# Introduction to Electric Power and Drive Systems

ISBN: 978-1-119-21425-0
256 pages
February 2017, Wiley-IEEE Press
For Instructors

## Description

An introduction to the analysis of electric machines, power electronic circuits, electric drive performance, and power systems

This book provides students with the basic physical concepts and analysis tools needed for subsequent coursework in electric power and drive systems with a focus on Tesla’s rotating magnetic field. Organized in a flexible format, it allows instructors to select material as needed to fit their school’s power program. The first chapter covers the fundamental concepts and analytical methods that are common to power and electric drive systems. The subsequent chapters offer introductory analyses specific to electric machines, power electronic circuits, drive system performance and simulation, and power systems. In addition, this book:

• Provides students with an analytical base on which to build in advanced follow-on courses
• Examines fundamental power conversions (dc-dc, ac-dc and dc-ac), harmonics, and distortion
• Describes the dynamic computer simulation of a brushless dc drive to illustrate its performance with both a sinusoidal inverter voltage approximation and more realistic stator six-step drive  applied voltages
• Includes in-chapter short problems, numerous worked examples, and end-of-chapter problems to help readers review and more fully understand each topic
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PREFACE AND ACKNOWLEDGMENT xi

CHAPTER 1 BASIC CONCEPTS 1

1.1 Introduction 1

1.2 Phasor Analysis and Power Calculations 1

Power and Reactive Power 5

1.3 Elementary Magnetic Circuits 8

Field Energy and Coenergy 13

1.4 Stationary Coupled Circuits 16

Magnetically Linear Transformer 16

Field Energy 20

1.5 Coupled Circuits in Relative Motion 22

Field Energy 25

1.6 Electromagnetic Force and Torque 26

1.7 Elementary Electromechanical Device 32

1.8 Two- and Three-Phase Systems 35

Two-Phase Systems 35

Three-Phase Systems 37

References 40

Problems 40

CHAPTER 2 ELECTRIC MACHINES 43

2.1 Introduction 43

2.2 Fundamentals of Electric Machine Analysis 44

Concentrated Winding 44

Distributed Windings 47

Rotating Air-Gap MMF – Tesla’s Rotating Magnetic Field 52

Two-Pole Two-Phase Stator 52

Three-Phase Stator 56

P-Pole Machines 58

Machine Inductances 62

2.3 Two-Phase Permanent-Magnet AC Machine 63

2.4 Analysis of a Two-Phase Permanent-Magnet AC Machine 69

Transformation 70

2.5 Three-Phase Permanent-Magnet AC Machine 81

Voltage Equations and Winding Inductances 82

Torque 83

The qsr-, dsr-, and 0s- Equations 84

References 89

Problems 89

CHAPTER 3 POWER ELECTRONICS 91

3.1 Introduction 91

3.2 Switching-Circuit Fundamentals 91

Power Conversion Principles 92

Fourier Analysis 95

Switches and Switching Functions 97

Energy Storage Elements 101

3.3 DC-DC Conversion 103

Buck Converter 104

Boost Converter 113

3.4 AC-DC Conversion 118

Half-Wave Rectifier 118

Full-Wave Rectifier 125

3.5 DC-AC Conversion 133

Single-Phase Inverter 133

Three-Phase Inverter 136

3.6 Harmonics and Distortion 144

References 147

Problems 147

CHAPTER 4 PERFORMANCE AND SIMULATION OF AN ELECTRIC DRIVE 149

4.1 Introduction 149

4.2 Operating Modes of a Brushless DC Motor 149

Brushless DC Motor Operation with 𝜙𝑣 = 0 150

Maximum Torque Per Volt Operation of a Brushless DC Motor (𝜙𝑣 = 𝜙𝑣MT¨MV ) 155

Maximum Torque Per Ampere Operation of a Brushless DC Motor (𝜙𝑣 = 𝜙𝑣MT¨MA) 160

4.3 Operation of a Brushless DC Drive 164

Operation of Brushless DC Drive with 𝜙𝑣 = 0 166

Operation of Brushless DC Drive with 𝜙𝑣 = 𝜙𝑣MT¨MV 170

Operation of Brushless DC Drive with 𝜙𝑣 = 𝜙𝑣MT¨MA 172

Modes of Control of a Brushless DC Drive 174

4.4 Simulation of a Brushless DC Drive 180

Simulation of Coupled Circuits 180

Simulation of Drive Inverter and Transformation 181

Simulation of Permanent-Magnet AC Machine 183

References 186

Problems 186

CHAPTER 5 POWER SYSTEMS 187

5.1 Introduction 187

5.2 Three-Phase Transformer Connections 187

Wye-Wye Connection 188

Delta-Delta Connection 190

Wye-Delta or Delta-Wye Connection 191

Ideal Transformers 192

5.3 Synchronous Generator 193

Damper Windings 198

Torque 198

Steady-State Operation and Rotor Angle 198

5.4 Reactive Power and Power Factor Correction 204

5.5 Per Unit System 209

Per Unitizing the Synchronous Generator 210

5.6 Discussion of Transient Stability 215

Three-Phase Fault 215

References 220

Problems 220

APPENDIXA TRIGONOMETRIC RELATIONS, CONSTANTS AND CONVERSION FACTORS, AND ABBREVIATIONS 221

APPENDIX B WINDING INDUCTANCES 225

APPENDIXC ANIMATIONS 229

INDEX 231

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## Author Information

Paul C. Krause is Board Chairman of PC Krause and Associates Inc. (PCKA), and a retired Professor of Electrical and Computer Engineering at Purdue University. He has authored or co-authored more than 100 technical papers and is the co-author of Analysis of Electric Machinery and Drive Systems, Third Edition (Wiley-IEEE Press), and Electromechanical Motion Devices, Second Edition (Wiley-IEEE Press).  He is a Life Fellow of the IEEE and was the 2010 recipient of the IEEE Nikola Tesla Award.

Oleg Wasynczuk is Professor of Electrical and Computer Engineering at Purdue University and Chief Technical Officer of PCKA. He has authored or co-authored more than 100 technical papers and is the co-author of Analysis of Electric Machinery and Drive Systems, Third Edition (Wiley-IEEE Press), and Electromechanical Motion Devices, Second Edition (Wiley-IEEE Press). He is a Fellow of the IEEE and was the 2008 recipient of the IEEE PES Cyril Veinott Electromechanical Energy Conversion Award.

Timothy O'Connell is a Senior Lead Engineer at PCKA, where he leads a multi-member industry modeling and simulation team supporting the design and analysis of more electric aircraft. He has authored or co-authored over 20 technical papers on electric machine analysis and design, aerospace power systems, and modeling and simulation. He is a Senior Member of IEEE.

Maher Hasan is a Senior Lead Engineer at PCKA, where he has led several software development efforts for the simulation of circuits and electromechanical and power systems, and is involved in modeling and simulation in support of multiple efforts. He has authored or co-authored several technical papers in the fields of dynamic simulation and numerical methods.
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