Title Details

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 3

1.3.1 Heat Engines 4

1.3.2 Power Plants 5

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 15

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

2.2 Resistors, Inductors and Capacitors 21

2.2.1 Reactive Power and Voltage 22

2.2.2 Reactive Power Voltage Support 23

2.3 Problems 26

3 Transmission Lines 31

3.1 Modeling: Telegrapher’s Equations 32

3.1.1 Traveling Waves 33

3.1.2 Characteristic Impedance 33

3.1.3 Power 35

3.1.4 Line Terminations and Reflections 35

3.1.5 Sinusoidal Steady State 40

3.2 Problems 42

4 Polyphase Systems 45

4.0.1 Two-Phase Systems 45

4.1 Three-Phase Systems 47

4.2 Line–Line Voltages 49

4.2.1 Example: Wye and Delta Connected Loads 50

4.2.2 Example: Use of Wye–Delta for Unbalanced Loads 52

4.3 Problems 54

5 Electrical and Magnetic Circuits 57

5.1 Electric Circuits 57

5.1.1 Kirchoff ’s Current Law (KCL) 57

5.1.2 Kirchoff ’s Voltage Law (KVL) 58

5.1.3 Constitutive Relationship: Ohm’s Law 58

5.2 Magnetic Circuit Analogies 60

5.2.1 Analogy to KCL 60

5.2.2 Analogy to KVL: Magnetomotive Force 61

5.2.3 Analogy to Ohm’s Law: Reluctance 61

5.2.4 Simple Case 62

5.2.5 Flux Confinement 63

5.2.6 Example: C-Core 63

5.2.7 Example: Core with Different Gaps 64

5.3 Problems 66

6 Transformers 71

6.1 Single-phase Transformers 71

6.1.1 Ideal Transformer 72

6.1.2 Deviations from Ideal Transformer 73

6.2 Three-Phase Transformers 75

6.2.1 Example 77

6.3 Problems 80

7 Polyphase Lines and Single-Phase Equivalents 85

7.1 Polyphase Transmission and Distribution Lines 85

7.1.1 Example 87

7.2 Introduction To Per-Unit Systems 88

7.2.1 Normalization Of Voltage and Current 88

7.2.2 Three-Phase Systems 90

7.2.3 Networks with Transformers 90

7.2.4 Transforming from one base to another 91

7.2.5 Example: Fault Study 92

7.3 Appendix: Inductances of Transmission Lines 94

7.3.1 Single Wire 94

7.3.2 Mutual Inductance 96

7.3.3 Bundles of Conductors 96

7.3.4 Transposed Lines 97

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

8.1.2 Coenergy 108

8.2 Continuum Energy Flow 110

8.2.1 Material Motion 111

8.2.2 Additional Issues in Energy Methods 112

8.2.3 Electric Machine Description 116

8.2.4 Field Description of Electromagnetic Force: The Maxwell Stress Tensor 118

8.2.5 Tying the MST and Poynting Approaches together 120

8.3 Surface Impedance of Uniform Conductors 124

8.3.1 Linear Case 124

8.3.2 Iron 128

8.3.3 Magnetization 128

8.3.4 Saturation and Hysteresis 129

8.3.5 Conduction, Eddy Currents and Laminations 131

8.3.6 Eddy Currents in Saturating Iron 133

8.4 Semi-Empirical Method of Handling Iron Loss 136

8.5 Problems 139

9 Synchronous Machines 145

9.1 Round Rotor Machines: Basics 146

9.1.1 Operation with a Balanced Current Source 147

9.1.2 Operation with a Voltage Source 147

9.2 Reconciliation of Models 150

9.2.1 Torque Angles 150

9.3 Per-Unit Systems 151

9.4 Normal Operation 152

9.4.1 Capability Diagram 153

9.4.2 Vee Curve 153

9.5 Salient Pole Machines: Two-Reaction Theory 154

9.6 Synchronous Machine Dynamics 157

9.7 Synchronous Machine Dynamic Model 159

9.7.1 Electromagnetic Model 159

9.7.2 Park’s Equations 160

9.7.3 Power and Torque 164

9.7.4 Per-Unit Normalization 164

9.7.5 Equivalent Circuits 167

9.7.6 Transient Reactances and Time Constants 168

9.8 Statement of Simulation Model 169

9.8.1 Example: Transient Stability 170

9.8.2 Equal Area Transient Stability Criterion 170

9.9 Appendix: Transient Stability Code 173

9.10 Appendix: Winding Inductance Calculation 176

9.10.1 Pitch Factor 180

9.10.2 Breadth Factor 180

9.11 Problems 182

10 System Analysis and Protection 185

10.1 The Symmetrical Component Transformation 185

10.2 Sequence Impedances 188

10.2.1 Balanced Transmission Lines 188

10.2.2 Balanced Load 189

10.2.3 Possibly Unbalanced Loads 190

10.2.4 Unbalanced Sources 191

10.2.5 Rotating Machines 193

10.2.6 Transformers 193

10.3 Fault Analysis 197

10.3.1 Single Line–neutral Fault 198

10.3.2 Double Line–neutral Fault 199

10.3.3 Line–Line Fault 200

10.3.4 Example of Fault Calculations 201

10.4 System Protection 205

10.4.1 Fuses 206

10.5 Switches 207

10.6 Coordination 208

10.6.1 Ground Overcurrent 208

10.7 Impedance Relays 208

10.7.1 Directional Elements 209

10.8 Differential Relays 210

10.8.1 Ground Fault Protection for Personnel 211

10.9 Zones of System Protection 212

10.10 Problems 212

11 Load Flow 219

11.1 Two Ports and Lines 219

11.1.1 Power Circles 221

11.2 Load Flow in a Network 222

11.3 Gauss–Seidel Iterative Technique 224

11.4 Bus Admittance 226

11.4.1 Bus Incidence 226

11.4.2 Alternative Assembly of Bus Admittance 227

11.5 Example: Simple Program 228

11.5.1 Example Network 228

11.6 MATLAB Script for the Load Flow Example 229

11.7 Problems 231

12 Power Electronics and Converters in Power Systems 235

12.1 Switching Devices 235

12.1.1 Diode 236

12.1.2 Thyristor 236

12.1.3 Bipolar Transistors 237

12.2 Rectifier Circuits 239

12.2.1 Full-Wave Rectifier 239

12.3 DC–DC Converters 247

12.3.1 Pulse Width Modulation 249

12.3.2 Boost Converter 249

12.4 Canonical Cell 255

12.4.1 Bidirectional Converter 255

12.4.2 H-Bridge 257

12.5 Three-Phase Bridge Circuits 259

12.5.1 Rectifier Operation 259

12.5.2 Phase Control 261

12.5.3 Commutation Overlap 262

12.5.4 AC Side Current Harmonics 265

12.6 High-Voltage DC Transmission 270

12.7 Basic Operation of a Converter Bridge 271

12.7.1 Turn-On Switch 272

12.7.2 Inverter Terminal 272

12.8 Achieving High Voltage 273

12.9 Problems 274

13 Induction Machines 281

13.1 Introduction 281

13.2 Induction Machine Transformer Model 283

13.2.1 Operation: Energy Balance 289

13.2.2 Example of Operation 294

13.2.3 Motor Performance Requirements 294

13.3 Squirrel-Cage Machines 296

13.4 Single-Phase Induction Motors 297

13.4.1 Rotating Fields 297

13.4.2 Power Conversion in the Single-Phase Induction Machine 298

13.4.3 Starting of Single-Phase Induction Motors 300

13.4.4 Split Phase Operation 301

13.5 Induction Generators 303

13.6 Induction Motor Control 306

13.6.1 Volts/Hz Control 306

13.6.2 Field Oriented Control 307

13.6.3 Elementary Model 308

13.6.4 Simulation Model 309

13.6.5 Control Model 310

13.6.6 Field-Oriented Strategy 311

13.7 Doubly Fed Induction Machines 313

13.7.1 Steady State Operation 315

13.8 Appendix 1: Squirrel-Cage Machine Model 318

13.8.1 Rotor Currents and Induced Flux 319

13.8.2 Squirrel-Cage Currents 320

13.9 Appendix 2: Single-Phase Squirrel Cage Model 325

13.10 Appendix 3: Induction Machine Winding Schemes 326

13.10.1 Winding Factor for Concentric Windings 329

13.11 Problems 331

14 DC (Commutator) Machines 337

14.1 Geometry 337

14.2 Torque Production 338

14.3 Back Voltage 339

14.4 Operation 341

14.4.1 Shunt Operation 342

14.4.2 Separately Excited 343

14.4.3 Machine Capability 345

14.5 Series Connection 346

14.6 Universal Motors 348

14.7 Commutator 349

14.7.1 Commutation Interpoles 351

14.7.2 Compensation 351

14.8 Compound Wound DC Machines 352

14.9 Problems 354

15 Permanent Magnets in Electric Machines 357

15.1 Permanent Magnets 357

15.1.1 Permanent Magnets in Magnetic Circuits 359

15.1.2 Load Line Analysis 360

15.2 Commutator Machines 363

15.2.1 Voltage 365

15.2.2 Armature Resistance 366

15.3 Brushless PM Machines 367

15.4 Motor Morphologies 367

15.4.1 Surface Magnet Machines 367

15.4.2 Interior Magnet, Flux Concentrating Machines 368

15.4.3 Operation 369

15.4.4 A Little Two-Reaction Theory 371

15.4.5 Finding Torque Capability 374

15.5 Problems 380

Index 385