The reference frame theory that was detailed in critically acclaimed first edition of Analysis of Electric Machinery and Drive Systems has become the universally accepted approach for the analysis of both electric machines and electric drive systems. This thoroughly updated third edition features numerous changes in the early chapters that make the derivation of many of the equations more direct and understandable. The authors have developed several new models and model structures for electric machines that improve the accuracy and computational efficiency of coupled machine/power electronic circuit models.

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

Reference 44

Problems 44

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

Reference 83

Problems 84

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

References 115

Problems 115

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

References 140

Problems 140

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

References 210

Problems 210

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

References 266

Problems 267

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

References 295

Problems 297

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

References 333

Problems 335

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

References 375

Problems 375

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

References 431

Problems 431

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

References 458

Problems 458

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

References 499

Problems 500

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

References 538

Problems 539

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

References 581

Problems 581

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