Electric Power Principles
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Electric Power Principles
Sources, Conversion, Distribution and Use
Kirtley, James L.
John Wiley & Sons Inc
02/2020
432
Dura
Inglês
9781119585176
15 a 20 dias
888
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Preface xv
About the Companion Website xvii
1 Electric Power Systems 1
1.1 Electric Utility Systems 2
1.2 Energy and Power 3
1.2.1 Basics and Units 3
1.3 Sources of Electric Power 5
1.3.1 Heat Engines 5
1.3.2 Power Plants 6
1.3.2.1 Environmental Impact of Burning Fossil Fuels 7
1.3.3 Nuclear Power Plants 8
1.3.4 Hydroelectric Power 9
1.3.5 Wind Turbines 10
1.3.6 Solar Power Generation 12
1.4 Electric Power Plants and Generation 14
1.5 Problems 15
2 AC Voltage, Current, and Power 17
2.1 Sources and Power 17
2.1.1 Voltage and Current Sources 17
2.1.2 Power 18
2.1.3 Sinusoidal Steady State 18
2.1.4 Phasor Notation 19
2.1.5 Real and Reactive Power 19
2.1.5.1 Root Mean Square (RMS) Amplitude 20
2.2 Resistors, Inductors, and Capacitors 20
2.2.1 Reactive Power and Voltage 22
2.2.1.1 Example 22
2.2.2 Reactive Power Voltage Support 22
2.3 Voltage Stability and Bifurcation 23
2.3.1 Voltage Calculation 24
2.3.2 Voltage Solution and Effect of Reactive Power 25
2.4 Problems 26
3 Transmission Lines 33
3.1 Modeling: Telegrapher's Equations 33
3.1.1 Traveling Waves 35
3.1.2 Characteristic Impedance 35
3.1.3 Power 36
3.1.4 Line Terminations and Reflections 36
3.1.4.1 Examples 37
3.1.4.2 Lightning 38
3.1.4.3 Inductive Termination 39
3.1.5 Sinusoidal Steady State 41
3.2 Problems 44
4 Polyphase Systems 47
4.1 Two-phase Systems 47
4.2 Three-phase Systems 48
4.3 Line-Line Voltages 51
4.3.1 Example: Wye- and Delta-connected Loads 52
4.3.2 Example: Use of Wye-Delta for Unbalanced Loads 53
4.4 Problems 55
5 Electrical and Magnetic Circuits 59
5.1 Electric Circuits 59
5.1.1 Kirchhoff's Current Law 59
5.1.2 Kirchhoff's Voltage Law 60
5.1.3 Constitutive Relationship: Ohm's Law 60
5.2 Magnetic Circuit Analogies 62
5.2.1 Analogy to KCL 62
5.2.2 Analogy to KVL: Magnetomotive Force 62
5.2.3 Analogy to Ohm's Law: Reluctance 63
5.2.4 Simple Case 64
5.2.5 Flux Confinement 64
5.2.6 Example: C-Core 65
5.2.7 Example: Core with Different Gaps 66
5.3 Problems 66
6 Transformers 71
6.1 Single-phase Transformers 71
6.1.1 Ideal Transformers 72
6.1.2 Deviations from an Ideal Transformer 73
6.1.3 Autotransformers 75
6.2 Three-phase Transformers 76
6.2.1 Example 78
6.2.2 Example: Grounding or Zigzag Transformer 80
6.3 Problems 81
7 Polyphase Lines and Single-phase Equivalents 87
7.1 Polyphase Transmission and Distribution Lines 87
7.1.1 Example 89
7.2 Introduction to Per-unit Systems 90
7.2.1 Normalization of Voltage and Current 90
7.2.2 Three-phase Systems 91
7.2.3 Networks with Transformers 92
7.2.4 Transforming from One Base to Another 92
7.2.5 Example: Fault Study 93
7.2.5.1 One-line Diagram of the Situation 93
7.3 Appendix: Inductances of Transmission Lines 95
7.3.1 Single Wire 95
7.3.2 Mutual Inductance 96
7.3.3 Bundles of Conductors 97
7.3.4 Transposed Lines 98
7.4 Problems 98
8 Electromagnetic Forces and Loss Mechanisms 103
8.1 Energy Conversion Process 103
8.1.1 Principle of Virtual Work 104
8.1.1.1 Example: Lifting Magnet 106
8.1.2 Co-energy 107
8.1.2.1 Example: Co-energy Force Problem 107
8.1.2.2 Electric Machine Model 108
8.2 Continuum Energy Flow 109
8.2.1 Material Motion 110
8.2.2 Additional Issues in Energy Methods 111
8.2.2.1 Co-energy in Continuous Media 111
8.2.2.2 Permanent Magnets 112
8.2.2.3 Energy in the Flux-Current Plane 113
8.2.3 Electric Machine Description 115
8.2.4 Field Description of Electromagnetic Force: The Maxwell Stress Tensor 117
8.2.5 Tying the Maxwell Stress Tensor and Poynting Approaches Together 119
8.2.5.1 Simple Description of a Linear Induction Motor 120
8.3 Surface Impedance of Uniform Conductors 122
8.3.1 Linear Case 123
8.3.2 Iron 125
8.3.3 Magnetization 126
8.3.4 Saturation and Hysteresis 126
8.3.5 Conduction, Eddy Currents, and Laminations 129
8.3.5.1 Complete Penetration Case 129
8.3.6 Eddy Currents in Saturating Iron 131
8.4 Semi-empirical Method of Handling Iron Loss 133
8.5 Problems 136
References 141
9 Synchronous Machines 143
9.1 Round Rotor Machines: Basics 144
9.1.1 Operation with a Balanced Current Source 145
9.1.2 Operation with a Voltage Source 145
9.2 Reconciliation of Models 147
9.2.1 Torque Angles 148
9.3 Per-unit Systems 148
9.4 Normal Operation 149
9.4.1 Capability Diagram 150
9.4.2 Vee Curve 150
9.5 Salient Pole Machines: Two-reaction Theory 151
9.6 Synchronous Machine Dynamics 155
9.7 Synchronous Machine Dynamic Model 155
9.7.1 Electromagnetic Model 156
9.7.2 Park's Equations 157
9.7.3 Power and Torque 160
9.7.4 Per-unit Normalization 160
9.7.5 Equivalent Circuits 163
9.7.6 Transient Reactances and Time Constants 164
9.8 Statement of Simulation Model 165
9.8.1 Example: Transient Stability 166
9.8.2 Equal Area Transient Stability Criterion 166
9.9 Appendix 1: Transient Stability Code 169
9.10 Appendix 2: Winding Inductance Calculation 172
9.10.1 Pitch Factor 175
9.10.2 Breadth Factor 175
9.11 Problems 177
10 System Analysis and Protection 181
10.1 The Symmetrical Component Transformation 181
10.2 Sequence Impedances 184
10.2.1 Balanced Transmission Lines 184
10.2.2 Balanced Load 185
10.2.3 Possibly Unbalanced Loads 186
10.2.4 Unbalanced Sources 187
10.2.5 Rotating Machines 189
10.2.6 Transformers 189
10.2.6.1 Example: Rotation of Symmetrical Component Currents 190
10.2.6.2 Example: Reconstruction of Currents 191
10.3 Fault Analysis 192
10.3.1 Single Line-Neutral Fault 192
10.3.2 Double Line-Neutral Fault 193
10.3.3 Line-Line Fault 193
10.3.4 Example of Fault Calculations 194
10.3.4.1 Symmetrical Fault 195
10.3.4.2 Single Line-Neutral Fault 195
10.3.4.3 Double Line-Neutral Fault 196
10.3.4.4 Line-Line Fault 197
10.3.4.5 Conversion to Amperes 198
10.4 System Protection 198
10.4.1 Fuses 199
10.5 Switches 199
10.6 Coordination 200
10.6.1 Ground Overcurrent 200
10.7 Impedance Relays 201
10.7.1 Directional Elements 202
10.8 Differential Relays 202
10.8.1 Ground Fault Protection for Personnel 203
10.9 Zones of System Protection 203
10.10 Problems 204
11 Load Flow 211
11.1 Two Ports and Lines 211
11.1.1 Power Circles 212
11.2 Load Flow in a Network 214
11.3 Gauss-Seidel Iterative Technique 216
11.4 Bus Types 217
11.5 Bus Admittance 217
11.5.1 Bus Incidence 217
11.5.2 Example Network 218
11.5.3 Alternative Assembly of Bus Admittance 219
11.6 Newton-Raphson Method for Load Flow 220
11.6.1 Generator Buses 222
11.6.2 Decoupling 222
11.6.3 Example Calculations 223
11.7 Problems 223
11.8 Appendix: Matlab Scripts to Implement Load Flow Techniques 226
11.8.1 Gauss-Seidel Routine 226
11.8.2 Newton-Raphson Routine 228
11.8.3 Decoupled Newton-Raphson Routine 230
12 Power Electronics and Converters in Power Systems 233
12.1 Switching Devices 233
12.1.1 Diodes 234
12.1.2 Thyristors 234
12.1.3 Bipolar Transistors 235
12.2 Rectifier Circuits 236
12.2.1 Full-wave Rectifier 237
12.2.1.1 Full-wave Bridge with Resistive Load 237
12.2.1.2 Phase-control Rectifier 238
12.2.1.3 Phase Control into an Inductive Load 240
12.2.1.4 AC Phase Control 242
12.2.1.5 Rectifiers for DC Power Supplies 242
12.3 DC-DC Converters 243
12.3.1 Pulse Width Modulation 246
12.3.2 Boost Converter 247
12.3.2.1 Continuous Conduction 247
12.3.2.2 Discontinuous Conduction 249
12.3.2.3 Unity Power Factor Supplies 250
12.4 Canonical Cell 251
12.4.1 Bidirectional Converter 251
12.4.2 H-Bridge 252
12.5 Three-phase Bridge Circuits 254
12.5.1 Rectifier Operation 254
12.5.2 Phase Control 257
12.5.3 Commutation Overlap 257
12.5.4 AC Side Current Harmonics 259
12.5.4.1 Power Supply Rectifiers 261
12.5.4.2 PWM Capable Switch Bridge 262
12.6 Unified Power Flow Controller 264
12.7 High-voltage DC Transmission 267
12.8 Basic Operation of a Converter Bridge 268
12.8.1 Turn-on Switch 268
12.8.2 Inverter Terminal 269
12.9 Achieving High Voltage 270
12.10 Problems 271
13 System Dynamics and Energy Storage 277
13.1 Load-Frequency Relationship 277
13.2 Energy Balance 277
13.2.1 Natural Response 278
13.2.2 Feedback Control 279
13.2.3 Droop Control 280
13.2.4 Isochronous Control 281
13.3 Synchronized Areas 282
13.3.1 Area Control Error 282
13.3.2 Synchronizing Dynamics 283
13.3.3 Feedback Control to Drive ACE to Zero 284
13.4 Inverter Connection 285
13.4.1 Overview of Connection 286
13.4.2 Filters 287
13.4.3 Measurement 288
13.4.4 Phase Locked Loop 289
13.4.5 Control Loops 290
13.4.6 Grid-following (Slave) Inverter 291
13.4.7 Grid-forming (Master) Inverter 291
13.4.8 Droop-controlled Inverter 292
13.5 Energy Storage 292
13.5.1 Time Scales 293
13.5.2 Batteries 293
13.5.2.1 Simplest Battery Model 294
13.5.2.2 Diffusion Model 294
13.5.2.3 Model Including State of Charge 295
13.6 Problems 296
14 Induction Machines 299
14.1 Introduction 299
14.2 Induction Machine Transformer Model 301
14.2.1 Operation: Energy Balance 307
14.2.1.1 Simplified Torque Estimation 309
14.2.1.2 Torque Summary 310
14.2.2 Example of Operation 310
14.2.3 Motor Performance Requirements 312
14.2.3.1 Effect of Rotor Resistance 312
14.3 Squirrel-cage Machines 313
14.4 Single-phase Induction Motors 314
14.4.1 Rotating Fields 314
14.4.2 Power Conversion in the Single-phase Induction Machine 315
14.4.3 Starting of Single-phase Induction Motors 316
14.4.3.1 Shaded Pole Motors 317
14.4.3.2 Split-phase Motors 317
14.4.4 Split-phase Operation 318
14.4.4.1 Example Motor 319
14.5 Induction Generators 321
14.6 Induction Motor Control 322
14.6.1 Volts/Hz Control 323
14.6.2 Field-oriented Control 323
14.6.3 Elementary Model 324
14.6.4 Simulation Model 325
14.6.5 Control Model 326
14.6.6 Field-oriented Strategy 327
14.7 Doubly-fed Induction Machines 329
14.7.1 Steady-state Operation 331
14.8 Appendix 1: Squirrel-cage Machine Model 334
14.8.1 Rotor Currents and Induced Flux 334
14.8.2 Squirrel-cage Currents 335
14.9 Appendix 2: Single-phase Squirrel-cage Model 339
14.10 Appendix 3: Induction Machine Winding Schemes 341
14.10.1 Winding Factor for Concentric Windings 344
14.11 Problems 345
References 350
15 DC (Commutator) Machines 351
15.1 Geometry 351
15.2 Torque Production 352
15.3 Back Voltage 353
15.4 Operation 354
15.4.1 Shunt Operation 355
15.4.2 Separately Excited 356
15.4.2.1 Armature Voltage Control 357
15.4.2.2 Field Weakening Control 357
15.4.2.3 Dynamic Braking 358
15.4.3 Machine Capability 358
15.5 Series Connection 359
15.6 Universal Motors 361
15.7 Commutator 362
15.7.1 Commutation Interpoles 362
15.7.2 Compensation 364
15.8 Compound-wound DC Machines 365
15.9 Problems 367
16 Permanent Magnets in Electric Machines 371
16.1 Permanent Magnets 371
16.1.1 Permanent Magnets in Magnetic Circuits 373
16.1.2 Load Line Analysis 373
16.1.2.1 Very Hard Magnets 374
16.1.2.2 Surface Magnet Analysis 375
16.1.2.3 Amperian Currents 376
16.2 Commutator Machines 376
16.2.1 Voltage 378
16.2.2 Armature Resistance 379
16.3 Brushless PM Machines 380
16.4 Motor Morphologies 380
16.4.1 Surface Magnet Machines 380
16.4.2 Interior Magnet, Flux-concentrating Machines 381
16.4.3 Operation 382
16.4.3.1 Voltage and Current: Round Rotor 382
16.4.4 A Little Two-reaction Theory 384
16.4.5 Finding Torque Capability 387
16.4.5.1 Optimal Currents 388
16.4.5.2 Rating 389
16.5 Problems 393
Reference 396
Index 397
About the Companion Website xvii
1 Electric Power Systems 1
1.1 Electric Utility Systems 2
1.2 Energy and Power 3
1.2.1 Basics and Units 3
1.3 Sources of Electric Power 5
1.3.1 Heat Engines 5
1.3.2 Power Plants 6
1.3.2.1 Environmental Impact of Burning Fossil Fuels 7
1.3.3 Nuclear Power Plants 8
1.3.4 Hydroelectric Power 9
1.3.5 Wind Turbines 10
1.3.6 Solar Power Generation 12
1.4 Electric Power Plants and Generation 14
1.5 Problems 15
2 AC Voltage, Current, and Power 17
2.1 Sources and Power 17
2.1.1 Voltage and Current Sources 17
2.1.2 Power 18
2.1.3 Sinusoidal Steady State 18
2.1.4 Phasor Notation 19
2.1.5 Real and Reactive Power 19
2.1.5.1 Root Mean Square (RMS) Amplitude 20
2.2 Resistors, Inductors, and Capacitors 20
2.2.1 Reactive Power and Voltage 22
2.2.1.1 Example 22
2.2.2 Reactive Power Voltage Support 22
2.3 Voltage Stability and Bifurcation 23
2.3.1 Voltage Calculation 24
2.3.2 Voltage Solution and Effect of Reactive Power 25
2.4 Problems 26
3 Transmission Lines 33
3.1 Modeling: Telegrapher's Equations 33
3.1.1 Traveling Waves 35
3.1.2 Characteristic Impedance 35
3.1.3 Power 36
3.1.4 Line Terminations and Reflections 36
3.1.4.1 Examples 37
3.1.4.2 Lightning 38
3.1.4.3 Inductive Termination 39
3.1.5 Sinusoidal Steady State 41
3.2 Problems 44
4 Polyphase Systems 47
4.1 Two-phase Systems 47
4.2 Three-phase Systems 48
4.3 Line-Line Voltages 51
4.3.1 Example: Wye- and Delta-connected Loads 52
4.3.2 Example: Use of Wye-Delta for Unbalanced Loads 53
4.4 Problems 55
5 Electrical and Magnetic Circuits 59
5.1 Electric Circuits 59
5.1.1 Kirchhoff's Current Law 59
5.1.2 Kirchhoff's Voltage Law 60
5.1.3 Constitutive Relationship: Ohm's Law 60
5.2 Magnetic Circuit Analogies 62
5.2.1 Analogy to KCL 62
5.2.2 Analogy to KVL: Magnetomotive Force 62
5.2.3 Analogy to Ohm's Law: Reluctance 63
5.2.4 Simple Case 64
5.2.5 Flux Confinement 64
5.2.6 Example: C-Core 65
5.2.7 Example: Core with Different Gaps 66
5.3 Problems 66
6 Transformers 71
6.1 Single-phase Transformers 71
6.1.1 Ideal Transformers 72
6.1.2 Deviations from an Ideal Transformer 73
6.1.3 Autotransformers 75
6.2 Three-phase Transformers 76
6.2.1 Example 78
6.2.2 Example: Grounding or Zigzag Transformer 80
6.3 Problems 81
7 Polyphase Lines and Single-phase Equivalents 87
7.1 Polyphase Transmission and Distribution Lines 87
7.1.1 Example 89
7.2 Introduction to Per-unit Systems 90
7.2.1 Normalization of Voltage and Current 90
7.2.2 Three-phase Systems 91
7.2.3 Networks with Transformers 92
7.2.4 Transforming from One Base to Another 92
7.2.5 Example: Fault Study 93
7.2.5.1 One-line Diagram of the Situation 93
7.3 Appendix: Inductances of Transmission Lines 95
7.3.1 Single Wire 95
7.3.2 Mutual Inductance 96
7.3.3 Bundles of Conductors 97
7.3.4 Transposed Lines 98
7.4 Problems 98
8 Electromagnetic Forces and Loss Mechanisms 103
8.1 Energy Conversion Process 103
8.1.1 Principle of Virtual Work 104
8.1.1.1 Example: Lifting Magnet 106
8.1.2 Co-energy 107
8.1.2.1 Example: Co-energy Force Problem 107
8.1.2.2 Electric Machine Model 108
8.2 Continuum Energy Flow 109
8.2.1 Material Motion 110
8.2.2 Additional Issues in Energy Methods 111
8.2.2.1 Co-energy in Continuous Media 111
8.2.2.2 Permanent Magnets 112
8.2.2.3 Energy in the Flux-Current Plane 113
8.2.3 Electric Machine Description 115
8.2.4 Field Description of Electromagnetic Force: The Maxwell Stress Tensor 117
8.2.5 Tying the Maxwell Stress Tensor and Poynting Approaches Together 119
8.2.5.1 Simple Description of a Linear Induction Motor 120
8.3 Surface Impedance of Uniform Conductors 122
8.3.1 Linear Case 123
8.3.2 Iron 125
8.3.3 Magnetization 126
8.3.4 Saturation and Hysteresis 126
8.3.5 Conduction, Eddy Currents, and Laminations 129
8.3.5.1 Complete Penetration Case 129
8.3.6 Eddy Currents in Saturating Iron 131
8.4 Semi-empirical Method of Handling Iron Loss 133
8.5 Problems 136
References 141
9 Synchronous Machines 143
9.1 Round Rotor Machines: Basics 144
9.1.1 Operation with a Balanced Current Source 145
9.1.2 Operation with a Voltage Source 145
9.2 Reconciliation of Models 147
9.2.1 Torque Angles 148
9.3 Per-unit Systems 148
9.4 Normal Operation 149
9.4.1 Capability Diagram 150
9.4.2 Vee Curve 150
9.5 Salient Pole Machines: Two-reaction Theory 151
9.6 Synchronous Machine Dynamics 155
9.7 Synchronous Machine Dynamic Model 155
9.7.1 Electromagnetic Model 156
9.7.2 Park's Equations 157
9.7.3 Power and Torque 160
9.7.4 Per-unit Normalization 160
9.7.5 Equivalent Circuits 163
9.7.6 Transient Reactances and Time Constants 164
9.8 Statement of Simulation Model 165
9.8.1 Example: Transient Stability 166
9.8.2 Equal Area Transient Stability Criterion 166
9.9 Appendix 1: Transient Stability Code 169
9.10 Appendix 2: Winding Inductance Calculation 172
9.10.1 Pitch Factor 175
9.10.2 Breadth Factor 175
9.11 Problems 177
10 System Analysis and Protection 181
10.1 The Symmetrical Component Transformation 181
10.2 Sequence Impedances 184
10.2.1 Balanced Transmission Lines 184
10.2.2 Balanced Load 185
10.2.3 Possibly Unbalanced Loads 186
10.2.4 Unbalanced Sources 187
10.2.5 Rotating Machines 189
10.2.6 Transformers 189
10.2.6.1 Example: Rotation of Symmetrical Component Currents 190
10.2.6.2 Example: Reconstruction of Currents 191
10.3 Fault Analysis 192
10.3.1 Single Line-Neutral Fault 192
10.3.2 Double Line-Neutral Fault 193
10.3.3 Line-Line Fault 193
10.3.4 Example of Fault Calculations 194
10.3.4.1 Symmetrical Fault 195
10.3.4.2 Single Line-Neutral Fault 195
10.3.4.3 Double Line-Neutral Fault 196
10.3.4.4 Line-Line Fault 197
10.3.4.5 Conversion to Amperes 198
10.4 System Protection 198
10.4.1 Fuses 199
10.5 Switches 199
10.6 Coordination 200
10.6.1 Ground Overcurrent 200
10.7 Impedance Relays 201
10.7.1 Directional Elements 202
10.8 Differential Relays 202
10.8.1 Ground Fault Protection for Personnel 203
10.9 Zones of System Protection 203
10.10 Problems 204
11 Load Flow 211
11.1 Two Ports and Lines 211
11.1.1 Power Circles 212
11.2 Load Flow in a Network 214
11.3 Gauss-Seidel Iterative Technique 216
11.4 Bus Types 217
11.5 Bus Admittance 217
11.5.1 Bus Incidence 217
11.5.2 Example Network 218
11.5.3 Alternative Assembly of Bus Admittance 219
11.6 Newton-Raphson Method for Load Flow 220
11.6.1 Generator Buses 222
11.6.2 Decoupling 222
11.6.3 Example Calculations 223
11.7 Problems 223
11.8 Appendix: Matlab Scripts to Implement Load Flow Techniques 226
11.8.1 Gauss-Seidel Routine 226
11.8.2 Newton-Raphson Routine 228
11.8.3 Decoupled Newton-Raphson Routine 230
12 Power Electronics and Converters in Power Systems 233
12.1 Switching Devices 233
12.1.1 Diodes 234
12.1.2 Thyristors 234
12.1.3 Bipolar Transistors 235
12.2 Rectifier Circuits 236
12.2.1 Full-wave Rectifier 237
12.2.1.1 Full-wave Bridge with Resistive Load 237
12.2.1.2 Phase-control Rectifier 238
12.2.1.3 Phase Control into an Inductive Load 240
12.2.1.4 AC Phase Control 242
12.2.1.5 Rectifiers for DC Power Supplies 242
12.3 DC-DC Converters 243
12.3.1 Pulse Width Modulation 246
12.3.2 Boost Converter 247
12.3.2.1 Continuous Conduction 247
12.3.2.2 Discontinuous Conduction 249
12.3.2.3 Unity Power Factor Supplies 250
12.4 Canonical Cell 251
12.4.1 Bidirectional Converter 251
12.4.2 H-Bridge 252
12.5 Three-phase Bridge Circuits 254
12.5.1 Rectifier Operation 254
12.5.2 Phase Control 257
12.5.3 Commutation Overlap 257
12.5.4 AC Side Current Harmonics 259
12.5.4.1 Power Supply Rectifiers 261
12.5.4.2 PWM Capable Switch Bridge 262
12.6 Unified Power Flow Controller 264
12.7 High-voltage DC Transmission 267
12.8 Basic Operation of a Converter Bridge 268
12.8.1 Turn-on Switch 268
12.8.2 Inverter Terminal 269
12.9 Achieving High Voltage 270
12.10 Problems 271
13 System Dynamics and Energy Storage 277
13.1 Load-Frequency Relationship 277
13.2 Energy Balance 277
13.2.1 Natural Response 278
13.2.2 Feedback Control 279
13.2.3 Droop Control 280
13.2.4 Isochronous Control 281
13.3 Synchronized Areas 282
13.3.1 Area Control Error 282
13.3.2 Synchronizing Dynamics 283
13.3.3 Feedback Control to Drive ACE to Zero 284
13.4 Inverter Connection 285
13.4.1 Overview of Connection 286
13.4.2 Filters 287
13.4.3 Measurement 288
13.4.4 Phase Locked Loop 289
13.4.5 Control Loops 290
13.4.6 Grid-following (Slave) Inverter 291
13.4.7 Grid-forming (Master) Inverter 291
13.4.8 Droop-controlled Inverter 292
13.5 Energy Storage 292
13.5.1 Time Scales 293
13.5.2 Batteries 293
13.5.2.1 Simplest Battery Model 294
13.5.2.2 Diffusion Model 294
13.5.2.3 Model Including State of Charge 295
13.6 Problems 296
14 Induction Machines 299
14.1 Introduction 299
14.2 Induction Machine Transformer Model 301
14.2.1 Operation: Energy Balance 307
14.2.1.1 Simplified Torque Estimation 309
14.2.1.2 Torque Summary 310
14.2.2 Example of Operation 310
14.2.3 Motor Performance Requirements 312
14.2.3.1 Effect of Rotor Resistance 312
14.3 Squirrel-cage Machines 313
14.4 Single-phase Induction Motors 314
14.4.1 Rotating Fields 314
14.4.2 Power Conversion in the Single-phase Induction Machine 315
14.4.3 Starting of Single-phase Induction Motors 316
14.4.3.1 Shaded Pole Motors 317
14.4.3.2 Split-phase Motors 317
14.4.4 Split-phase Operation 318
14.4.4.1 Example Motor 319
14.5 Induction Generators 321
14.6 Induction Motor Control 322
14.6.1 Volts/Hz Control 323
14.6.2 Field-oriented Control 323
14.6.3 Elementary Model 324
14.6.4 Simulation Model 325
14.6.5 Control Model 326
14.6.6 Field-oriented Strategy 327
14.7 Doubly-fed Induction Machines 329
14.7.1 Steady-state Operation 331
14.8 Appendix 1: Squirrel-cage Machine Model 334
14.8.1 Rotor Currents and Induced Flux 334
14.8.2 Squirrel-cage Currents 335
14.9 Appendix 2: Single-phase Squirrel-cage Model 339
14.10 Appendix 3: Induction Machine Winding Schemes 341
14.10.1 Winding Factor for Concentric Windings 344
14.11 Problems 345
References 350
15 DC (Commutator) Machines 351
15.1 Geometry 351
15.2 Torque Production 352
15.3 Back Voltage 353
15.4 Operation 354
15.4.1 Shunt Operation 355
15.4.2 Separately Excited 356
15.4.2.1 Armature Voltage Control 357
15.4.2.2 Field Weakening Control 357
15.4.2.3 Dynamic Braking 358
15.4.3 Machine Capability 358
15.5 Series Connection 359
15.6 Universal Motors 361
15.7 Commutator 362
15.7.1 Commutation Interpoles 362
15.7.2 Compensation 364
15.8 Compound-wound DC Machines 365
15.9 Problems 367
16 Permanent Magnets in Electric Machines 371
16.1 Permanent Magnets 371
16.1.1 Permanent Magnets in Magnetic Circuits 373
16.1.2 Load Line Analysis 373
16.1.2.1 Very Hard Magnets 374
16.1.2.2 Surface Magnet Analysis 375
16.1.2.3 Amperian Currents 376
16.2 Commutator Machines 376
16.2.1 Voltage 378
16.2.2 Armature Resistance 379
16.3 Brushless PM Machines 380
16.4 Motor Morphologies 380
16.4.1 Surface Magnet Machines 380
16.4.2 Interior Magnet, Flux-concentrating Machines 381
16.4.3 Operation 382
16.4.3.1 Voltage and Current: Round Rotor 382
16.4.4 A Little Two-reaction Theory 384
16.4.5 Finding Torque Capability 387
16.4.5.1 Optimal Currents 388
16.4.5.2 Rating 389
16.5 Problems 393
Reference 396
Index 397
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<p>Principles of electric power; introduction to electric power systems; physics of electric power systems circuit theory electric power; sources of electric power; conversion of electric power; distribution of electrical power</p>
Preface xv
About the Companion Website xvii
1 Electric Power Systems 1
1.1 Electric Utility Systems 2
1.2 Energy and Power 3
1.2.1 Basics and Units 3
1.3 Sources of Electric Power 5
1.3.1 Heat Engines 5
1.3.2 Power Plants 6
1.3.2.1 Environmental Impact of Burning Fossil Fuels 7
1.3.3 Nuclear Power Plants 8
1.3.4 Hydroelectric Power 9
1.3.5 Wind Turbines 10
1.3.6 Solar Power Generation 12
1.4 Electric Power Plants and Generation 14
1.5 Problems 15
2 AC Voltage, Current, and Power 17
2.1 Sources and Power 17
2.1.1 Voltage and Current Sources 17
2.1.2 Power 18
2.1.3 Sinusoidal Steady State 18
2.1.4 Phasor Notation 19
2.1.5 Real and Reactive Power 19
2.1.5.1 Root Mean Square (RMS) Amplitude 20
2.2 Resistors, Inductors, and Capacitors 20
2.2.1 Reactive Power and Voltage 22
2.2.1.1 Example 22
2.2.2 Reactive Power Voltage Support 22
2.3 Voltage Stability and Bifurcation 23
2.3.1 Voltage Calculation 24
2.3.2 Voltage Solution and Effect of Reactive Power 25
2.4 Problems 26
3 Transmission Lines 33
3.1 Modeling: Telegrapher's Equations 33
3.1.1 Traveling Waves 35
3.1.2 Characteristic Impedance 35
3.1.3 Power 36
3.1.4 Line Terminations and Reflections 36
3.1.4.1 Examples 37
3.1.4.2 Lightning 38
3.1.4.3 Inductive Termination 39
3.1.5 Sinusoidal Steady State 41
3.2 Problems 44
4 Polyphase Systems 47
4.1 Two-phase Systems 47
4.2 Three-phase Systems 48
4.3 Line-Line Voltages 51
4.3.1 Example: Wye- and Delta-connected Loads 52
4.3.2 Example: Use of Wye-Delta for Unbalanced Loads 53
4.4 Problems 55
5 Electrical and Magnetic Circuits 59
5.1 Electric Circuits 59
5.1.1 Kirchhoff's Current Law 59
5.1.2 Kirchhoff's Voltage Law 60
5.1.3 Constitutive Relationship: Ohm's Law 60
5.2 Magnetic Circuit Analogies 62
5.2.1 Analogy to KCL 62
5.2.2 Analogy to KVL: Magnetomotive Force 62
5.2.3 Analogy to Ohm's Law: Reluctance 63
5.2.4 Simple Case 64
5.2.5 Flux Confinement 64
5.2.6 Example: C-Core 65
5.2.7 Example: Core with Different Gaps 66
5.3 Problems 66
6 Transformers 71
6.1 Single-phase Transformers 71
6.1.1 Ideal Transformers 72
6.1.2 Deviations from an Ideal Transformer 73
6.1.3 Autotransformers 75
6.2 Three-phase Transformers 76
6.2.1 Example 78
6.2.2 Example: Grounding or Zigzag Transformer 80
6.3 Problems 81
7 Polyphase Lines and Single-phase Equivalents 87
7.1 Polyphase Transmission and Distribution Lines 87
7.1.1 Example 89
7.2 Introduction to Per-unit Systems 90
7.2.1 Normalization of Voltage and Current 90
7.2.2 Three-phase Systems 91
7.2.3 Networks with Transformers 92
7.2.4 Transforming from One Base to Another 92
7.2.5 Example: Fault Study 93
7.2.5.1 One-line Diagram of the Situation 93
7.3 Appendix: Inductances of Transmission Lines 95
7.3.1 Single Wire 95
7.3.2 Mutual Inductance 96
7.3.3 Bundles of Conductors 97
7.3.4 Transposed Lines 98
7.4 Problems 98
8 Electromagnetic Forces and Loss Mechanisms 103
8.1 Energy Conversion Process 103
8.1.1 Principle of Virtual Work 104
8.1.1.1 Example: Lifting Magnet 106
8.1.2 Co-energy 107
8.1.2.1 Example: Co-energy Force Problem 107
8.1.2.2 Electric Machine Model 108
8.2 Continuum Energy Flow 109
8.2.1 Material Motion 110
8.2.2 Additional Issues in Energy Methods 111
8.2.2.1 Co-energy in Continuous Media 111
8.2.2.2 Permanent Magnets 112
8.2.2.3 Energy in the Flux-Current Plane 113
8.2.3 Electric Machine Description 115
8.2.4 Field Description of Electromagnetic Force: The Maxwell Stress Tensor 117
8.2.5 Tying the Maxwell Stress Tensor and Poynting Approaches Together 119
8.2.5.1 Simple Description of a Linear Induction Motor 120
8.3 Surface Impedance of Uniform Conductors 122
8.3.1 Linear Case 123
8.3.2 Iron 125
8.3.3 Magnetization 126
8.3.4 Saturation and Hysteresis 126
8.3.5 Conduction, Eddy Currents, and Laminations 129
8.3.5.1 Complete Penetration Case 129
8.3.6 Eddy Currents in Saturating Iron 131
8.4 Semi-empirical Method of Handling Iron Loss 133
8.5 Problems 136
References 141
9 Synchronous Machines 143
9.1 Round Rotor Machines: Basics 144
9.1.1 Operation with a Balanced Current Source 145
9.1.2 Operation with a Voltage Source 145
9.2 Reconciliation of Models 147
9.2.1 Torque Angles 148
9.3 Per-unit Systems 148
9.4 Normal Operation 149
9.4.1 Capability Diagram 150
9.4.2 Vee Curve 150
9.5 Salient Pole Machines: Two-reaction Theory 151
9.6 Synchronous Machine Dynamics 155
9.7 Synchronous Machine Dynamic Model 155
9.7.1 Electromagnetic Model 156
9.7.2 Park's Equations 157
9.7.3 Power and Torque 160
9.7.4 Per-unit Normalization 160
9.7.5 Equivalent Circuits 163
9.7.6 Transient Reactances and Time Constants 164
9.8 Statement of Simulation Model 165
9.8.1 Example: Transient Stability 166
9.8.2 Equal Area Transient Stability Criterion 166
9.9 Appendix 1: Transient Stability Code 169
9.10 Appendix 2: Winding Inductance Calculation 172
9.10.1 Pitch Factor 175
9.10.2 Breadth Factor 175
9.11 Problems 177
10 System Analysis and Protection 181
10.1 The Symmetrical Component Transformation 181
10.2 Sequence Impedances 184
10.2.1 Balanced Transmission Lines 184
10.2.2 Balanced Load 185
10.2.3 Possibly Unbalanced Loads 186
10.2.4 Unbalanced Sources 187
10.2.5 Rotating Machines 189
10.2.6 Transformers 189
10.2.6.1 Example: Rotation of Symmetrical Component Currents 190
10.2.6.2 Example: Reconstruction of Currents 191
10.3 Fault Analysis 192
10.3.1 Single Line-Neutral Fault 192
10.3.2 Double Line-Neutral Fault 193
10.3.3 Line-Line Fault 193
10.3.4 Example of Fault Calculations 194
10.3.4.1 Symmetrical Fault 195
10.3.4.2 Single Line-Neutral Fault 195
10.3.4.3 Double Line-Neutral Fault 196
10.3.4.4 Line-Line Fault 197
10.3.4.5 Conversion to Amperes 198
10.4 System Protection 198
10.4.1 Fuses 199
10.5 Switches 199
10.6 Coordination 200
10.6.1 Ground Overcurrent 200
10.7 Impedance Relays 201
10.7.1 Directional Elements 202
10.8 Differential Relays 202
10.8.1 Ground Fault Protection for Personnel 203
10.9 Zones of System Protection 203
10.10 Problems 204
11 Load Flow 211
11.1 Two Ports and Lines 211
11.1.1 Power Circles 212
11.2 Load Flow in a Network 214
11.3 Gauss-Seidel Iterative Technique 216
11.4 Bus Types 217
11.5 Bus Admittance 217
11.5.1 Bus Incidence 217
11.5.2 Example Network 218
11.5.3 Alternative Assembly of Bus Admittance 219
11.6 Newton-Raphson Method for Load Flow 220
11.6.1 Generator Buses 222
11.6.2 Decoupling 222
11.6.3 Example Calculations 223
11.7 Problems 223
11.8 Appendix: Matlab Scripts to Implement Load Flow Techniques 226
11.8.1 Gauss-Seidel Routine 226
11.8.2 Newton-Raphson Routine 228
11.8.3 Decoupled Newton-Raphson Routine 230
12 Power Electronics and Converters in Power Systems 233
12.1 Switching Devices 233
12.1.1 Diodes 234
12.1.2 Thyristors 234
12.1.3 Bipolar Transistors 235
12.2 Rectifier Circuits 236
12.2.1 Full-wave Rectifier 237
12.2.1.1 Full-wave Bridge with Resistive Load 237
12.2.1.2 Phase-control Rectifier 238
12.2.1.3 Phase Control into an Inductive Load 240
12.2.1.4 AC Phase Control 242
12.2.1.5 Rectifiers for DC Power Supplies 242
12.3 DC-DC Converters 243
12.3.1 Pulse Width Modulation 246
12.3.2 Boost Converter 247
12.3.2.1 Continuous Conduction 247
12.3.2.2 Discontinuous Conduction 249
12.3.2.3 Unity Power Factor Supplies 250
12.4 Canonical Cell 251
12.4.1 Bidirectional Converter 251
12.4.2 H-Bridge 252
12.5 Three-phase Bridge Circuits 254
12.5.1 Rectifier Operation 254
12.5.2 Phase Control 257
12.5.3 Commutation Overlap 257
12.5.4 AC Side Current Harmonics 259
12.5.4.1 Power Supply Rectifiers 261
12.5.4.2 PWM Capable Switch Bridge 262
12.6 Unified Power Flow Controller 264
12.7 High-voltage DC Transmission 267
12.8 Basic Operation of a Converter Bridge 268
12.8.1 Turn-on Switch 268
12.8.2 Inverter Terminal 269
12.9 Achieving High Voltage 270
12.10 Problems 271
13 System Dynamics and Energy Storage 277
13.1 Load-Frequency Relationship 277
13.2 Energy Balance 277
13.2.1 Natural Response 278
13.2.2 Feedback Control 279
13.2.3 Droop Control 280
13.2.4 Isochronous Control 281
13.3 Synchronized Areas 282
13.3.1 Area Control Error 282
13.3.2 Synchronizing Dynamics 283
13.3.3 Feedback Control to Drive ACE to Zero 284
13.4 Inverter Connection 285
13.4.1 Overview of Connection 286
13.4.2 Filters 287
13.4.3 Measurement 288
13.4.4 Phase Locked Loop 289
13.4.5 Control Loops 290
13.4.6 Grid-following (Slave) Inverter 291
13.4.7 Grid-forming (Master) Inverter 291
13.4.8 Droop-controlled Inverter 292
13.5 Energy Storage 292
13.5.1 Time Scales 293
13.5.2 Batteries 293
13.5.2.1 Simplest Battery Model 294
13.5.2.2 Diffusion Model 294
13.5.2.3 Model Including State of Charge 295
13.6 Problems 296
14 Induction Machines 299
14.1 Introduction 299
14.2 Induction Machine Transformer Model 301
14.2.1 Operation: Energy Balance 307
14.2.1.1 Simplified Torque Estimation 309
14.2.1.2 Torque Summary 310
14.2.2 Example of Operation 310
14.2.3 Motor Performance Requirements 312
14.2.3.1 Effect of Rotor Resistance 312
14.3 Squirrel-cage Machines 313
14.4 Single-phase Induction Motors 314
14.4.1 Rotating Fields 314
14.4.2 Power Conversion in the Single-phase Induction Machine 315
14.4.3 Starting of Single-phase Induction Motors 316
14.4.3.1 Shaded Pole Motors 317
14.4.3.2 Split-phase Motors 317
14.4.4 Split-phase Operation 318
14.4.4.1 Example Motor 319
14.5 Induction Generators 321
14.6 Induction Motor Control 322
14.6.1 Volts/Hz Control 323
14.6.2 Field-oriented Control 323
14.6.3 Elementary Model 324
14.6.4 Simulation Model 325
14.6.5 Control Model 326
14.6.6 Field-oriented Strategy 327
14.7 Doubly-fed Induction Machines 329
14.7.1 Steady-state Operation 331
14.8 Appendix 1: Squirrel-cage Machine Model 334
14.8.1 Rotor Currents and Induced Flux 334
14.8.2 Squirrel-cage Currents 335
14.9 Appendix 2: Single-phase Squirrel-cage Model 339
14.10 Appendix 3: Induction Machine Winding Schemes 341
14.10.1 Winding Factor for Concentric Windings 344
14.11 Problems 345
References 350
15 DC (Commutator) Machines 351
15.1 Geometry 351
15.2 Torque Production 352
15.3 Back Voltage 353
15.4 Operation 354
15.4.1 Shunt Operation 355
15.4.2 Separately Excited 356
15.4.2.1 Armature Voltage Control 357
15.4.2.2 Field Weakening Control 357
15.4.2.3 Dynamic Braking 358
15.4.3 Machine Capability 358
15.5 Series Connection 359
15.6 Universal Motors 361
15.7 Commutator 362
15.7.1 Commutation Interpoles 362
15.7.2 Compensation 364
15.8 Compound-wound DC Machines 365
15.9 Problems 367
16 Permanent Magnets in Electric Machines 371
16.1 Permanent Magnets 371
16.1.1 Permanent Magnets in Magnetic Circuits 373
16.1.2 Load Line Analysis 373
16.1.2.1 Very Hard Magnets 374
16.1.2.2 Surface Magnet Analysis 375
16.1.2.3 Amperian Currents 376
16.2 Commutator Machines 376
16.2.1 Voltage 378
16.2.2 Armature Resistance 379
16.3 Brushless PM Machines 380
16.4 Motor Morphologies 380
16.4.1 Surface Magnet Machines 380
16.4.2 Interior Magnet, Flux-concentrating Machines 381
16.4.3 Operation 382
16.4.3.1 Voltage and Current: Round Rotor 382
16.4.4 A Little Two-reaction Theory 384
16.4.5 Finding Torque Capability 387
16.4.5.1 Optimal Currents 388
16.4.5.2 Rating 389
16.5 Problems 393
Reference 396
Index 397
About the Companion Website xvii
1 Electric Power Systems 1
1.1 Electric Utility Systems 2
1.2 Energy and Power 3
1.2.1 Basics and Units 3
1.3 Sources of Electric Power 5
1.3.1 Heat Engines 5
1.3.2 Power Plants 6
1.3.2.1 Environmental Impact of Burning Fossil Fuels 7
1.3.3 Nuclear Power Plants 8
1.3.4 Hydroelectric Power 9
1.3.5 Wind Turbines 10
1.3.6 Solar Power Generation 12
1.4 Electric Power Plants and Generation 14
1.5 Problems 15
2 AC Voltage, Current, and Power 17
2.1 Sources and Power 17
2.1.1 Voltage and Current Sources 17
2.1.2 Power 18
2.1.3 Sinusoidal Steady State 18
2.1.4 Phasor Notation 19
2.1.5 Real and Reactive Power 19
2.1.5.1 Root Mean Square (RMS) Amplitude 20
2.2 Resistors, Inductors, and Capacitors 20
2.2.1 Reactive Power and Voltage 22
2.2.1.1 Example 22
2.2.2 Reactive Power Voltage Support 22
2.3 Voltage Stability and Bifurcation 23
2.3.1 Voltage Calculation 24
2.3.2 Voltage Solution and Effect of Reactive Power 25
2.4 Problems 26
3 Transmission Lines 33
3.1 Modeling: Telegrapher's Equations 33
3.1.1 Traveling Waves 35
3.1.2 Characteristic Impedance 35
3.1.3 Power 36
3.1.4 Line Terminations and Reflections 36
3.1.4.1 Examples 37
3.1.4.2 Lightning 38
3.1.4.3 Inductive Termination 39
3.1.5 Sinusoidal Steady State 41
3.2 Problems 44
4 Polyphase Systems 47
4.1 Two-phase Systems 47
4.2 Three-phase Systems 48
4.3 Line-Line Voltages 51
4.3.1 Example: Wye- and Delta-connected Loads 52
4.3.2 Example: Use of Wye-Delta for Unbalanced Loads 53
4.4 Problems 55
5 Electrical and Magnetic Circuits 59
5.1 Electric Circuits 59
5.1.1 Kirchhoff's Current Law 59
5.1.2 Kirchhoff's Voltage Law 60
5.1.3 Constitutive Relationship: Ohm's Law 60
5.2 Magnetic Circuit Analogies 62
5.2.1 Analogy to KCL 62
5.2.2 Analogy to KVL: Magnetomotive Force 62
5.2.3 Analogy to Ohm's Law: Reluctance 63
5.2.4 Simple Case 64
5.2.5 Flux Confinement 64
5.2.6 Example: C-Core 65
5.2.7 Example: Core with Different Gaps 66
5.3 Problems 66
6 Transformers 71
6.1 Single-phase Transformers 71
6.1.1 Ideal Transformers 72
6.1.2 Deviations from an Ideal Transformer 73
6.1.3 Autotransformers 75
6.2 Three-phase Transformers 76
6.2.1 Example 78
6.2.2 Example: Grounding or Zigzag Transformer 80
6.3 Problems 81
7 Polyphase Lines and Single-phase Equivalents 87
7.1 Polyphase Transmission and Distribution Lines 87
7.1.1 Example 89
7.2 Introduction to Per-unit Systems 90
7.2.1 Normalization of Voltage and Current 90
7.2.2 Three-phase Systems 91
7.2.3 Networks with Transformers 92
7.2.4 Transforming from One Base to Another 92
7.2.5 Example: Fault Study 93
7.2.5.1 One-line Diagram of the Situation 93
7.3 Appendix: Inductances of Transmission Lines 95
7.3.1 Single Wire 95
7.3.2 Mutual Inductance 96
7.3.3 Bundles of Conductors 97
7.3.4 Transposed Lines 98
7.4 Problems 98
8 Electromagnetic Forces and Loss Mechanisms 103
8.1 Energy Conversion Process 103
8.1.1 Principle of Virtual Work 104
8.1.1.1 Example: Lifting Magnet 106
8.1.2 Co-energy 107
8.1.2.1 Example: Co-energy Force Problem 107
8.1.2.2 Electric Machine Model 108
8.2 Continuum Energy Flow 109
8.2.1 Material Motion 110
8.2.2 Additional Issues in Energy Methods 111
8.2.2.1 Co-energy in Continuous Media 111
8.2.2.2 Permanent Magnets 112
8.2.2.3 Energy in the Flux-Current Plane 113
8.2.3 Electric Machine Description 115
8.2.4 Field Description of Electromagnetic Force: The Maxwell Stress Tensor 117
8.2.5 Tying the Maxwell Stress Tensor and Poynting Approaches Together 119
8.2.5.1 Simple Description of a Linear Induction Motor 120
8.3 Surface Impedance of Uniform Conductors 122
8.3.1 Linear Case 123
8.3.2 Iron 125
8.3.3 Magnetization 126
8.3.4 Saturation and Hysteresis 126
8.3.5 Conduction, Eddy Currents, and Laminations 129
8.3.5.1 Complete Penetration Case 129
8.3.6 Eddy Currents in Saturating Iron 131
8.4 Semi-empirical Method of Handling Iron Loss 133
8.5 Problems 136
References 141
9 Synchronous Machines 143
9.1 Round Rotor Machines: Basics 144
9.1.1 Operation with a Balanced Current Source 145
9.1.2 Operation with a Voltage Source 145
9.2 Reconciliation of Models 147
9.2.1 Torque Angles 148
9.3 Per-unit Systems 148
9.4 Normal Operation 149
9.4.1 Capability Diagram 150
9.4.2 Vee Curve 150
9.5 Salient Pole Machines: Two-reaction Theory 151
9.6 Synchronous Machine Dynamics 155
9.7 Synchronous Machine Dynamic Model 155
9.7.1 Electromagnetic Model 156
9.7.2 Park's Equations 157
9.7.3 Power and Torque 160
9.7.4 Per-unit Normalization 160
9.7.5 Equivalent Circuits 163
9.7.6 Transient Reactances and Time Constants 164
9.8 Statement of Simulation Model 165
9.8.1 Example: Transient Stability 166
9.8.2 Equal Area Transient Stability Criterion 166
9.9 Appendix 1: Transient Stability Code 169
9.10 Appendix 2: Winding Inductance Calculation 172
9.10.1 Pitch Factor 175
9.10.2 Breadth Factor 175
9.11 Problems 177
10 System Analysis and Protection 181
10.1 The Symmetrical Component Transformation 181
10.2 Sequence Impedances 184
10.2.1 Balanced Transmission Lines 184
10.2.2 Balanced Load 185
10.2.3 Possibly Unbalanced Loads 186
10.2.4 Unbalanced Sources 187
10.2.5 Rotating Machines 189
10.2.6 Transformers 189
10.2.6.1 Example: Rotation of Symmetrical Component Currents 190
10.2.6.2 Example: Reconstruction of Currents 191
10.3 Fault Analysis 192
10.3.1 Single Line-Neutral Fault 192
10.3.2 Double Line-Neutral Fault 193
10.3.3 Line-Line Fault 193
10.3.4 Example of Fault Calculations 194
10.3.4.1 Symmetrical Fault 195
10.3.4.2 Single Line-Neutral Fault 195
10.3.4.3 Double Line-Neutral Fault 196
10.3.4.4 Line-Line Fault 197
10.3.4.5 Conversion to Amperes 198
10.4 System Protection 198
10.4.1 Fuses 199
10.5 Switches 199
10.6 Coordination 200
10.6.1 Ground Overcurrent 200
10.7 Impedance Relays 201
10.7.1 Directional Elements 202
10.8 Differential Relays 202
10.8.1 Ground Fault Protection for Personnel 203
10.9 Zones of System Protection 203
10.10 Problems 204
11 Load Flow 211
11.1 Two Ports and Lines 211
11.1.1 Power Circles 212
11.2 Load Flow in a Network 214
11.3 Gauss-Seidel Iterative Technique 216
11.4 Bus Types 217
11.5 Bus Admittance 217
11.5.1 Bus Incidence 217
11.5.2 Example Network 218
11.5.3 Alternative Assembly of Bus Admittance 219
11.6 Newton-Raphson Method for Load Flow 220
11.6.1 Generator Buses 222
11.6.2 Decoupling 222
11.6.3 Example Calculations 223
11.7 Problems 223
11.8 Appendix: Matlab Scripts to Implement Load Flow Techniques 226
11.8.1 Gauss-Seidel Routine 226
11.8.2 Newton-Raphson Routine 228
11.8.3 Decoupled Newton-Raphson Routine 230
12 Power Electronics and Converters in Power Systems 233
12.1 Switching Devices 233
12.1.1 Diodes 234
12.1.2 Thyristors 234
12.1.3 Bipolar Transistors 235
12.2 Rectifier Circuits 236
12.2.1 Full-wave Rectifier 237
12.2.1.1 Full-wave Bridge with Resistive Load 237
12.2.1.2 Phase-control Rectifier 238
12.2.1.3 Phase Control into an Inductive Load 240
12.2.1.4 AC Phase Control 242
12.2.1.5 Rectifiers for DC Power Supplies 242
12.3 DC-DC Converters 243
12.3.1 Pulse Width Modulation 246
12.3.2 Boost Converter 247
12.3.2.1 Continuous Conduction 247
12.3.2.2 Discontinuous Conduction 249
12.3.2.3 Unity Power Factor Supplies 250
12.4 Canonical Cell 251
12.4.1 Bidirectional Converter 251
12.4.2 H-Bridge 252
12.5 Three-phase Bridge Circuits 254
12.5.1 Rectifier Operation 254
12.5.2 Phase Control 257
12.5.3 Commutation Overlap 257
12.5.4 AC Side Current Harmonics 259
12.5.4.1 Power Supply Rectifiers 261
12.5.4.2 PWM Capable Switch Bridge 262
12.6 Unified Power Flow Controller 264
12.7 High-voltage DC Transmission 267
12.8 Basic Operation of a Converter Bridge 268
12.8.1 Turn-on Switch 268
12.8.2 Inverter Terminal 269
12.9 Achieving High Voltage 270
12.10 Problems 271
13 System Dynamics and Energy Storage 277
13.1 Load-Frequency Relationship 277
13.2 Energy Balance 277
13.2.1 Natural Response 278
13.2.2 Feedback Control 279
13.2.3 Droop Control 280
13.2.4 Isochronous Control 281
13.3 Synchronized Areas 282
13.3.1 Area Control Error 282
13.3.2 Synchronizing Dynamics 283
13.3.3 Feedback Control to Drive ACE to Zero 284
13.4 Inverter Connection 285
13.4.1 Overview of Connection 286
13.4.2 Filters 287
13.4.3 Measurement 288
13.4.4 Phase Locked Loop 289
13.4.5 Control Loops 290
13.4.6 Grid-following (Slave) Inverter 291
13.4.7 Grid-forming (Master) Inverter 291
13.4.8 Droop-controlled Inverter 292
13.5 Energy Storage 292
13.5.1 Time Scales 293
13.5.2 Batteries 293
13.5.2.1 Simplest Battery Model 294
13.5.2.2 Diffusion Model 294
13.5.2.3 Model Including State of Charge 295
13.6 Problems 296
14 Induction Machines 299
14.1 Introduction 299
14.2 Induction Machine Transformer Model 301
14.2.1 Operation: Energy Balance 307
14.2.1.1 Simplified Torque Estimation 309
14.2.1.2 Torque Summary 310
14.2.2 Example of Operation 310
14.2.3 Motor Performance Requirements 312
14.2.3.1 Effect of Rotor Resistance 312
14.3 Squirrel-cage Machines 313
14.4 Single-phase Induction Motors 314
14.4.1 Rotating Fields 314
14.4.2 Power Conversion in the Single-phase Induction Machine 315
14.4.3 Starting of Single-phase Induction Motors 316
14.4.3.1 Shaded Pole Motors 317
14.4.3.2 Split-phase Motors 317
14.4.4 Split-phase Operation 318
14.4.4.1 Example Motor 319
14.5 Induction Generators 321
14.6 Induction Motor Control 322
14.6.1 Volts/Hz Control 323
14.6.2 Field-oriented Control 323
14.6.3 Elementary Model 324
14.6.4 Simulation Model 325
14.6.5 Control Model 326
14.6.6 Field-oriented Strategy 327
14.7 Doubly-fed Induction Machines 329
14.7.1 Steady-state Operation 331
14.8 Appendix 1: Squirrel-cage Machine Model 334
14.8.1 Rotor Currents and Induced Flux 334
14.8.2 Squirrel-cage Currents 335
14.9 Appendix 2: Single-phase Squirrel-cage Model 339
14.10 Appendix 3: Induction Machine Winding Schemes 341
14.10.1 Winding Factor for Concentric Windings 344
14.11 Problems 345
References 350
15 DC (Commutator) Machines 351
15.1 Geometry 351
15.2 Torque Production 352
15.3 Back Voltage 353
15.4 Operation 354
15.4.1 Shunt Operation 355
15.4.2 Separately Excited 356
15.4.2.1 Armature Voltage Control 357
15.4.2.2 Field Weakening Control 357
15.4.2.3 Dynamic Braking 358
15.4.3 Machine Capability 358
15.5 Series Connection 359
15.6 Universal Motors 361
15.7 Commutator 362
15.7.1 Commutation Interpoles 362
15.7.2 Compensation 364
15.8 Compound-wound DC Machines 365
15.9 Problems 367
16 Permanent Magnets in Electric Machines 371
16.1 Permanent Magnets 371
16.1.1 Permanent Magnets in Magnetic Circuits 373
16.1.2 Load Line Analysis 373
16.1.2.1 Very Hard Magnets 374
16.1.2.2 Surface Magnet Analysis 375
16.1.2.3 Amperian Currents 376
16.2 Commutator Machines 376
16.2.1 Voltage 378
16.2.2 Armature Resistance 379
16.3 Brushless PM Machines 380
16.4 Motor Morphologies 380
16.4.1 Surface Magnet Machines 380
16.4.2 Interior Magnet, Flux-concentrating Machines 381
16.4.3 Operation 382
16.4.3.1 Voltage and Current: Round Rotor 382
16.4.4 A Little Two-reaction Theory 384
16.4.5 Finding Torque Capability 387
16.4.5.1 Optimal Currents 388
16.4.5.2 Rating 389
16.5 Problems 393
Reference 396
Index 397
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