Analysis of Electric Machinery and Drive Systems

PAUL KRAUSE, PhD, is founder of P.C. Krause and Associates. He is the sole author of the first edition of this book, an IEEE Fellow, and a winner of the prestigious Tesla Award. He is also the coauthor of Electromechanical Motion Devices, Second Edition, from Wiley-IEEE Press. OLEG WASYNCZUK, PhD, is a Professor of Electrical and Computer Engineering at Purdue University. He is a Fellow of IEEE, an award-winning author of numerous papers, and is co-author of Electromechanical Motion Devices, Second Edition, from Wiley-IEEE Press. SCOTT SUDHOFF, PhD, is Editor-in-Chief of IEEE Transactions on Energy Conversion and a Fellow of IEEE. He is also a Professor at Purdue University. He has produced extensive writings in the areas of electric machinery and power electronic converter analysis, simulation, and design. STEVEN PEKAREK, PhD, is a Fellow of the IEEE and has served on the organizing committee of several conferences focusing on electric machinery and power electronics. He and his students have published many papers in these areas. He presently serves as a faculty member in ECE at Purdue University.

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