Introduction to the Analysis of Electromechanical Systems (eBook)

Paul C. Krause, Oleg Wasynczuk, Timothy O'Connell (Autoren)

eBook Download: EPUB

2021
John Wiley & Sons (Verlag)
978-1-119-83001-6 (ISBN)

Infos

Discover the analytical foundations of electric machine, power electronics, electric drives, and electric power systems 

In Introduction to the Analysis of Electromechanical Systems, an accomplished team of engineers delivers an accessible and robust analysis of fundamental topics in electrical systems and electrical machine modeling oriented to their control with power converters. The book begins with an introduction to the electromagnetic variables in rotatory and stationary reference frames before moving onto descriptions of electric machines. 

The authors discuss direct current, round-rotor permanent-magnet alternating current, and induction machines, as well as brushless direct current and induction motor drives. Synchronous generators and various other aspects of electric power system engineering are covered as well, showing readers how to describe the behavior of electromagnetic variables and how to approach their control with modern power converters. 

Introduction to the Analysis of Electromechanical Systems presents analysis techniques at an introductory level and at sufficient detail to be useful as a prerequisite for higher level courses. It also offers supplementary materials in the form of online animations and videos to illustrate the concepts contained within. Readers will also enjoy: 

• A thorough introduction to basic system analysis, including phasor analysis, power calculations, elementary magnetic circuits, stationary coupled circuits, and two- and three-phase systems 
• Comprehensive explorations of the basics of electric machine analysis and power electronics, including switching-circuit fundamentals, conversion, and electromagnetic force and torque 
• Practical discussions of power systems, including three-phase transformer connections, synchronous generators, reactive power and power factor correction, and discussions of transient stability 

Perfect for researchers and industry professionals in the area of power and electric drives, Introduction to the Analysis of Electromechanical Systems will also earn its place in the libraries of senior undergraduate and graduate students and professors in these fields. 

Autor

Paul C. Krause, PhD, retired after 39 years as a professor at Purdue University School of Electrical and Computer Engineering. He founded P.C. Krause & Associates in 1983. He is a Life Fellow of IEEE and has authored or co-authored over 100 technical papers and five textbooks on electric machines. He was the 2010 recipient of the IEEE Nikola Tesla Award. He and the co-authors are also co-authors of Electromechanical Motion Devices: Rotating Magnetic Field-Based Analysis with Online Animations, 3rd Edition. Oleg Wasynczuk, PhD, is Professor of Electrical and Computer Engineering at Purdue University. He has authored or co-authored over 100 technical papers and four 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. Timothy O'Connell, PhD, is a Senior Lead Engineer at P.C. Krause & Associates and an Adjunct Research Assistant Professor of Electrical and Computer Engineering at the University of Illinois at Urbana-Champaign. He is a Senior Member of IEEE and an Associate Editor of the IEEE Transactions on Aerospace and Electronic Systems. He has authored or co-authored over 20 technical papers and three textbooks on electric machines and has co-edited a book on electrified aircraft propulsion.

Inhalt

Preface ix

About the Authors xi

1 Basic System Analysis 1

1.1 Introduction 1

1.2 Phasor Analysis and Power Calculations 1

1.2.1 Power and Reactive Power 6

1.3 Elementary Magnetic Circuits 8

1.3.1 Field Energy and Coenergy 12

1.4 Stationary Coupled Circuits - The Transformer 16

1.4.1 Magnetically Linear Transformer 17

1.4.2 Field Energy 20

1.5 Two- and Three-phase Systems 23

1.5.1 Two-phase Systems 23

1.5.2 Three-phase Systems 25

1.6 Problems 29

2 Fundamentals of Electric Machine Analysis 31

2.1 Introduction 31

2.2 Coupled Circuits in Relative Motion 32

2.2.1 Field Energy 35

2.3 Electromagnetic Force and Torque 36

2.4 Winding Configurations 42

2.4.1 Concentrated Winding 42

2.4.2 Distributed Windings 46

2.5 Rotating Air-gap mmf - Tesla's Rotating Magnetic Field 49

2.5.1 Two-pole Two-phase Stator 50

2.5.2 Three-phase Stator 55

2.6 Change of Variables 57

2.6.1 Two-phase Transformation 57

2.6.2 Three-phase Transformation 59

2.7 Stator Voltage Equations in Arbitrary Reference Frame 61

2.8 Instantaneous and Steady-state Phasors 63

2.9 P-pole Machines 65

2.10 Problems 70

References 72

3 Electric Machines 73

3.1 Introduction 73

3.2 Direct-current Machine 73

3.2.1 Commutation 74

3.2.2 Voltage and Torque Equations 77

3.2.3 Permanent-magnet dc Machine 79

3.3 Permanent-magnet ac Machine 82

3.3.1 Two-phase Permanent-magnet ac Machine 82

3.3.2 Reference Frame Analysis of a Permanent-magnet ac Machine 86

3.3.3 Three-phase Permanent-magnet ac Machine 90

3.3.4 Steady-state Analysis 90

3.4 Symmetrical Induction Machines 95

3.4.1 Two-phase Induction Machine 96

3.4.2 Symmetrical Rotor Windings 98

3.4.3 Substitute Variables for Symmetrical Rotating Circuits 101

3.4.4 Torque 105

3.4.5 Phasors and Steady-state Equivalent Circuit 108

3.5 Problems 115

References 117

4 Power Electronics 119

4.1 Introduction 119

4.2 Switching-circuit Fundamentals 120

4.2.1 Power Conversion Principles 120

4.2.2 Switches and Switching Functions 121

4.2.3 Energy Storage Elements 125

4.3 dc-dc Conversion 127

4.3.1 Buck Converter 127

4.3.2 Boost Converter 137

4.3.3 Advanced Circuit Topologies 141

4.4 ac-dc Conversion 141

4.4.1 Half-wave Rectifier 141

4.4.2 Full-wave Rectifier 148

4.5 dc-ac Conversion 156

4.5.1 Single-phase Inverter 156

4.6 Problems 160

References 163

5 Electric Drives 165

5.1 Introduction 165

5.2 dc Drive 165

5.2.1 Average-value Time-domain Block Diagram 168

5.2.2 Torque Control 170

5.3 Brushless dc Drive 172

5.3.1 Operation of Brushless Dc Drive with Phi V = 0 175

5.3.2 Torque Control 177

5.4 Induction Motor Drive 182

5.4.1 Torque Control 187

5.5 Problems 191

References 191

6 Power Systems 193

6.1 Introduction 193

6.2 Three-phase Transformer Connections 193

6.2.1 Wye-Wye Connection 194

6.2.2 Delta-Delta Connection 196

6.2.3 Wye-Delta or Delta-Wye Connection 197

6.2.4 Ideal Transformers 198

6.3 Synchronous Generator 200

6.3.1 Damper Windings 204

6.3.2 Torque 205

6.3.3 Steady-state Operation and Rotor Angle 206

6.4 Reactive Power and Power-Factor Correction 212

6.5 Per Unit System 218

6.6 Discussion of Transient Stability 221

6.6.1 Three-phase Fault 222

6.7 Problems 226

References 227

Appendix A Abbreviations, Constants, Conversions, and Identities 229

Index 233

Textauszug

1
Basic System Analysis

1.1 Introduction

The twentieth century began with the electric power industry in its infancy; Thomas Edison and Nikola Tesla were locked in battle with Edison advocating direct current (dc) and Tesla alternating current (ac). The century ended with the electric power industry expanding rapidly from the traditional power generation, transmission, and utilization into propulsion of air, ground, and sea transportation. The advent of the computer and the silicon-controlled rectifier in the mid-1900s brought about an expansion of the power area to include the smart-grid, microgrids, efficient and robust electric drives, more electric aircraft, ships, and land vehicles. A growth which is likely to continue into the foreseeable future.

Before the advent of the computer, engineers were essentially limited to steady-state analysis and therefore unable to conveniently deal with the analytical challenges of the expanding power industry. This chapter sets forth some of the basic concepts and analysis tools that are part of the present-day power and electric drives area. Although not inclusive, the material covered in this chapter is representative and common to most disciplines of the power area.

1.2 Phasor Analysis and Power Calculations

Since the early twentieth century, we have lived in an ac world. Thanks to George Westinghouse and Nikola Tesla, power systems are predominately ac; power is generated by large ac generators, transmitted by high-voltage transmission lines, and transformed to a low voltage and distributed to homes and factories. The evolution of the ac power system brought about many engineering challenges and, as we look back, it is difficult to comprehend how these problems were solved without a computer. Even steady-state ac-circuit analysis posed a problem until the early 1900s when Charles Stienmetz, who was a less flamboyant colleague of Edison and Tesla, came up with the concept of what is now known as phasors. Some may consider the phasor a casualty of the computer age along with the slide rule. It is, however, still a very useful means for understanding and portraying the steady-state performance of electric machines, power systems, and electric drives. Moreover, the phasor concept provides a means of visualizing sinusoidal variations from different frames of reference, and in Chapter 2 we will find that the voltage and current phasors combined with Tesla's rotating magnetic field provides a straightforward means of analyzing and portraying the steady-state operation of ac machines.

The phasor can be established by expressing a steady-state sinusoidal variable as

(1.1)

where the a subscript is used here to denote sinusoidal quantities. The sinusoidal variations are expressed as cosines, capital letters are used to denote steady-state quantities, and Fp is the peak value of the sinusoidal variation. Generally, F or f represents voltage (V or ) or current (I or i) in circuit analysis, but it could be any sinusoidal variable. For steady-state conditions, θef may be written as

(1.2)

where ωe is the electrical angular velocity in rad/s (2π times the frequency) and θef(0) is the time-zero position of the electrical variable. Substituting (1.2) into (1.1) yields

(1.3)

Now, Euler's identity is

(1.4)

and since we are expressing the sinusoidal variation as a cosine, (1.3) may be written as

(1.5)

where Re is shorthand for the “real part of.” Equations (1.3) and (1.5) are equivalent. Let us rewrite (1.5) as

(1.6)

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

(1.7)

where F is the rms value of Fa(t) and T is the period of the sinusoidal variation. It is left to the reader to show that the rms value of (1.3) is . Therefore, we can express (1.6) as

(1.8)

By definition, the phasor representing Fa(t), which is denoted with a raised tilde, is

(1.9)

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 (1.6) may now be written as

(1.10)

A shorthand notation for (1.9) is

(1.11)

Equation (1.11) is commonly referred to as the polar form of the phasor. The Cartesian form is

(1.12)

When using phasors to calculate steady-state voltages and currents, we think of the phasors as being stationary at t = 0; however, we know from (1.10) that a phasor is related to the instantaneous value of the sinusoidal quantity it represents. In other words, the real projection of the phasor rotating counterclockwise at ωe is the instantaneous value of . Thus, with θef(0) = 0 in (1.3)

(1.13)

the phasor representing (1.13) is

(1.14)

For

(1.15)

the phasor is

(1.16)

We will use degrees and radians interchangeably when expressing phasors. Although there are several ways to arrive at (1.16) from (1.15), it is helpful to ask yourself where must the rotating phasor be positioned at time zero so that, when it rotates counterclockwise at ωe, its real projection is ? It follows that a phasor of amplitude F positioned at 90° represents .

In other words, we are viewing a sinusoidal variation as the real projection in the real-imaginary plane of a rotating line equal in magnitude to the positive peak value of the variation and rotating at the electrical angular velocity of the sinusoidal variation. Since we are dealing with a steady-state variation, we can stop the rotation at any time and view it as a fixed line, but knowing full well that it, in fact, represents a sinusoidal variations and to represent the sinusoidal variation we must rotate it counterclockwise at ωe and take the real projection. Please understand that if we ran at ωe in unison with the rotating line it would appear as a constant to us. Therefore, this is no different than stopping the phasor at some arbitrary time zero; but realizing that it actually represents a sinusoidal variation. We'll talk more about this important aspect as we go along. See Example 1A.

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 L and a capacitance C. Thus, using uppercase letters to indicate steady-state variables

(1.17)

Throughout the text, we will use either R or r to represent resistance. For steady-state operation, let

(1.18)

(1.19)

where we have dropped the functional notation, and the subscript a helps to distinguish the instantaneous value from the rms value of the steady-state variables. The steady-state voltage equation may be obtained by substituting (1.18) and (1.19) into (1.17), whereupon we can write

(1.20)

The second term on the right-hand side of (1.20), which is , can be written

(1.21)

Since , from (1.21), we can write

(1.22)

Since , (1.22) may be written

(1.23)

If we follow a similar procedure, we can show that

(1.24)

Differentiation of a steady-state sinusoidal variable rotates the phasor counterclockwise by or j; integration rotates the phasor clockwise by or −j.

The steady-state voltage equation given by (1.20) can now be written in phasor form as

(1.25)

We can express (1.25) compactly as

(1.26)

where the impedance, Z, is a complex number; it is not a phasor. It may be expressed as

(1.27)

where XL = ωeL is the inductive reactance and is the capacitive reactance. We should be careful here. Some prefer to write (1.27) as R + jX where X is XL + XC and let XC be negative. This is essentially a matter of choice and does not change the end result. We will deal primarily with XL and not XC,...

Produkt-Details

• Erscheint lt. Verlag: 6.12.2021
• Reihe/Serie: IEEE Press Series on Power and Energy Systems
• Reihe/Serie: IEEE Press Series on Power Engineering
• Reihe/Serie: IEEE Press Series on Power Engineering
• Sprache: englisch
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Schlagworte: Electrical & Electronics Engineering • electrical machine modeling • Electrical Systems • electric drives textbook • Electric machines textbook • electric power systems • electric power systems textbook • Electromagnetic Compatibility • Elektrische Energietechnik • Elektromagnetische Verträglichkeit • Elektromechanik • Elektrotechnik u. Elektronik • Energie • Energy • induction motor drives • Leistungselektronik • <p>Electric machines textbook • Power converters • Power Electronics • Power electronics textbook • synchronous generators • synchronous generators </p>
• ISBN-10: 1-119-83001-X / 111983001X
• ISBN-13: 978-1-119-83001-6 / 9781119830016