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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