Analysis and Details of the Subject
There is one book reviewed in this issue. The third edition of this text on electric machinery has reference-frame theory at its core, the reviewer states, and is recommended for “those with a need for electric machinery modeling and simulation.”
Analysis of Electric Machinery and Drive Systems, Third Edition
by Paul Krause, Oleg Wasynczuk, Scott Sudhoff, and Steven Pekarek
Analysis is a word that means a scrutiny, enquiry, explanation, or dissection. Analysis is the perfect word to describe this book. This work gets to the details of modeling electric machines, motors and generators, and drives systems. As stated in the preface, “…reference-frame theory is at the core of this book.” The changes and additions in this third edition are important.
Chapter 1 begins with a basic but thorough discussion of the theory behind electromechanical energy conversion and magnetically coupled circuits starting out, of course, with the transformer and moving on to the rotating machine. One of the interesting issues is that some of the inductances are a function of the rotor position. Chapter 2 introduces distributed winding and rotating air-gap magnetomotive force. This chapter also addresses flux linkages, e.g., the magnetizing flux that crosses the air gap and couples the rotor and stator, and the leakage flux that does not cross the air gap. Then we come to Chapter 3, a study of reference-frame theory.
The chapter starts out with a brief but interesting background on reference frames. It all began in the late 1920s by R.H. Park. Four basic reference frames are discussed: 1) reference fixed to the rotor, 2) reference fixed to the stator, 3) a synchronously rotating reference frame, and 4) the arbitrary reference frame. This chapter is relatively short but one to be studied well to understand how these reference frames can be used and why one may be preferred over another. Keep in mind that some of these go by a different name, e.g., the rotor fixed frame may be called the “dq frame” and the stator fixed frame may be simply the “fixed frame.”
After explaining the material in the first three chapters, the authors put the material to work on permanent-magnet (PM), synchronous, and induction machines in the next three chapters. Chapter 4 addresses the PM motor, which lends itself ideally to controlled voltage or current source inverter applications. The authors point out that, with the proper control strategy, the PM motor and drive can be used to 1) improve the performance of the PM motor, 2) operate at maximum torque per amp, 3) provide field weakening to increase the speed range for constant power, and 4) shift the voltage phase to obtain the maximum torque at any speed.
The synchronous machine is covered in Chapter 5. First the synchronous motor (current into the stator) is discussed, and then the synchronous generator (current out of the stator), both steam and hydro, are evaluated. The discussion of torque-angle and critical clearing time are especially interesting. The authors seem to imply that large synchronous generators are equipped with damper windings on the rotor. It is my experience that dedicated copper damper windings are not provided on two- and four-pole generator rotors. Manufacturers use a variety of rotor wedge materials to act as a damper winding to allow the rotor to withstand the negative sequence currents identified in IEEE C50.13 without injurious overheating. In Chapter 6 we get to the industry’s work horse, the induction motor. The chapter starts with the classical equations using machine variables and moves in the reference-frame evaluations. Of particular interest are Figures 6.11-1–6.11-5, showing the free acceleration characteristics of an induction motor using the machine variables and the five different reference-frame theories. Needless to say, it was nice that the output torque curve was the same for all six simulations.
Chapter 7 goes into more detail; addressing the operational impedances and time constants. The introduction suggests that, for solid iron rotor machines, you may need as many as four rotor windings in each axis to evaluate transient dynamics. This chapter looks into the synchronous machine reactances, time constants, and short-circuit characteristics. Finally the chapter discusses the pros and cons of parameters from frequency-response characteristics. The authors point out that the frequency range from 0.05 to 5 Hz should be carefully evaluated to insure accuracy in dynamic and transient studies.
Chapter 8 addresses three alternate forms of machine equations: 1) linearized (small-displacement) formulation for operating point stability, 2) neglecting stator current transients for large-excursion transient studies, and 3) the voltage-behind reactance formulation. The chapter goes into the details of each transformation for the synchronous and induction machines.
Chapter 9 takes up the issue of unbalanced operation and the single-phase induction motor. The chapter starts out with a brief discussion of symmetrical components, the unbalance analysis tool from the 1900s. The authors go on to show that unbalance phase variables can be expressed as a series of balanced sets in the arbitrary reference frame with coefficients that may be constraint or time varying. As the authors point out, there are a plethora of textbooks on dc machines. Chapter 10 reviews the theory of the dc and PM machines. The last half of the chapter contains a thorough discussion of converter drives.
Chapter 11 begins the development of basic converter operation. The semicontrolled single- and three-phase load commutated converters are introduced. Models for the average-value and dynamic average-value converters are developed.
Throughout this text, a three-phase variable-frequency source was often mentioned; well here it is in Chapter 12. The chapter gets right into the operation of a six-stepped, three-phase bridge. This is commonly known as pulse-width modulation. Several
other modulation strategies are introduced. The previous two chapters paved the way for Chapter 13, which gets to the heart of the popular induction motor drive. Several control strategies are evaluated. The first is the volts-per-hertz control. Volts-per-hertz control is simple, inexpensive, and open loop; the control does not require a speed feedback. Constant slip control, with proper modulation, can provide a current-based operation; this will achieve an optimal torque for a given value of stator current with maximum efficiency. The field-orientated control will make the drive act as a torque transducer. The direct torque control is another method of regulating torque. Finally, we know that increasing rotor resistance can increase starting torque and lower reactive power during starting. The slip energy recovery drive achieves these advantages but without increasing losses at operating speed.
Chapter 14 covers, perhaps, the second most-used adjustable speed drive, the PM ac motor. In this chapter the three-phase bridge rectifier described in Chapter 12 is the converter drive used; here it is referred to as an inverter. Both the voltage-source and the current-regulated drives are studied. Average-value models for each drive are developed. This chapter points out that the current-regulated inverter drive has a few advantages. Since torque is a function of current, the torque can be easily controlled. This drive is not susceptible to changes in the machines parameters. Also, current-regulated drives are current limiting so fault currents and starting current can be automatically limited.
Chapter 15 is a new chapter to this third edition; it tackles the topic of motor design. The authors chose the PM motor on a dc bus. I am a bit puzzled—why didn’t they select the very popular induction motor on an ac bus? Another issue, although the reader is forewarned, structural and thermal issues as well as several loss mechanisms are not taken into consideration. Thermal issues are one of the leading causes of motor failures. Who would purchase a motor under these circumstances? Having said this; the chapter is filled with very useful information on a host of issues that a motor designer has to balance to create a quality product meeting all the performance requirements. I especially enjoyed reviewing this chapter as it is an excellent introduction to motor design.
One of the features of this volume, not often found in other technical books, is the amount of explanation offered. There is a lot of text, a lot of excellent and informative discussion about each chapter and the concepts covered.
For those with a need for electric machinery modeling and simulation, you will enjoy this book. The in-depth explanation of the various reference-frame theories is outstanding. The authors went to great length to detail the use of each reference frame to the evaluation of synchronous, induction, and PM machines. However, if you are a utility plant engineer looking for information about motor types, application, operation, testing, or maintenance, this is not the book for you. Again, for those interested in modeling and the fundamentals of reference-frame theory for the analysis of motors, generators, and drive systems, I recommend this excellent text.