كتاب Handbook of Power System Engineering

اخوانى واصدقائى اليكم هذا الكتاب
Handbook of Power
System Engineering
Contents
PREFACE xix
ACKNOWLEDGEMENTS xxi
ABOUT THE AUTHOR xxiii
INTRODUCTION xxv
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 of three-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 Supplement: Additional Explanation for Equation 1.27 17
Coffee break 1: Electricity, its substance and methodology 19
2 SYMMETRICAL COORDINATE METHOD
(SYMMETRICAL COMPONENTS) 21
2.1 Fundamental Concept of Symmetrical Components 21
2.2 Definition of Symmetrical Components 23
2.2.1 Definition 23
2.2.2 Implication of symmetrical components 25
2.3 Conversion of Three-phase Circuit into Symmetrical Coordinated Circuit 26
2.4 Transmission Lines by Symmetrical Components 28
2.4.1 Single circuit line with LR constants 28
2.4.2 Double circuit line with LR constants 30
2.4.3 Single circuit line with stray capacitance C 33
2.4.4 Double circuit line with C constants 36
2.5 Typical Transmission Line Constants 38
2.5.1 Typical line constants 38
2.5.2 L, C constant values derived from typical travelling-wave
velocity and surge impedance 40
2.6 Generator by Symmetrical Components (Easy Description) 41
2.6.1 Simplified symmetrical equations 41
2.6.2 Reactance of generator 43
2.7 Description of Three-phase Load Circuit by Symmetrical Components 44
3 FAULT ANALYSIS BY SYMMETRICAL COMPONENTS 45
3.1 Fundamental Concept of Symmetrical Coordinate Method 45
3.2 Line-to-ground Fault (Phase a to Ground Fault: 1fG) 46
3.2.1 Condition before the fault 47
3.2.2 Condition of phase a to ground fault 48
3.2.3 Voltages and currents at virtual terminal point f in the
0–1–2 domain 48
3.2.4 Voltages and currents at an arbitrary point
under fault conditions 49
3.2.5 Fault under no-load conditions 50
3.3 Fault Analysis at Various Fault Modes 51
3.4 Conductor Opening 51
3.4.1 Single phase (phase a) conductor opening 51
3.4.2 Two-phases (phase b, c) conductor opening 57
Coffee break 2: Dawn of the world of electricity, from Coulomb
to Ampe`re and Ohm 58
4 FAULT ANALYSIS OF PARALLEL CIRCUIT LINES
(INCLUDING SIMULTANEOUS DOUBLE CIRCUIT FAULT) 61
4.1 Two-phase Circuit and its Symmetrical Coordinate Method 61
4.1.1 Definition and meaning 61
4.1.2 Transformation process of double circuit line 63
4.2 Double Circuit Line by Two-phase Symmetrical Transformation 65
4.2.1 Transformation of typical two-phase circuits 65
4.2.2 Transformation of double circuit line 67
4.3 Fault Analysis of Double Circuit Line (General Process) 69
4.4 Single Circuit Fault on the Double Circuit Line 70
4.4.1 Line-to-ground fault (1fG) on one side circuit 70
4.4.2 Various one-side circuit faults 73
4.5 Double Circuit Fault at Single Point f 73
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 73
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) 74
4.5.3 Circuit 1 phase a line-to-ground fault and circuit 2 phase b
line-to-ground fault at point f (method 2) 75
4.5.4 Various double circuit faults at single point f 77
4.6 Simultaneous Double Circuit Faults at Different Points f,
F on the Same Line 77
4.6.1 Circuit condition before fault 77
4.6.2 Circuit 1 phase a line-to-ground fault and circuit 2 phase b
line-to-ground fault at different points f, F 80
4.6.3 Various double circuit faults at different points 81
5 PER UNIT METHOD AND INTRODUCTION OF TRANSFORMER CIRCUIT 83
5.1 Fundamental Concept of the PU Method 83
5.1.1 PU method of single phase circuit 84
5.1.2 Unitization of a single phase three-winding transformer
and its equivalent circuit 85
5.2 PU Method for Three-phase Circuits 89
5.2.1 Base quantities by PU method for three-phase circuits 89
5.2.2 Unitization of three-phase circuit equations 90
5.3 Three-phase Three-winding Transformer, its Symmetrical Components
Equations and the Equivalent Circuit 91
5.3.1 f f D-connected three-phase transformer 91
5.3.2 Three-phase transformers with various winding connections 97
5.3.3 Core structure and the zero-sequence excitation impedance 97
5.3.4 Various winding methods and the effect of delta windings 97
5.3.5 Harmonic frequency voltages/currents in the 0–1–2 domain 100
5.4 Base Quantity Modification of Unitized Impedance 101
5.4.1 Note on % IZ of three-winding transformer 102
5.5 Autotransformer 102
5.6 Numerical Example to Find the Unitized Symmetrical
Equivalent Circuit 104
5.7 Supplement: Transformation from Equation 5.18 to Equation 5.19 114
Coffee break 3: Faraday and Henry, the discoverers of the principle
of electric energy application 116
6 The a–b–0 COORDINATE METHOD (CLARKE COMPONENTS)
AND ITS APPLICATION 119
6.1 Definition of a–b–0 Coordinate Method (a–b–0 Components) 119
6.2 Interrelation Between a–b–0 Components and Symmetrical Components 120
6.2.1 The transformation of arbitrary waveform quantities 122
6.2.2 Interrelation between a–b–0 and symmetrical components 123
6.3 Circuit Equation and Impedance by the a–b–0 Coordinate Method 125
6.4 Three-phase Circuit in a–b–0 Components 126
6.4.1 Single circuit transmission line 126
6.4.2 Double circuit transmission line 127
6.4.3 Generator 129
6.4.4 Transformer impedances and load impedances in the
a–b–0 domain 130
6.5 Fault Analysis by a–b–0 Components 131
6.5.1 The b–c phase line to ground fault 131
6.5.2 Other mode short-circuit faults 133
6.5.3 Open-conductor mode faults 133
7 SYMMETRICAL AND a–b–0 COMPONENTS AS ANALYTICAL TOOLS
FOR TRANSIENT PHENOMENA 135
7.1 The Symbolic Method and its Application to Transient Phenomena 135
7.2 Transient Analysis by Symmetrical and a–b–0 Components 137
7.3 Comparison of Transient Analysis by Symmetrical and a–b–0 Components 138
Coffee break 4: Weber and other pioneers 141
8 NEUTRAL GROUNDING METHODS 143
8.1 Comparison of Neutral Grounding Methods 143
8.2 Overvoltages on the Unfaulted Phases Caused by
a Line-to-ground Fault 148
8.3 Possibility of Voltage Resonance 149
8.4 Supplement: Arc-suppression Coil (Petersen Coil)
Neutral Grounded Method 150
9 VISUAL VECTOR DIAGRAMS OF VOLTAGES AND CURRENTS UNDER
FAULT CONDITIONS 151
9.1 Three-phase Fault: 3fS, 3fG (Solidly Neutral Grounding System,
High-resistive Neutral Grounding System) 151
9.2 Phase b–c Fault: 2fS (for Solidly Neutral Grounding System,
High-resistive Neutral Grounding System) 152
9.3 Phase a to Ground Fault: 1fG (Solidly Neutral Grounding System) 155
9.4 Double Line-to-ground (Phases b and c) Fault: 2fG
(Solidly Neutral Grounding System) 157
9.5 Phase a Line-to-ground Fault: 1fG (High-resistive Neutral
Grounding System) 160
9.6 Double Line-to-ground (Phases b and c) Fault: 2fG (High-resistive
Neutral Grounding System) 162
Coffee break 5: Maxwell, the greatest scientist of the nineteenth century 164
10 THEORY OF GENERATORS 169
10.1 Mathematical Description of a Synchronous Generator 169
10.1.1 The fundamental model 169
10.1.2 Fundamental three-phase circuit equations 171
10.1.3 Characteristics of inductances in the equations 173
10.2 Introduction of d–q–0 Method (d–q–0 Components) 177
10.2.1 Definition of d–q–0 method 177
10.2.2 Mutual relation of d–q–0, a–b–c and 0–1–2 domains 179
10.2.3 Characteristics of d–q–0 domain quantities 179
10.3 Transformation of Generator Equations from a–b–c to d–q–0 Domain 181
10.3.1 Transformation of generator equations to d–q–0 domain 181
10.3.2 Unitization of generator d–q–0 domain equations 184
10.3.3 Introduction of d–q–0 domain equivalent circuits 188
10.4 Generator Operating Characteristics and it’s Vector Diagrams
on d-and q-axes plain 190
10.5 Transient Phenomena and the Generator’s Transient Reactances 194
10.5.1 Initial condition just before sudden change 194
10.5.2 Assorted d-axis and q-axis reactances for transient phenomena 195
10.6 Symmetrical Equivalent Circuits of Generators 196
10.6.1 Positive-sequence circuit 197
10.6.2 Negative-sequence circuit 199
10.6.3 Zero-sequence circuit 202
10.7 Laplace-transformed Generator Equations and the Time Constants 202
10.7.1 Laplace-transformed equations 202
10.8 Relations Between the d–q–0 and a–b–0 Domains 206
10.9 Detailed Calculation of Generator Short-circuit Transient Current
under Load Operation 206
10.9.1 Transient fault current by sudden three-phase terminal fault
under no-load condition 211
10.10 Supplement 1: The Equations of the Rational Function and
Their Transformation into Expanded Sub-sequential Fractional Equations 211
10.11 Supplement 2: Calculation of the Coefficients of Equation 10.120 212
10.11.1 Calculation of Equation rk1; k2; k3; k4ffd; k4ff d 212
10.11.2 Calculation of equation 10.120 sk5; k6; k7ff d7 214
10.12 Supplement 3: The Formulae of the Laplace Transform 214
11 APPARENT POWER AND ITS EXPRESSION IN THE 0–1–2
AND d–q–0 DOMAINS 215
11.1 Apparent Power and its Symbolic Expression for Arbitrary
Waveform Voltages and Currents 215
11.1.1 Definition of apparent power 215
11.1.2 Expansion of apparent power for arbitrary waveform
voltages and currents 217
11.2 Apparent Power of a Three-phase Circuit in the 0–1–2 Domain 217
11.3 Apparent Power in the d–q–0 Domain 220
Coffee break 6: Hertz, the discoverer and inventor of radio waves 222
12 GENERATING POWER AND STEADY-STATE STABILITY 223
12.1 Generating Power and the P–d and Q–d Curves 223
12.2 Power Transfer Limit between a Generator and Power System Network 226
12.2.1 Equivalency between one-machine to infinite-bus system
and two-machine system 226
12.2.2 Apparent power of a generator 227
12.2.3 Power transfer limit of a generator (steady-state stability) 228
12.2.4 Visual description of generator’s apparent power transfer limit 229
12.3 Supplement: Derivation of Equation 12.17 231
13 THE GENERATOR AS ROTATING MACHINERY 233
13.1 Mechanical (Kinetic) Power and Generating (Electrical) Power 233
13.1.1 Mutual relation between mechanical input power and
electrical output power 233
13.2 Kinetic Equation of the Generator 235
13.2.1 Dynamic characteristics of the generator
(kinetic motion equation) 235
13.2.2 Dynamic equation of generator as an electrical expression 237
13.2.3 Speed governors, the rotating speed control equipment for
generators 237
Coffee break 7: Heaviside, the great benefactor of electrical engineering 241
14 TRANSIENT/DYNAMIC STABILITY, P–Q–V CHARACTERISTICS
AND VOLTAGE STABILITY OF A POWER SYSTEM 245
14.1 Steady-state Stability, Transient Stability, Dynamic Stability 245
14.1.1 Steady-state stability 245
14.1.2 Transient-state stability 245
14.1.3 Dynamic stability 246
14.2 Mechanical Acceleration Equation for the Two-generator System,
and Disturbance Response 246
14.3 Transient Stability and Dynamic Stability (Case Study) 247
14.3.1 Transient stability 248
14.3.2 Dynamic stability 249
14.4 Four-terminal Circuit and the P–d Curve under Fault Conditions 250
14.4.1 Circuit 1 251
14.4.2 Circuit 2 252
14.4.3 Trial calculation under assumption of x1 ¼ x2 ¼ x; x01
¼ x02
¼ x0 253
14.5 P–Q–V Characteristics and Voltage Stability
(Voltage Instability Phenomena) 254
14.5.1 Apparent power at sending terminal and receiving terminal 254
14.5.2 Voltage sensitivity by small disturbance DP, DQ 255
14.5.3 Circle diagram of apparent power 256
14.5.4 P–Q–V characteristics, and P–V and Q–V curves 257
14.5.5 P–Q–V characteristics and voltage instability phenomena 258
14.6 Supplement 1: Derivation of Equation 14.20 from Equation 14.19 262
14.7 Supplement 2: Derivation of Equation 14.30 from Equation 14.18 s 262
15 GENERATOR CHARACTERISTICS WITH AVR AND STABLE
OPERATION LIMIT 263
15.1 Theory of AVR, and Transfer Function of Generator System with AVR 263
15.1.1 Inherent transfer function of generator 263
15.1.2 Transfer function of generator þ load 265
15.2 Duties of AVR and Transfer Function of Generator þ AVR 267
15.3 Response Characteristics of Total System and
Generator Operational Limit 270
15.3.1 Introduction of s functions for AVR þ exciter þ generator þ load 270
15.3.2 Generator operational limit and its p–q coordinate expression 272
15.4 Transmission Line Charging by Generator with AVR 274
15.4.1 Line charging by generator without AVR 275
15.4.2 Line charging by generator with AVR 275
15.5 Supplement 1: Derivation of Equation 15.9 from Equations 15.7 and 15.8 275
15.6 Supplement 2: Derivation of Equation 15.10 from
Equations 15.8 and 15.9 276
Coffee break 8: The symbolic method by complex numbers and Arthur Kennelly,
the prominent pioneer 277
16 OPERATING CHARACTERISTICS AND THE CAPABILITY
LIMITS OF GENERATORS 279
16.1 General Equations of Generators in Terms of p–q Coordinates 279
16.2 Rating Items and the Capability Curve of the Generator 282
16.2.1 Rating items and capability curve 282
16.2.2 Generator’s locus in the p–q coordinate plane under various
operating conditions 285
16.3 Leading Power-factor (Under-excitation Domain) Operation,
and UEL Function by AVR 287
16.3.1 Generator as reactive power generator 287
16.3.2 Overheating of stator core end by leading power-factor
operation (low excitation) 289
16.3.3 UEL (under-excitation limit) protection by AVR 292
16.3.4 Operation in the over-excitation domain 293
16.4 V–Q (Voltage and Reactive Power) Control by AVR 293
16.4.1 Reactive power distribution for multiple generators and
cross-current control 293
16.4.2 P–f control and V–Q control 295
16.5 Thermal Generators’ Weak Points (Negative-sequence Current,
Higher Harmonic Current, Shaft-torsional Distortion) 296
16.5.1 Features of large generators today 296
16.5.2 The thermal generator: smaller I2-withstanding capability 297
16.5.3 Rotor overheating caused by d.c. and higher harmonic
currents 299
16.5.4 Transient torsional twisting torque of TG coupled shaft 302
16.6 General Description of Modern Thermal/Nuclear TG Unit 305
16.6.1 Steam turbine (ST) unit for thermal generation 305
16.6.2 Combined cycle system with gas/steam turbines 306
16.6.3 ST unit for nuclear generation 309
16.7 Supplement: Derivation of Equation 16.14 310
17 R–X COORDINATES AND THE THEORY OF DIRECTIONAL
DISTANCE RELAYS 313
17.1 Protective Relays, Their Mission and Classification 313
17.1.1 Duties of protective relays 314
17.1.2 Classification of major relays 314
17.2 Principle of Directional Distance Relays and R–X Coordinates Plane 315
17.2.1 Fundamental function of directional distance relays 315
17.2.2 R–X coordinates and their relation to P–Q coordinates and p–q
coordinates 316
17.2.3 Characteristics of DZ-Rys 317
17.3 Impedance Locus in R–X Coordinates in Case of a Fault
(under No-load Condition) 318
17.3.1 Operation of DZ(S)-Ry for phase b–c line-to-line fault ð2fSÞ 318
17.3.2 Response of DZ(G)-Ry to phase a line-to-ground fault ð1fGÞ 321
17.4 Impedance Locus under Normal States and Step-out Condition 325
17.4.1 R–X locus under stable and unstable conditions 325
17.4.2 Step-out detection and trip-lock of DZ-Rys 328
17.5 Impedance Locus under Faults with Load Flow Conditions 329
17.6 Loss of Excitation Detection by DZ-Rys 330
17.6.1 Loss of excitation detection 330
17.7 Supplement 1: The Drawing Method for the Locus _ Z ¼ _A =ð1 kejdÞ
of Equation 17.22 332
17.7.1 The locus for the case d: constant, k:0 to 1 332
17.7.2 The locus for the case k: constant, d: 0 to 360 332
17.8 Supplement 2: The Drawing Method for _Z ¼ 1=ð1=_A þ 1=_BÞ
of Equation 17.24 334
18 TRAVELLING-WAVE (SURGE) PHENOMENA 339
18.1 Theory of Travelling-wave Phenomena along Transmission Lines
(Distributed-constants Circuit) 339
18.1.1 Waveform equation of a transmission line
(overhead line and cable) and the image of a travelling wave 339
18.1.2 The general solution for voltage and current
by Laplace transforms 345
18.1.3 Four-terminal network equation between two arbitrary points 346
18.1.4 Examination of line constants 348
18.2 Approximation of Distributed-constants Circuit and Accuracy
of Concentrated-constants Circuit 349
18.3 Behaviour of Travelling Wave at a Transition Point 351
18.3.1 Incident, transmitted and reflected waves at a transition point 351
18.3.2 Behaviour of voltage and current travelling waves at typical
transition points 352
18.4 Behaviour of Travelling Waves at a Lightning-strike Point 354
18.5 Travelling-wave Phenomena of Three-phase Transmission Line 356
18.5.1 Surge impedance of three-phase line 356
18.5.2 Surge analysis by symmetrical coordinates
(lightning strike on phase a conductor) 357
18.6 Line-to-ground and Line-to-line Travelling Waves 358
18.7 The Reflection Lattice and Transient Behaviour Modes 361
18.7.1 The reflection lattice 361
18.7.2 Oscillatory and non-oscillatory convergence 362
18.8 Supplement 1: General Solution Equation 18.10 for
Differential Equation 18.9 362
18.9 Supplement 2: Derivation of Equation 18.19 from Equation 18.18 363
19 SWITCHING SURGE PHENOMENA BY CIRCUIT-BREAKERS
AND LINE SWITCHES 365
19.1 Transient Calculation of a Single Phase Circuit by Breaker Opening 365
19.1.1 Calculation of fault current tripping (single phase circuit) 365
19.1.2 Calculation of current tripping (double power source circuit) 369
19.2 Calculation of Transient Recovery Voltages Across a Breaker’s
Three Poles by 3fS Fault Tripping 374
19.2.1 Recovery voltage appearing at the first phase (pole) tripping 375
19.2.2 Transient recovery voltage across a breaker’s three poles
by 3fS fault tripping 377
19.3 Fundamental Concepts of High-voltage Circuit-breakers 384
19.3.1 Fundamental concept of breakers 384
19.3.2 Terminology of switching phenomena and breaker
tripping capability 385
19.4 Actual Current Tripping Phenomena by Circuit-breakers 387
19.4.1 Short-circuit current (lagging power-factor current) tripping 387
19.4.2 Leading power-factor small-current tripping 389
19.4.3 Short-distance line fault tripping (SLF)19.4.4 Current chopping phenomena by tripping small current
with lagging power factor 394
19.4.5 Step-out tripping 396
19.4.6 Current-zero missing 396
19.5 Overvoltages Caused by Breaker Closing (Close-switching Surge) 397
19.5.1 Principles of overvoltage caused by breaker closing 397
19.6 Resistive Tripping and Resistive Closing by Circuit-breakers 399
19.6.1 Resistive tripping and closing 399
19.6.2 Overvoltage phenomena caused by tripping of breaker
with resistive tripping mechanism 401
19.6.3 Overvoltage phenomena caused by closing of breaker
with resistive closing mechanism 403
19.7 Switching Surge Caused by Line Switches (Disconnecting Switches) 406
19.7.1 LS switching surge: the mechanism appearing 407
19.8 Supplement 1: Calculation of the Coefficients k1k4 of Equation 19.6 408
19.9 Supplement 2: Calculation of the Coefficients k1k6 of Equation 19.17 408
Coffee break 10: Fortescue’s symmetrical components 409
20 OVERVOLTAGE PHENOMENA 411
20.1 Classification of Overvoltage Phenomena 411
20.2 Fundamental (Power) Frequency Overvoltages
(Non-resonant Phenomena) 411
20.2.1 Ferranti effect 411
20.2.2 Self-excitation of a generator 413
20.2.3 Sudden load tripping or load failure 414
20.2.4 Overvoltages of unfaulted phases by one line-to-ground fault 415
20.3 Lower Frequency Harmonic Resonant Overvoltages 415
20.3.1 Broad-area resonant phenomena
(lower order frequency resonance) 415
20.3.2 Local area resonant phenomena 417
20.3.3 Interrupted ground fault of cable line in a neutral
ungrounded distribution system 419
20.4 Switching Surges 419
20.4.1 Overvoltages caused by breaker closing (breaker closing surge) 420
20.4.2 Overvoltages caused by breaker tripping (breaker tripping surge) 421
20.4.3 Switching surge by line switches 421
20.5 Overvoltage Phenomena by Lightning Strikes 421
20.5.1 Direct strike on phase conductors (direct flashover) 422
20.5.2 Direct strike on OGW or tower structure (inverse flashover) 422
20.5.3 Induced strokes (electrostatic induced strokes,
electromagnetic induced strokes) 423
21 INSULATION COORDINATION 425
21.1 Overvoltages as Insulation Stresses 425
21.1.1 Conduction and insulation 425
21.1.2 Classification of overvoltages 426
21.2 Fundamental Concept of Insulation Coordination 431
21.2.1 Concept of insulation coordination 431
21.2.2 Specific principles of insulation strength and breakdown 431
21.3 Countermeasures on Transmission Lines to Reduce Overvoltages
and Flashover 432
21.3.1 Countermeasures 433
21.4 Overvoltage Protection at Substations 436
21.4.1 Surge protection by metal–oxide surge arresters 436
21.4.2 Separation effects of station arresters 441
21.4.3 Station protection by OGWs, and grounding resistance reduction 443
21.5 Insulation Coordination Details 446
21.5.1 Definition and some principal matters of standards 446
21.5.2 Insulation configuration 447
21.5.3 Insulation withstanding level and BIL, BSL 449
21.5.4 Standard insulation levels and the principles 450
21.5.5 Comparison of insulation levels for systems under
and over 245 kV 450
21.6 Transfer Surge Voltages Through the Transformer, and
Generator Protection 456
21.6.1 Electrostatic transfer surge voltage 456
21.6.2 Generator protection against transfer surge voltages through
transformer 464
21.6.3 Electromagnetic transfer voltage 465
21.7 Internal High-frequency Voltage Oscillation of Transformers
Caused by Incident Surge 465
21.7.1 Equivalent circuit of transformer in EHF domain 465
21.7.2 Transient oscillatory voltages caused by incident surge 465
21.7.3 Reduction of internal oscillatory voltages 470
21.8 Oil-filled Transformers Versus Gas-filled Transformers 471
21.9 Supplement: Proof that Equation 21.21 is the solution of Equation 21.20 473
Coffee break 11: Edith Clarke, the prominent woman electrician 474
22 WAVEFORM DISTORTION AND LOWER ORDER HARMONIC
RESONANCE 475
22.1 Causes and Influences of Waveform Distortion 475
22.1.1 Classification of waveform distortion 475
22.1.2 Causes of waveform distortion 477
22.2 Fault Current Waveform Distortion Caused on Cable Lines 478
22.2.1 Introduction of transient current equation 478
22.2.2 Evaluation of the transient fault current 481
22.2.3 Waveform distortion and protective relays 484
23 POWER CABLES 485
23.1 Power Cables and Their General Features 485
23.1.1 Classification 485
23.1.2 Unique features and requirements of power cables 488
23.2 Circuit Constants of Power Cables 491
23.2.1 Inductances of cables 491
23.2.2 Capacitance and surge impedance of cables 495
23.3 Metallic Sheath and Outer Covering 498
23.3.1 Role of metallic sheath and outer covering 498
23.3.2 Metallic sheath earthing methods 499
23.4 Cross-bonding Metallic-shielding Method 500
23.4.1 Cross-bonding method 500
23.4.2 Surge voltage analysis on the cable sheath circuit
and jointing boxes 501
23.5 Surge Voltages Arising on Phase Conductors and Sheath Circuits 504
23.5.1 Surge voltages at the cable connecting point m 504
23.5.2 Surge voltages at the cable terminal end point n 506
23.6 Surge Voltages on Overhead Line and Cable Combined Networks 507
23.6.1 Overvoltage behaviour on cable line caused by lightning
surge from overhead line 507
23.6.2 Switching surges arising on cable line 508
23.7 Surge Voltages at Cable End Terminal Connected to GIS 509
Coffee break 12: Park’s equations, the birth of the d–q–0 method 512
24 APPROACHES FOR SPECIAL CIRCUITS 513
24.1 On-load Tap-changing Transformer (LTC Transformer) 513
24.2 Phase-shifting Transformer 515
24.2.1 Introduction of fundamental equations 516
24.2.2 Application for loop circuit line 518
24.3 Woodbridge Transformer and Scott Transformer 519
24.3.1 Woodbridge winding transformer 519
24.3.2 Scott winding transformer 522
24.4 Neutral Grounding Transformer 522
24.5 Mis-connection of Three-phase Orders 524
24.5.1 Cases 524
Coffee break 13: Power system engineering and insulation coordination 529
APPENDIX A – MATHEMATICAL FORMULAE 531
APPENDIX B – MATRIX EQUATION FORMULAE 533
ANALYTICAL METHODS INDEX 539
COMPONENTS INDEX 541
SUBJECT INDEX 545
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