Introduction to the Analysis of Electromechanical Systems

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. 

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.

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 𝜙_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

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