Post on 18-Apr-2018
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