E-book

# AC Circuits and Power Systems in Practice

ISBN: 978-1-118-92461-7
592 pages
September 2017

## Description

The essential guide that combines power system fundamentals with the practical aspects of equipment design and operation in modern power systems

Written by an experienced power engineer, AC Circuits and Power Systems in Practice offers a comprehensive guide that reviews power system fundamentals and network theorems while exploring the practical aspects of equipment design and application. The author covers a wide-range of topics including basic circuit theorems, phasor diagrams, per-unit quantities and symmetrical component theory, as well as active and reactive power and their effects on network stability, voltage support and voltage collapse. Magnetic circuits, reactor and transformer design are analyzed, as is the operation of step voltage regulators. In addition, detailed introductions are provided to earthing systems in LV and MV networks, the adverse effects of harmonics on power equipment and power system protection. Finally, European and American engineering standards are presented where appropriate throughout the text, to familiarize the reader with their use and application.

This book is written as a practical power engineering text for engineering students and recent graduates. It contains more than 400 illustrations and is designed to provide the reader with a broad introduction to the subject and to facilitate further study. Many of the examples included come from industry and are not normally covered in undergraduate syllabi. They are provided to assist in bridging the gap between tertiary study and industrial practice, and to assist the professional development of recent graduates. The material presented is easy to follow and includes both mathematical and visual representations using phasor diagrams. Problems included at the end of most chapters are designed to walk the reader through practical applications of the associated theory.

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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

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 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 Sources 144

4.19 Problems 144

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 Star to Delta 171

5.6 Sequence Components Remote from a Fault 173

5.7 Problems 175

5.7 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 Sources 207

6.9 Problems 207

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 243

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 362

10.3 Metering Errors 367

10.4 Ratio Correction Factors 373

10.5 Reactive Power Measurement Error 379

10.6 Evaluation of the Overall Error for an Installation 379

10.7 Commissioning and Auditing of Metering Installations 382

10.8 Problems 383

10.9 Sources 389

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

References 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

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## Author Information

GRAEME VERTIGAN is a consulting engineer working in the Australian power supply industry. He has delivered courses on Energy Metering for the national electricity market operator since 2009, and was formerly the senior electrical engineer at a large Tasmanian zinc refinery. He was also employed as a part time lecturer at the University of Tasmania for many years.

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## Reviews

"This book combines the author?s rich experience in industry and teaching expertise in university. It covers the fundamental topics of AC circuits, and the application of those theories are discussed with numerous examples as well as the requirements of Engineering Standards. The writing style is logical and explicit, while illustrations and diagrams are with great accuracy, facilitating readers to have a systematic and in-depth understanding. Overall, I think this book can be an invaluable guide for recent graduate engineers working in power industry." -- Adrian Chen, Electrical Engineer, Moolarben Coal Operations Pty Ltd, Australia
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