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Kalsi-SS-1970-Phd-Thesis.Pdf UNIVERSITY OF LONDON IMPERIAL COLLIDE OF SCIENCE AND TECHNOLOGY Department of Electrical Engineering TRANSIENT PHENOMENA IN LARGE INDUCTION MOTORS IN A POWER SYSTEM by Swann Singh KALSI, B.Tech.(Hons.),M.Sc.(Eng.) Thesis submitted for the degree of Doctor of Philosophy in the Faculty of Ensineering LONDON, July 1970. 2 TO DEEP AND ICARAM 3 ABSTRACT As the size of the individual induction motor has increased significantly in the last few years, the behaviour of induction motors-in a power system under fault condition has assumed importance. The two main problems considered are the immediate fault current, which determines the rating of switchgear and the subsequent stability of the system. A standard method of determining the fault contribution made by 1 induction motors to the fault currents in a system is recommended . The basis of the proposals is that an induction motor can be treated in the same way as a synchronous machine. The recommendations are supported by a detailed theory of induction motor transients, in which accurate formulae are derived for the current following a sudden short circuit. The decpbar effectin the squirrel cage motors is theoretically simulated by two equivalent windings on the rotor. The proposed method is a simple one and is particularly useful for determining switchgear ratings in a mixed system containing both synchronous and induction machines, since it uses parameters of. the same kind for both, and permits existing procedures and method of computation to be used without change. The other problems studied on constant speed assumption are listed in Sect. 1.6. The study has been extended to the transient stability of a large induction motor when it forms part of a composite system. A full mathematical derivation of the equations is given, together with a comparison with previously suggested methods. The analysis has been extended to a general multi-machine system also containing synchronous machines. A comparison between the test and calculated results with various methods of machine representation was made on a single model 4 induction motor, and on a simple system containing the motor and a micro-alternator, which is representative of a large generator. The model induction motor was especially designed to simulate a 1800 h.p. induction motor on a per-unit basis, and its main features are the low resistances and the use of a dcepbar cage winding. The accurate representation of induction motors has been shown to be important in a system stability study for reliable and accurate results. It is shown that the stray load losses have an important effect on the prediction of individual machine behaviour, and on the overall system• behaviour when the two types of machines are present. At an early stage of the project, some work was carried out on synchronous machine stability2. This work, described in Part 1V, was a valuable preparation for the investigations as a whole and particularly for the combined system described in Chapter 11. 5 ACKTOWLEDGEnTITS The work presented in this thesis was carried out under the supervision of Dr. B. Adkins, M.A., D.Sc. (Eng.), C.Eng., F.I.E.E. of the Electrical Engineering Department, Imperial College of Science and Technology, London. I wish to thank Dr. Adkins for his helpful guidance and constant encouragement. I am grateful to the Science Research Council (U.K.) and the Electrical Engineering Department, Imperial College of Science and Technology, London, for the research assistantship under a grant from the S.R.C., and for the facilities, including the use of the IBM-70941I and CD6-6600 computers, to pursue the :•rork. The sincere appreciation is also extented to the S.R.C. for permission to register for the higher degree of the University. The author also thanks Messrs. E.E.- A.E.I. Machines Ltd., Rugby, for the information on the large motors. I also wish to thank Mr. A.J. Parsons of Messrs. Mawdsley's Ltd., Dursley and Mr. D.D. Stephen of Messrs. E.E.-A.E.I. Machines Ltd., Rugby for valuable discussions. Finally, I thank my colleagues who have contributed, directly or indirectly, to the success of the project. 6 TABLE OF CONTERS Abstract 3 Acknowledgements 5 List of symbols 12 CHAPTE2 1 INIRODUCTION. 16 1.1 General 16 1.2 Problems associated with large induction motors 16 1.3 Review of the investigations 17 1.4 The model induction motor 19 1.5 Method of analysis 19 1.6 Problems studied and the new conclusions 20 PART I: THE LABORATORY EC4UIP1-EiT 26 CHAPTER 2 THE MODZI, INDUCTION MOTOR 27 2.1 Introduction 27 2.2 Comparison of large and small induction motors 29 2.3 Theory of deerbar induction motor 33 2.3.1 Basic design of an induction motor having retangular 33 deepbars. 2.3.1.1 A.C. impedance 35 2.3.1.2 General procedure for designing an induction motor 37 having rectangular deepbars 2.3.2 The design of the model induction motor 38 2.3.3 Inverted T-shared bar 70 2.3.4 Compound bars made of tapered and rectangular sections 43 2.3.4.1 Exact solution for estimatinn: the imnedonce of a L.5 tanered bar 2.3.4.2 An approximate solution for tho in edance of tancred •-vu and comnosite bars 7 2.3.4.3 Step-by-step method of calculating the bar impedance 47 2.3.4.4 Circuit-analysis method of calculating the bar 49 impedance 2.3.4.5 Formulae for computing the other parameters 50 2.3.5 Comparison of results computed by various methods 50 2.3.6 The model induction motor set 62 2.4 Measurements for checking the computed results 68 2.4.1 No-load test 68 2.4.2 Locked rotor test 68 2.4.3 Torque speed characteristic 68 2.4.3.1 Calculation of the secondary impedance 73 2.4.4 Stray load losses 82 2.5 Conclusions 82 CHAPTER 3 OTHLa EXPERIMENTAL EQUIP= 85 3.1 The model motor system 85 3.2 Induction motor load simulation 87 3.3 Measurement of motor speed 87 3.4 Simulation of the transformer and the transmission line 91 impedances 3.5 Synchronous machine model 91 PART II: THE FAULT STUDIES OF LARGE INDUCTION roToRs 96 CHAPTER 4 INTRODUCTION 97 4.1 Review of investigations 97 4.2 The'object of the thesis 99 4.2.1 Fault currents in a system containing synchronous machines 99 4.2.2 Fault currents in a system containing induction motors 101 4.2.3 D7.termination of the sub-transient reactance or an induction 102 4 motor 8 4.2.3.1 The sudden short-circuit test 102 4.2.3.2 The standstill impedance test 102 4.2.3.3 Measurement of the frequency response characteristic 103 CHAPTIM 5 TRANSIENT THEORY OF A DEEP3AR INDUCTION MOTOR 105 5.1 Representation of a deepbar induction motor 105 5.2 Short circuit of an induction motor 107 5.2.1 Current and torque after a direct short circuit 107 5.2.2 Indirect short circuit 111 5.2.2.1 Terminal voltage after disconnection 111 5.2,2.2 Current and torque after a short circuit 112 5.3 Switching an induction machine to the supply 113 5.3.1 Machine running with trapped flux in the rotor 114 5.3.2 Machine running without trapped flux in the rotor 116 5.3.3 Machine initially at standstill 118 CHAPTER 6 EXPERIMENTAL PROCEDURE 121 6.1 Determination of transient parameters from the admittance 121 locus 6.2 Model test results and comparison with calculations 123 6.2.1 The direct short circuit test 125 6.2.2 The indirect short circuit test 125 6.2.3 Variable frequency impedance test 125 6.2.4 Variable speed impedance test 128 6.2.5 Approximate determination of operational admittance from 128 standard tests 6.2.6 Comparion of transient parameters determined by various 131 methods CHAPTER 7 coNalusoN OF CMPUTED AND TEST RESULTS 1364 7.1 The model motor 136 9 7.1.1 Direct short circuit test 136 7.1.2 Electrical torque during the short circuit 138 7.2 Application of the method of calculation to the large machines 138 7.3 Indirect short circuit test 143 7.4 Transient current and torque following the sudden connection 148 of a machine to the supply 7.4.1 Machine initially running with trapped flux 148 7.4.2 Machine initially running without trapped flux 152 7.4.3 Machine initially at .standstill 152 CHAPTER 8 CONCLUSIONS 158 PART III: TRANSIENT STABILITY OF POWER SYSTEMS CONTAINING BOTH 160 SYNCHRONOUS AND INDUCTION MACHINES CHAPTER 9 INTRODUCTION 161 9.1 General 161 9.2 Influence of digital computer on system studies 162 9.3 The past work 162 9.4 The object of the thesis 163 CHAPTER 10 STUDY OF A SINGLE INDUCTION MACHINE SYSTEM 165 10.1 General 165 10.2 Mathematical derivations 165 10.2.1 Accurate representation 165 10.2.2 Approximate representation 167 10.2.2.1 Method A (pli, and s terms neglected) 167 10.2.2.2 Method B (pyl term neglected) 168 10.2.2.3 Method C (Steady state equivalent circuit) 168 10.3 Comparison of computed and test results 169 10.3.1 Effect of rotor trapped flux 170 10.3.2, Three phase short circuit at full load 170 10 10.3.3 Effect of stray load losses 173 10.3.4 Open circuit fault at full load 175 10.4 Numerical integration techniques 175 10.5 Conclusions 182 CHAPTER 11 MULTI MACHINE SYSTEM STUDIES 184 11.1 System under investigation 184 11.2 Synchronous machine representation 186 11.2.1 Alternator equations 186 11.2.2 Accurate representation 188 11.2.3 Approximate representations 189 11.2.3.1 Method A (ppd, pTcl, and s terms neglected) 189 11.2.3.2 Method B (pY and ptP qterms neglected) d 190 11.2.3.3 Method C (Damping neglected) 191 11.3 System network representation 192 11.3.1 Transformation from the machine axis (d, q) 192 variables to the system ( cc, p axes) variables 11.3.2 Accurate representation of the network 193 11.3.3 Approximate representation of the network 194 11.4 The method of analysis for the system under investigation 194 11.4.1 Method-X 195 11.4.1.1 Method-Xi (Accurate) 195 11.4.1.2 Method-X2(APproximate) ' 201 11.4.2 Method-Y 205 11.4.3 Method-Z 208 11.5 Application of the method of calculations to a general 211 n--machine system.
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