Analysis of Electric Machinery and Drive Systems

About the Authors xi Preface xiii Acknowledgments xv About the Companion Website xvii 1 Introductory Concepts 1 1.1 Introduction 1 1.2 Stationary Magnetically Coupled Circuits 1 1.2.1 Nonlinear Magnetic System 8 1.3 Energy Balance Relationships 13 1.4 Energy in Coupling Field 18 1.5 Electromagnetic Forces 24 1.6 Steady-State and Dynamic Performance of an Electromechanical System 27 References 33 Problems 33 2 Symmetrical Three-Phase Stator 37 2.1 Introduction 37 2.2 Stator Winding Configuration and Air-Gap mmf 37 2.3 Transformation Equations 41 2.4 Voltage Equations in Arbitrary Reference Frame 46 2.4.1 Electric Power 49 2.5 Transformation Between Reference Frames 49 2.6 P-Pole Machines 51 2.7 Transformation of a Balanced Set 52 2.8 Instantaneous and Steady-State Phasors 56 2.9 Variables Observed from Several Frames of Reference 57 References 63 Problems 63 3 Symmetrical Induction Machine 65 3.1 Introduction 65 3.2 Induction Machine 65 3.3 Transformation of Rotor Windings to the Arbitrary Reference Frame 67 3.4 Voltage, Flux-Linkage Equations, and Equivalent Circuit 70 3.5 Torque Expressed in Arbitrary Reference Frame Variables 75 3.6 Computer Simulation in the Arbitrary Reference Frame 77 3.7 Per Unit System 78 3.8 Steady-State Equivalent Circuit and Common Modes of Operation 81 3.9 Free-Acceleration Torque Versus Speed Characteristics 89 3.10 Free-Acceleration Characteristics Viewed from Various Reference Frames 97 3.11 Dynamic Performance During Sudden Changes in Load Torque 102 References 105 Problems 105 4 Brushless DC Machine 109 4.1 Introduction 109 4.2 Voltage Equations in Machine Variables 109 4.3 Voltage and Torque Equations in Rotor Reference Frame Variables 113 4.4 Instantaneous and Steady-State Phasors 116 4.5 Field Orientation of a Brushless DC Drive 117 4.5.1 Brushless Dc Motor Operation with Φ V = 0 118 4.5.2 Maximum-Torque-Per-Volt Operation of a Brushless dc Drive (φ V = Φ Vmt/v) 121 4.5.3 Maximum-Torque-Per-Ampere Operation of a Brushless dc Drive (φ V = Φ Vmt/a) 124 References 125 Problems 126 5 Synchronous Machines 127 5.1 Introduction 127 5.2 Windings of a Synchronous Machine 128 5.3 Voltage Equations in Rotor Reference Frame Variables 130 5.4 Torque Expressions Positive for Motor Action 133 5.5 Time-Domain Block Diagram 133 5.6 Rotor Angle and Angle Between Rotors 136 5.7 Per Unit System 137 5.8 Analysis of Steady-State Operation 138 5.9 Stator Currents Positive out of Machine—Synchronous Generator Operation 143 5.9.1 Dynamic Performance during a Sudden Change in Input Torque 147 5.9.2 Dynamic Performance during a Three-Phase Fault at the Machine Terminals 153 References 158 Problems 158 6 Neglecting Electric Transients 163 6.1 Introduction 163 6.2 Neglecting Stator Electric Transients 163 6.3 Induction Machine with Stator Transients Neglected 166 6.3.1 Free-Acceleration Characteristics 166 6.4 The Synchronous Machine with Stator Transients Neglected 170 6.4.1 Three-Phase Fault at Machine Terminals 171 References 175 Problems 175 7 Machine Equations in Operational Impedances and Time Constants 177 7.1 Introduction 177 7.2 Park’s Equations in Operational form 178 7.3 Operational Impedances and G(P) for a Synchronous Machine with Four Rotor Windings 178 7.4 Standard Synchronous Machine Reactances 182 7.5 Standard Synchronous Machine Time Constants 184 7.6 Derived Synchronous Machine Time Constants 185 7.7 Parameters from Short-Circuit Characteristics 188 7.8 Parameters from Frequency-Response Characteristics 196 References 202 Problems 204 8 Eigenvalues and Voltage-Behind-Reactance Machine Equations 207 8.1 Introduction 207 8.2 Machine Equations to be Linearized 208 8.2.1 Induction Machine 208 8.2.2 Synchronous Machine 209 8.3 Linearization of Machine Equations 210 8.3.1 Induction Machine 211 8.3.2 Synchronous Machines 213 8.4 Small-Displacement Stability—Eigenvalues 216 8.5 Eigenvalues of Typical Induction Machines 216 8.6 Eigenvalues of Typical Synchronous Machines 220 8.7 Detailed Voltage-Behind-Reactance Model 221 8.8 Reduced-Order Voltage-Behind-Reactance Model 230 References 231 Problems 232 9 Semi-Controlled Bridge Converters 233 9.1 Introduction 233 9.2 Single-Phase Load Commutated Converter 233 9.3 Three-Phase Load Commutated Converter 245 9.4 Conclusions and Extensions 256 References 257 Problems 258 10 Fully Controlled Three-Phase Bridge Converters 259 10.1 Introduction 259 10.2 The Three-Phase Bridge Converter 259 10.3 Six-Step Operation 265 10.4 Six-Step Modulation 273 10.5 Sine-Triangle Modulation 278 10.6 Extended Sine-Triangle Modulation 283 10.7 Space-Vector Modulation 285 10.8 Hysteresis Modulation 289 10.9 Delta Modulation 292 10.10 Open-Loop Voltage and Current Regulation 293 10.11 Closed-Loop Voltage and Current Regulation 296 References 300 Problems 302 11 Direct-Current Machine and Drive 305 11.1 Introduction 305 11.2 Commutation 306 11.3 Voltage and Torque Equations 309 11.4 Permanent-Magnet dc Machine 311 11.5 dc Drive 313 11.5.1 Average-Value Time-Domain Block Diagram 316 11.5.2 Torque Control 318 Reference 319 Problems 319 12 Torque Control of Permanent-Magnet and Synchronous Reluctance Machines 321 12.1 Introduction 321 12.2 Torque Control of a Permanent-Magnet AC Machine 322 12.2.1 Maximum Steady-State Torque Versus Speed 324 12.3 Simulation of a Permanent-Magnet AC Machine with Torque Control 331 12.3.1 Electrical Dynamics 333 12.3.2 Mechanical Dynamics 333 12.3.3 System-Level Simulation Block Diagram 334 12.3.4 System Studies 335 12.3.5 Reduced-Order Simulation 339 12.4 Torque Control of a Synchronous Reluctance Machine 339 References 347 Problems 348 13 Induction Motor Drives 351 13.1 Introduction 351 13.2 Volts-Per-Hertz Control 351 13.3 Constant Slip Current Control 358 13.4 Field-Oriented Control 365 13.5 Direct Field-Oriented Control 369 13.6 Robust Direct Field-Oriented Control 371 13.7 Indirect Rotor Field-Oriented Control 376 13.8 Direct Torque Control 379 13.9 Slip Energy Recovery Drives 383 13.10 Conclusions 386 References 386 Problems 387 14 Permanent-Magnet AC Motor Drives 389 14.1 Introduction 389 14.2 Voltage-Source Inverter Drives 390 14.3 Equivalence of Voltage-Source Inverters to an Idealized Source 391 14.4 Average-Value Analysis of Voltage-Source Inverter Drives 400 14.5 Steady-State Performance of Voltage-Source Inverter Drives 403 14.6 Transient and Dynamic Performance of Voltage-Source Inverter Drives 406 14.7 Case Study: Voltage-Source Inverter-Based Speed Control 411 14.8 Current-Regulated Inverter Drives 417 14.9 Voltage Limitations of Current-Regulated Inverter Drives 421 14.10 Current Command Synthesis 423 14.11 Average-Value Modeling of Current-Regulated Inverter Drives 426 14.12 Case Study: Current-Regulated Inverter-Based Speed Controller 428 References 431 Problems 431 Appendix A Abbreviations, Constants, Conversions, and Identities 433 Appendix B Phasors and Phasor Diagrams 437 Index 441