Analysis of Electric Machinery and Drive Systems

by Paul C. Krause, Oleg Wasynczuk, Scott D. Sudhoff, Steven D. Pekarek

Overview

New edition of the popular reference on machine analysis, focusing on reference frame theory with techniques for derivation of equations

Analysis of Electric Machinery and Drive Systems covers the concepts needed to understand the evolution of electrical and magnetic variables for designing the power-electronic circuits that supply or extract electrical energy from a variety of machines, comprehensively addressing the varied needs of readers in the electric machinery, electric drives, and electric power industries.

This fourth edition has been extensively revised and updated to include nine new or updated chapters on symmetrical three-phase stators, symmetrical induction machines, brushless DC machines, synchronous machines, neglecting electric transients, eigenvalues and voltage-behind-reactive machine equations, direct current machine and drive, and torque control of permanent-magnet and synchronous reluctance machines.

Introductory concepts related to the subject have also been expanded upon, detailing stationary magnetically coupled circuits, energy balance relationships, energy in coupling field, and steady-state and dynamic performance of electromechanical systems. The fourth edition also includes illustrations of the free-acceleration characteristics of induction and brushless dc machines viewed from various reference frames and many other topics.

With problems at the end of each chapter to reinforce learning, the book explores additional topics including:

• Operational impedances and time constraints of synchronous machines, covering Park's equations in operational form and parameters from short-circuit and frequency-response characteristics
• Fully controlled three-phase bridge converters, covering six-step, sine-triangle, space-vector, hysteresis, and delta modulations, along with open- and closed-loop voltage and current regulations
• Motor drives, covering volts-per-hertz, constant slip current, field-oriented, and direct torque control as well as slip energy recovery drives
• Brushless DC motor drives, covering average-value analysis, steady-state performance, and transient and dynamic performance of voltage-source inverter drives

Analysis of Electric Machinery and Drive Systems, Fourth Edition, is a perfect resource for electrical engineering students and an essential, up-to-date reference for electrical and mechanical engineers working with drives.

Product Details

ISBN-13:	9781394293865
Publisher:	Wiley
Publication date:	03/11/2025
Series:	IEEE Press Series on Power and Energy Systems
Pages:	688
Product dimensions:	6.50(w) x 1.50(h) x 9.50(d)

About the Author

Paul C. Krause is a former Professor at Purdue University School of Electrical and Computer Engineering. He is the founder of PC Krause and Associates Inc. and recipient of the 2010 IEEE Nikola Tesla Award.

Oleg Wasynczuk is a Professor Emeritus of Electrical and Computer Engineering at Purdue University. He also served as Chief Technical Officer of PC Krause and Associates Inc. and is the recipient of the 2008 IEEE PES Cyril Veinott Electromechanical Energy Conversion Award.

Scott D. Sudhoff is the Michael and Katherine Birck Distinguished Professor of Electrical and Computer Engineering at Purdue University. He is a former Editor-in-Chief of the IEEE Transactions on Energy Conversion and recipient of the 2024 IEEE Nikola Tesla Award.

Steven Pekarek is the Edmund O. Schweitzer, III, Professor of Electrical and Computer Engineering at Purdue University. He has served as an Editor of the IEEE Transactions on Energy Conversion and the IEEE Transactions on Power Electronics, and is the recipient of the 2018 IEEE PES Cyril Veinott Electromechanical Energy Conversion Award.

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Table of Contents

Preface xiii

1 THEORY OF ELECTROMECHANICAL ENERGY CONVERSION 1

1.1. Introduction 1

1.2. Magnetically Coupled Circuits 1

1.3. Electromechanical Energy Conversion 12

1.4. Elementary ac Machines 35

2 DISTRIBUTED WINDINGS IN AC MACHINERY 53

2.1. Introduction 53

2.2. Describing Distributed Windings 54

2.3. Winding Functions 64

2.4. Air-Gap Magnetomotive Force 67

2.5. Rotating MMF 71

2.6. Flux Linkage and Inductance 73

2.7. Resistance 76

2.8. Voltage and Flux Linkage Equations for Distributed Winding Machines 77

3 REFERENCE-FRAME THEORY 86

3.1. Introduction 86

3.2. Background 87

3.3. Equations of Transformation: Change of Variables 88

3.4. Stationary Circuit Variables Transformed to the Arbitrary Reference Frame 90

3.5. Commonly Used Reference Frames 97

3.6. Transformation of a Balanced Set 98

3.7. Balanced Steady-State Phasor Relationships 99

3.8. Balanced Steady-State Voltage Equations 102

3.9. Variables Observed from Several Frames of Reference 105

3.10. Transformation Between Reference Frames 110

3.11. Specialty Transformations 111

3.12. Space-Phasor Notation 113

4 PERMANENT-MAGNET AC MACHINES 121

4.1. Introduction 121

4.2. Voltage and Torque Equations in Machine Variables 122

4.3. Voltage and Torque Equations in Rotor Reference-Frame Variables 125

4.4. Analysis of Steady-State Operation 127

4.5. Brushless dc Motor 129

4.6. Phase Shifting of Applied Voltages of a Permanent-Magnet ac Machine 134

4.7. Control of Stator Currents 138

5 SYNCHRONOUS MACHINES 142

5.1. Introduction 142

5.2. Voltage Equations in Machine Variables 143

5.3. Torque Equation in Machine Variables 149

5.4. Stator Voltage Equations in Arbitrary Reference-Frame Variables 149

5.5. Voltage Equations in Rotor Reference-Frame Variables 151

5.6. Torque Equations in Substitute Variables 157

5.7. Rotor Angle and Angle Between Rotors 158

5.8. Per Unit System 159

5.9. Analysis of Steady-State Operation 160

5.10. Stator Currents Positive Out of Machine: Synchronous Generator Operation 171

5.11. Computer Simulation 201

6 SYMMETRICAL INDUCTION MACHINES 215

6.1. Introduction 215

6.2. Voltage Equations in Machine Variables 216

6.3. Torque Equation in Machine Variables 220

6.4. Equations of Transformation for Rotor Circuits 222

6.5. Voltage Equations in Arbitrary Reference-Frame Variables 224

6.6. Torque Equation in Arbitrary Reference-Frame Variables 229

6.7. Commonly Used Reference Frames 232

6.8. Per Unit System 233

6.9. Analysis of Steady-State Operation 235

6.10. Free Acceleration Characteristics 244

6.11. Free Acceleration Characteristics Viewed from Various Reference Frames 251

6.12. Dynamic Performance During Sudden Changes in Load Torque 257

6.13. Dynamic Performance During a Three-Phase Fault at the Machine Terminals 260

6.14. Computer Simulation in the Arbitrary Reference Frame 261

7 MACHINE EQUATIONS IN OPERATIONAL IMPEDANCES AND TIME CONSTANTS 271

7.1. Introduction 271

7.2. Park’s Equations in Operational Form 272

7.3. Operational Impedances and G(p) for a Synchronous Machine with Four Rotor Windings 273

7.4. Standard Synchronous Machine Reactances 276

7.5. Standard Synchronous Machine Time Constants 278

7.6. Derived Synchronous Machine Time Constants 278

7.7. Parameters from Short-Circuit Characteristics 283

7.8. Parameters from Frequency-Response Characteristics 290

8 ALTERNATIVE FORMS OF MACHINE EQUATIONS 299

8.1. Introduction 299

8.2. Machine Equations to Be Linearized 300

8.3. Linearization of Machine Equations 302

8.4. Small-Displacement Stability: Eigenvalues 308

8.5. Eigenvalues of Typical Induction Machines 309

8.6. Eigenvalues of Typical Synchronous Machines 312

8.7. Neglecting Electric Transients of Stator Voltage Equations 313

8.8. Induction Machine Performance Predicted with Stator Electric Transients Neglected 318

8.9. Synchronous Machine Performance Predicted with Stator Electric Transients Neglected 322

8.10. Detailed Voltage Behind Reactance Model 325

8.11. Reduced Order Voltage Behind Reactance Model 332

9 UNBALANCED OPERATION AND SINGLE-PHASE INDUCTION MACHINES 336

9.1. Introduction 336

9.2. Symmetrical Component Theory 337

9.3. Symmetrical Component Analysis of Induction Machines 338

9.4. Unbalanced Stator Conditions of Induction Machines: Reference-Frame Analysis 339

9.5. Typical Unbalanced Stator Conditions of Induction Machines 346

9.6. Unbalanced Rotor Conditions of Induction Machines 351

9.7. Unbalanced Rotor Resistors 354

9.8. Single-Phase Induction Machines 358

9.9. Asynchronous and Unbalanced Operation of Synchronous Machines 368

10 DC MACHINES AND DRIVES 377

10.1. Introduction 377

10.2. Elementary dc Machine 377

10.3. Voltage and Torque Equations 384

10.4. Basic Types of dc Machines 386

10.5. Time-Domain Block Diagrams and State Equations 394

10.6. Solid-State Converters for dc Drive Systems 398

10.7. One-Quadrant dc/dc Converter Drive 400

10.8. Two-Quadrant dc/dc Converter Drive 418

10.9. Four-Quadrant dc/dc Converter Drive 421

10.10. Machine Control with Voltage-Controlled dc/dc Converter 423

10.11. Machine Control with Current-Controlled dc/dc Converter 426

11 SEMI-CONTROLLED BRIDGE CONVERTERS 434

11.1. Introduction 434

11.2. Single-Phase Load Commutated Converter 434

11.3. Three-Phase Load Commutated Converter 445

11.4. Conclusions and Extensions 456

12 FULLY CONTROLLED THREE-PHASE BRIDGE CONVERTERS 460

12.1. Introduction 460

12.2. The Three-Phase Bridge Converter 460

12.3. Six-Step Operation 466

12.4. Six-Step Modulation 474

12.5. Sine-Triangle Modulation 477

12.6. Extended Sine-Triangle Modulation 483

12.7. Space-Vector Modulation 485

12.8. Hysteresis Modulation 489

12.9. Delta Modulation 492

12.10. Open-Loop Voltage and Current Regulation 493

12.11. Closed-Loop Voltage and Current Regulation 495

13 INDUCTION MOTOR DRIVES 503

13.1. Introduction 503

13.2. Volts-per-Hertz Control 504

13.3. Constant Slip Current Control 510

13.4. Field-Oriented Control 517

13.5. Direct Field-Oriented Control 521

13.6. Robust Direct Field-Oriented Control 523

13.7. Indirect Rotor Field-Oriented Control 528

13.8. Direct Torque Control 532

13.9. Slip Energy Recovery Drives 535

13.10. Conclusions 538

14 PERMANENT-MAGNET AC MOTOR DRIVES 541

14.1. Introduction 541

14.2. Voltage-Source Inverter Drives 542

14.3. Equivalence of Voltage-Source Inverters to an Idealized Source 543

14.4. Average-Value Analysis of Voltage-Source Inverter Drives 552

14.5. Steady-State Performance of Voltage-Source Inverter Drives 555

14.6. Transient and Dynamic Performance of Voltage-Source Inverter Drives 557

14.7. Case Study: Voltage-Source Inverter-Based Speed Control 562

14.8. Current-Regulated Inverter Drives 567

14.9. Voltage Limitations of Current-Regulated Inverter Drives 571

14.10. Current Command Synthesis 572

14.11. Average-Value Modeling of Current-Regulated Inverter Drives 576

14.12. Case Study: Current-Regulated Inverter-Based Speed Controller 578

15 INTRODUCTION TO THE DESIGN OF ELECTRIC MACHINERY 583

15.1. Introduction 583

15.2. Machine Geometry 585

15.3. Stator Windings 590

15.4. Material Parameters 593

15.5. Stator Currents and Control Philosophy 596

15.6. Radial Field Analysis 597

15.7. Lumped Parameters 602

15.8. Ferromagnetic Field Analysis 603

15.9. Formulation of Design Problem 609

15.10. Case Study 614

15.11. Extensions 618

Acknowledgments 619

References 620

Problems 621

Appendix A Trigonometric Relations, Constants and Conversion Factors, and Abbreviations 623

A.1. Basic Trigonometric Relations 623

A.2. Three-Phase Trigonometric Relations 624

A.3. Constants and Conversion Factors 624

A.4. Abbreviations 625

Appendix B Carter’s Coeffi cient 626

Appendix C Leakage Inductance 629

References 635

Index 636

Editorial Reviews

A textbook for students who have completed an introductory course in electric machines. The 1986 first edition, published by McGraw Hill, focused on analysis using reference frame theory and emphasized the concept of the arbitrary reference frame. IEEE published the second edition in 1989. The third edition expands the application of reference-frame theory to analyzing the complete drive system—machine, converter, and control. Annotation c. Book News, Inc., Portland, OR (booknews.com)