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Modeling, Analogue and Tests of an Electric Machine

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Modeling, Analogue and Tests of an Electric Machine MODELING, ANALOGUE AND TESTS OF AN ELECTRIC MACHINE VOLTAGE CONTROL SYSTEM 'by GRAHAM E.' DAWSON ( j B.A.Sc, University of British. Columbia, 1963. A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS, FOR THE DEGREE OF MASTER OF APPLIED SCIENCE. in the Department of Electrical Engineering We accept this thesis as conforming to the required standard Members of the Committee Head of the Department .»»«... Members of the Department of Electrical Engineering THE UNIVERSITY OF BRITISH COLUMBIA September, 1966 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely.avai1able for reference and study. I further agree that permission for ex• tensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives.. It is understood that copying or publication of this thesis for finan• cial gain shall not be allowed without my.written permission. Department of Electrical Engineering The University of British Columbia Vancou ve r.,8, Canada Date 7. MM ABSTRACT This thesis is concerned with the modeling, analogue and tests of an interconnected four electric machine voltage control system. Many analogue studies of electric machines have been done but most are concerned with the development of analogue techniques and only a few give substantiation of the validity of the analogue models through comparison of results from analogue studies and from real machine tests. Chapter 2 describes the procedure and the system under study. Chapter 3 describes the methods used for the determination of the electrical and mechanical system parameters. The analogue model of the interconnected system is developed by studying the induction motor-amplidyne subsystem in Chapter 4 and the synchronous motor-dc generator subsystem in Chapter 5. Both transient and steady state tests are carried out on the analogue and on real machines to substantiate the validity of the analogue models. The subsystems are then interconnected and the interconnected system analogue is further verified from transient and steady state tests on the analogue and real machines. Although the system under study is specific, the methods of modeling, analogue and testing are general, there• fore, they can be applied to the transient and steady state studies of other electric machine systems. ii TABLE OP CONTENTS Page ABSTRACT ii TABLE OF'CONTENTS iii LIST OF ILLUSTRATIONS v LIST OF TABLES vii ACKNOWLEDGEMENT ix 1. INTRODUCTION 1 2. PROCEDURE AND SYSTEM UNDER STUDY 2-1 Procedure 3 2- 2 System Under Study 5 3. PARAMETER DETERMINATION 3- 1 Self Inductance 7 3-2 Mutual Inductance 9 3-3 Speed Voltage Coefficient 11 3-4 Resistance H 3-5 Friction Coefficient, . 12 3-6 Moment of Inertia , 15 3-7 Induction Motor Torque 16 3- 8 Synchronous Motor Torque 17 4. STUDY OF INDUCTION M0T0R-AMP1IDYNE SET 4- 1 Voltage and Torque Equations 19 4-2 Parameters 22 4-3 Analogue Setup 22 4- 4 Comparison of Analogue Study and Real Machine Tests 25 5. STUDY OF SYNCHRONOUS MOTOR-DC GENERATOR SET 5- 1 Voltage and Torque Equations 31 5-2 Parameters ; • 33 5-3 Analogue Setup 33 5-4 Comparison of Analogue Study and Real Machine .. Tests 34 iii Page 6. STUDY OP THE INTERCONNECTED POUR MACHINE VOLTAGE CONTROL SYSTEM 6-1 System Equations 39 6-2 Parameters 41 6-3 Analogue Setup 42 6-4 Comparison of Analogue Study and Real Machine Tests 44 6-5 Effect of Anti-Hunting Potentiometer Setting on System Stability 47 I 7. CONCLUSION 62 APPENDIX Machine Ratings 64 REFERENCES 65 iv LIST OF ILLUSTRATIONS Page Figure 2-1 Procedure for Modeling, Analogue and Tests 4 2- 2 Interconnected Voltage Control System • 5 3- 1 Circuit for Self Inductance Measurement 7 3-2 Amplidyne Field Winding Current Response 8 3-3 Circuit for Mutual Inductance Measurement 9 3-4 Circuit for Speed Voltage Coefficient Measurement 11 3-5 Plot to Obtain Speed Voltage Coefficient 12 3-6 Effect of Iron Losses on Friction Calculations .. 14 3- 7 linear Approximation of the Induction Motor Torque Curve 17 4- 1 Circuit of the Amplidyne 20 4-2 Amplidyne No load Test 27 4-3 Amplidyne load Test 27 4-4 Amplidyne Output Voltage Transients 28 4-5 Amplidyne load Current Transients 29 4- 6 Amplidyne Anti-Hunting Current Transients ....... 30 5- 1 Circuit of the DC Generator 31 5-2 DC Generator Open Circuit Characteristic 36 5-3 DC Generator Load Test 36 5-4 DC Generator Ouput Voltage Transients 37 5-5 DC Generator load Current Transients 37 5- 6 Synchronous Motor Speed Transients 38 6- 1 Circuit of the Interconnected Voltage Control System 40 v Figure Page 6-2 Thevenin Equivalent of DC Generator Armature and Feedback Circuit 41 6-3 Analogue Setup of the Interconnected Voltage Control System 43 6-4 Interconnected System at No Load 45 6-5 Interconnected System with Load 46 6-6 Amplidyne Field Current Transients Interconnected System, a = 1.0 48 6-7 Amplidyne Field Current Transients Interconnected System , a = 0.40 49 6-8 Amplidyne d-Axis Current Transients Interconnected System, a = 1.0 50 6-9 Amplidyne d-Axis Current Transients Interconnected System, a = 0.40,. 51 6-10 Amplidyne'Anti-Hunting Current Transients Interconnected System, a = 1.0 52 6-11 Amplidyne Anti-Hunting Current Transients Interconnected System, a = 0.40 53 6-12 DC Generator Field Voltage Transients Interconnected System, a = 1.0 54 6-13 DC Generator Field Voltage Transients Interconnected System, a = 0.40 55 6-14 DC Generator Output Voltage Transients Interconnected System, a = 1.0 56 6-15 DC Generator Output Voltage Transients Interconnected System, a = 0.40 57 6-16 Synchronous Motor Speed Transients Interconnected System, a = 1.0 58 6-17 Synchronous Motor Speed Transients Interconnected System, a = 0.40 59 6-18 Amplidyne Field Current Oscillations Interconnected System 60 6-19 Amplidyne Anti-Hunting Current Oscillations Interconnected System 60 vi Figure Page 6-20 Amplidyne d-Axis Current Oscillations Interconnected System 61 6-21 DC Generator Output Voltage Oscillations Interconnected System 61 6-22 Induction Motor Speed Oscillations Interconnected System 61 vii LIST OF TABLES Table Page 3- 1 Measurements and Calculations of Mutual Inductance 10 4- 1 Parameters of Induction Motor-Amplidyne Set 23 5- 1 Parameters of Synchronous Motor-DC Generator Set. 33 viii ] ACKNOWLEDGEMENTS I want to acknowledge with gratitude the guidance and encouragement given to me by Dr. Y.N. Yu during this thesis study. Acknowledgement is given to the University of British Columbia and the National Research Council of Canada for fin• ancial support of the research. I would like to thank Mr. A. MacKenzie for drafting the illustrations and Miss H. Klassen for typing the thesis in final form. I am also indebted to Beverley, my wife, for her encouragement and for preparing the original manuscript. ix 1. INTRODUCTION Many analogue studies of electric machines have been done. Physical models are obtained, equations are written and analogue studies are carried out. However, these studies are mostly concerned with the development of analogue techniques. Verification of system behaviour from analogue studies by comparison with machine tests is seldom given,especially for interconnected machine systems. Krause and Thomas (l), applying the d-q:coordinate transformations, studied on the analogue computer transient phenomena of a 3-phase induction motor with unbalanced stator voltages and unequal rotor resistors. Krause (2) also carried out transient studies of 2-phase and various types of single- phase induction motors. Dineley and Glover (3) modeled a synchronous generator on an analogue computer to study voltage effects of capacitive loading. The effect of saturation of the main axis flux was simulated by a function generator. O'Plaherty and Aldred (4), using the analogue computer, studied a synchronous-machine and transmission system with symmetrical and unsymmetrical faults. Stabilities of various faults at different locations along the transmission line were determined. Symmetrical components and Park's equations were used to set up the system on the analogue computer. In all the previous studies no comparison was made between the results from the analogue computer and those from the actual tests. 2 To carry out transient analysis of 2-phase and 3- phase induction motors on the analogue computer, Hughes and Aldred (5) used measured parameters. They verified their model hy a comparison of results from steady state studies on the analogue with those from real tests. With this model they studied starting transients of a 2-phase induction motor and unbalanced and single phase operation of a 3-phase induction motor. Riaz (6) in his voltage regulation studies gave a detailed analogue presentation for a synchronous generator including saliency, amortisseur winding and saturation. With approximations, he studied a zero power factor load. His computer results of no load and load steady state voltages and transient response times.compared favourably with test results. Although the techniques of analogue computer studies of electric machine systems have been very well developed, a complete comparison of results from analogue studies with those from actual machine tests is still lacking. In this thesis, an interconnected four machine system, consisting of a synchronous motor-dc generator set and an induction motor-amplidyne set, is used to carry out the study. Both steady state and transient performances from analogue studies and real machine tests will be compared for the individual sets and for the interconnected system. A Pace 231R analogue computer is used to carry out the study. 3 2. PROCEDURE AND SYSTEM UNDER STUDY 2-1 Procedure The development of a complete analogue of an electric machine system for both the steady state and transient studies involves modeling, analogue, and comparison of analogue results with those from performance tests on real machines.
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