Design of Rotating Electrical Machines By Juha Pyrhonen and Tapani Jokinen and Val eria Hrabovcova (1) PDF

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OTE/SPH OTE/SPH FM JWBK312-Pyrhönen November 23, 2008 13:4 Printer Name: Yet to Come DESIGN OF ROTATING ELECTRICAL MACHINES Design of Rotating Electrical Machines Juha Pyrhönen, Tapani Jokinen and Valéria Hrabovcová © 2008 John Wiley & Sons, Ltd. ISBN: 978-0-470-69516-6 i OTE/SPH OTE/SPH FM...

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OTE/SPH OTE/SPH FM JWBK312-Pyrh¨onen

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DESIGN OF ROTATING ELECTRICAL MACHINES

Design of Rotating Electrical Machines Juha Pyrh¨onen, Tapani Jokinen and Val´eria Hrabovcov´a © 2008 John Wiley & Sons, Ltd. ISBN: 978-0-470-69516-6

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DESIGN OF ROTATING ELECTRICAL MACHINES Juha Pyrh¨onen Department of Electrical Engineering, Lappeenranta University of Technology, Finland

Tapani Jokinen Department of Electrical Engineering, Helsinki University of Technology, Finland

Val´eria Hrabovcov´a Department of Power Electrical Systems, Faculty of Electrical Engineering, ˇ University of Zilina, Slovak Republic

Translated by Hanna Niemel¨a Department of Electrical Engineering, Lappeenranta University of Technology, Finland

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This edition first published 2008
C 2008 John Wiley & Sons, Ltd Adapted from the original version in Finnish written by Juha Pyrh¨onen and published by Lappeenranta University C Juha Pyrh¨ of Technology
onen, 2007 Registered office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com. The right of the authors to be identified as the authors of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. Library of Congress Cataloging-in-Publication Data Pyrh¨onen, Juha. Design of rotating electrical machines / Juha Pyrh¨onen, Tapani Jokinen, Val´eria Hrabovcov´a ; translated by Hanna Niemel¨a. p. cm. Includes bibliographical references and index. ISBN 978-0-470-69516-6 (cloth) 1. Electric machinery–Design and construction. 2. Electric generators–Design and construction. 3. Electric motors–Design and construction. 4. Rotational motion. I. Jokinen, Tapani, 1937– II. Hrabovcov´a, Val´eria. III. Title. TK2331.P97 2009 621.31 042–dc22 2008042571 A catalogue record for this book is available from the British Library. ISBN: 978-0-470-69516-6 (H/B) Typeset in 10/12pt Times by Aptara Inc., New Delhi, India. Printed in Great Britain by CPI Antony Rowe, Chippenham, Wiltshire

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Contents About the Authors

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Preface

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Abbreviations and Symbols

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1 1.1 1.2 1.3

1 1 9 12 17 22

1.4 1.5 1.6 1.7 1.8

Principal Laws and Methods in Electrical Machine Design Electromagnetic Principles Numerical Solution The Most Common Principles Applied to Analytic Calculation 1.3.1 Flux Line Diagrams 1.3.2 Flux Diagrams for Current-Carrying Areas Application of the Principle of Virtual Work in the Determination of Force and Torque Maxwell’s Stress Tensor; Radial and Tangential Stress Self-Inductance and Mutual Inductance Per Unit Values Phasor Diagrams Bibliography

2 Windings of Electrical Machines 2.1 Basic Principles 2.1.1 Salient-Pole Windings 2.1.2 Slot Windings 2.1.3 End Windings 2.2 Phase Windings 2.3 Three-Phase Integral Slot Stator Winding 2.4 Voltage Phasor Diagram and Winding Factor 2.5 Winding Analysis 2.6 Short Pitching 2.7 Current Linkage of a Slot Winding 2.8 Poly-Phase Fractional Slot Windings 2.9 Phase Systems and Zones of Windings 2.9.1 Phase Systems 2.9.2 Zones of Windings

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25 33 36 40 43 45 47 48 48 52 53 54 56 63 71 72 81 92 95 95 98

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Contents

2.10 Symmetry Conditions 2.11 Base Windings 2.11.1 First-Grade Fractional Slot Base Windings 2.11.2 Second-Grade Fractional Slot Base Windings 2.11.3 Integral Slot Base Windings 2.12 Fractional Slot Windings 2.12.1 Single-Layer Fractional Slot Windings 2.12.2 Double-Layer Fractional Slot Windings 2.13 Single- and Two-Phase Windings 2.14 Windings Permitting a Varying Number of Poles 2.15 Commutator Windings 2.15.1 Lap Winding Principles 2.15.2 Wave Winding Principles 2.15.3 Commutator Winding Examples, Balancing Connectors 2.15.4 AC Commutator Windings 2.15.5 Current Linkage of the Commutator Winding and Armature Reaction 2.16 Compensating Windings and Commutating Poles 2.17 Rotor Windings of Asynchronous Machines 2.18 Damper Windings Bibliography

99 102 103 104 104 105 105 115 122 126 127 131 134 137 140

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153 159 159 164 169 171 173 173 177 177

Design of Magnetic Circuits 3.1 Air Gap and its Magnetic Voltage 3.1.1 Air Gap and Carter Factor 3.1.2 Air Gaps of a Salient-Pole Machine 3.1.3 Air Gap of Nonsalient-Pole Machine 3.2 Equivalent Core Length 3.3 Magnetic Voltage of a Tooth and a Salient Pole 3.3.1 Magnetic Voltage of a Tooth 3.3.2 Magnetic Voltage of a Salient Pole 3.4 Magnetic Voltage of Stator and Rotor Yokes 3.5 No-Load Curve, Equivalent Air Gap and Magnetizing Current of the Machine 3.6 Magnetic Materials of a Rotating Machine 3.6.1 Characteristics of Ferromagnetic Materials 3.6.2 Losses in Iron Circuits 3.7 Permanent Magnets in Rotating Machines 3.7.1 History and Characteristics of Permanent Magnets 3.7.2 Operating Point of a Permanent Magnet Circuit 3.7.3 Application of Permanent Magnets in Electrical Machines 3.8 Assembly of Iron Stacks 3.9 Magnetizing Inductance Bibliography

142 145 147 150 152

180 183 187 193 200 200 205 213 219 221 224

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Contents

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Flux Leakage 4.1 Division of Leakage Flux Components 4.1.1 Leakage Fluxes Not Crossing an Air Gap 4.1.2 Leakage Fluxes Crossing an Air Gap 4.2 Calculation of Flux Leakage 4.2.1 Air-Gap Leakage Inductance 4.2.2 Slot Leakage Inductance 4.2.3 Tooth Tip Leakage Inductance 4.2.4 End Winding Leakage Inductance 4.2.5 Skewing Factor and Skew Leakage Inductance Bibliography Resistances 5.1 DC Resistance 5.2 Influence of Skin Effect on Resistance 5.2.1 Analytical Calculation of Resistance Factor 5.2.2 Critical Conductor Height 5.2.3 Methods to Limit the Skin Effect 5.2.4 Inductance Factor 5.2.5 Calculation of Skin Effect Using Circuit Analysis 5.2.6 Double-Sided Skin Effect Bibliography

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Main Dimensions of a Rotating Machine 6.1 Mechanical Loadability 6.2 Electrical Loadability 6.3 Magnetic Loadability 6.4 Air Gap Bibliography Design Process and Properties of Rotating Electrical Machines 7.1 Asynchronous Motor 7.1.1 Current Linkage and Torque Production of an Asynchronous Machine 7.1.2 Impedance and Current Linkage of a Cage Winding 7.1.3 Characteristics of an Induction Machine 7.1.4 Equivalent Circuit Taking Asynchronous Torques and Harmonics into Account 7.1.5 Synchronous Torques 7.1.6 Selection of the Slot Number of a Cage Winding 7.1.7 Construction of an Induction Motor 7.1.8 Cooling and Duty Types 7.1.9 Examples of the Parameters of Three-Phase Industrial Induction Motors

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225 227 227 228 230 230 234 245 246 250 253 255 255 256 256 265 266 267 267 274 280 281 291 293 294 297 300 301 313 315 320 327 332 337 339 342 343 348

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7.1.10 Asynchronous Generator 7.1.11 Asynchronous Motor Supplied with Single-Phase Current 7.2 Synchronous Machine 7.2.1 Inductances of a Synchronous Machine in Synchronous Operation and in Transients 7.2.2 Loaded Synchronous Machine and Load Angle Equation 7.2.3 RMS Value Phasor Diagrams of a Synchronous Machine 7.2.4 No-Load Curve and Short-Circuit Test 7.2.5 Asynchronous Drive 7.2.6 Asymmetric-Load-Caused Damper Currents 7.2.7 Shift of Damper Bar Slotting from the Symmetry Axis of the Pole 7.2.8 V Curve of a Synchronous Machine 7.2.9 Excitation Methods of a Synchronous Machine 7.2.10 Permanent Magnet Synchronous Machines 7.2.11 Synchronous Reluctance Machines 7.3 DC Machines 7.3.1 Configuration of DC Machines 7.3.2 Operation and Voltage of a DC Machine 7.3.3 Armature Reaction of a DC Machine and Machine Design 7.3.4 Commutation 7.4 Doubly Salient Reluctance Machine 7.4.1 Operating Principle of a Doubly Salient Reluctance Machine 7.4.2 Torque of an SR Machine 7.4.3 Operation of an SR Machine 7.4.4 Basic Terminology, Phase Number and Dimensioning of an SR Machine 7.4.5 Control Systems of an SR Motor 7.4.6 Future Scenarios for SR Machines Bibliography 8 Insulation of Electrical Machines 8.1 Insulation of Rotating Electrical Machines 8.2 Impregnation Varnishes and Resins 8.3 Dimensioning of an Insulation 8.4 Electrical Reactions Ageing Insulation 8.5 Practical Insulation Constructions 8.5.1 Slot Insulations of Low-Voltage Machines 8.5.2 Coil End Insulations of Low-Voltage Machines 8.5.3 Pole Winding Insulations 8.5.4 Low-Voltage Machine Impregnation 8.5.5 Insulation of High-Voltage Machines 8.6 Condition Monitoring of Insulation 8.7 Insulation in Frequency Converter Drives Bibliography

Contents

351 353 358 359 370 376 383 386 391 392 394 394 395 400 404 404 405 409 411 413 414 415 416 419 422 425 427 429 431 436 440 443 444 445 445 446 447 447 449 453 455

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Contents

Heat Transfer 9.1 Losses 9.1.1 Resistive Losses 9.1.2 Iron Losses 9.1.3 Additional Losses 9.1.4 Mechanical Losses 9.2 Heat Removal 9.2.1 Conduction 9.2.2 Radiation 9.2.3 Convection 9.3 Thermal Equivalent Circuit 9.3.1 Analogy between Electrical and Thermal Quantities 9.3.2 Average Thermal Conductivity of a Winding 9.3.3 Thermal Equivalent Circuit of an Electrical Machine 9.3.4 Modelling of Coolant Flow 9.3.5 Solution of Equivalent Circuit 9.3.6 Cooling Flow Rate Bibliography

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457 458 458 460 460 460 462 463 466 470 476 476 477 479 488 493 495 496

Appendix A

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Appendix B

501

Index

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About the Authors Juha Pyrh¨onen is a Professor in the Department of Electrical Engineering at Lappeenranta University of Technology, Finland. He is engaged in the research and development of electric motors and drives. He is especially active in the fields of permanent magnet synchronous machines and drives and solid-rotor high-speed induction machines and drives. He has worked on many research and industrial development projects and has produced numerous publications and patents in the field of electrical engineering. Tapani Jokinen is a Professor Emeritus in the Department of Electrical Engineering at Helsinki University of Technology, Finland. His principal research interests are in AC machines, creative problem solving and product development processes. He has worked as an electrical machine design engineer with Oy Str¨omberg Ab Works. He has been a consultant for several companies, a member of the Board of High Speed Tech Ltd and Neorem Magnets Oy, and a member of the Supreme Administrative Court in cases on patents. His research projects include, among others, the development of superconducting and large permanent magnet motors for ship propulsion, the development of high-speed electric motors and active magnetic bearings, and the development of finite element analysis tools for solving electrical machine problems. Val´eria Hrabovcov´a is a Professor of Electrical Machines in the Department of Power ˇ Electrical Systems, Faculty of Electrical Engineering, at the University of Zilina, Slovak Republic. Her professional and research interests cover all kinds of electrical machines, electronically commutated electrical machines included. She has worked on many research and development projects and has written numerous scientific publications in the field of electrical engineering. Her work also includes various pedagogical activities, and she has participated in many international educational projects.

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Preface Electrical machines are almost entirely used in producing electricity, and there are very few electricity-producing processes where rotating machines are not used. In such processes, at least auxiliary motors are usually needed. In distributed energy systems, new machine types play a considerable role: for instance, the era of permanent magnet machines has now commenced. About half of all electricity produced globally is used in electric motors, and the share of accurately controlled motor drives applications is increasing. Electrical drives provide probably the best control properties for a wide variety of processes. The torque of an electric motor may be controlled accurately, and the efficiencies of the power electronic and electromechanical conversion processes are high. What is most important is that a controlled electric motor drive may save considerable amounts of energy. In the future, electric drives will probably play an important role also in the traction of cars and working machines. Because of the large energy flows, electric drives have a significant impact on the environment. If drives are poorly designed or used inefficiently, we burden our environment in vain. Environmental threats give electrical engineers a good reason for designing new and efficient electric drives. Finland has a strong tradition in electric motors and drives. Lappeenranta University of Technology and Helsinki University of Technology have found it necessary to maintain and expand the instruction given in electric machines. The objective of this book is to provide students in electrical engineering with an adequate basic knowledge of rotating electric machines, for an understanding of the operating principles of these machines as well as developing elementary skills in machine design. However, due to the limitations of this material, it is not possible to include all the information required in electric machine design in a single book, yet this material may serve as a manual for a machine designer in the early stages of his or her career. The bibliographies at the end of chapters are intended as sources of references and recommended background reading. The Finnish tradition of electrical machine design is emphasized in this textbook by the important co-authorship of Professor Tapani Jokinen, who has spent decades in developing the Finnish machine design profession. An important view of electrical machine design is provided by Professor Val´eria Hrabovcov´a from Slovak Republic, which also has a strong industrial tradition. We express our gratitude to the following persons, who have kindly provided material for this book: Dr Jorma Haataja (LUT), Dr Tanja Hedberg (ITT Water and Wastewater AB), Mr Jari J¨appinen (ABB), Ms Hanne Jussila (LUT), Dr Panu Kurronen (The Switch Oy), Dr Janne Nerg (LUT), Dr Markku Niemel¨a (ABB), Dr Asko Parviainen (AXCO Motors Oy),

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Preface

Mr Marko Rilla (LUT), Dr Pia Salminen (LUT), Mr Ville Sihvo and numerous other colleagues. Dr Hanna Niemel¨a’s contribution to this edition and the publication process of the manuscript is highly acknowledged. Juha Pyrh¨onen Tapani Jokinen Val´eria Hrabovcov´a

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Abbreviations and Symbols A A A AC AM A1–A2 a B Br Bsat B B1–B2 b b0c bc bd bdr bds br bs bv b0 C C C1–C2 Cf c cp cth CTI cv D DC

linear current density [A/m] magnetic vector potential [V s/m] temperature class 105 ◦ C alternating current asynchronous machine armature winding of a DC machine number of parallel paths in windings without commutator: per phase, in windings with a commutator: per half armature, diffusivity magnetic flux density, vector [V s/m2 ], [T] remanence flux density [T] saturation flux density [T] temperature class 130 ◦ C commutating pole winding of a DC machine width [m] conductor width [m] conductor width [m] tooth width [m] rotor tooth width [m] stator tooth width [m] rotor slot width [m] stator slot width [m] width of ventilation duct [m] slot opening [m] capacitance [F], machine constant, integration constant temperature class >180 ◦ C compensating winding of a DC machine friction coefficient specific heat capacity [J/kg K], capacitance per unit of length, factor, divider, constant specific heat capacity of air at constant pressure heat capacity Comparative Tracking Index specific volumetric heat [kJ/K m3 ] electric flux density [C/m2 ], diameter [m] direct current

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Dr Dri Ds Dse D1–D2 d dt E Ea E E E E1–E2 e e F F F FEA Fg Fm F1–F2 f g G G th H Hc , HcB HcJ H h h 0c hc hd hp h p2 hs h yr h ys I IM Ins Io Is

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Abbreviations and Symbols

outer diameter of the rotor [m] inner diameter of the rotor [m] inner diameter of the stator [m] outer diameter of the stator [m] series magnetizing winding of a DC machine thickness [m] thickness of the fringe of a pole shoe [m] electromotive force (emf) [V], RMS, electric field strength [V/m], scalar, elastic modulus, Young’s modulus [Pa] activation energy [J] electric field strength, vector [V/m] temperature class 120 ◦ C irradiation shunt winding of a DC machine electromotive force [V], instantaneous value e(t) Napier’s constant force [N], scalar force [N], vector temperature class 155 ◦ C finite element analysis geometrical factor
magnetomotive force H · dl [A], (mmf) separate magnetizing winding of a DC machine or a synchronous machine frequency [Hz], Moody friction factor coefficient, constant, thermal conductance per unit length electrical conductance thermal conductance magnetic field strength [A/m] coercivity related to flux density [A/m] coercivity related to magnetization [A/m] temperature class 180 ◦ C, hydrogen hei...