^rms/A U rms/V P mech/W P out/W 77 in % 2000 -4.10 34.0 14.03 -858.7 477.0 55.6 2500 -3.00 32.6 13.98 -785.4 455.7 58.0 3000 -2.48 32.8 13.98 -779.1 458.5 58.9 3500 -2.14 32.5 13.99 -784.4 454.7 58.0 4000 -1.93 32.8 14.00 -808.4 459.2 56.8 Appendix A: Measuring Results of an Alternator 115

Table A.7: Measuring results of the alternator for load 3 at high speeds

v/rpm 77Nm ■f rms/A t/rms/V P mech/W Pout/W 77 in % 3611 -4.808 57.5 14.14 -1818.3 813.1 44.7 4493 -3.592 55.0 13.98 -1689.9 768.9 45.5 4994 -3.518 54.0 13.95 -1839.7 753.3 40.9 5496 -3.204 53.9 13.95 -1844.1 751.9 40.8 5999 -3.138 54.5 13.96 -1971.3 760.8 38.6 6473 -3.054 54.2 13.96 -2070.3 756.6 36.5 6997 -2.994 54.2 13.96 -2193.9 756.6 34.5 7518 -2.884 53.4 13.95 -2270.6 744.9 32.8 8022 -2.800 53.7 13.96 -2352.1 749.7 31.9 8688 -2.780 53.4 13.95 -2362.1 744.9 31.5 9028 -2.850 54.0 13.97 -2469.4 754.4 30.5 9543 -2.754 53.6 13.93 -2382.4 746.6 31.3 10249 -2.736 53.5 13.92 -2465.7 744.7 30.2

Table A.8: Measuring results of the alternator for load 3 at low speeds

v/rpm T/Nm 7 rms /A 7/ rms/V P mech/W P out/W 77 in % 1340 10.0 1500 14.0 2000 34.0 2500 -4.52 45.5 13.11 -1183.3 596.5 50.4 3000 -4.71 52.5 13.86 -1479.7 727.7 49.2 3500 -4.49 55.4 14,01 -1645.7 776.2 47.2 4000 -3.80 55.0 13.95 -1591.7 767.3 48.2 Appendix A: Measuring Results of an Alternator 116

Table A.9: Measuring results of the alternator without excitation at high speeds

v/rpm 77Nm P mech /W 3000 -0.32 -101 3500 -0.37 -136 4000 -0.42 -176 4500 -0.48 -226 5000 -0.55 -288 5500 -0.62 -357 6000 -0.70 -440 6500 -0.78 -531 7020 -0.87 -640 7475 -0.99 -775 8015 -1.16 -974 8500 -1.30 -1157

Table A.10: Measuring results of the alternator without excitation and fan at high speeds

v/rpm T/Nm -Pmech/W 3000 -0.08 -25 3500 -0.08 -29 4000 -0.09 -38 4505 -0.09 -42 5000 -0.11 -58 5495 -0.13 -75 oo OO 6000 -0.14 t 6505 -0.15 -102 7000 -0.22 -161 7500 -0.26 -204 8005 -0.35 -293 Appendix A: Measuring Results of an Alternator 117

Table A.ll: Derived fan losses from the alternator measurements

v/rpm P mech/W 3000 75 3500 105 4000 140 4500 185 5000 230 5500 280 6000 350 6500 430 7000 480 7500 570 8000 680 118

Appendix B: True Scale Figures of the Generator

Scale: mm

Figure B.l: Cross section of the generator Appendix B: True Scale Figures of the Generator 119

Scale: 1:1 Unit: mm

Figure B.2: Longitudinal cross section of the generator 120

Appendix C: Conclusion of Characteristic and Dimension Values

Nominal voltage Z7n =14V

Nominal current 7n = 107 A Nominal output power PN= 1.5 kW Minimum speed Vmin= 1,200 rpm Maximum speed Vmax= 12,000 rpm Number of stator poles Ns = 4 Number of rotor poles Nr= 2 Shaft radius RSh = 10 mm Minor rotor radius Ro = 24 mm Rotor radius R\ = 37.5 mm Radius of stator slot bottom i?2 = 56 mm

Stator outside radius i?3 = 74 mm Stack length L$tk = 75 nun Overall length Le= 133.5 mm Air gap length <5= 0.3 mm Stator pole arc A = 45° Rotor pole arc A =47.5° Radius of comer at stator slot bottom r-5 mm

Lamination stacking factor /stk = 0.97 Layer thickness of the lamination stacking rstk= 0.5 mm Number of parallel path per phase Npath = 1 Number of turns per pole Nv = 12 Slot fill factor Sfin= 0.576 Thickness of insulation layer d = 0.2 mm Slot area Asiot= 786 mm2 Copper area Acu = 226 mm2 Direct-current phase resistance (20 °C) PphDC(20) = 6.3 m£2 Direct-current phase resistance (90 °C) PphDC(9o> =8.0 mQ Iron weight WFe= 6.7 kg Copper weight Wcu = 2.4 kg Total weight Wtot = 9.1 kg Moment of inertia / = 7.94*1 0"4 kgm 2 121

Appendix D: Tables of the Simulation Results

Table D.l: Simulation results of the generator at maximum output power (part 1)

v/rpm shaii/Nm T P shaf/W T] gen HI % I dc /A 6oin° 0cin° fiVW P ou,/W 77 tot in % 1200 13.0 1633 82.8 89.5 157 210 408 1253 76.7 1300 13.5 1840 82.5 100.5 153 210 461 1407 76.5 1400 13.3 1954 82.9 107.0 150 210 479 1498 76.7 1500 12.0 1881 84.2 105.0 149 210 432 1470 78.1 2000 9.0 1877 86.3 107.5 142 210 384 1505 80.2 3000 5.7 1801 87.9 105.0 140 215 340 1470 81.6 4500 3.8 1799 88.8 106.0 135 220 324 1484 82.5 6000 2.9 1824 88.8 107.5 130 225 335 1505 82.5 7000 2.5 1827 88.8 107.5 121 225 336 1505 82.4 8000 2.0 1716 88.0 100.0 115 227 337 1400 81.6 9000 1.6 1537 88.8 90.5 115 227 289 1267 82.4 12000 0.9 1176 90.1 70.0 115 227 205 980 83.3

Table D.2: Simulation results of the generator at maximum output power (part 2)

v/rpm / p/A /pocak/A IcJA /rocak/A I Doeafc/A fcu/W PeVW P cott/W Pwit/W 1200 67.0 315 22.6 253 315 263.5 17.7 126.4 0.14 1300 73.8 334 23.9 253 334 302.3 19.0 139.1 0.17 1400 76.8 341 23.5 237 341 315.1 19.5 143.9 0.20 1500 72.6 327 20.3 196 327 279.1 18.8 134.1 0.23 2000 69.7 307 16.1 113 307 238.9 17.9 127.0 0.40 3000 66.1 275 13.7 86 275 202.3 15.6 120.9 0.90 4500 67.0 246 14.0 97 246 184.2 15.2 122.6 2.03 6000 71.4 231 17.9 144 231 185.3 15.6 130.4 3.60 7000 73.5 221 19.9 132 221 182.3 16.6 132.1 4.90 8000 73.7 216 24.0 153 216 182.6 17.3 130.5 6.40 9000 66.1 194 21.1 134 194 147.3 16.6 116.5 8.10 12000 50.7 150 15.7 97 150 86.7 15.1 88.4 14.40

Table D.3: Simulation results of the generator at 1 kW output power (part 1)

v/rpm T shafi/Nm P shaf/W 7? sen in % /dc /A 0o in" 0c in" P u=t/W Pout/W 7? tot in % 1200 9.66 1214 85.8 69.2 162.5 210 264 " 969 79.8 1300 8.96 1219 86.5 70.1 161.0 210 253 981 80.5 1400 8.36 1226 87.1 70.9 159.5 210 247 993 81.0 1500 7.86 1235 87.5 71.8 158.0 210 242 1005 81.4 2000 5.81 1217 88.8 71.7 152.0 210 220 1004 82.5 3000 3.84 1207 89.9 71.8 142.0 210 205 1005 83.3 4500 2.54 1195 90.8 71.9 140.0 215 191 1007 84.2 6000 1.86 1165 91.4 70.5 131.0 215 181 987 84.7 7000 1.62 1184 91.6 71.9 135.0 220 OO 1007 85.0 8000 1.41 1185 91.7 72.3 130.0 220 180 1012 85.4 9000 1.23 1163 91.6 70.8 134.0 225 180 991 85.2 12000 0.94 1176 90.1 70.2 115.0 227 205 983 83.6 Appendix D: Tables of the Simulation Results 122

Table D.4: Simulation results of the generator at 1 kW output power (part 2)

v/rpm /p/A I Pocak/A / cx(/A ■Itdoi /A 1 Doeak/A PcuAV PrAV f con/W /’winAV 1200 49.8 262 ' 15.4 178 262 158.1 14.2 91.1 0.14 1300 49.0 261 14.1 153 261 150.1 14.0 89.1 0.17 1400 48.5 259 13.2 133 259 144.5 13.9 87.9 0.20 1500 48.3 257 12.5 117 257 140.8 13.8 87.4 0.23 2000 46.3 243 10.5 61 243 122.3 13.4 83.7 0.40 3000 45.8 220 10.0 32 220 108.0 13.5 82.8 0.90 4500 44.9 195 9.0 31 195 95.1 12.6 81.7 2.03 6000 44.5 174 9.3 28 174 83.4 13.2 80.6 3.60 7000 44.7 167 8.8 34 167 81.9 12.7 81.4 4.90 8000 45.2 159 9.0 32 159 78.4 13.1 82.0 6.40 9000 45.2 154 9.9 75 154 77.1 12.7 82.0 8.10 12000 50.7 150 15.7 97 150 86.7 15.1 88.4 14.40

Table D.5: Simulation results of the generator at 0.5 lcW output power (part 1)

Pshaf/W v/rpm rshafl /Nm V gen in % /dc /A 0O in0 0c in” P Lto/W Pou/W 7? tot in % 1200 4.87 612 90.0 37.0 172.5 210 108 518 84.6 1300 4.24 577 90.5 34.7 171.5 210 98 486 84.2 1400 4.07 596 90.6 35.9 170.0 210 100 503 84.3 1500 3.85 604 90.8 36.4 169.0 210 100 510 84.4 2000 2.77 579 91.4 35.3 165.0 210 92 494 85.4 3000 1.91 600 92.0 36.5 157.0 210 92 511 85.2 4500 1.25 590 92.6 36.2 149.0 210 86 507 85.9 6000 0.92 578 92.9 35.5 143.0 210 82 497 86.0 7000 0.80 586 92.9 36.1 139.0 210 83 505 86.2 8000 0.70 589 92.9 36.3 145.0 215 83 508 86.3 9000 0.62 584 92.8 35.9 142.0 215 83 503 86.1 12000 0.47 584 92.1 35.7 143.0 220 86 500 85.6

Table D.6: Simulation results of the generator at 0.5 kW output power (part 2)

v/rpm / p/A f Pocak/A Axe/A ■^Tocak/A I Dpeal/A Pcu/W PreAV Pcon/W PwinAV 1200 26.3 176 7.8 84 176 52.0 9.2 46.3 0.14 1300 24.7 170 7.4 65 170 45.4 9.0 43.3 0.17 1400 25.2 173 7.3 5.7 173 46.5 9.1 44.2 0.20 1500 25.3 174 7.1 50 174 46.4 9.1 44.5 0.23 2000 24.0 165 6.4 32 165 40.7 8.9 42.3 0.40 3000 24.4 153 6.1 27 153 38.2 9.2 43.2 0.90 4500 23.7 133 5.6 22 133 32.2 9.5 42.2 2.03 6000 23.0 119 5.2 19 119 27.9 9.7 41.1 3.60 7000 23.2 113 5.2 18 113 26.9 10.0 41.5 4.90 8000 22.9 109 4.7 20 109 26.2 9.4 41.3 6.40 9000 22.6 103 4.6 19 103 24.5 9.6 40.8 8.10 12000 22.3 93 4.5 22 93 22.2 9.5 40.4 14.40 Appendix D: Tables of the Simulation Results 123

Table D.7: Simulation results of the generator at 0.1 kW output power (part 1)

v/rpm T sbaf/Nm P shaf/W 1} gen in % I dc /A 0o in° 9cin° fuo/W P ou/W T] lot in % 1200 0.91 115 90.3 6.8 174.0 205 23.2 95 82.2 1300 0.97 126 90.9 7.6 173.5 205 24.1 106 84.4 1400 0.83 122 91.0 7.2 173.0 205 23.1 101 83.2 1500 0.76 119 91.1 7.1 172.5 205 22.3 99 83.4 2000 0.55 116 91.7 7.0 171.0 205 20.5 98 84.2 3000 0.38 119 92.7 7.3 178.0 210 18.6 102 85.8 4500 0.25 117 92.2 7.1 175.0 210 18.4 100 85.4 6000 0.19 121 91.3 7.3 172.0 210 19.8 102 84.5 7000 0.16 119 90.2 7.1 171.0 210 20.5 100 84.2 8000 0.15 122 89.2 7.2 169.0 210 22.1 101 82.8 9000 0.13 123 87.9 7.2 168.0 210 23.5 101 82.1 12000 0.10 127 83.5 7.0 164.0 210 29.3 98 77.4

Table D.8: Simulation results of the generator at 0.1 kW output power (part 2)

v/rpm / p/A I Plicak/A WA / TDcal/A I Doeak/A PcuAV Pr/W Pcom/W Pwu/W 1200 8.1 60 4.7 30 60 4.4 6.6 12.0 0.14 1300 8.3 66 4.5 29 66 4.8 6.5 12.6 0.17 1400 8.0 64 4.4 28 64 4.4 6.4 12.1 0.20 1500 7.8 63 4.3 26 63 4.1 6.2 11.8 0.23 .2000 7.1 59 3.6 22 59 3.4 5.8 10.9 0.40 3000 6.2 59 2.6 19 59 3.2 4.6 10.0 0.90 4500 5.6 52 2.1 14 52 2.5 4.5 9.3 2.03 6000 5.5 48 1.8 12 48 2.3 4.7 9.2 3.60 7000 5.2 45 1.8 11 45 2.1 4.6 8.8 4.90 8000 5.2 43 1.6 10 43 2.0 4.8 8.9 640 9000 5.1 41 1.5 9 41 1.9 4.8 87 8.10

12000 4.8 36 1.3 8 36 1.6 4.9 84 14 40