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 11.1. Introduction 11.2. Magnetically Coupled Circuits 11.3. Electromechanical Energy Conversion 121.4. Elementary ac Machines 352 DISTRIBUTED WINDINGS IN AC MACHINERY 532.1. Introduction 532.2. Describing Distributed Windings 542.3. Winding Functions 642.4. Air-Gap Magnetomotive Force 672.5. Rotating MMF 712.6. Flux Linkage and Inductance 732.7. Resistance 762.8. Voltage and Flux Linkage Equations for Distributed Winding Machines 773 REFERENCE-FRAME THEORY 863.1. Introduction 863.2. Background 873.3. Equations of Transformation: Change of Variables 883.4. Stationary Circuit Variables Transformed to the Arbitrary Reference Frame 903.5. Commonly Used Reference Frames 973.6. Transformation of a Balanced Set 983.7. Balanced Steady-State Phasor Relationships 993.8. Balanced Steady-State Voltage Equations 1023.9. Variables Observed from Several Frames of Reference 1053.10. Transformation Between Reference Frames 1103.11. Specialty Transformations 1113.12. Space-Phasor Notation 1134 PERMANENT-MAGNET AC MACHINES 1214.1. Introduction 1214.2. Voltage and Torque Equations in Machine Variables 1224.3. Voltage and Torque Equations in Rotor Reference-Frame Variables 1254.4. Analysis of Steady-State Operation 1274.5. Brushless dc Motor 1294.6. Phase Shifting of Applied Voltages of a Permanent-Magnet ac Machine 1344.7. Control of Stator Currents 1385 SYNCHRONOUS MACHINES 1425.1. Introduction 1425.2. Voltage Equations in Machine Variables 1435.3. Torque Equation in Machine Variables 1495.4. Stator Voltage Equations in Arbitrary Reference-Frame Variables 1495.5. Voltage Equations in Rotor Reference-Frame Variables 1515.6. Torque Equations in Substitute Variables 1575.7. Rotor Angle and Angle Between Rotors 1585.8. Per Unit System 1595.9. Analysis of Steady-State Operation 1605.10. Stator Currents Positive Out of Machine: Synchronous Generator Operation 1715.11. Computer Simulation 2016 SYMMETRICAL INDUCTION MACHINES 2156.1. Introduction 2156.2. Voltage Equations in Machine Variables 2166.3. Torque Equation in Machine Variables 2206.4. Equations of Transformation for Rotor Circuits 2226.5. Voltage Equations in Arbitrary Reference-Frame Variables 2246.6. Torque Equation in Arbitrary Reference-Frame Variables 2296.7. Commonly Used Reference Frames 2326.8. Per Unit System 2336.9. Analysis of Steady-State Operation 2356.10. Free Acceleration Characteristics 2446.11. Free Acceleration Characteristics Viewed from Various Reference Frames 2516.12. Dynamic Performance During Sudden Changes in Load Torque 2576.13. Dynamic Performance During a Three-Phase Fault at the Machine Terminals 2606.14. Computer Simulation in the Arbitrary Reference Frame 2617 MACHINE EQUATIONS IN OPERATIONAL IMPEDANCES AND TIME CONSTANTS 2717.1. Introduction 2717.2. Park’s Equations in Operational Form 2727.3. Operational Impedances and G( p) for a Synchronous Machine with Four Rotor Windings 2737.4. Standard Synchronous Machine Reactances 2767.5. Standard Synchronous Machine Time Constants 2787.6. Derived Synchronous Machine Time Constants 2787.7. Parameters from Short-Circuit Characteristics 2837.8. Parameters from Frequency-Response Characteristics 2908 ALTERNATIVE FORMS OF MACHINE EQUATIONS 2998.1. Introduction 2998.2. Machine Equations to Be Linearized 3008.3. Linearization of Machine Equations 3028.4. Small-Displacement Stability: Eigenvalues 3088.5. Eigenvalues of Typical Induction Machines 3098.6. Eigenvalues of Typical Synchronous Machines 3128.7. Neglecting Electric Transients of Stator Voltage Equations 3138.8. Induction Machine Performance Predicted with Stator Electric Transients Neglected 3188.9. Synchronous Machine Performance Predicted with Stator Electric Transients Neglected 3228.10. Detailed Voltage Behind Reactance Model 3258.11. Reduced Order Voltage Behind Reactance Model 3329 UNBALANCED OPERATION AND SINGLE-PHASE INDUCTION MACHINES 3369.1. Introduction 3369.2. Symmetrical Component Theory 3379.3. Symmetrical Component Analysis of Induction Machines 3389.4. Unbalanced Stator Conditions of Induction Machines: Reference-Frame Analysis 3399.5. Typical Unbalanced Stator Conditions of Induction Machines 3469.6. Unbalanced Rotor Conditions of Induction Machines 3519.7. Unbalanced Rotor Resistors 3549.8. Single-Phase Induction Machines 3589.9. Asynchronous and Unbalanced Operation of Synchronous Machines 36810 DC MACHINES AND DRIVES 37710.1. Introduction 37710.2. Elementary dc Machine 37710.3. Voltage and Torque Equations 38410.4. Basic Types of dc Machines 38610.5. Time-Domain Block Diagrams and State Equations 39410.6. Solid-State Converters for dc Drive Systems 39810.7. One-Quadrant dc/dc Converter Drive 40010.8. Two-Quadrant dc/dc Converter Drive 41810.9. Four-Quadrant dc/dc Converter Drive 42110.10. Machine Control with Voltage-Controlled dc/dc Converter 42310.11. Machine Control with Current-Controlled dc/dc Converter 42611 SEMI-CONTROLLED BRIDGE CONVERTERS 43411.1. Introduction 43411.2. Single-Phase Load Commutated Converter 43411.3. Three-Phase Load Commutated Converter 44511.4. Conclusions and Extensions 45612 FULLY CONTROLLED THREE-PHASE BRIDGE CONVERTERS 46012.1. Introduction 46012.2. The Three-Phase Bridge Converter 46012.3. Six-Step Operation 46612.4. Six-Step Modulation 47412.5. Sine-Triangle Modulation 47712.6. Extended Sine-Triangle Modulation 48312.7. Space-Vector Modulation 48512.8. Hysteresis Modulation 48912.9. Delta Modulation 49212.10. Open-Loop Voltage and Current Regulation 49312.11. Closed-Loop Voltage and Current Regulation 49513 INDUCTION MOTOR DRIVES 50313.1. Introduction 50313.2. Volts-per-Hertz Control 50413.3. Constant Slip Current Control 51013.4. Field-Oriented Control 51713.5. Direct Field-Oriented Control 52113.6. Robust Direct Field-Oriented Control 52313.7. Indirect Rotor Field-Oriented Control 52813.8. Direct Torque Control 53213.9. Slip Energy Recovery Drives 53513.10. Conclusions 53814 PERMANENT-MAGNET AC MOTOR DRIVES 54114.1. Introduction 54114.2. Voltage-Source Inverter Drives 54214.3. Equivalence of Voltage-Source Inverters to an Idealized Source 54314.4. Average-Value Analysis of Voltage-Source Inverter Drives 55214.5. Steady-State Performance of Voltage-Source Inverter Drives 55514.6. Transient and Dynamic Performance of Voltage-Source Inverter Drives 55714.7. Case Study: Voltage-Source Inverter-Based Speed Control 56214.8. Current-Regulated Inverter Drives 56714.9. Voltage Limitations of Current-Regulated Inverter Drives 57114.10. Current Command Synthesis 57214.11. Average-Value Modeling of Current-Regulated Inverter Drives 57614.12. Case Study: Current-Regulated Inverter-Based Speed Controller 57815 INTRODUCTION TO THE DESIGN OF ELECTRIC MACHINERY 58315.1. Introduction 58315.2. Machine Geometry 58515.3. Stator Windings 59015.4. Material Parameters 59315.5. Stator Currents and Control Philosophy 59615.6. Radial Field Analysis 59715.7. Lumped Parameters 60215.8. Ferromagnetic Field Analysis 60315.9. Formulation of Design Problem 60915.10. Case Study 61415.11. Extensions 618Acknowledgments 619References 620Problems 621Appendix A Trigonometric Relations, Constants and Conversion Factors, and Abbreviations 623A.1. Basic Trigonometric Relations 623A.2. Three-Phase Trigonometric Relations 624A.3. Constants and Conversion Factors 624A.4. Abbreviations 625Appendix B Carter’s Coeffi cient 626Appendix C Leakage Inductance 629References 635Index 636