Electric Machines

CHARLES A. GROSS Aubum University

Auburn, Alabama, U.S.A.

LßP) CRC Press V v * / Taylor & Francis Croup

Boca Raton London New York

CRC Press is an imprint of the Taylor & Francis Group, an informa business

Contents

Chapter 1 Basic Electromagnetic Concepts 1.1 Basic Magnetic Concepts 2 1.2 Magnetically Linear Systems: Magnetic Circuits 4 1.3 Voltage, Current, and Magnetic Field Interactions 8 1.4 Magnetic Properties of Materials 10 1.5 Nonlinear Magnetic Circuit Analysis 14 1.6 Permanent Magnets 19 1.7 Superconducting Magnets 20 1.8 The Fundamental Translational EM Machine 22

1.8.1 The Biot-Savart Law 28 1.9 The Fundamental Rotational EM Machine 28 1.10 Multiwinding EM Systems 30 1.11 Leakage Flux 36 1.12 The Concept of Ratings in EM Systems 38 1.13 Summary 38 Problems 39

Chapter 2 Transformers 2.1 The Ideal n-Winding Transformer 43 2.2 Transformer Ratings and Per-Unit Scaling 46 2.3 The Nonideal Three-Winding Transformer 48 2.4 The Nonideal Two-Winding Transformer 51 2.5 Transformer Efficiency and Voltage Regulation 51 2.6 Practical Considerations 54 2.7 The Autotransformer 56 2.8 Operation of Transformers in Three-Phase Environments 57

2.8.1 The Wye-Wye Scheme 59 2.8.2 The Wye-Delta Scheme 60 2.8.3 The Delta-Wye Scheme 61 2.8.4 The Delta-Delta Scheme 61 2.8.5 The Open Delta Scheme 62 2.8.6 The Zig-Zag Scheme 62

2.9 Sequence Circuit Models for Three-Phase Transformer Analysis 66 2.10 Harmonics in Transformers 71 2.11 Summary 74 Problems 75

Chapter 3 Basic Mechanical Considerations 3.1 Some General Perspectives 79 3.2 Efficiency 83 3.3 Load Torque-Speed Characteristics 84

3.3.1 Constant Torque Loads (n = 0; TL = A0) 84

3.3.2 Linear (First-Order) Torque Loads (n = 1; TL = AjwJ 85 3.3.3 Parabolic (Second-Order) Torque Loads (n = 2; TL = A2<D£) 85 3.3.4 The General nth-Order Case (TL = A0 + A ^ + A2<w£ + • • • + A„ft>£) 86 3.3.5 The Constant Power Load 88

3.4 Mass Polar Moment of Inertia 88 3.5 Gearing 90 3.6 Operating Modes 93 3.7 Translational Systems 94 3.8 A Comprehensive Example: The Elevator 95 3.9 PrimeMovers 101

3.9.1 Hydraulic Turbines 101 3.9.2 Steam Turbines 102 3.9.3 Gas Turbines 102 3.9.4 Wind Turbines 103 3.9.5 M-GSets 106 3.9.6 Standalone Emergency Power Supplies 106 3.9.7 Vehicular Electrical Systems 106

3.10 Summary 107 Problems 108

Chapter 4 The Polyphase Induction Machine: Balanced Operation 4.1 Machine Construction 113

4.1.1 Stator Design 113 4.1.2 Rotor Design 115

4.2 Stator Winding Layout 116 4.3 The Rotating Magnetic Field 120 4.4 Stator-Rotor Interactions 124 4.5 Performance Analysis Using the Equivalent Circuit 128 4.6 Equivalent Circuit Constants from Tests 133

4.6.1 The DC Test 134 4.6.2 The Blocked Rotor (BR) Test 135 4.6.3 The No-Load (NL) Test 135

4.7 Operating Modes: Motor, Generator, and Braking 137 4.8 Dynamic Performance 141 4.9 Cage Rotor Machines 146 4.10 Thermal Considerations 151 4.11 Summary 156 Problems 156

Chapter 5 Control of AC Motors 5.1 Control of the Load Torque-Speed Characteristic 161 5.2 Control of the Motor Torque-Speed Characteristic 162 5.3 Controlling Voltage and Frequency 164 5.4 Power Semiconductor Switching Components 166

5.4.1 The Power Semiconductor Diode 167 5.4.2 The Power Semiconductor Thyristor 167 5.4.3 The Insulated Gated Bipolar Junction Transistor 169 5.4.4 Semiconductor Component Ratings 170

5.5 The Single-Phase Inverter 170

5.6 The Three-Phase Inverter 174 5.7 AC to DC Conversion: Rectifiers 179 5.8 Three-Phase Rectifiers 182 5.9 Controlled Rectifiers 184

5.9.1 Controlled Thyristor Rectifiers 184 5.9.2 Controlled IGBT Rectifiers 185

5.10 AC Motor Drives 187 5.11 AC Motor Drives: Dynamic Performance 190 5.12 Motor Reverse Performance 192 5.13 The Cycloconverter 193 5.14 Summary 193 Problems 195

Chapter 6 The Polyphase Induction Machine: Unbalanced Operation 6.1 Unbalanced Operation 199

6.1.1 Positive Sequence Response 201 6.1.2 Negative Sequence Response 201 6.1.3 Zero Sequence Response 202

6.2 Single Phasing 205 6.3 Running Three-Phase Motors from Single-Phase Sources 208 6.4 Operation on Nonsinusoidal Voltage 211 6.5 The Two-Phase Induction Motor 214 6.6 The Single-Phase Induction Motor 215 6.7 The Single-Phase Induction Motor Operating on One Winding 224 6.8 Equivalent Circuit Constants from Tests 227

6.8.1 The DC Test 228 6.8.2 The Blocked Rotor (BR) Tests 228 6.8.3 The No-Load Test 229

6.9 Dynamic Performance 229 6.10 Summary 232 Problems 232

Chapter 7 The Polyphase Synchronous Machine: Balanced Operation 7.1 Machine Construction 235

7.1.1 Stator Design 236 7.1.2 Rotor Design , 236

7.2 Evolution of the Machine Model from the Induction Machine 237 7.3 Interaction of the Rotor and Stator Circuits: The Magnetization Characteristic ....239 7.4 The Nonsalient Pole Synchronous Machine: Generator Operation 241 7.5 The Nonsalient Pole Synchronous Machine: Motor Operation 246 7.6 The Salient Pole Synchronous Machine 251 7.7 Synchronous Machine Constants from Tests 260

7.7.1 The DC Test: Ra 260 7.7.2 The Open-Circuit Test: The Magnetization Characteristic and Field

Resistance 260 7.7.3 The Short-Circuit Test: Xd 262 7.7.4 The Slip Test: X, 262 7.7.5 The No-Load Test: Rotational Losses 263 7.7.6 The Zero-Power Factor Lagging Test: Xt 263 7.7.7 VeeCurves 268

7.8 The Synchronous Generator Operating in a Utility Environment 269 7.8.1 PrimeMovers 269 7.8.2 Excitation Systems 270 7.8.3 Capability Curves 272

7.8.3.1 Stator Thermal Limits 273 7.8.3.2 Rotor Thermal Limits 273 7.8.3.3 End-Region Hearing 273 7.8.3.4 Steady-State Stability Limits 274 7.8.3.5 Boiler Thermal Limits 274

7.8.4 Pumped Storage 276 7.9 Permanent Magnetic Synchronous Machines 277 7.10 The Polyphase Synchronous-Reluctance Machine 279 7.11 The Brushless DC Motor 280 7.12 Summary 282 Problems 282

Chapter 8 The Polyphase Synchronous Machine: The General Coupled Circuit Model

8.1 The General Coupled Circuit Model of the Synchronous Machine 287 8.2 The Odq Transformation 292 8.3 Powers and Torques in the OdqFDQ Model 298 8.4 The OdqFDQ Model Using Generator Sign Conventions 299 8.5 Balanced Three-Phase Constant Speed Generator Performance 301 8.6 Per-Unit Scaling as Applied to Synchronous Machines 305 8.7 The Tee Equivalent Circuits 309 8.8 OdqFDQU Constants Derived from Manufacturer's Data 312 8.9 OdqFDQU Model Performance 320 8.10 Summary 322 Problems 323

Chapter 9 The DC Machine 9.1 Machine Construction 327

9.1.1 Stator Design 327 9.1.2 Rotor (Armature) Design 329

9.1.2.1 The Lap Winding 331 9.1.2.2 The Wave Winding 331

9.2 Generation of DC Voltage 331 9.3 The DC Machine Model: Generator Operation 338 9.4 The DC Machine Model: Motor Operation 341 9.5 Speed Control of DC Motors 343

9.5.1 Field Control 343 9.5.2 Armature Control 345 9.5.3 Four Quadrant Operation 346 9.5.4 Reversing DC Motors 346

9.6 DC Machine Constants from Tests 347 9.6.1 The DC Test: Ra 347 9.6.2 The Transient Test: La 347 9.6.3 The Open-Circuit Test: The Magnetization Characteristic

and Field Resistance 347 9.6.4 The No-Load Test: Rotational Losses 348

9.7 DC Motor Drives: Half-Wave Converters 348 9.7.1 The Half-Wave Diode DC Motor Drive 349 9.7.2 The Half-Wave Thyristor DC Motor Drive 350 9.7.3 The Half-Wave IGBT DC Motor Drive 352

9.8 DC Motor Drives: Full-Wave Converters 353 9.8.1 The Full-Wave Diode DC Motor Drive 353 9.8.2 The Full-Wave Thyristor DC Motor Drive 355 9.8.3 The Six-Step Three-Phase Thyristor DC Motor Drive 356

9.9 Four-Quadrant Performance 358 9.10 DC Motor Dynamic Performance 358 9.11 An Elevator Application 362 9.12 A More General DC Machine Model 364 9.13 Summary 366 Problems 366

Chapter 10 Translational Electromechanical Machines 10.1 Linear Induction Machine Construction 373

10.1.1 Primary Design 373 10.1.2 Secondary Design 374 10.1.3 Electromagnetic Levitation 375 10.1.4 Electrodynamic Levitation 379

10.2 Linear Induction Machine Modeling: The Equivalent Circuit 380 10.3 The High Speed Rail (HSR) Application 382 10.4 Linear Synchronous Machine Construction 385

10.4.1 Linear Synchronous Machine Armature Design 386 10.4.2 Linear Synchronous Machine Field Design 386

10.5 Linear Synchronous Machine Nonsalient Pole Model 386 10.6 Linear Electromechanical Machine Applications in Elevators 389 10.7 Summary 393 Problems 394

Chapter 11 Special Purpose Machines and Sensors 11.1 The Universal Motor 397 11.2 The Shaded Pole Motor 398 11.3 The Hysteresis Motor 398 11.4 The Stepper Motor 399 11.5 Encoders 401 11.6 Resolvers 404 11.7 Microelectromechanical Systems 407 11.8 Summary 410 Problems 411

Epilogue 413

Appendix A: Units and Conversion Factors 415

Appendix B: A Review of Electrical Circuit Concepts B.l DC Circuit Concepts 420 B.2 AC Circuit Concepts 421 B.3 Balanced Three-Phase AC Circuit Concepts 424 B.4 Symmetrical Components 427

Appendix C: Harmonie Concepts C.l Basic Concepts 431 C.2 Coefficient Calculations 432 C.3 Rms (Effective) Values 433 C.4 Symmetries 434 C.5 Spectral Plots 434 C.6 Response of Linear Circuits to Nonsinusoidal Excitation 437

References in Electric Machines, Transformers, and Power Electronics 439

Index 445