Preface xiii
Acknowledgements xvii
Part I 1
1 Power Systems: A General Overview 3
1.1 Three?phase System of AC Voltages 3
1.2 Low Voltage Distribution 6
1.3 Examples of Distribution Transformers 8
1.4 Practical Magnitude Limits for LV Loads 10
1.5 Medium Voltage Network 11
1.6 Transmission and Sub?Transmission Networks 24
1.7 Generation of Electrical Energy 32
1.8 Sources 41
Further Reading 41
2 Review of AC Circuit Theory and Application of Phasor Diagrams 43
2.1 Representation of AC Voltages and Currents 43
2.2 RMS Measurement of Time Varying AC Quantities 44
2.3 Phasor Notation (Phasor Diagram Analysis) 45
2.4 Passive Circuit Components: Resistors, Capacitors and Inductors 49
2.5 Review of Sign Conventions and Network Theorems 55
2.6 AC Circuit Analysis Examples 61
2.7 Resonance in AC Circuits 74
2.8 Problems 83
2.9 Practical Experiment 88
3 Active Power, Reactive Power and Power Factor 91
3.1 Single?Phase AC Power 91
3.2 Active Power 92
3.3 Reactive Power 93
3.4 Apparent Power or the volt?amp Product, S 96
3.5 Three?Phase Power 97
3.6 Power Factor 99
3.7 Power Factor Correction 100
3.8 Typical Industrial Load Profiles 105
3.9 Directional Power Flows 107
3.10 Energy Retailing 110
3.11 Problems 111
4 Magnetic Circuits, Inductors and Transformers 115
4.1 Magnetic Circuits 115
4.2 Magnetic Circuit Model 116
4.3 Gapped Cores and Effective Permeability 119
4.4 Inductance Calculations 120
4.5 Core Materials 121
4.6 Magnetising Characteristics of GOSS 122
4.7 Energy Stored in the Air Gap 125
4.8 EMF Equation 126
4.9 Magnetic Circuit Topologies 127
4.10 Magnetising Losses 129
4.11 Two?Winding Transformer Operation 131
4.12 Transformer VA Ratings and Efficiency 133
4.13 Two?Winding Transformer Equivalent Circuit 134
4.14 The Per?Unit System 137
4.15 Transformer Short?Circuit and Open?Circuit Tests 138
4.16 Transformer Phasor Diagram 140
4.17 Current Transformers 142
4.18 Problems 144
4.19 Sources 153
5 Symmetrical Components 155
5.1 Symmetrical Component Theory 156
5.2 Sequence Networks and Fault Analysis 160
5.3 Network Fault Connections 163
5.4 Measurement of Zero?sequence Components (Residual Current and Voltage) 170
5.5 Phase?to?Ground Fault Currents Reflected from a Star to a Delta Connected Winding 171
5.6 Sequence Components Remote from a Fault 173
5.7 Problems 175
5.8 Sources 185
6 Power Flows in AC Networks 187
6.1 Power Flow Directions 188
6.2 Synchronous Condenser 188
6.3 Synchronous Motor 191
6.4 Generalised Power Flow Analysis 192
6.5 Low X/R Networks 197
6.6 Steady State Transmission Stability Limit 201
6.7 Voltage Collapse in Power Systems 202
6.8 Problems 207
6.9 Sources 209
Part II 211
7 Three?Phase Transformers 213
7.1 Positive and Negative Sequence Impedance 213
7.2 Transformer Zero?Sequence Impedance 219
7.3 Transformer Vector Groups 221
7.4 Transformer Voltage Regulation 222
7.5 Magnetising Current Harmonics 228
7.6 Tap?changing Techniques 233
7.7 Parallel Connection of Transformers 245
7.8 Transformer Nameplate 249
7.9 Step Voltage Regulator 251
7.10 Problems 264
7.11 Sources 272
8 Voltage Transformers 273
8.1 Inductive and Capacitive Voltage Transformers 273
8.2 Voltage Transformer Errors 276
8.3 Voltage Transformer Equivalent Circuit 281
8.4 Voltage Transformer ‘Error Lines’ 284
8.5 Re?rating Voltage Transformers 288
8.6 Accuracy Classes for Protective Voltage Transformers 289
8.7 Dual?Wound Voltage Transformers 292
8.8 Earthing and Protection of Voltage Transformers 292
8.9 Non?Conventional Voltage Transformers 297
8.10 Problems 299
8.11 Sources 301
9 Current Transformers 303
9.1 CT Secondary Currents and Ratios 304
9.2 Current Transformer Errors and Standards 306
9.3 IEEE C57.13 Metering Class Magnitude and Phase Errors 309
9.4 Current Transformer Equivalent Circuit 312
9.5 Magnetising Admittance Variation and CT Compensation Techniques 315
9.6 Composite Error 319
9.7 Instrument Security Factor for Metering CTs 322
9.8 Protection Current Transformers 324
9.9 Inter?Turn Voltage Ratings 337
9.10 Non?Conventional Current Transformers 338
9.11 Problems 341
9.12 Sources 349
10 Energy Metering 351
10.1 Metering Intervals 353
10.2 General Metering Analysis using Symmetrical Components 361
10.3 Metering Errors 367
10.4 Ratio Correction Factors 373
10.5 Reactive Power Measurement Error 378
10.6 Evaluation of the Overall Error for an Installation 379
10.7 Commissioning and Auditing of Metering Installations 381
10.8 Problems 383
10.9 Sources 388
11 Earthing Systems 391
11.1 Effects of Electricity on the Human Body 391
11.2 Residual Current Devices 399
11.3 LV Earthing Systems 402
11.4 LV Earthing Systems used Worldwide 413
11.5 Medium Voltage Earthing Systems 413
11.6 High Voltage Earthing 423
11.7 Exercise 423
11.8 Problems (Earthing Grid Design) 425
11.9 Sources 434
12 Introduction to Power System Protection 437
12.1 Fundamental Principles of Protection 437
12.2 Protection Relays 438
12.3 Primary and Backup Protection (Duplicate Protection) 439
12.4 Protection Zones 441
12.5 Overcurrent Protection 443
12.6 Differential Protection 451
12.7 Frame Leakage and Arc Flash Busbar Protection 462
12.8 Distance Protection (Impedance Protection) 464
12.9 Problems 469
12.10 Sources 475
13 Harmonics in Power Systems 477
13.1 Measures of Harmonic Distortion 479
13.2 Resolving a Non?linear Current or Voltage into its Harmonic Components (Fourier Series) 480
13.3 Harmonic Phase Sequences 484
13.4 Triplen Harmonic Currents 487
13.5 Harmonic Losses in Transformers 487
13.6 Power Factor in the Presence of Harmonics 492
13.7 Management of Harmonics 495
13.8 Harmonic Standards 504
13.9 Measurement of Harmonics 514
13.10 Problems 515
13.11 Sources 519
14 Operational Aspects of Power Engineering 521
14.1 Device Numbers 521
14.2 One Line Diagram (OLD) 523
14.3 Switchgear Topologies 526
14.4 Switching Plans, Equipment Isolation and Permit to Work Procedures 537
14.5 Electrical Safety 542
14.6 Measurements with an Incorrectly Configured Multimeter 549
14.7 Sources 551
Index 553
