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Fitzgerald & Kingsley's Electric Machinery (IRWIN ELEC&COMPUTER ENGINERING)

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In SI units, the magnetic stored energy W is measured in j o u l e s (J). For a single-winding system of constant inductance, the change in magnetic Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY 10020. Copyright (~) 2003, 1990, 1983, 1971, 1961, 1952 by The McGraw-Hill Companies, Inc. All rights reserved. Copyright renewed 1980 by Rosemary Fitzgerald and Charles Kingsley, Jr. All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning. Figure 1.12 Exciting rms voltamperes per kilogram at 60 Hz for M-5 grain-oriented electrical steel 0.012 in thick. (Armco Inc.) T he objective of this book is to study the devices used in the interconversion of electric and mechanical energy. Emphasis is placed on electromagnetic rotating machinery, by means of which the bulk of this energy conversion For practical magnetic materials (as is discussed in Sections 1.3 and 1.4), Bc and Hc are not simply related by a known constant permeability/z as described by Eq. 1.7. In fact, Bc is often a nonlinear, multivalued function of Hc. Thus, although Eq. 1.10 continues to hold, it does not lead directly to a simple expression relating the mmf and the flux densities, such as that of Eq. 1.11. Instead the specifics of the nonlinear Bc-He relation must be used, either graphically or analytically. However, in many cases, the concept of constant material permeability gives results of acceptable engineering accuracy and is frequently used.

To produce magnetic flux in the core requires current in the exciting winding known as the exciting current, i~o. 6 The nonlinear magnetic properties of the core re- quire that the waveform of the exciting current differs from the sinusoidal waveform of the flux. A curve of the exciting current as a function of time can be found graphically from the magnetic characteristics of the core material, as illustrated in Fig. 1.1 la. Since Bc and Hc are related to ~o and i~ by known geometric constants, the ac hys- teresis loop of Fig. 1.1 lb has been drawn in terms of ~o = BcAc and is i~0 = Hclc/N. Sine waves of induced voltage, e, and flux, ~o, in accordance with Eqs. 1.48 and 1.49, are shown in Fig. 1.11 a. From Eq. 1.1, the relationship between the mmf acting on a magnetic circuit and the magnetic field intensity in that circuit is. 3 chapter introduces the basic concept of electromechanical energy conversion. The fourth chapter then provides an overview of and on introduction to the various machine types. Some instructors choose to omit all or most of the material in Chapter 3 from an introductory course. This can be done without a significant impact to the understanding of much of the material in the remainder of the book. Although very little in the way of sophisticated mathematics is required of the reader of this book, the mathematics can get somewhat messy and tedious. This is especially true in the analyis of ac machines in which there is a significant amount of algebra involving complex numbers. One of the significant positive developments in the last decade or so is the widespread availability of programs such as MATLAB which greatly facilitate the solution of such problems. MATLAB is widely used in many universities and is available in a student version. 2INTERNATIONAL EDITION ISBN 0-07-112193-5 Copyright ~ 2003. Exclusive rights by The McGraw-Hill Companies, Inc., for manufacture and export. This book cannot be re-exported from the country to which it is sold by McGraw-Hill. The International Edition is not available in North America.

S o l u t i o n Notice that there are two air gaps in series, of total length 2g, and that by symmetry the flux Professor Kingsley first asked this author to participate in the fourth edition of Electric Machinery; the professor was actively involved in that edition. He participated in an advisory capacity for the fifth edition. Unfortunately, Professor Kingsley passed away since the publication of the fifth edition and did not live to see the start of the work on this edition. He was a fine gentleman, a valued teacher and friend, and he is missed.in a magnetic circuit in the absence of external excitation (such as winding currents). This is a familiar phenomenon to anyone who has afixed notes to a refrigerator with small magnets and is widely used in devices such as loudspeakers and permanent- Consider the magnetic circuit of Fig. 1.20. This includes a section of hard mag- netic material in a core of highly permeable soft magnetic material as well as an N-turn excitation winding. With reference to Fig. 1.21, we assume that the hard Inductance is measured in henrys (H) or weber-turns per ampere. Equation 1.31 shows the dimensional form of expressions for inductance; inductance is proportional to the square of the number of turns, to a magnetic permeability, and to a cross- sectional area and is inversely proportional to a length. It must be emphasized that, strictly speaking, the concept of inductance requires a linear relationship between flux and mmf. Thus, it cannot be rigorously applied in situations where the nonlinear characteristics of magnetic materials, as is discussed in Sections 1.3 and 1.4, dominate the performance of the magnetic system. However, in many situations of practical interest, the reluctance of the system is dominated by that of an air gap (which is of course linear) and the nonlinear effects of the magnetic material can be ignored. In other cases it may be perfectly acceptable to assume an average value of magnetic permeability for the core material and to calculate a corresponding average inductance which can be used for calculations of reasonable engineering accuracy. Example 1.3 illustrates the former situation and Example 1.4 the latter. Flux linkage is measured in units of webers (or equivalently weber-turns). The symbol q9 is used to indicate the instantaneous value of a time-varying flux. pts) Draw a schematic of this scenario. For now, consider the load as a single impedance, Z, at some

The instructor should note that a complete presentation of field-oriented control requires the use of the dq0 transformation. This transformation, which appeared for synchronous machines in Chapter 6 of the previous edition, is now found in Appendix C of this edition. In addition, the discussion in this appendix has been expanded to include a derivation of the dq0 transformation for induction machines in which both stator and rotor quantities must be transformed. Finally, I wish to thank the reviewers who participated in this project and whose comments and suggestions played a valuable role in the final form of this edition. These include Professors: The exciting new sixth edition of “Electric Machinery” has been extensively updated while retaining the emphasis on fundamental principles and physical understanding that has been the outstanding feature of this classic book. The ac excitation characteristics of core materials are often described in terms of rms voltamperes rather than a magnetization curve relating B and H. The theory behind this representation can be explained by combining Eqs. 1.52 and 1.53. Thus, from Eqs. 1.52 and 1.53, the rms voltamperes required to excite the core of Fig. 1.1 to a specified flux density is equal to In addition, it should be noted that even in cases where it is not specifically suggested, most of the end-of-chapter problems in the book can be worked using MATLAB or an equivalent program. Thus, students who are comfortable using such tools should be encouraged to do so to save themselves the need to grind through messy calculations by hand. This approach is a logical extension to the use of calculators to facilitate computation. When solving homework problems, the students should still, of course, be required to show on paper how they formulated their solution, since it is the formulation of the solution that is key to understanding the material. However, once a problem is properly formulated, there is typically little additional to be learned from the number crunching itself. The learning process then continues with an examination of the results, both in terms of understanding what they mean with regard to the topic being studied as well as seeing if they make physical sense.

PROBLEM SOLUTIONS: Chapter 1

The magnetic circuit of Fig. 1.6a consists of an N-turn winding on a magnetic core of infinite permeability with two parallel air gaps of lengths g~ and g2 and areas A~ and A2, respectively. Many motor-drive systems are based upon the technique of field-oriented con- trol (also known as vector control). A significant addition to this new edition is the discussion of field-oriented control which now appears in Chapter 11. This is some- what advanced material which is not typically found in introductory presentations of electric machinery. As a result, the chapter is structured so that this material can be omitted or included at the discretion of the instructor. It first appears in the section on torque control of synchronous motors, in which the basic equations are derived and the analogy with the control of dc machines is discussed. It appears again in its most commonly used form in the section on the torque control of induction motors.

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