Handbook of power systems engineering with power ... · Engineering with Power Electronics Applications ... 1.3.4 MKSrational unitsystem andthevariousMKSpractical units ... Power

Handbookof Power SystemsEngineering with PowerElectronics ApplicationsSecond Edition

Yoshihide Hase

Power System Engineering Consultant, Tokyo, Japan

WILEYAJohn Wiley&Sons, Ltd., Publication

Contents

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

1.1.1 Three-phase single circuit line without overhead grounding wire 1

1.1.2 Three-phase single circuit line with OGW, OPGW 8

1.1.3 Three-phase double circuit line with LR constants 9

1.2 Stray Capacitance of Overhead Transmission Lines 10

1.2.1 Stray capacitance ofthree-phase single circuit line 10

1.2.2 Three-phase single circuit line with OGW 16

1.2.3 Three-phase double circuit line 16

1.3 Working Inductance and Working Capacitance 18

1.3.1 Introduction of working inductance 18

1.3.2 Introduction of working capacitance 20

1.3.3 Special properties of working inductance and workingcapacitance 22

1.3.4 MKS rational unit system and the various MKS practical units

in electrical engineering field 23

1.4 Supplement: Proof of Equivalent Radius r^, = r'/" • w""'/n for a

Multi-bundled Conductor 25

1.4.1 Equivalent radius for inductance calculation 25

1.4.2 Equivalent radius of capacitance calculation 26

Coffee break 1: Electricity, its substance and methodology 27

2 SYMMETRICAL COORDINATE METHOD (SYMMETRICAL COMPONENTS) 29

2.1 Fundamental Concept of Symmetrical Components 29

2.2 Definition of Symmetrical Components 31

2.2.1 Definition 31

2.2.2 Implication of symmetrical components 33

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

viii CONTENTS

2.4 Transmission Lines by Symmetrical Components 36

2.4.1 Single circuit line with LR constants 36

2.4.2 Double circuit line with LR constants 38

2.4.3 Single circuit line with stray capacitance C 41

2.4.4 Double circuit line with C constants 44

2.5 Typical Transmission Line Constants 46

2.5.1 Typical line constants 46

2.5.2 L, C constant values derived from typical travelling-wavevelocity and surge impedance 48

2.6 Generator by Symmetrical Components (Easy Description) 49

2.6.1 Simplified symmetrical equations 49

2.6.2 Reactance of generator 51

2.7 Description of Three-phase Load Circuit by SymmetricalComponents 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: 10G) 54

3.2.1 Condition before the fault 55

3.2.2 Condition of phase a to ground fault 56

3.2.3 Voltages and currents at virtual terminal point f inthe 0-1-2 domain 56

3.2.4 Voltages and currents at an arbitrary point underfault conditions 57

3.2.5 Fault under no-load conditions 58

3.3 Fault Analysis at Various Fault Modes 59

3.4 Conductor Opening 59

3.4.1 Single-phase (phase a) conductor opening 59

3.4.2 Two-phases (phase b, c) conductor opening 65

Coffee break 2: Dawn of the world of electricity, from Coulombto Ampere and Ohm 66

4 FAULT ANALYSIS OF PARALLEL CIRCUIT LINES

(INCLUDING SIMULTANEOUS DOUBLE CIRCUIT FAULT) 69

4.1 Two-phase Circuit and its Symmetrical Coordinate Method 69

4.1.1 Definition and meaning 69

4.1.2 Transformation process of double circuit line 71

4.2 Double Circuit Line by Two-phase Symmetrical Transformation 73

4.2.1 Transformation of typical two-phase circuits 73

4.2.2 Transformation of double circuit line 75

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

4.4 Single Circuit Fault on the Double Circuit Line 80

4.4.1 Line-to-ground fault (1#G) on one-side circuit 80

4.4.2 Various one-side circuit faults 81

4.5 Double Circuit Fault at Single Point f 81

4.5.1 Circuit 1 phase a line-to-ground fault and circuit 2 phases b

and c line-to-line faults at point f 81

4.5.2 Circuit 1 phase a line-to-ground fault and circuit 2 phase b

line-to-ground fault at point f (method 1) 82

CONTENTS ix

4.5.3 Circuit 1 phase a line-to-ground fault and circuit 2 phase bline-to-ground fault at point f (method 2) 83

4.5.4 Various double circuit faults at single point f 85

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

4.6.1 Circuit condition before fault 85

4.6.2 Circuit 1 phase a line-to-ground fault and circuit 2 phase bline-to-ground fault atdifferent points f, F 88

4.6.3 Various double circuit faults at different points 89

5 PER UNIT METHOD AND INTRODUCTION OF TRANSFORMER CIRCUIT 91

5.1 Fundamental Concept of the PU Method 91

5.1.1 PU method of single-phase circuit 92

5.1.2 Unitization of a single-phase three-winding transformer andits equivalent circuit 93

5.2 PU Method for Three-phase Circuits 97

5.2.1 Base quantities by PU method for three-phase circuits 97

5.2.2 Unitization of three-phase circuit equations 98

5.3 Three-phase Three-winding Transformer, its SymmetricalComponents Equations, and the Equivalent Circuit 99

5.3.1 X. — X — A-connected three-phase transformer 99

5.3.2 Three-phase transformers with various winding connections 105

5.3.3 Core structure and the zero-sequence excitation impedance 105

5.3.4 Various winding methods and the effect of delta windings 105

5.3.5 Harmonic frequency voltages/currents in the 0-1-2 domain 108

5.4 Base Quantity Modification of Unitized Impedance 110

5.4.1 Note on % IZ of three-winding transformer 110

5.5 Autotransformer 111

5.6 Numerical Example to Find the Unitized SymmetricalEquivalent Circuit 112

5.7 Supplement: Transformation from Equation 5.18 to Equation 5.19 122

Coffee break 3: Faraday and Henry, the discoverers of the principle ofelectric energy application 124

6 THE a-0-0 COORDINATE METHOD (CLARKE COMPONENTS) ANDITS APPLICATION 127

6.1 Definition of Coordinate Method (a-p-0 Components) 127

6.2 Interrelation Between a-p-Q Components and Symmetrical Components 130

6.2.1 The transformation of arbitrary waveform quantities 130

6.2.2 Interrelation between a—/8—0 and symmetrical components 132

6.3 Circuit Equation and Impedance by the a—f}—0 Coordinate Method 134

6.4 Three-phase Circuit in a—/6—0 Components 134

6.4.1 Single circuit transmission line 134

6.4.2 Double circuit transmission line 136

6.4.3 Generator 137

6.4.4 Transformer impedances and load impedancesin the a-fi-O domain 139

6.5 Fault Analysis by a-/8-0 Components 139

6.5.1 Line-to-ground fault (phase a to ground fault: 1 <p G) 139

6.5.2 The b-c phase line to ground fault 140

6.5.3 Other mode short-circuit faults 141

X CONTENTS

6.5.4 Open-conductor mode faults 141

6.5.5 Advantages of a-fi-0 method 141

7 SYMMETRICAL AND a-p- 0 COMPONENTSAS 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 a—ft—0 Components 147

7.3 Comparison of Transient Analysis by Symmetrical and a—f)—0

Components 150

Coffee break 4: Weber and other pioneers 151

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

Coffee break 5: Maxwell, the greatest scientist of the nineteenth century 161

9 VISUAL VECTOR DIAGRAMS OF VOLTAGES AND CURRENTS UNDER

FAULT CONDITIONS 169

9.1 Three-phase Fault: 30S, 3$G (Solidly Neutral Grounding System,High-resistive Neutral Grounding System) 169

9.2 Phase b-c Fault: 2$S (for Solidly Neutral Grounding System,High-resistive Neutral Grounding System) 170

9.3 Phase a to Ground Fault: 10G (Solidly Neutral Grounding System) 173

9.4 Double Line-to-ground (Phases b and c) Fault:

2#G (Solidly Neutral Grounding System) 175

9.5 Phase a Line-to-ground Fault: 10G (High-resistive Neutral

Grounding System) 178

9.6 Double Line-to-ground (Phases b and c) Fault:

2<pG (High-resistive Neutral Grounding System) 180

10 THEORY OF GENERATORS 183

10.1 Mathematical Description of a Synchronous Generator 183

10.1.1 The fundamental model 183

10.1.2 Fundamental three-phase circuit equations 185

10.1.3 Characteristics of inductances in the equations 187

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

10.2.1 Definition of d-q-0 method 191

10.2.2 Mutual relation of d-q-0, a-b-c, and 0-1 -2 domains 193

10.2.3 Characteristics of d-q-0 domain quantities 194

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

10.3.1 Transformation of generator equations to d-q-0 domain 195

10.3.2 Physical meanings of generator's fundamental equations on

the d-q-0 domain 198

10.3.3 Unitization of generator d-q-0 domain equations 201

10.3.4 Introduction of d-q-0 domain equivalent circuits 206

CONTENTS xi

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

10.5.1 Initial condition just before sudden change 211

10.5.2 Assorted d-axis and q-axis reactances for transient phenomena 212

10.6 Symmetrical Equivalent Circuits of Generators 213

10.6.1 Positive-sequence circuit 214

10.6.2 Negative-sequence circuit 217

10.6.3 Zero-sequence circuit 219

10.7 Laplace-transformed Generator Equations and the Time Constants 220

10.7.1 Laplace-transformed equations 220

10.8 Measuring of Generator Reactances 224

10.8.1 Measuring method of d-axis reactance xj and short-circuit ratio SCR 224

10.8.2 Measuring method of d-axis reactance X2 and xq 227

10.9 Relations Between the d-q-0 and a-j6-0 Domains 228

10.10 Detailed Calculation of Generator Short-circuit Transient Current

under Load Operation 228

10.10.1 Transient short circuit calculation by Laplace transform 228

10.10.2 Transient fault current by sudden three-phase terminal faultunder no-load condition 234

10.11 Supplement 234

10.11.1 Supplement 1: Physical concept of linking flux and flux linkage 234

10.11.2 Supplement 2: Proof of time constants T'd, Tj, Vequation (10.108b) 235

10.11.3 Supplement 3: The equations of the rational function andtheir transformation into expanded sub-sequentialfractional equations 237

10.11.4 Supplement 4: Calculation of the coefficients of equation 10.127 238

10.11.5 Supplement 5: The formulae of the laplace transform

(see also Appendix A) 240

11 APPARENT POWERAND ITS EXPRESSION IN THE 0-1 -2 AND

d-q-0 DOMAINS 241

11.1 Apparent Power and its Symbolic Expression for Arbitrary WaveformVoltages and Currents 241

11.1.1 Definition of apparent power 241

11.1.2 Expansion of apparent power for arbitrary waveform voltagesand currents 243

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

Coffee break 6: Hertz, the discoverer and inventor of radio waves 248

12 GENERATING POWER AND STEADY-STATE STABILITY 251

12.1 Generating Power and the P-S and Q-S Curves 251

12.2 Power Transfer Limit between a Generator and a

Power System Network 254

12.2.1 Equivalency between one-machine to infinite-bus system and

two-machine system 254

12.2.2 Apparent power of a generator 255

xii CONTENTS

12.2.3 Power transfer limit of a generator (steady-state stability) 256

12.2.4 Visual description of a generator's apparent power transfer limit 257

12.2.5 Mechanical analogy of steady-state stability 259

12.3 Supplement: Derivation of Equation 12.17

from Equations 12.15 (2) CD and 12.16 261

13 THE GENERATOR AS ROTATING MACHINERY 263

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

13.1.1 Mutual relation between mechanical input power andelectrical output power 263

13.2 Kinetic Equation of the Generator 265

13.2.1 Dynamic characteristics of the generator(kinetic motion equation) 265

13.2.2 Dynamic equation of generator as an electrical expression 267

13.3 Mechanism of Power Conversion from Rotor Mechanical Power

to Stator Electrical Power 268

13.4 Speed Governors, the Rotating Speed Control Equipmentfor Generators 274

Coffee break 7: Brilliant dawn of the modern electrical age and the newtwentieth century: 1885-1900 277

14 TRANSIENT/DYNAMIC STABILITY, P-Q-V CHARACTERISTICS ANDVOLTAGE STABILITY OF A POWERSYSTEM 281

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

14.1.1 Steady-state stability 281

14.1.2 Transient stability 281

14.1.3 Dynamic stability 282

14.2 Mechanical Acceleration Equation for the Two-generator System andDisturbance Response 282

14.3 Transient Stability and Dynamic Stability (Case Study) 284

14.3.1 Transient stability 284

14.3.2 Dynamic stability 286

14.4 Four-terminal Circuit and the P—S Curve under Fault Conditions and

Operational Reactance 286

14.4.1 Circuit 1 287

14.4.2 Circuit 2 288

14.4.3 Trial calculation of P-S curve 289

14.5 P-Q-V Characteristics and Voltage Stability(Voltage Instability Phenomena) 290

14.5.1 Apparent power at sending terminal and receiving terminal 290

14.5.2 Voltage sensitivity by small disturbance AP, AQ 291

14.5.3 Circle diagram of apparent power 292

14.5.4 P-Q-V characteristics, and P-V and Q-V curves 293

14.5.5 P-Q-V characteristics and voltage instability phenomena 295

14.5.6 V-Q control (voltage and reactive power control) of power systems 298

14.6 Supplement 1: Derivation of AV/AP, AV/AQ 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 CD) 299

CONTENTS

15 GENERATOR CHARACTERISTICS WITH AVR AND STABLE

OPERATION LIMIT 301

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

15.1.1 Inherent transfer function ofgenerator 301

15.1.2 Transfer function ofgenerator+load 303

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

15.3 Response Characteristics of Total System and Generator

Operational Limit 308

15.3.1 Introduction of s functions for AVR + exciter+generator + load 308

15.3.2 Generator operational limit and its p-

q coordinate expression 310

15.4 Transmission Line Charging by Generator with AVR 312

15.4.1 Line charging by generator without AVR 313

15.4.2 Line charging by generator with AVR 313

15.5 Supplement 1: Derivation of ej(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 eo(s) as Function of ef(s) (Equation 15.10 from

Equations 15.8 and 15.9) 314

Coffee break 8: Heaviside, the great benefactor of electrical engineering 315

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

16.2.1 Rating items and capability curve 322

16.2.2 Generator's locus in the p-q coordinate plane under various

operating conditions 325

16.3 Leading Power-factor (Under-excitation Domain) Operation, andUEL Function by AVR 328

16.3.1 Generator as reactive power generator 328

16.3.2 Overheating of stator core end by leading power-factoroperation (low excitation) 329

16.3.3 UEL (under-excitation limit) protection by AVR 333

16.3.4 Operation in the over-excitation domain 334

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

16.4.1 Reactive power distribution for multiple generators and

cross-current control 334

16.4.2 P-f control and V-Q control 336

16.5 Thermal Generators' Weak Points (Negative-sequence Current,

Higher Harmonic Current, Shaft-torsional Distortion) 337

16.5.1 Features of large generators today 337

16.5.2 The thermal generator: smaller /2-withstanding capability 338

16.5.3 Rotor overheating caused by d.c. and higherharmonic currents 340

16.5.4 Transient torsional twisting torque of TG coupled shaft 343

16.6 General Description of Modern Thermal/Nuclear TG Unit 346

16.6.1 Steam turbine (ST) unit for thermal generation 347

16.6.2 Combined Cycle (CC) system with gas/steam turbines 349

16.6.3 ST unit for nuclear generation 351

16.7 Supplement: Derivation of Equation 16.14 from Equation 16.9 ® 351

xiv CONTENTS

17 R-X COORDINATESAND THE THEORY OF DIRECTIONAL

DISTANCE RELAYS 35317.1 Protective Relays, Their Mission and Classification 353

17.1.1 Duties of protective relays 354

17.1.2 Classification of major relays 35417.2 Principle of Directional Distance Relays and R-X Coordinates Plane 355

17.2.1 Fundamental function of directional distance relays 355

17.2.2 R-X coordinates and their relation to P-Q coordinatesand p-q coordinates 356

17.2.3 Characteristics of DZ-Relays 35717.3 Impedance Locus in R-X Coordinates in Case of a Fault

(under No-load Condition) 35817.3.1 Operation of DZ{S)-Relay for phase b-c line-to-line fault \2<j>S) 35817.3.2 Response of DZ(G)-Relay to phase a line-to-ground fault (1#G) 36117.3.3 Response of DZ(G)-Relay against phase b to c (line-to-line)

short circuit fault (2$S) 36317.3.4 DZ-Ry for high-impedance neutral grounded system 365

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

17.4.1 R-X locus under stable and unstable conditions 36517.4.2 Step-out detection and trip-lock of DZ-Relays 369

17.5 Impedance Locus under Faults with Load Flow Conditions 37017.6 Loss of Excitation Detection by DZ-Relays 371

17.6.1 Loss of excitation detection 37117.7 Supplement 1: The Drawing Method for the Locus Z = A/(l - ke'{)

of Equation 17.22 372

17.7.1 The locus for the case 8: constant, k: 0 to oo 37217.7.2 The locus for the case k: constant, 8:0 to 360° 373

17.8 Supplement 2: The Drawing Method for Z = 1 /(I /A + 1 /B)of Equation 17.24 374

Coffee break 9: The symbolic method by complex numbers and

Arthur Kennelly, the prominent pioneer 376

18 TRAVELLING-WAVE (SURGE) PHENOMENA 37918.1 Theory of Travelling-wave Phenomena along Transmission Lines

(Distributed-constants Circuit) 37918.1.1 Waveform equation of a transmission line

(overhead line and cable) and the image of a travelling wave 379

18.1.2 The general solution for voltage and current by Laplacetransforms 385

18.1.3 Four-terminal network equation between two arbitrary points 387

18.1.4 Examination of line constants 38918.2 Approximation of Distributed-constants Circuit and Accuracy

of Concentrated-constants Circuit 39018.3 Behaviour of Travelling Wave at a Transition Point 391

18.3.1 Incident wave, transmitted wave and reflected wave at a

transition point 39118.3.2 Behaviour of voltage and current travelling waves

at typical transition points 39218.4 Surge Overvoltages and their Three Different and Confusing Notations 39518.5 Behaviour of Travelling Waves at a Lightning-strike Point 396

CONTENTS xv

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

18.6.1 Surge impedance of three-phase line 398

18.6.2 Surge analysis of lightning by symmetrical coordinates

(lightning strike on phase a conductor) 399

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

18.8 The Reflection Lattice and Transient Behaviour Modes 402

18.8.1 The reflection lattice 402

18.8.2 Oscillatory and non-oscillatory convergence 404

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

Coffee break 10: Steinmetz, prominent benefactor of circuit theoryand high-voltage technology 408

19 SWITCHING SURGE PHENOMENA BY CIRCUIT-BREAKERS AND

LINE SWITCHES 411

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

19.1.1 Calculation of fault current tripping (single-phase circuit) 411

19.1.2 Calculation of current tripping (double power source circuit) 415

19.2 Calculation of Transient Recovery Voltages Across a Breaker's ThreePoles by 30S Fault Tripping 420

19.2.1 Recovery voltage appearing at the first phase (pole) tripping 421

19.2.2 Transient recovery voltage across a breaker's three polesby 3$S fault tripping 423

19.3 Fundamental Concepts of High-voltage Circuit-breakers 430

19.3.1 Fundamental concept of breakers 430

19.3.2 Terminology of switching phenomena and breaker trippingcapability 431

19.4 Current Tripping by Circuit-breakers: Actual Phenomena 434

19.4.1 Short-circuit current (lagging power-factor current)

tripping 434

19.4.2 Leading power-factor small-current tripping 436

19.4.3 Short-distance line fault tripping (SLF) 440

19.4.4 Current chopping phenomena by tripping small current

with lagging power factor 441

19.4.5 Step-out tripping 443

19.4.6 Current-zero missing 444

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

19.5.1 Principles ofovervoltage caused by breaker closing 444

19.6 Resistive Tripping and Resistive Closing by Circuit-breakers 447

19.6.1 Resistive tripping and resistive closing 447

19.6.2 Standardized switching surge level requested byEHV/UHV breakers 447

19.6.3 Overvoltage phenomena caused by tripping of breakerwith resistive tripping mechanism 448

19.6.4 Overvoltage phenomena caused by closing of breakerwith resistive closing mechanism 451

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

19.7.1 LS-switching surge: the phenomena and mechanism 453

19.7.2 Caused Influence of LS-switching surge 454

xvi CONTENTS

19.8 Supplement 1: Calculation of the Coefficients k-\— /C4 of Equation 19.6 455

19.9 Supplement 2: Calculation of the Coefficients k^-kf, of Equation 19.17 455

Coffee break 11: Fortescue's symmetrical components 457

20 OVERVOLTAGE PHENOMENA 459

20.1 Classification of Overvoltage Phenomena 459

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

20.2.1 Ferranti effect 459

20.2.2 Self-excitation of a generator 461

20.2.3 Sudden load tripping or load failure 462

20.2.4 Overvoltages of unfaulted phases by one line-to-ground fault 463

20.3 Lower Frequency Harmonic Resonant Overvoltages 463

20.3.1 Broad-area resonant phenomena (lower order frequencyresonance) 463

20.3.2 Local area resonant phenomena 465

20.3.3 Interrupted ground fault of cable line in a neutral ungroundeddistribution system 467

20.4 Switching Surges 467

20.4.1 Overvoltages caused by breaker closing (breaker closing surge) 468

20.4.2 Overvoltages caused by breaker tripping (breaker tripping surge) 469

20.4.3 Switching surge by line switches 469

20.5 Overvoltage Phenomena by Lightning Strikes 469

20.5.1 Direct strike on phase conductors (direct flashover) 470

20.5.2 Direct strike on OGW or tower structure (inverse flashover) 470

20.5.3 Induced strokes (electrostatic induced strokes, electromagneticinduced strokes) 471

21 INSULATION COORDINATION 475

21.1 Overvoltages as Insulation Stresses 475

21.1.1 Conduction and insulation 475

21.1.2 Classification ofovervoltages 476

21.2 Fundamental Concept of Insulation Coordination 481

21.2.1 Concept of insulation coordination 481

21.2.2 Specific principles of insulation strength and breakdown 482

21.3 Countermeasures on Transmission Lines to Reduce Overvoltagesand Flashover 483

21.3.1 Adoption of a possible large number of overhead groundingwires (OGWs, OPGWs) 483

21.3.2 Adoption of reasonable allocation and air clearances for

conductors/grounding wires 484

21.3.3 Reduction of surge impedance of the towers 484

21.3.4 Adoption of arcing horns (arcing rings) 484

21.3.5 Tower mounted arrester devices 485

21.3.6 Adoption of unequal circuit insulation (double circuit line) 487

21.3.7 Adoption of high-speed reclosing 487

21.4 Overvoltage Protection at Substations 488

21.4.1 Surge protection by metal-oxide surge arresters 488

21.4.2 Metal-oxide arresters 490

21.4.3 Ratings, classification and selection of arrester? 494

CONTENTS xvii

21.4.4 Separation effects of station arresters 495

21.4.5 Station protection by OGWs, and grounding resistance reduction 497

21.5 Insulation Coordination Details 500

21.5.1 Definition and some principal matters of standards 500

21.5.2 Insulation configuration 502

21.5.3 Insulation withstanding level and BIL, BSL 502

21.5.4 Standard insulation levels and their principles 504

21.5.5 Insulation levels for power systems under 245 kV (Table 21.2A) 504

21.5.6 Insulation levels for power systems over 245 kV (Tables 21.2B and C) 507

21.5.7 Evaluation of degree of insulation coordination 509

21.5.8 Insulation of power cable 511

21.6 Transfer Surge Voltages Through the Transformer, and Generator

Protection 511

21.6.1 Electrostatic transfer surge voltage 511

21.6.2 Generator protection against transfer surge voltages throughtransformer 519

21.6.3 Electromagnetic transfer voltage 520

21.7 Internal High-frequency Voltage Oscillation of TransformersCaused by Incident Surge 520

21.7.1 Equivalent circuit of transformer in EHF domain 520

21.7.2 Transient oscillatory voltages caused by incident surge 521

21.7.3 Reduction of internal oscillatory voltages 525

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

Coffee break 12: Edith Clarke, the prominent woman electrician 530

22 WAVEFORMDISTORTION ANDLOWER ORDER HARMONIC

RESONANCE 531

22.1 Causes and Influences of Waveform Distortion 531

22.1.1 Classification ofwaveform distortion 531

22.1.2 Causes ofwaveform distortion 533

22.2 Fault Current Waveform Distortion Caused on Cable Lines 534

22.2.1 Introduction of transient current equation 534

22.2.2 Evaluation of the transient fault current 537

22.2.3 Waveform distortion and protective relays 540

23 POWER CABLES AND POWER CABLE CIRCUITS 541

23.1 Power Cables and Their General Features 541

23.1.1 Classification 541

23.2 Distinguishing Features of Power Cable 545

23.2.1 Insulation 545

23.2.2 Production process 546

23.2.3 Various environmental layout conditions and requiredwithstanding stresses 547

23.2.4 Metallic sheath circuit and outer-covering insulation 548

23.2.5 Electrical specification and factory testing levels 549

23.3 Circuit Constants of Power Cables 550

23.3.1 Inductances of cables 550

23.3.2 Capacitance and surge impedance of cables 554

xviii CONTENTS

23.4 Metallic Sheath and Outer Covering 55723.4.1 Role of metallic sheath and outer covering 55723.4.2 Metallic sheath earthing methods 558

23.5 Cross-bonding Metallic-shielding Method 55923.5.1 Cross-bonding method 55923.5.2 Surge voltage analysis on the cable sheath circuit and

jointing boxes 56023.6 Surge Voltages: Phenomena Travelling Through a Power Cable 563

23.6.1 Surge voltages at the cable infeed terminal point m 56323.6.2 Surge voltages at the cable outfeed terminal point n 565

23.7 Surge Voltages Phenomena on Cable and Overhead Line JointingTerminal 56623.7.1 Overvoltage behaviour on cable line caused by lightning

surge from overhead line 56623.7.2 Switching surges arising on cable line 567

23.8 Surge Voltages at Cable End Terminal Connected to GIS 568

Coffee break 13: Park's equations, the birth of the d-q-0 method 571

24 APPROACHES FOR SPECIAL CIRCUITS 57324.1 On-load Tap-changing Transformer (LTC Transformer) 57324.2 Phase-shifting Transformer 575

24.2.1 Introduction of fundamental equations 57624.2.2 Application for loop circuit lines 578

24.3 Woodbridge Transformer and Scott Transformer 57924.3.1 Woodbridge winding transformer 57924.3.2 Scottwinding transformer 582

24.4 Neutral Grounding Transformer 58324.5 Mis-connection of Three-phase Orders 585

24.5.1 Case 1: phase a-b-c to a-c-b mis-connection 58524.5.2 Case 2: phase a-b-c to b-c-a mis-connection 587

Coffee break 14: Power system engineering and insulation coordination 589

25 THEORY OF INDUCTION GENERATORS AND MOTORS 59125.1 Introduction of Induction Motors and Their Driving Control 59125.2 Theory of Three-phase Induction Machines |IM) with Wye-connected

Rotor Windings 59225.2.1 Equations of induction machine in obc domain 59225.2.2 dqO domain transformed equations 59625.2.3 Phasor expression of dqO domain transformed equations 60525.2.4 Driving power and torque of induction machines 60625.2.5 Steady-state operation 610

25.3 Squirrel-cage Type Induction Motors 61225.3.1 Circuit equation 61225.3.2 Characteristics of squirrel-cage induction machine 61525.3.3 Torque, air-gap flux, speed and power as basis of

power electronic control 61725.3.4 Start-up operation 62425.3.5 Rated speed operation 62625.3.6 Over speed operation and braking operation 627

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

CONTENTS xix

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

26.5.1 Classification and features of various power semiconductor devices 635

26.5.2 Diodes 637

26.5.3 Thyristors 638

26.5.4 GTO (Gate turn-off thyristors) 639

26.5.5 Bipolar junction transistor (BJT) or power transistor 640

26.5.6 Power MOSFET (metal oxide semiconductor field effect transistor) 641

26.5.7 IGBT (insulated gate bipolar transistors) 642

26.5.8 IPM (intelligent power module) 642

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

27.1.1 Single-phase rectifierwith pure resistive load R 651

27.1.2 Inductive load and the role of series connected inductance L 653

27.1.3 Roles of freewheeling diodes and current smoothing reactors 655

27.1.4 Single-phase diode bridge full-wave rectifier 656

27.1.5 Roles ofvoltage smoothing capacitors 657

27.1.6 Three-phase half-bridge rectifier 658

27.1.7 Current over-lapping 660

27.1.8 Three-phase full-bridge rectifier 661

27.2 AC to DC Controlled Conversion: Rectifier by Thyristors 661

27.2.1 Single-phase half-bridge rectifier by a thyristor 661

27.2.2 Single-phase full-bridge rectifier with thyristors 664

27.2.3 Three-phase full-bridge rectifier by thyristors 667

27.2.4 Higher harmonics and ripple ratio 667

27.2.5 Commutating reactances: effects of source side reactances 670

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

27.3.1 Voltage step-down converter (Buck chopper) 672

27.3.2 Step up (boost) converter (Boost chopper) 674

27.3.3 Buck-boostconverter (step-down/step-up converter) 676

27.3.4 Two-/four-quadrant converter (Composite chopper) 677

27.3.5 Pulse width modulation control (PWM) of a dc-dc converter 678

27.3.6 Multi-phase converter 679

27.4 DC to AC Inverters 680

27.4.1 Overview of inverters 680

27.4.2 Single-phase type inverter 682

27.4.3 Three-phase type inverter 684

27.5 PWM (Pulse Width Modulation) Control of Inverters 687

27.5.1 Principles of PWM (Pulse width modulation) control

(Triangle modulation) 687

27.5.2 Another PWM control schemes (tolerance band control) 690

27.6 AC to AC Converter (Cycloconverter) 691

27.7 Supplement: Transformer Core Flux Saturation (Flux Bias Caused

by DC Biased Current Component) 692

XX CONTENTS

28 POWER ELECTRONICS APPLICATIONS IN UTILITY POWERSYSTEMS

AND SOME INDUSTRIES 69528.1 Introduction 69528.2 Motor Drive Application 695

28.2.1 Concept of induction motor driving control 695

28.2.2 Volts per hertz (V/f) control (or AVAF inverter control) 69728.2.3 Constant torque and constant speed control 70028.2.4 Space vector PWM control of induction motor

(sinusoidal control method) 700

28.2.5 Phasevector PWM control (rotor flux oriented control) 702

28.2.6 d-q- Sequence current PWM control (sinusoidal control practice) 70328.3 Generator Excitation System 70428.4 (Double-fed) Adjustable Speed Pumped Storage Generator-motor Unit 706

28.5 Wind Generation 710

28.6 Small Hydro Generation 71528.7 Solar Generation (Photovoltaic Generation) 716

28.8 Static Var Compensators (SVC: Thyristor Based External

Commutated Scheme) 717

28.8.1 SVC (Static var compensators) 718

28.8.2 TCR (Thyristor controlled reactors) and TCC

(Thyristor controlled capacitors) 719

28.8.3 Asymmetrical control method with PWM control for SVC 721

28.8.4 STATCOM or SVG (Static var generator) 722

28.9 Active Filters 726

28.9.1 Base concept of active filters 726

28.9.2 Active filter by d-q method 727

28.9.3 Vector PWM control based on d-q method 730

28.9.4 Converter modelling as d-q-coordinates Laplace transfer function 730

28.9.5 Active filter by p-q method or by a-jS-method 73228.10 High-Voltage DC Transmission (HVDC Transmission) 734

28.11 FACTS (Flexible AC Transmission Systems) Technology 736

28.11.1 Overview of FACTS 73628.11.2 TCSC (Thyristor-controlled series capacitor) and TPSC

(Thyristor-protected series capacitor) 738

28.12 Railway Applications 74128.12.1 Railway substation systems 741

28.12.2 Electric train engine motor driving systems 742

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