Formerly known as Handbook of Power System Engineering, this second edition provides rigorous revisions to the original treatment of systems analysis together with a substantial new four–chapter section on power electronics applications. Encompassing a whole range of equipment, phenomena, and analytical approaches, this handbook offers a complete overview of power systems and their power electronics applications, and presents a thorough examination of the fundamental principles, combining theories and technologies that are usually treated in separate specialised fields, in a single unified hierarchy.

Key features of this new edition:

- Updates throughout the entire book with new material covering applications to current topics such as blushless generators, speed adjustable pumped storage hydro generation, wind generation, small–hydro generation, solar generation, DC–transmission, SVC, SVG (STATCOM), FACTS, active–filters, UPS and advanced railway traffic applications

- Theories of electrical phenomena ranging from DC and power frequency to lightning–/switching–surges, and insulation coordination now with reference to IEC Standards 2010

- New chapters presenting advanced theories and technologies of power electronics circuits and their control theories in combination with various characteristics of power systems as well as induction–generator/motor driving systems

- Practical engineering technologies of generating plants, transmission lines, sub–stations, load systems and their combined network that includes schemes of high voltage primary circuits, power system control and protection

PREFACE xxi

ACKNOWLEDGEMENTS xxiii

ABOUT THE AUTHOR xxv

INTRODUCTION xxvii

1 OVERHEAD TRANSMISSION LINES AND THEIR CIRCUIT CONSTANTS 1

1.1 Overhead Transmission Lines with LR Constants 1

1.2 Stray Capacitance of Overhead Transmission Lines 10

1.3 Working Inductance and Working Capacitance 18

1.4 Supplement: Proof of Equivalent Radius req () for a Multi–bundled Conductor 25

2 SYMMETRICAL COORDINATE METHOD (SYMMETRICAL COMPONENTS) 29

2.1 Fundamental Concept of Symmetrical Components 29

2.2 Definition of Symmetrical Components 31

2.3 Conversion of Three–phase Circuit into Symmetrical Coordinated Circuit 34

2.4 Transmission Lines by Symmetrical Components 36

2.5 Typical Transmission Line Constants 46

2.6 Generator by Symmetrical Components (Easy Description) 49

2.7 Description of Three–phase Load Circuit by Symmetrical Components 52

3 FAULT ANALYSIS BY SYMMETRICAL COMPONENTS 53

3.1 Fundamental Concept of Symmetrical Coordinate Method 53

3.2 Line–to–ground Fault (Phase a to Ground Fault: 1fG) 54

3.3 Fault Analysis at Various Fault Modes 59

3.4 Conductor Opening 59

4 FAULT ANALYSIS OF PARALLEL CIRCUIT LINES (INCLUDING SIMULTANEOUS DOUBLE CIRCUIT FAULT) 69

4.1 Two–phase Circuit and its Symmetrical Coordinate Method 69

4.2 Double Circuit Line by Two–phase Symmetrical Transformation 73

4.3 Fault Analysis of Double Circuit Line (General Process) 77

4.4 Single Circuit Fault on the Double Circuit Line 80

4.5 Double Circuit Fault at Single Point f 81

4.6 Simultaneous Double Circuit Faults at Different Points f, F on the Same Line 85

5 PER UNIT METHOD AND INTRODUCTION OF TRANSFORMER CIRCUIT 91

5.1 Fundamental Concept of the PU Method 91

5.2 PU Method for Three–phase Circuits 97

5.3 Three–phase Three–winding Transformer, its Symmetrical Components Equations, and the Equivalent Circuit 99

5.4 Base Quantity Modification of Unitized Impedance 110

5.5 Autotransformer 111

5.6 Numerical Example to Find the Unitized Symmetrical Equivalent Circuit 112

5.7 Supplement: Transformation from Equation 5.18 to Equation 5.19 122

6 THE ab0 COORDINATE METHOD (CLARKE COMPONENTS) AND ITS APPLICATION 127

6.1 Definition of ab0 Coordinate Method (ab0 Components) 127

6.2 Interrelation Between ab0 Components and Symmetrical Components 130

6.3 Circuit Equation and Impedance by the ab0 Coordinate Method 134

6.4 Three–phase Circuit in ab0 Components 134

6.5 Fault Analysis by ab0 Components 139

7 SYMMETRICAL AND ab0 COMPONENTS AS ANALYTICAL TOOLS FOR TRANSIENT PHENOMENA 145

7.1 The Symbolic Method and its Application to Transient Phenomena 145

7.2 Transient Analysis by Symmetrical and ab0 Components 147

7.3 Comparison of Transient Analysis by Symmetrical and ab0 Components 150

8 NEUTRAL GROUNDING METHODS 153

8.1 Comparison of Neutral Grounding Methods 153

8.2 Overvoltages on the Unfaulted Phases Caused by a Line–to–ground fault 158

8.3 Arc–suppression Coil (Petersen Coil) Neutral Grounded Method 159

8.4 Possibility of Voltage Resonance 160

9 VISUAL VECTOR DIAGRAMS OF VOLTAGES AND CURRENTS UNDER FAULT CONDITIONS 169

9.1 Three–phase Fault: 3fS, 3fG (Solidly Neutral Grounding System, High–resistive Neutral Grounding System) 169

9.2 Phase b c Fault: 2fS (for Solidly Neutral Grounding System, High–resistive Neutral Grounding System) 170

9.3 Phase a to Ground Fault: 1fG (Solidly Neutral Grounding System) 173

9.4 Double Line–to–ground (Phases b and c) Fault: 2fG (Solidly Neutral Grounding System) 175

9.5 Phase a Line–to–ground Fault: 1fG (High–resistive Neutral Grounding System) 178

9.6 Double Line–to–ground (Phases b and c) Fault: 2fG (High–resistive Neutral Grounding System) 180

10 THEORY OF GENERATORS 183

10.1 Mathematical Description of a Synchronous Generator 183

10.2 Introduction of d q 0 Method (d q 0 Components) 191

10.3 Transformation of Generator Equations from a b c to d q 0 Domain 195

10.4 Generator Operating Characteristics and its Vector Diagrams on d– and q–axes Plane 208

10.5 Transient Phenomena and the Generator s Transient Reactances 211

10.6 Symmetrical Equivalent Circuits of Generators 213

10.7 Laplace–transformed Generator Equations and the Time Constants 220

10.8 Measuring of Generator Reactances 224

10.9 Relations Between the d q 0 and a b 0 Domains 228

10.10 Detailed Calculation of Generator Short–circuit Transient Current under Load Operation 228

10.11 Supplement 234

11 APPARENT POWER AND ITS EXPRESSION IN THE 0 1 2 AND d q 0 DOMAINS 241

11.1 Apparent Power and its Symbolic Expression for Arbitrary Waveform Voltages and Currents 241

11.2 Apparent Power of a Three–phase Circuit in the 0 1 2 Domain 243

11.3 Apparent Power in the d q 0 Domain 246

12 GENERATING POWER AND STEADY–STATE STABILITY 251

12.1 Generating Power and the P d and Q d Curves 251

12.2 Power Transfer Limit between a Generator and a Power System Network 254

12.3 Supplement: Derivation of Equation 12.17 from Equations 12.15st and 12.16 261

13 THE GENERATOR AS ROTATING MACHINERY 263

13.1 Mechanical (Kinetic) Power and Generating (Electrical) Power 263

13.2 Kinetic Equation of the Generator 265

13.3 Mechanism of Power Conversion from Rotor Mechanical Power to Stator Electrical Power 268

13.4 Speed Governors, the Rotating Speed Control Equipment for Generators 274

14 TRANSIENT/DYNAMIC STABILITY, P Q V CHARACTERISTICS AND VOLTAGE STABILITY OF A POWER SYSTEM 281

14.1 Steady–state Stability, Transient Stability, Dynamic Stability 281

14.2 Mechanical Acceleration Equation for the Two–generator System and Disturbance Response 282

14.3 Transient Stability and Dynamic Stability (Case Study) 284

14.4 Four–terminal Circuit and the Pd Curve under Fault Conditions and Operational Reactance 286

14.5 PQV Characteristics and Voltage Stability (Voltage Instability Phenomena) 290

14.6 Supplement 1: Derivation of DV/DP, DV/DQ Sensitivity Equation (Equation 14.20 from Equation 14.19) 298

14.7 Supplement 2: Derivation of Power Circle Diagram Equation (Equation 14.31 from Equation 14.18 s) 299

15 GENERATOR CHARACTERISTICS WITH AVR AND STABLE OPERATION LIMIT 301

15.1 Theory of AVR, and Transfer Function of Generator System with AVR 301

15.2 Duties of AVR and Transfer Function of Generator + AVR 305

15.3 Response Characteristics of Total System and Generator Operational Limit 308

15.4 Transmission Line Charging by Generator with AVR 312

15.5 Supplement 1: Derivation of ed (s), eq(s) as Function of ef (s) (Equation 15.9 from Equations 15.7 and 15.8) 313

15.6 Supplement 2: Derivation of eG(s) as Function of ef (s) (Equation 15.10 from Equations 15.8 and 15.9) 314

16 OPERATING CHARACTERISTICS AND THE CAPABILITY LIMITS OF GENERATORS 319

16.1 General Equations of Generators in Terms of p q Coordinates 319

16.2 Rating Items and the Capability Curve of the Generator 322

16.3 Leading Power–factor (Under–excitation Domain) Operation, and UEL Function by AVR 328

16.4 V Q (Voltage and Reactive Power) Control by AVR 334

16.5 Thermal Generators Weak Points (Negative–sequence Current, Higher Harmonic Current, Shaft–torsional Distortion) 337

16.6 General Description of Modern Thermal/Nuclear TG Unit 346

16.7 Supplement: Derivation of Equation 16.14 from Equation 16.9 351

17 R X COORDINATES AND THE THEORY OF DIRECTIONAL DISTANCE RELAYS 353

17.1 Protective Relays, Their Mission and Classification 353

17.2 Principle of Directional Distance Relays and R X Coordinates Plane 355

17.3 Impedance Locus in R X Coordinates in Case of a Fault (under No–load Condition) 358

17.4 Impedance Locus under Normal States and Step–out Condition 365

17.5 Impedance Locus under Faults with Load Flow Conditions 370

17.6 Loss of Excitation Detection by DZ–Relays 371

17.7 Supplement 1: The Drawing Method for the Locus () of Equation 17.22 372

17.8 Supplement 2: The Drawing Method for () of Equation 17.24 374

18 TRAVELLING–WAVE (SURGE) PHENOMENA 379

18.1 Theory of Travelling–wave Phenomena along Transmission Lines (Distributed–constants Circuit) 379

18.2 Approximation of Distributed–constants Circuit and Accuracy of Concentrated–constants Circuit 390

18.3 Behaviour of Travelling Wave at a Transition Point 391

18.4 Surge Overvoltages and their Three Different and Confusing Notations 395

18.5 Behaviour of Travelling Waves at a Lightning–strike Point 396

18.6 Travelling–wave Phenomena of Three–phase Transmission Line 398

18.7 Line–to–ground and Line–to–line Travelling Waves 400

18.8 The Reflection Lattice and Transient Behaviour Modes 402

18.9 Supplement 1: General Solution Equation 18.10 for Differential Equation 18.9 405

18.10 Supplement 2: Derivation of Equation 18.19 from Equation 18.18 407

19 SWITCHING SURGE PHENOMENA BY CIRCUIT–BREAKERS AND LINE SWITCHES 411

19.1 Transient Calculation of a Single–Phase Circuit by Breaker Opening 411

19.2 Calculation of Transient Recovery Voltages Across a Breaker's Three Poles by 3fS Fault Tripping 420

19.3 Fundamental Concepts of High–voltage Circuit–breakers 430

19.4 Current Tripping by Circuit–breakers: Actual Phenomena 434

19.5 Overvoltages Caused by Breaker Closing (Close–switching Surge) 444

19.6 Resistive Tripping and Resistive Closing by Circuit–breakers 447

19.7 Switching Surge Caused by Line Switches (Disconnecting Switches) 453

19.8 Supplement 1: Calculation of the Coefficients k1k4 of Equation 19.6 455

19.9 Supplement 2: Calculation of the Coefficients k1k6 of Equation 19.17 455

20 OVERVOLTAGE PHENOMENA 459

20.1 Classification of Overvoltage Phenomena 459

20.2 Fundamental (Power) Frequency Overvoltages (Non–resonant Phenomena) 459

20.3 Lower Frequency Harmonic Resonant Overvoltages 463

20.4 Switching Surges 467

20.5 Overvoltage Phenomena by Lightning Strikes 469

21 INSULATION COORDINATION 475

21.1 Overvoltages as Insulation Stresses 475

21.2 Fundamental Concept of Insulation Coordination 481

21.3 Countermeasures on Transmission Lines to Reduce Overvoltages and Flashover 483

21.4 Overvoltage Protection at Substations 488

21.5 Insulation Coordination Details 500

21.6 Transfer Surge Voltages Through the Transformer, and Generator Protection 511

21.7 Internal High–frequency Voltage Oscillation of Transformers Caused by Incident Surge 520

21.8 Oil–filled Transformers Versus Gas–filled Transformers 526

21.9 Supplement: Proof that Equation 21.21 is the Solution of Equation 21.20 529

22 WAVEFORM DISTORTION AND LOWER ORDER HARMONIC RESONANCE 531

22.1 Causes and Influences of Waveform Distortion 531

22.2 Fault Current Waveform Distortion Caused on Cable Lines 534

23 POWER CABLES AND POWER CABLE CIRCUITS 541

23.1 Power Cables and Their General Features 541

23.2 Distinguishing Features of Power Cable 545

23.3 Circuit Constants of Power Cables 550

23.4 Metallic Sheath and Outer Covering 557

23.5 Cross–bonding Metallic–shielding Method 559

23.6 Surge Voltages: Phenomena Travelling Through a Power Cable 563

23.7 Surge Voltages Phenomena on Cable and Overhead Line Jointing Terminal 566

23.8 Surge Voltages at Cable End Terminal Connected to GIS 568

24 APPROACHES FOR SPECIAL CIRCUITS 573

24.1 On–load Tap–changing Transformer (LTC Transformer) 573

24.2 Phase–shifting Transformer 575

24.3 Woodbridge Transformer and Scott Transformer 579

24.4 Neutral Grounding Transformer 583

24.5 Mis–connection of Three–phase Orders 585

25 THEORY OF INDUCTION GENERATORS AND MOTORS 591

25.1 Introduction of Induction Motors and Their Driving Control 591

25.2 Theory of Three–phase Induction Machines (IM) with Wye–connected Rotor Windings 592

25.3 Squirrel–cage Type Induction Motors 612

25.4 Supplement 1: Calculation of Equations (25.17), (25.18), and (25.19) 627

26 POWER ELECTRONIC DEVICES AND THE FUNDAMENTAL CONCEPT OF SWITCHING 629

26.1 Power Electronics and the Fundamental Concept 629

26.2 Power Switching by Power Devices 630

26.3 Snubber Circuit 633

26.4 Voltage Conversion by Switching 635

26.5 Power Electronic Devices 635

26.6 Mathematical Backgrounds for Power Electronic Application Analysis 643

27 POWER ELECTRONIC CONVERTERS 651

27.1 AC to DC Conversion: Rectifier by a Diode 651

27.2 AC to DC Controlled Conversion: Rectifier by Thyristors 661

27.3 DC to DC Converters (DC to DC Choppers) 671

27.4 DC to AC Inverters 680

27.5 PWM (Pulse Width Modulation) Control of Inverters 687

27.6 AC to AC Converter (Cycloconverter) 691

27.7 Supplement: Transformer Core Flux Saturation (Flux Bias Caused by DC Biased Current Component) 692

28 POWER ELECTRONICS APPLICATIONS IN UTILITY POWER SYSTEMS AND SOME INDUSTRIES 695

28.1 Introduction 695

28.2 Motor Drive Application 695

28.3 Generator Excitation System 704

28.4 (Double–fed) Adjustable Speed Pumped Storage Generator–motor Unit 706

28.5 Wind Generation 710

28.6 Small Hydro Generation 715

28.7 Solar Generation (Photovoltaic Generation) 716

28.8 Static Var Compensators (SVC: Thyristor Based External Commutated Scheme) 717

28.9 Active Filters 726

28.10 High–Voltage DC Transmission (HVDC Transmission) 734

28.11 FACTS (Flexible AC Transmission Systems) Technology 736

28.12 Railway Applications 741

28.13 UPSs (Uninterruptible Power Supplies) 745

APPENDIX A MATHEMATICAL FORMULAE 747

APPENDIX B MATRIX EQUATION FORMULAE 751

ANALYTICAL METHODS INDEX 757

COMPONENTS INDEX 759

SUBJECT INDEX 763

YOSHIHIDE HASE, Power System Engineering Consultant, Tokyo, Japan