A new formulation of machine equations for imp
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
