electric motors and drive, Formulas and forms for Engineering. University of Lagos

electric motors and drive, Formulas and forms for Engineering. University of Lagos

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Electric Motors and Drives

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Electric Motors and Drives Fundamentals, Types and Applications

Third edition

Austin Hughes Senior Fellow, School of Electronic and Electrical Engineering, University of Leeds



Newnes is an imprint of Elsevier

Newnes is an imprint of Elsevier

Linacre House, Jordan Hill, Oxford OX2 8DP

30 Corporate Drive, Suite 400, Burlington, MA 01803

First edition 1990

Second edition 1993

Third edition 2006

Copyright  1990, 1993, 2006, Austin Hughes. Published by Elsevier Ltd. All rights reserved

The right of Austin Hughes to be identified as the author of this work

has been asserted in accordance with the Copyright, Designs and

Patents Act 1988.

No part of this publication may be reproduced, stored in a retrieval system or transmitted in any

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Oxford, UK: phone (+44) (0) 1865 843830; fax (+44) (0) 1865 853333; email: [email protected]

vier.com. Alternatively you can submit your request online by visiting the Elsevier web site at http://

elsevier.com/locate/permissions, and selecting Obtaining permission to use Elsevier material

British Library Cataloguing in Publication Data

A catalogue record for this book is available from the British Library

Library of Congress Cataloguing in Publication Data

A catalogue record for this book is available from the Library of Congress

ISBN-13: 978-0-7506-4718-2

ISBN-10: 0-7506-4718-3

For information on all Newnes publications

visit our website at http://books.elsevier.com/

Printed and bound in Great Britain

06 07 08 09 10 10 9 8 7 6 5 4 3 2 1


Preface xvi


Introduction 1

Producing Rotation 2 Magnetic field and magnetic flux 3 Magnetic flux density 4 Force on a conductor 6

Magnetic Circuits 7 Magnetomotive force (MMF) 9 Electric circuit analogy 10 The air-gap 11 Reluctance and air-gap flux densities 12 Saturation 14 Magnetic circuits in motors 15

Torque Production 16 Magnitude of torque 18 The beauty of slotting 19

Specific Loadings and Specific Output 21 Specific loadings 21 Torque and motor volume 23 Specific output power – importance of speed 23

Energy Conversion – Motional EMF 25 Elementary motor – stationary conditions 26 Power relationships – conductor moving at constant speed 28

Equivalent Circuit 30 Motoring condition 32 Behaviour with no mechanical load 32 Behaviour with a mechanical load 35 Relative magnitudes of V and E, and efficiency 37 Analysis of primitive motor – conclusions 38

General Properties of Electric Motors 39 Operating temperature and cooling 39 Torque per unit volume 40 Power per unit volume – importance of speed 41 Size effects – specific torque and efficiency 41 Efficiency and speed 41 Rated voltage 41 Short-term overload 42

Review Questions 42


Introduction 45 General arrangement of drives 45

Voltage Control – D.C. Output from D.C. Supply 47 Switching control 48 Transistor chopper 49 Chopper with inductive load – overvoltage protection 52

Features of power electronic converters 54

D.C. from A.C. – Controlled Rectification 55 The thyristor 55 Single-pulse rectifier 56 Single-phase fully controlled converter – output voltage and control 57

3-phase fully controlled converter 62 Output voltage range 64 Firing circuits 64

A.C. from D.C. SP – SP Inversion 65 Single-phase inverter 65 Output voltage control 67 Sinusoidal PWM 68 3-phase inverter 69

vi Contents

Forced and natural commutation – historical perspective 69

Matrix converters 70

Inverter Switching Devices 72 Bipolar junction transistor (BJT) 72 Metal oxide semiconductor field effect transistor (MOSFET) 73

Insulated gate bipolar transistor (IGBT) 74 Gate turn-off thyristor (GTO) 74

Converter Waveforms and Acoustic Noise 75

Cooling of Power Switching Devices 75 Thermal resistance 75 Arrangement of heatsinks and forced air cooling 77 Cooling fans 78

Review Questions 79


Introduction 82

Torque Production 84 Function of the commutator 86 Operation of the commutator – interpoles 88

Motional E.M.F. 90 Equivalent circuit 94

D.C. motor – Steady-State Characteristics 95 No-load speed 95 Performance calculation – example 96 Behaviour when loaded 98 Base speed and field weakening 103 Armature reaction 105 Maximum output power 106

Transient Behaviour – Current Surges 107 Dynamic behaviour and time-constants 108

Shunt, Series and Compound Motors 111 Shunt motor – steady-state operating characteristics 113

Series motor – steady-state operating characteristics 115

Contents vii

Universal motors 118 Compound motors 119

Four-Quadrant Operation and Regenerative Braking 119 Full speed regenerative reversal 122 Dynamic braking 124

Toy Motors 124

Review Questions 126


Introduction 133

Thyristor D.C. Drives – General 134 Motor operation with converter supply 136 Motor current waveforms 136 Discontinuous current 139 Converter output impedance: overlap 141 Four-quadrant operation and inversion 143 Single-converter reversing drives 144 Double SP-converter reversing drives 146 Power factor and supply effects 146

Control Arrangements for D.C. Drives 148 Current control 150 Torque control 152 Speed control 152 Overall operating region 154 Armature voltage feedback and IR compensation 155

Drives without current control 155

Chopper-Fed D.C. Motor Drives 155 Performance of chopper-fed d.c. motor drives 156 Torque–speed characteristics and control arrangements 159

D.C. Servo Drives 159 Servo motors 160 Position control 162

Digitally Controlled Drives 163

Review Questions 164

viii Contents


Introduction 167 Outline of approach 168

The Rotating Magnetic Field 170 Production of rotating magnetic field 172 Field produced by each phase winding 172 Resultant field 176 Direction of rotation 177 Main (air-gap) flux and leakage flux 177 Magnitude of rotating flux wave 179 Excitation power and VA 182 Summary 183

Torque Production 183 Rotor construction 183 Slip 185 Rotor induced e.m.f., current and torque 185 Rotor currents and torque – small slip 187 Rotor currents and torque – large slip 189

Influence of Rotor Current on Flux 191 Reduction of flux by rotor current 192

Stator Current-Speed Characteristics 193

Review Questions 196


Methods of Starting Cage Motors 198 Direct Starting – Problems 198 Star/delta (wye/mesh) starter 202 Autotransformer starter 202 Resistance or reactance starter 203 Solid-state soft starting 204 Starting using a variable-frequency inverter 206

Run-up and Stable Operating Regions 206 Harmonic effects – skewing 208 High inertia loads – overheating 209 Steady-state rotor losses and efficiency 209

Contents ix

Steady-state stability – pullout torque and stalling 210

Torque–Speed Curves – Influence of Rotor Parameters 211 Cage rotor 211 Double cage rotors 213 Deep bar rotors 214 Starting and run-up of slipring motors 215

Influence of Supply Voltage on Torque–Speed Curve 217

Generating and Braking 218 Generating region – overhauling loads 219 Plug reversal and plug braking 220 Injection braking 221

Speed Control 221 Pole-changing motors 222 Voltage control of high-resistance cage motors 223 Speed control of wound-rotor motors 224

Power Factor Control and Energy Optimisation 225 Voltage control 225 Slip energy recovery (wound rotor motors) 227

Single-Phase Induction Motors 227 Principle of operation 227 Capacitor-run motors 229 Split-phase motors 230 Shaded-pole motors 231

Size Range 232 Scaling down – the excitation problem 232

Review Questions 233


Introduction 236 Outline of approach 237

Similarity Between Induction Motor and Transformer 238

The Ideal Transformer 240 Ideal transformer – no-load condition, flux and magnetising current 240

x Contents

Ideal transformer – no-load condition, voltage ratio 245

Ideal transformer on load 246

The Real Transformer 248 Real transformer – no-load condition, flux and magnetising current 248

Real transformer – leakage reactance 251 Real transformer on load – exact equivalent circuit 252

Real transformer – approximate equivalent circuit 254

Measurement of parameters 256 Significance of equivalent circuit parameters 257

Development of the Induction Motor Equivalent Circuit 258 Stationary conditions 258 Modelling the electromechanical energy conversion process 259

Properties of Induction Motors 261 Power balance 262 Torque 262

Performance Prediction – Example 263 Line current 264 Output power 264 Efficiency 265 Phasor diagram 266

Approximate Equivalent Circuits 267 Starting and full-load relationships 268 Dependence of pull out torque on motor parameters 269

Analysis 270 Graphical interpretation via phasor diagram 271

Measurement of Parameters 274

Equivalent Circuit Under Variable-Frequency Conditions 274

Review Questions 277

Contents xi


Introduction 279 Comparison with d.c. drive 280 Inverter waveforms 282 Steady-state operation – importance of achieving full flux 284

Torque–Speed Characteristics – Constant V/f Operation 286 Limitations imposed by the inverter – constant power and constant torque regions 288

Limitations imposed by motor 289

Control Arrangements for Inverter-Fed Drives 290 Open-loop speed control 291 Closed-loop speed control 293

Vector (Field-Oriented) Control 296 Transient torque control 297

Cycloconverter Drives 300

Review Questions 303


Introduction 305 Open-loop position control 306 Generation of step pulses and motor response 307

High-speed running and ramping 308

Principle of Motor Operation 311 Variable reluctance motor 312 Hybrid motor 314 Summary 317

Motor Characteristics 318 Static torque–displacement curves 318 Single-stepping 319 Step position error and holding torque 320 Half stepping 321 Step division – mini-stepping 323

xii Contents

Steady-State Characteristics – Ideal (Constant-Current) Drive 324 Requirements of drive 324 Pull-out torque under constant-current conditions 326

Drive Circuits and Pull-Out Torque–Speed Curves 328 Constant-voltage drive 328 Current-forced drive 330 Chopper drive 331 Resonances and instability 333

Transient Performance 335 Step response 335 Starting from rest 336 Optimum acceleration and closed-loop control 337

Review Questions 338


Introduction 340

Synchronous Motors 341 Excited-rotor motors 343 Equivalent circuit of excited-rotor synchronous motor 344

Phasor diagram and Power-factor control 347 Starting 349 Permanent magnet synchronous motors 350 Hysteresis motors 351 Reluctance motors 351

Controlled-Speed Synchronous Motor Drives 352 Open-loop inverter-fed synchronous motor drives 353

Self-synchronous (closed-loop) operation 354 Operating characteristics and control 355

Brushless D.C. Motors 357

Contents xiii

Switched Reluctance Motor Drives 358 Principle of operation 359 Torque prediction and control 360 Power converter and overall drive characteristics 363

Review Questions 363


Introduction 366

Power Range for Motors and Drives 366 Maximum speed and speed range 368

Load Requirements – Torque–Speed Characteristics 369 Constant-torque load 369 Inertia matching 374 Fan and pump loads 374

General Application Considerations 375 Regenerative operation and braking 375 Duty cycle and rating 376 Enclosures and cooling 377 Dimensional standards 378 Supply interaction and harmonics 378

Review Questions 379


Reasons for Adopting a Simplified Approach 381

Closed-Loop (Feedback) Systems 382 Error-activated feedback systems 383 Closed-loop systems 384

Steady-State Analysis of Closed-Loop Systems 386

Importance of Loop Gain – Example 390

Steady-State Error – Integral Control 392

PID Controller 394

xiv Contents

Stability 396

Disturbance Rejection – Example Using D.C. Machine 397

Further Reading 400

Answers to Numerical Review Questions 401

Index 404

Contents xv


Like its predecessors, the third edition of this book is intended primarily for non-specialist users and students of electric motors and drives. My original aim was to bridge the gap between specialist textbooks (which are pitched at a level too academic for the average user) and the more prosaic ‘handbooks’, which are full of useful detail but provide little opportunity for the development of any real insight or understand- ing. The fact that the second edition was reprinted ten times indicated that there had indeed been a gap in the market, and that a third edition would be worthwhile. It was also gratifying to learn that although the original book was not intended as yet another undergraduate textbook, teachers and students had welcomed the book as a gentle introduction to the subject. The aim throughout is to provide the reader with an understanding of

how each motor and drive system works, in the belief that it is only by knowing what should happen that informed judgements and sound comparisons can be made. Given that the book is aimed at readers from a range of disciplines, introductory material on motors and power electronics is clearly necessary, and this is presented in the first two chapters. Many of these basic ideas crop up frequently throughout the book, so unless the reader is well-versed in the fundamentals it would be wise to absorb the first two chapters before tackling the later material. In addition, an awareness of the basic ideas underlying feedback and closed-loop control is necessary in order to follow the sections dealing with drives, and this has now been provided as an Appendix. The book explores most of the widely used modern types of motors

and drives, including conventional and brushless d.c., induction motors (mains and inverter-fed), stepping motors, synchronous motors (mains and converter-fed) and reluctance motors. The d.c. motor drive and the induction motor drive are given most importance, reflecting their dom- inant position in terms of numbers. Understanding the d.c. drive is particularly important because it is still widely used as a frame of

reference for other drives: those who develop a good grasp of the d.c. drive will find their know-how invaluable in dealing with all other types, particularly if they can establish a firm grip on the philosophy of the control scheme. Younger readers may be unaware of the radical changes that have

taken place over the past 40 years, so perhaps a couple of paragraphs are appropriate to put the current scene into perspective. For more than a century, many different types of motors were developed, and each be- came closely associated with a particular application. Traction, for ex- ample, was seen as the exclusive preserve of the series d.c. motor, whereas the shunt d.c. motor, though outwardly indistinguishable, was seen as being quite unsuited to traction applications. The cage induction motor was (and still is) the most widely used but was judged as being suited only for applications that called for constant speed. The reason for the pleth- ora of motor types was that there was no easy way of varying the supply voltage and/or frequency to obtain speed control, and designers were therefore forced to seek ways of providing speed control within the motor itself. All sorts of ingenious arrangements and interconnections of motor windings were invented, but even the best motors had a limited range of operating characteristics, and all of them required bulky control equipment gear-control, which was manually or electromechanically op- erated, making it difficult to arrange automatic or remote control. All this changed from the early 1960s when power electronics began to

make an impact. The first major breakthrough came with the thyristor, which provided a relatively cheap, compact and easily controlled variable-speed drive using the d.c. motor. In the 1970s, the second major breakthrough resulted from the development of power-electronic inverters, providing a three-phase variable-frequency supply for the cage induction motor and thereby enabling its speed to be controlled. These major developments resulted in the demise of many of the

special motors, leaving the majority of applications in the hands of comparatively few types, and the emphasis has now shifted from complexity inside the motor to sophistication in supply and control arrangements. From the user’s point of view this is a mixed blessing. Greater flexi-

bility and superior levels of performance are available, and there are fewer motor types to consider. But if anything more than constant speed is called for, the user will be faced with the purchase of a complete drive system, consisting of a motor together with its associated power elec- tronics package. To choose wisely requires not only some knowledge of motors, but also the associated power-electronics and the control op- tions that are normally provided.

Preface xvii

Development in the world of electrical machines tends to be steady rather than spectacular, which means that updating the second edition has called for only modest revision of the material covering the how and why of motors, though in most areas explanations have been extended, especially where feedback indicated that more clarity was called for. After much weighing the pros and cons I decided to add a chapter on the equivalent circuit of the induction motor, because familiarity with the terminology of the equivalent circuit is necessary in order to engage in serious dialogue with induction motor suppliers or experts. However those who find the circuit emphasis not to their liking can be reassured that they can skip Chapter 7 without prejudicing their ability to tackle the subsequent chapter on induction motor drives. The power electronics area has matured since the 1993 edition of the

book, but although voltage and current ratings of individual switching devices continue to improve, and there is greater integration of drive electronics and power devices, there has been no strategic shift that would call for a radical revision of the material in the second edition. The majority of drive converters now use IGBT or MOSFET devices, but the old-fashioned bipolar transistor symbol has been retained in most of the diagrams because it has the virtue of showing the direction of current flow, and is therefore helpful in understanding circuit operation. The style of the book reflects my own preference for an informal

approach, in which the difficulty of coming to grips with new ideas is not disguised. Deciding on the level at which to pitch the material was originally a headache, but experience suggested that a mainly descriptive approach with physical explanations would be most appropriate, with mathematics kept to a minimum to assist digestion. The most important concepts (such as the inherent e.m.f. feedback in motors, or the need for a switching strategy in converters) are deliberately reiterated to reinforce understanding, but should not prove too tiresome for readers who have already ‘got the message’. I had hoped to continue without numbered headings, as this always seems to me to make the material seem lighter, but cross referencing is so cumbersome without numbering that in the end I had to give in. I have deliberately not included any computed magnetic field plots,

nor any results from the excellent motor simulation packages that are now available because experience suggests that simplified diagrams are actually better as learning vehicles. All of the diagrams have been redrawn, and many new ones have been added. Review questions have been added at the end of each chapter. The

number of questions broadly reflects my judgement of the relative

xviii Preface

importance of each chapter, and they are intended to help build confi- dence and to be used selectively. A drives user might well not bother with the basic machine-design questions in the first two chapters, but could benefit by tackling the applications-related questions in subse- quent chapters. Judicious approximations are called for in most of the questions, and in some cases there is either insufficient explicit informa- tion or redundant data: this is deliberate and designed to reflect reality. Answers to the numerical questions are printed in the book, with

fully worked and commented solutions on the accompanying website http://books.elsevier.com/companions/0750647183. The best way to learn is to make an unaided attempt before consulting a worked solu- tion, so the extra effort in consulting the website will perhaps encourage best practice. In any event, my model solution may not be the best!

Austin Hughes

Preface xix

This Page Intentionally Left Blank



Electric motors are so much a part of everyday life that we seldom give them a second thought. When we switch on an electric drill, for example, we conWdently expect it to run rapidly up to the correct speed, and we do not question how it knows what speed to run at, or how it is that once enough energy has been drawn from the supply to bring it up to speed, the power drawn falls to a very low level. When we put the drill to work it draws more power, and when we Wnish the power drawn from the mains reduces automatically, without intervention on our part. The humble motor, consisting of nothing more than an arrangement

of copper coils and steel laminations, is clearly rather a clever energy converter, which warrants serious consideration. By gaining a basic understanding of how the motor works, we will be able to appreciate its potential and its limitations, and (in later chapters) see how its already remarkable performance can be further enhanced by the addi- tion of external electronic controls. This chapter deals with the basic mechanisms of motor operation, so

readers who are already familiar with such matters as magnetic Xux, magnetic and electric circuits, torque, and motional e.m.f can probably aVord to skim over much of it. In the course of the discussion, however, several very important general principles and guidelines emerge. These apply to all types of motors and are summarised in Section 1.8. Experi- ence shows that anyone who has a good grasp of these basic principles will be well equipped to weigh the pros and cons of the diVerent types of motor, so all readers are urged to absorb them before tackling other parts of the book.


Nearly all motors exploit the force which is exerted on a current- carrying conductor placed in a magnetic Weld. The force can be demonstrated by placing a bar magnet near a wire carrying current (Figure 1.1), but anyone trying the experiment will probably be dis- appointed to discover how feeble the force is, and will doubtless be left wondering how such an unpromising eVect can be used to make eVective motors. We will see that in order to make the most of the mechanism, we need

to arrange a very strong magnetic Weld, and make it interact with many conductors, each carrying as much current as possible. We will also see later that although the magnetic Weld (or ‘excitation’) is essential to the working of the motor, it acts only as a catalyst, and all of the mechanical output power comes from the electrical supply to the conductors on which the force is developed. It will emerge later that in some motors the parts of the machine responsible for the excitation and for the energy converting functions are distinct and self-evident. In the d.c. motor, for example, the excitation is provided either by permanent magnets or by Weld coils wrapped around clearly deWned projecting Weld poles on the stationary part, while the conductors on which force is developed are on the rotor and supplied with current via sliding brushes. In many motors, however, there is no such clear-cut physical distinction between the ‘excitation’ and the ‘energy-converting’ parts of the machine, and a single stationary winding serves both purposes. Nevertheless, we will Wnd that identifying and separating the excitation and energy-converting functions is always helpful in understanding how motors of all types operate. Returning to the matter of force on a single conductor, we will Wrst

look at what determines the magnitude and direction of the force,



Current in conductor

Figure 1.1 Mechanical force produced on a current-carrying wire in a magnetic Weld

2 Electric Motors and Drives

before turning to ways in which the mechanism is exploited to produce rotation. The concept of the magnetic circuit will have to be explored, since this is central to understanding why motors have the shapes they do. A brief introduction to magnetic Weld, magnetic Xux, and Xux density is included before that for those who are not familiar with the ideas involved.

Magnetic field and magnetic flux

When a current-carrying conductor is placed in amagnetic Weld, it experi- ences a force. Experiment shows that the magnitude of the force depends directly on the current in the wire, and the strength of the magnetic Weld, and that the force is greatestwhen themagneticWeld isperpendicular to the conductor. In the set-up shown in Figure 1.1, the source of the magnetic Weld

is a bar magnet, which produces a magnetic Weld as shown in Figure 1.2. The notion of a ‘magnetic Weld’ surrounding a magnet is an abstract

idea that helps us to come to grips with the mysterious phenomenon of








Figure 1.2 Magnetic Xux lines produced by a permanent magnet

Electric Motors 3

magnetism: it not only provides us with a convenient pictorial way of picturing the directional eVects, but it also allows us to quantify the ‘strength’ of the magnetism and hence permits us to predict the various eVects produced by it. The dotted lines in Figure 1.2 are referred to as magnetic Xux lines, or

simply Xux lines. They indicate the direction along which iron Wlings (or small steel pins) would align themselves when placed in the Weld of the bar magnet. Steel pins have no initial magnetic Weld of their own, so there is no reason why one end or the other of the pins should point to a particular pole of the bar magnet. However, when we put a compass needle (which is itself a permanent

magnet) in the Weld we Wnd that it aligns itself as shown in Figure 1.2. In the upper half of the Wgure, the S end of the diamond-shaped compass settles closest to the N pole of the magnet, while in the lower half of the Wgure, the N end of the compass seeks the S of the magnet. This immediately suggests that there is a direction associated with the lines of Xux, as shown by the arrows on the Xux lines, which conventionally are taken as positively directed from the N to the S pole of the bar magnet. The sketch in Figure 1.2 might suggest that there is a ‘source’ near the

top of the bar magnet, from which Xux lines emanate before making their way to a corresponding ‘sink’ at the bottom. However, if we were to look at the Xux lines inside the magnet, we would Wnd that they were continuous, with no ‘start’ or ‘Wnish’. (In Figure 1.2 the internal Xux lines have been omitted for the sake of clarity, but a very similar Weld pattern is produced by a circular coil of wire carrying a d.c. See Figure 1.6 where the continuity of the Xux lines is clear.). Magnetic Xux lines always form closed paths, as we will see when we look at the ‘magnetic circuit’, and draw a parallel with the electric circuit, in which the current is also a continuous quantity. (There must be a ‘cause’ of the magnetic Xux, of course, and in a permanent magnet this is usually pictured in terms of atomic-level circulating currents within the magnet material. Fortunately, discussion at this physical level is not necessary for our purpose.)

Magnetic flux density

Along with showing direction, the Xux plots also convey information about the intensity of the magnetic Weld. To achieve this, we introduce the idea that between every pair of Xux lines (and for a given depth into the paper) there is a same ‘quantity’ of magnetic Xux. Some people have no diYculty with such a concept, while others Wnd that the notion of quanti-

4 Electric Motors and Drives

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