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Access provided by: anon Sign Out. Analysis of Electric Machinery and Drive Systems. Book Abstract: An updated approach to reference frame analysis of electric machines and drive systems Since the first edition of Analysis of Electric Machinery was published, the reference frame theory that was detailed in the book has become the universally accepted approach for the analysis of both electric machines and electric drive systems. Copyright Year: Topics: Power, Energy and Industry Applications. Online ISBN: Author s : Paul C. Krause; Oleg Wasynczuk; Scott D. Need Help?

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Analysis Of Electric Machinery and Drive Systems

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Thrinadh Thota , Student at Nit Warangal. Show More. No Downloads. Views Total views. Actions Shares. Embeds 0 No embeds. No notes for slide. Pc krause analysis-of-electrical-machines 1. Krause Oleg Wasynczuk Scott D. Kartalopoulos, Editor in Chief M. Akay M. Eden M. Padgett J. Anderson M. E1-Hawary M. Newman R. Baker R. Herrick W. Reeve J. Brewer R. Hoyt G. Zobrist D. Bartnikas and K. E1-Hawary Hardcover pp I 4. PAUL C. This book is printed on acid-free paper. 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, scanning or otherwise, except as permitted under Section or of the United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Rosewood Drive, Danvers, MA , , fax Library of Congress Cataloging-in-Publication is available.

Krause and published in by McGraw-Hill. Sudhoff added as co-authors. Not only has this approach been embraced by the vast majority of electric machine analysts, it has also become the approach used in the analysis of electric drive systems. For the most part, the material in Chapters on electric drive systems is new.

In particular, the ana- lysis of converters used in electric drive systems is presented in Chapters 11 and 13 while dc, induction, and brushless dc motor drives are analyzed in Chapters 12, 14, and 15, respectively. Central to the analysis used in this text is the transformation to the arbitrary refer- ence frame.


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All real and complex transformations used in machine and drive ana- lyses can be shown to be special cases of this general transformation. The modern electric machine and drive analyst must understand reference frame theory. For this reason, the complete performance of all electric machines and drives considered are illustrated by computer traces wherein variables are often portrayed in different xiii For this purpose, considerable time should be devoted to the basic principles discussed in Chapter 1, perhaps some of Chapter 2 covering basic dc machines, most of Chapter 3 covering reference frame theory, and the beginning sections of Chapters 4, 5, and 6 covering induction, syn- chronous, and brushless dc machines.

We would like to acknowledge the efforts and assistance of the reviewers, in par- ticular Mohamed E. The principle of electromechanical energy conversion is perhaps the comerstone of machine analysis. This theory allows us to establish an expression of electromagnetic torque in terms of machine variables, generally the currents and the displacement of the mechanical system.

Other principles that must be established are 1 the derivation of equivalent circuit representations of magnetically coupled circuits, 2 the concept of a sinusoidally distributed winding, 3 the concept of a rotating air-gap magnetomotive force MMF , and 4 the deri- vation of winding inductances.

The above-mentioned basic principles are presented in this chapter, concluding with the voltage equations of a 3-phase synchronous machine and a 3-phase induction machine. This establishes an awareness of the complexity of these vol- tage equations and sets the stage for the change of variables Chapter 3 , which reduces the complexity of the voltage equations by eliminating the time-dependent inductances.

In the case of transformers, stationary circuits are 1 In the case of electric machines, circuits in relative motion are magnetically coupled for the purpose of transferring energy between mechanical and electrical systems. Because magnetically coupled circuits play such an important role in power trans- mission and conversion, it is important to establish the equations that describe their behavior and to express these equations in a form convenient for analysis.

These goals may be achieved by starting with two stationary electric circuits that are mag- netically coupled as shown in Fig.


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  6. The two coils consist of turns N, and N2, respectively, and they are wound on a common core that is generally a ferromagnetic material with permeability large relative to that of air. In the case of transformer steel the relative permeability may be as high to Often, in transformer analysis, i2 is selected positive out of the top of coil 2, and a dot is placed at that terminal. In this case, one coil is said to be magnetizing the core, the other demagnetizing. Before proceeding, it is appropriate to point out that this is an idealization of the actual magnetic system. To acknowledge this practical aspect of the magnetic system, the number of turns is considered to be an equivalent number rather than the actual number.

    This fact should cause us little concern because the inductances of the electric circuit resulting from the magnetic coupling are generally determined from tests.

    Pc krause analysis-of-electrical-machines

    The voltage equations may be expressed in matrix form as , dl V—l'l-I-E 1. The reluctance of the magnetizing path of the core shown in Fig. Substituting 1. An analogous state- ment may be made regarding l. From 1. The mutual inductances may be related to the magnetizing inductances. This is said to be referring the current in coil 2 to coil 1 whereupon coil 1 becomes the reference coil. This change of variables is said to refer the current of coil 1 to coil 2.

    We will demonstrate the derivation of the equivalent T circuit by referring the current of coil 2 to coil 1; thus from 1. In particular, 2; : If we substitute 1. The above voltage equations suggest the T equivalent circuit shown in Fig. It is apparent that this method may be extended to include any number of coils wound on the same core.

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    Example 1A It is instructive to illustrate the method of deriving an equiva- lent T circuit from open- and short-circuit measurements. For this purpose let us assume that when coil 2 of the two-winding transformer shown in Fig. The power during this test is 22 W. A transformer is generally designed so that some saturation occurs during normal operation. Electric machines are also designed similarly in that a machine generally operates slightly in the saturated region during normal, rated operating conditions.

    Our purpose here is not to set forth methods of analyzing nonlinear magnetic systems. This pro- cedure is quite straightforward for steady-state operation, but it cannot be used when analyzing the dynamics of electromechanical devices [1]. A method of incorporating the effects of saturation into a computer representation is of interest. Computer Simulation of Coupled Circuits Formulating the voltage equations of stationary coupled windings appropriate for computer simulation is straightforward and yet this technique is fundamental to the computer simulation of ac machines.

    Therefore it is to our advantage to consider this method here. In the com- puter simulation, 1. The currents can then be obtained from 1. It is clear that 1. From Fig. In particular, f Am is a function of Am as shown in Fig. It is desirable, however, to establish methods of analysis that may be applied to all electromechanical devices.