Electromechanical Motion Devices
Description
The thoroughly revised and updated third edition of Electromechanical Motion Devices contains an introduction to modern electromechanical devices and offers an understanding of the uses of electric machines in emerging applications such as in hybrid and electric vehicles. The authors--noted experts on the topic--put the focus on modern electric drive applications. The book includes basic theory, illustrative examples, and contains helpful practice problems designed to enhance comprehension.
The text offers information on Tesla's rotating magnetic field, which is the foundation of reference frame theory and explores in detail the reference frame theory. The authors also review permanent-magnet ac, synchronous, and induction machines. In each chapter, the material is arranged so that if steady-state operation is the main concern, the reference frame derivation can be de-emphasized and focus placed on the steady state equations that are similar in form for all machines. This important new edition:
* Features an expanded section on Power Electronics
* Covers Tesla's rotating magnetic field
* Contains information on the emerging applications of electric machines, and especially, modern electric drive applications
* Includes online animations and a solutions manual for instructors
Written for electrical engineering students and engineers working in the utility or automotive industry, Electromechanical Motion Devices offers an invaluable book for students and professionals interested in modern machine theory and applications.
More details
Other editions
Additional editions
Persons
PAUL KRAUSE, PHD, is Chairman of the Board of P.C. Krause & Associates, having retired after 39 years as a professor at Purdue University School of Electrical and Computer Engineering. He is a Life Fellow of IEEE and has authored or co-authored over 100 technical papers and three textbooks on electric machines. He was the 2010 recipient of the IEEE Nikola Tesla Award.
OLEG WASYNCZUK, PHD, is a Professor of Electrical and Computer Engineering at Purdue University. He has authored or co-authored over 100 technical papers and two textbooks on electric machines. He is a Fellow of IEEE and was the 2008 recipient of the IEEE Cyril Veinott Award. He also serves as Chief Technical Officer of P.C. Krause & Associates.
STEVEN D. PEKAREK, PHD, is the Edmund O. Schweitzer III Professor of Electrical and Computer Engineering at Purdue University. He is the co-author of two textbooks on electric machinery, an IEEE Fellow, and an active member of the IEEE Power and Energy Society. He is an Editor for the IEEE Transactions on Energy Conversion and the recipient of the 2018 IEEE Cyril Veinott Award.
TIMOTHY O'CONNELL, PHD, is a Senior Lead Engineer at P.C. Krause & Associates, where he has over ten years' experience in the modeling, simulation, analysis and design of more electric aircraft. He is an Adjunct Professor of Electrical and Computer Engineering at the University of Illinois at Urbana-Champaign. He is a Senior Member of IEEE, an Associate Editor of the IEEE Transactions on Aerospace and Electronic Systems, and has co-authored two textbooks on electric machinery.
Content
Preface ix
Chapter 1 Magnetic and Magnetically Coupled Circuits 1
1.1 Introduction 1
1.2 Phasor Analysis 2
1.3 Magnetic Circuits 8
1.4 Properties of Magnetic Materials 14
1.5 Stationary Magnetically Coupled Circuits 18
1.6 Open- and Short-Circuit Characteristics of Stationary Magnetically Coupled Circuits 25
1.7 Magnetic Systems with Mechanical Motion 28
1.8 Recapping 35
Chapter 2 Electromechanical Energy Conversion 39
2.1 Introduction 39
2.2 Energy Balance Relationships 40
2.3 Energy in Coupling Field 45
2.4 Graphical Interpretation of Energy Conversion 52
2.5 Electromagnetic and Electrostatic Forces 55
2.6 Operating Characteristics of an Elementary Electromagnet 60
2.7 Single-Phase Reluctance Machine 65
2.8 Windings in Relative Motion 70
2.9 Recapping 72
Chapter 3 Direct-Current Machines and the Dc Drive 77
3.1 Introduction 77
3.2 Elementary Direct-Current Machine 78
3.3 Voltage and Torque Equations 85
3.4 Permanent-Magnet DC Machine 88
3.5 Time-Domain Block Diagram and State Equations for the Permanent-Magnet DC Machine 92
3.6 Dynamic Characteristics of Permanent-Magnet DC Motors 94
3.7 DC Drive 97
3.8 Recapping 103
Chapter 4 Winding Distribution and Tesla's Rotating Magnetic Field 105
4.1 Introduction 105
4.2 Winding Distribution 106
4.3 Air-Gap MMF 109
4.4 Tesla's Rotating Magnetic Field - Symmetrical Stator Circuits 113
4.5 Tesla's Rotating Fields and Torque with Unsymmetrical and Symmetrical Rotor Circuits 121
4.6 P-Pole Machines 126
4.7 Recapping 131
Chapter 5 Introduction to Reference Frame Theory 137
5.1 Introduction 137
5.2 Background 138
5.3 Change of Variables for Symmetrical Stator Circuits 138
5.4 Transformation of Two-Phase Stator Variables to the Arbitrary Reference Frame 143
5.5 Balanced Steady-State Stator Variables Viewed from any Reference Frame 148
5.6 Stator Variables Observed from Different Reference Frames 152
5.7 Instantaneous Phasor 156
5.8 Transformation of Three-Phase Stator Variables to the Arbitrary Reference Frame 159
5.9 Substitute Variables for Symmetrical Rotating Circuits 162
5.10 Recapping 164
Chapter 6 Permanent-Magnet AC Machine and Field Orientation of a Brushless DC Drive 167
6.1 Introduction 167
6.2 Two-Phase Permanent-Magnet AC Machine 168
6.3 Voltage Equations and Winding Inductances 170
6.4 Torque 172
6.5 Machine Equations in the Rotor Reference Frame 173
6.6 Instantaneous and Steady-State Phasors 177
6.7 Three-Phase Permanent-Magnet AC Machine 181
6.8 Unequal Direct- and Quadrature-Axis Inductances 186
6.9 Field Orientation of a Brushless DC Drive 189
6.10 Inverter-Supplied Brushless DC Drive 208
6.11 Recapping 221
Chapter 7 Synchronous Machines 223
7.1 Introduction 223
7.2 Windings of the Synchronous Machine 224
7.3 Two-Phase Round-Rotor Synchronous Machine 228
7.4 Analysis of Steady-State Operation 234
7.5 Analysis of Steady-State Operation in Power Systems 238
7.6 Two-Phase Reluctance Machine 247
7.7 Dynamic and Steady-State Performance 254
7.8 Three-Phase Round-Rotor Synchronous Machine 260
7.9 Recapping 266
Chapter 8 Symmetrical Induction Machines and Field Orientation 269
8.1 Introduction 269
8.2 Two-Phase Induction Machine 270
8.3 Voltage Equations and Winding Inductances 274
8.4 Torque 280
8.5 Voltage Equations in the Arbitrary Reference Frame 281
8.6 Magnetically Linear Flux-Linkage Equations and Equivalent Circuits 284
8.7 Torque Equations in Arbitrary Reference Frame Variables 286
8.8 Phasors and Steady-State Operating Modes 286
8.9 Dynamic and Steady-State Performance - Machine Variables 299
8.10 Free Acceleration Viewed from Stationary, Rotor, and Synchronously Rotating Reference Frames 307
8.11 Three-Phase Induction Machine 312
8.12 Principles of Field Orientation 319
8.13 Recapping 331
Chapter 9 Stepper Motors 335
9.1 Introduction 335
9.2 Basic Configurations of Multistack Variable-Reluctance Stepper Motors 335
9.3 Equations for Multistack Variable-Reluctance Stepper Motors 342
9.4 Operating Characteristics of Multistack Variable-Reluctance Stepper Motors 345
9.5 Single-Stack Variable-Reluctance Stepper Motors 348
9.6 Basic Configuration of Permanent-Magnet Stepper Motors 352
9.7 Equations for Permanent-Magnet Stepper Motors 356
9.8 Equations of Permanent-Magnet Stepper Motors in Rotor Reference Frame - Reluctance Torques Neglected 359
9.9 Recapping 363
Chapter 10 Power Electronics 365
10.1 Introduction 365
10.2 Switching-Circuit Fundamentals 365
10.3 DC-DC Conversion 376
10.4 AC-DC Conversion 389
10.5 DC-AC Conversion 403
10.6 Recapping 407
Appendix A 411
Appendix B 415
Index 417
CHAPTER 1
MAGNETIC AND MAGNETICALLY COUPLED CIRCUITS
1.1 INTRODUCTION
Before diving into the analysis of electromechanical motion devices, it is helpful to review briefly some of our previous work in physics and in basic electric circuit analysis. In particular, the analysis of magnetic circuits, the basic properties of magnetic materials, and the derivation of equivalent circuits of stationary, magnetically coupled circuits are topics presented in this chapter. Much of this material will be a review for most, since it is covered either in a sophomore physics course for engineers or in introductory electrical engineering courses in circuit theory. Nevertheless, reviewing this material and establishing concepts and terms for later use sets the appropriate stage for our study of electromechanical motion devices.
Perhaps the most important new concept presented in this chapter is the fact that in all electromechanical devices, mechanical motion must occur, either translational or rotational, and this motion is reflected into the electric system either as a change of flux linkages in the case of an electromagnetic system or as a change of charge in the case of an electrostatic system. We will deal primarily with electromagnetic systems. If the magnetic system is linear, then the change in flux linkages results, owing to a change in the inductance. In other words, we will find that the inductances of the electric circuits associated with electromechanical motion devices are functions of the mechanical motion. In this chapter, we shall learn to express the self- and mutual inductances for simple translational and rotational electromechanical devices, and to handle these changing inductances in the voltage equations describing the electric circuits associated with the electromechanical system.
Throughout this text, we will give short problems (SPs) with answers following most sections. If we have done our job, each SP should take less than ten minutes to solve. Also, it may be appropriate to skip or de-emphasize some material in this chapter depending upon the background or interest of the students. At the close of each chapter, we shall take a moment to look back over some of the important aspects of the material that we have just covered and mention what is coming next and how we plan to fit things together as we go along.
1.2 PHASOR ANALYSIS
Phasors are used to analyze steady-state performance of ac circuits and devices. This concept can be readily established by expressing a steady-state sinusoidal variable as
(1.2-1)where capital letters are used to denote steady-state quantities and is the peak value of the sinusoidal variation, which is generally voltage or current but could be any electrical or mechanical sinusoidal variable. For steady-state conditions, may be written as
(1.2-2)where is the electrical angular velocity and is the time-zero position of the electrical variable. Substituting (1.2-2) into (1.2-1) yields
(1.2-3)Since
(1.2-4)equation (1.2-3) may also be written as
(1.2-5)where is shorthand for the "real part of." Equations (1.2-3) and (1.2-5) are equivalent. Let us rewrite (1.2-5) as
(1.2-6)Thus, we need to take a moment to define what is referred to as the root mean square (rms) of a sinusoidal variation. In particular, the rms value is defined as
(1.2-7)where is the rms value of and is the period of the sinusoidal variation. It is left to the reader to show that the rms value of (1.2-3) is . Therefore, we can express (1.2-6) as
(1.2-8)By definition, the phasor representing , which is denoted with a raised tilde, is
(1.2-9)which is a complex number. The reason for using the rms value as the magnitude of the phasor will be addressed later in this section. Equation (1.2-6) may now be written as
(1.2-10)A shorthand notation for (1.2-9) is
(1.2-11)Equation (1.2-11) is commonly referred to as the polar form of the phasor. The Cartesian form is
(1.2-12)When using phasors to calculate steady-state voltages and currents, we think of the phasors as being stationary at t = 0. On the other hand, a phasor is related to the instantaneous value of the sinusoidal quantity it represents. Let us take a moment to consider this aspect of the phasor and, thereby, give some physical meaning to it. From (1.2-4), we realize that is a constant-amplitude line of unity length rotating counterclockwise at an angular velocity of . Therefore,
(1.2-13)is a constant-amplitude line in length rotating counterclockwise at an angular velocity of with a time-zero displacement from the positive real axis of . Since is the peak value of the sinusoidal variation, the instantaneous value of is the real part of (1.2-13). In other words, the real projection of the phasor is the instantaneous value of at time zero. As time progresses, rotates at in the counterclockwise direction, and its real projection, in accordance with (1.2-10), is the instantaneous value of . Thus, for
(1.2-14)the phasor representing is
(1.2-15)For
(1.2-16)the phasor is
(1.2-17)Although there are several ways to arrive at (1.2-17) from (1.2-16), it is helpful to ask yourself where must the rotating phasor be positioned at time zero so that, when it rotates counterclockwise at , its real projection is ? Is it clear that a phasor of amplitude F positioned at represents ?
In order to show the facility of the phasor in the analysis of steady-state performance of ac circuits and devices, it is useful to consider a series circuit consisting of a resistance, an inductance, and a capacitance. Thus,
(1.2-18)For steady-state operation, let
(1.2-19) (1.2-20)where the subscript a is used to distinguish the instantaneous value from the rms value of the steady-state variable. The steady-state voltage equation may be obtained by substituting (1.2-19) and (1.2-20) into (1.2-18), whereupon we can write
(1.2-21)The second term on the right-hand side of (1.2-21), which is , can be written as
(1.2-22)Since , we can write
(1.2-23)Since , (1.2-23) may be written as
(1.2-24)If we follow a similar procedure, we can show that
(1.2-25)It is interesting that differentiation of a steady-state sinusoidal variable rotates the phasor counterclockwise by , whereas integration rotates the phasor clockwise by .
The steady-state voltage equation given by (1.2-21) can be written in phasor form as
(1.2-26)We can express (1.2-26) compactly as
(1.2-27)where Z, the impedance, is a complex number; it is not a phasor. It is often expressed as
(1.2-28)where XL = ?eL is the inductive reactance and is the capacitive reactance.
The instantaneous power is
(1.2-29)After some manipulation, we can write (1.2-29) as
(1.2-30)Therefore, the average power may be written as
(1.2-31)where and are the magnitude of the phasors (rms value), is the power factor angle , and is referred to as the power factor. If current is positive in the direction of voltage drop then (1.2-31) is positive if power is consumed and negative if power is generated. It is interesting to point out that in going from (1.2-29) to (1.2-30), the coefficient of the two right-hand terms is or one-half the product of the peak values of the sinusoidal variables. Therefore, it was considered more convenient to use the rms values for the phasors, whereupon average power could be calculated by the product of the magnitude of the voltage and current phasors as given by (1.2-31).
We see from (1.2-30) that the instantaneous power of a single-phase ac circuit oscillates at about an average value. Let us take a moment to calculate the steady-state power of a two-phase ac system. Balanced, steady-state, two-phase variables (a and b phase) may be expressed as
(1.2-32) (1.2-33) (1.2-34) (1.2-35)The total instantaneous power is
(1.2-36)Substituting (1.2-32) through (1.2-35) into (1.2-36) and after some trigonometric manipulation, the total power for a balanced two-phase system...
