Finite Element Analysis of Electrical Machines
In Finite Element Analysis of Electrical Machines the author covers two-dimensional analysis, emphasizing the use of finite elements to perform the most common calculations required of machine designers and analysts. The book explains what is inside a fin
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THE KLUWER INTERNATIONAL SERIES IN ENGINEERING AND COMPUTER SCIENCE POWER ELECTRONICS AND POWER SYSTEMS Consulting Editor Thomas A. Lipo
Other books in the series: ENERGY FUNCTION ANALYSIS FOR POWER SYSTEM STABILITY, M. A. Pai ISBN: 0-7923-9035-0 ELECTROMAGNETIC MODELLING OF POWER ELECTRONIC CONVERTERS, J. A. Ferreira ISBN: 0-7923-9034-2 MODERN POWER SYSTEMS CONTROL AND OPERATION, A. S. Debs ISBN: 0-89838-265-3 RELIABILITY ASSESSMENT OF LARGE ELECTRIC POWER SYSTEMS, R. Billington, R. N. Allan ISBN: 0-89838-266-1 SPOT PRICING OF ELECTRICITY, F. C. Schweppe, M. C. Caramanis, R. D. Tabors, R. E. Bohn ISBN: 0-89838-260-2 INDUSTRIAL ENERGY MANAGEMENT: Principles and Applications, Giovanni Petrecca ISBN: 0-7923-9305-8 THE FIELD ORffiNTATION PRINCIPLE IN CONTROL OF INDUCTION MOTORS, Andrzej M. Trzynadlowski ISBN: 0-7923-9420-8
FI N ITE ELEM ENT ANALYSIS OF ELECTRICAL MACHINES
S. J. SALON Rensselaer POlytechnic Institute Troy, New York
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SPRINGER SCIENCE+BUSINESS MEDIA, LLC
ISBN 978-1-4613-5996-8 ISBN 978-1-4615-2349-9 (eBook) DOI 10.1007/978-1-4615-2349-9 Library of Congress Cataloging-in-Publication Data A C.I.P. Catalogue record for this book is available from the Library of Congress.
Copyright © 1995 by Springer Science+Business Media New York Originally published by Kluwer Academic Publishers in 1995 Softcover reprint ofthe hardcover lst edition 1995 AH rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, Springer Science+Business Media. LLC.
Printed on acid-free paper.
CONTENTS
PREFACE 1
INTRODUCTION TO FINITE ELEMENTS 1.1 1.2 1.3 1.4
2
Introduction The Galerkin Finite Element Method Boundary Conditions Magnetostatic Example
NONLINEAR PROBLEMS 2.1 Introduction 2.2 Representation of the B-H Curve 2.3 The Basic Newton-Raphson Method for a Single Equation 2.4 Application of the Newton-Raphson Method to a First Order 2.5
3
PERMANENT MAGNETS 3.1 3.2 3.3 3.4 3.5
4
Element Cubic Splines
Introduction Magnetization Models of Permanent Magnets Current Sheet Equivalents Example With Permanent Magnet Intrinsic and Normal Hysteresis Characteristics
EDDY CURRENT ANALYSIS 4.1 4.2 4.3 4.4 4.5
Introduction Eddy Currents and Skin Effect Finite Element Example Elliptical Description of Flux Density Eddy Currents In Nonlinear Materials
ix
1 1 1 10 12
17 17 19 20 24 28 33 33 35 39 46 47
51 51 52 55 57 58
FINITE ELEMENT ANALYSIS OF ELECTRICAL MACHINES
4.6 4.7 4.8 4.9
5
Nonlinear Permeability Models Coupling Finite Elements To External Circuits Numerical Example Modeling Considerations
COMPUTATION OF LOSSES, RESISTANCE
AND INDUCTANCE 5.1 5.2 5.3 5.4 5.5 5.6
6
7
61 63 68 72
Introduction Computation of Eddy Current Loss Losses In A Series Winding Inductance and Reactance Poynting Vector Nonlinear Problems
75 75 75 79 84 93 93
CALCULATION OF FORCE AND TORQUE
97
6.1 6.2 6.3 6.4 6.5 6.6 6.7
97 98 98 104 116 11
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