Analysis of Synchronous Machines Second Edition by T. A. Lipo
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Analysis of Synchronous Machines Second Edition by T. A. Lipo


The material in this book has evolved from a course taught yearly to senior/ graduate students entitled “Theory and Control of Synchronous Machines” at the University of Wisconsin. Begun in 1980, the essence of the course material has not changed substantially. However, the means by which the course is taught has changed dramatically with the evolution of computing tools. The ready availability of MATLAB® and MATHCAD® has rendered many of the traditional methods of problem solving, such as analog simulation, FORTRAN programming, constructional phasor diagrams and so forth, to be mere anecdotes.

As a result of these powerful tools, over the years material has been Thomas A. Lipo Madison, WI MATLAB ® is a registered trademark of The MathWorks, Inc. For product information, please contact: The MathWorks, Inc. 3 Apple Hill Drive Natick, MA 01760-2098 USA Tel: 508 647 7000 Fax: 508-647-7001 E-mail: [email protected] Web: increasingly added to challenge the student and provide a deeper appreciation of the underlying theory of the subject. In particular, the material contained in Chapters 8–11 is rarely included in an introductory course and, if desired, could easily be omitted from a 3-credit course on this subject.

These chapters are typically presented by the author as the background material for a lengthy “class problem” near the end of the semester which serves to cap the student’s learning experience. I might add, with some delight, that these computational tools have even added to the “fun” of learning a challenging new subject.

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The author is indebted to his many graduate students, some of whom have contributed to the production of this book via their MSc. and Ph.D. theses. In addition, numerous other graduate students have also assisted both through their technical contributions as well as thorough proofreading of this text. The author also wishes to thank the David Grainger Foundation for funding and facilities provided at the University of Wisconsin. He is also indebted for facilities provided by the Center for Applied Power Systems, Florida State University during final rewrite of the text. Finally, this book is dedicated to Christine Lipo, wonderful and loving wife, who passed away August 18, 2004.

All conventional machines rely upon magnetic fields for the purpose of energy conversion. Windings are arranged on the periphery of a stationary member (stator) and a rotating member (rotor) so as to set up a field distribution of magnetic flux density in the space which separates them (air gap). By appropriate excitation of the windings, this field can be made to rotate relative to the stationary member (synchronous machine), relative to the rotating member (DC machine) or relative to both members (induction machine). The interaction of the flux components produced by the stator and rotor members result in the production of torque. Subsequent rotation of the rotor results in electromechanical energy conversion.
A valid approach to the study of electric machines is to deal directly with the electromagnetic fields. Knowledge of the field distribution leads to a deeper understanding of where flux is concentrated, where currents flow, where forces appear, and where heat is generated within the machine.

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Such detailed information is very important, since relatively small alterations in the design can often lead to substantial improvements in efficiency, cost, or reliability of the machine. The serious student of machine design must eventually be required to delve into the electromagnetic fields associated with rotating machines. Unfortunately, the analysis of machines as a fields problem involves the solution of Laplace’s or Poisson’s equation. The geometry of machines leads to complicated boundary conditions even for simplified cases. A digital computer must generally be used to find complete field distributions.
The approach of this book is to characterize the machine in terms of coupled magnetic circuits rather than magnetic fields. Our interest is then restricted primarily to the terminal rather than internal characteristics of machines. Although one loses sight of the exact spatial distribution of currents and fluxes, the problem becomes immensely simplified. However, to ensure an understanding of the simplifying assumptions, one must initially deal directly with the fields. The significant effects of the rotating fields must be expressed properly in terms of flux linkages in rotating coupled circuits. Since flux linkage is proportional to inductance, the ability to characterize winding distributions and utilize this characterization in the calculation of winding inductances is of central importance.

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