Electric Power Principles – Sources, Conversion, Distribution and Use 2nd Edition

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