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Electrical Design of Overhead Power Transmission Lines Masoud Farzaneh Shahab Farokhi William A. Chisholm
Mc Graw Hill New York Lisbon
Chicago
London Milan
Seoul
Madrid
San Francisco Mexico
New Delhi
Singapore Sydney
City
San Juan Toronto
Contents Preface
xiii
Acknowledgments Chapter
1
xv
Introduction
1
1.1
1
1.2
History of Electric Power Systems Organization of Modern Electric Power
2
Systems
1.3 Modern Transmission 1.4 1.5
Components
System Alternatives
...
of Overhead Transmission Lines
6
of the Book
8
Organization 1.5.1 The Learning Objective Initiative 1.5.2
8
Links to Industrial Resources and Standards
1.5.3
9
Level of Treatment
9
1: Introduction
1.5.4
Chapter
1.5.5
Chapter 2:
AC Circuits and
10
Sequence
Circuits of Power Networks
1.5.6 1.5.7
Chapter 3:
Matrix Methods in
AC Power
System Analysis
10 11
Chapter 4: Overhead Transmission Line Parameters
1.5.8
11
Chapter 5: Modeling of 11
Transmission Lines 1.5.9
6: AC Power-Flow
Chapter Analysis Using Iterative Methods 1.5.10 Chapter 7: Symmetrical Faults 1.5.11 Chapter 8: Unsymmetrical Faults 1.5.12
Chapter 9:
11 12
12
Control of Voltage and
Power Flow
12
1.5.13
Chapter 10: Stability in AC Networks
1.5.14
Chapter 11: HVDC
1.5.15
Chapter Chapter
1.5.16
Transmission
12: AC-Corona Effects 13
Lightning
Chapter Chapter
12 12 13
13
14: Transmission Line
Insulation and Coordination 1.5.18
..
Performance
of Transmission Lines 1.5.17
3
15:
Ampacity
13
of
Overhead Line Conductors
14
V
yj
Electrical
Chapter
2
Design of Overhead Power Transmission
AC Circuits and
Sequence
Circuits of
Power Networks 2.1
Introduction
2.2
Single-Phase
2.3
2.4
15 15 Circuits
Power in
Single-Phase Circuits
2.2.2
Complex
Power
2.3.1
Balanced Three-Phase Circuits
22
2.3.2
Unbalanced Three-Phase Circuits
27
Single-Line Diagram Per-Unit
3
and Per-Phase
Presentation
33
Representation
35
Definition
35
Advantages
of Per-Unit Presentation
...
36
Symmetrical Sequence Impedance of Power
Chapter
19 22
2.5.2
2.7
15
Three-Phase Circuits
2.5.1
2.6
15
2.2.1
Equivalent Circuit 2.5
Lines
System Components Load
39
2.6.1
Symmetrical
2.6.2
Synchronous
2.6.3
Power Transformers
46
2.6.4
Transmission Lines
49
39
Impedances
Generators
44
Sequence Networks
50
Problems
52
References
53
Matrix Methods in AC Power
System
Analysis 3.1 3.2
55
Introduction
Representation
55 of Generators
and
Impedances Analysis and Bus-ittance Matrix, Ybus Loop Analysis and Bus-Impedance
55
3.3 Bus 3.4
Matrix, '
3.5
56
Z.
60
bus
Node Elimination
3.6 Thevenin's
by Kron Reduction
63
Equivalent Impedance and
Elements of Z.
Matrix
64
^>us
3.7
3.8
Modifications of Z. ^>U5
Algorithm
for Direct Construction of
Problems
Chapter
4
70 73
Zbus
79
References
80
Overhead Transmission Line Parameters
81
4.1
Introduction
81
4.2
Resistance
81
4.2.1
DC Resistance
82
4.2.2
Alternating-Current (AC) Resistance
4.3
...
83
Inductance
84
4.3.1
88
Two-Wire Solid-Conductor Line
Contents
4.3.2
Composite
Conductor
Using 90
Geometric Mean Radius 4.3.3
Three-Phase Lines with Conductor
4.3.4
4.4
93
Three-Phase Lines with Conductor
Equal
Spacing Unequal
94
Spacing Groups of Conductors
4.3.5
Lines with
4.3.6
Double-Circuit Lines
4.3.7
Earth Return
96 98 101
101
Capacitance 4.4.1
Two-Wire Solid-Conductor Line
4.4.2
Three-Phase Lines with
103
Equal
Conductor Spacing Conductor
Unequal 105
Spacing
4.4.4
Bundled Conductor
4.4.5
Transmission Lines with Neutral
4.4.6
Chapter 5
104
Three-Phase Lines with
4.4.3
Using
106
GMR
Conductor and Earth Return
107
Double-Circuit Lines
115
Problems
116
References
117
Modeling of Transmission
119
Lines
119
5.1
Introduction
5.2
Transmission Line Representation
as a
119
Two-Port Network
121
5.3 Short Transmission Lines 5.4 5.5
Long 5.5.2 5.5.3
Chapter
6
130
Transmission Lines
5.5.1
5.6
126
Medium Transmission Lines
Exponential Hyperbolic
130
Form
133
Form
140
n-Circuit
Equivalent through a Transmission
Power Flow
Line
....
141
5.6.1
Maximum Power Flow
141
5.6.2
Surge-Impedance Loading
143
5.6.3
Ferranti Effect
146
5.6.4
Transmission Line
148
Loadability
Problems
151
References
152
AC Power-Flow
Analysis Using
Iterative
Methods
153
6.1
Introduction
153
6.2
Power-Flow Problem
153 156
6.3 The Gauss-Seidel Method 6.4 6.5
The
168
Method
Newton-Raphson Decoupled Newton-Raphson
Power Flow
....
179
vii
vijj
Electrical Design of Overhead Power Transmission Lines
6.6
Fast
Decoupled Newton-Raphson
Power Flow
181
Problems
184
References
Chapter
7
185
Symmetrical
Faults
187
7.1
Introduction
187
7.2
Fault in
a
188
7.3
Fault in
an
7.4
Series R-L Circuit Unloaded Transmission
Line with
a
Fault in
Loaded Transmission Line
with
a
7.5.2
Single Synchronous
Machine
Single Synchronous Machine
7.5 Fault in 7.5.1
a
a
Network
Fault Calculation
Using Synchronous
Machine Internal
Voltage Using the Thevenin
Equivalent Circuit
Chapter
8
Using Impedance Matrix Zbus
the Bus
208
Problems
217
References
218
Unsymmetrical Faults
219
8.1
219
Introduction
Types of Unsymmetrical Faults 8.3 Fault Calculation Using Interconnection of
Sequence
Networks
219
221
8.3.1
Single
8.3.2
Line-to-Line (L-L) Fault
8.3.3
Double Line-to-Ground (L-L-G)
Line-to-Ground (L-G) Fault
Fault 8.3.4
9
203
206
Fault Calculation
8.2
Chapter
200
203
Fault Calculation
7.5.3
193
224
230 233
Open-Conductor
Fault
236
Problems
240
References
241
Control of
Voltage and Power Flow
9.1
Introduction
9.2
Generation and
243
Absorption
of Reactive
Power
243
9.2.1
Loads
9.2.2
Overhead Transmission Lines
9.2.3
Underground
9.2.4
Power Transformers
244
Cables
9.2.5
Capacitor
9.2.6
Shunt Reactors
9.2.7
243
Banks
Machines
244 244 244 244 244
Series
Synchronous Compensation
244
9.3 9.4
Shunt
Compensation
251
9.4.1
Shunt
251
Capacitors
246
Contents
9.4.2 9.5
Shunt Reactors
254
Voltage Control Methods 9.5.1
256
Generator's Excitation Control
9.5.2
9.5.3
System Injection of Reactive Power Tap-Changing and Regulating
256
Transformers
259
Problems
266
References
Chapter
10
Stability
267
in AC Networks
10.1
Introduction
10.2
of
Dynamics
269 269
a Synchronous Swing Equation Steady-State Stability
Machine
and 10.3
270 276
10.4 Transient Stability 10.4.1
Equal-Area
280 Criterion
10.4.2 Numerical Solution of 10.5
282
Swing Equation
301
Stability Improvement Techniques
307
10.5.1
High-Speed Reclosing Single Pole Operation of Circuit
307
Breakers
307
Increasing Steady-State Stability Limit
307
10.5.2
10.5.3
10.5.4 Fast Fault
Clearing
10.5.5 Fast Excitation
10.5.6
Chapter
257
Systems
307 307
FastValving
307
10.5.7 HVDC Links
308
Problems
308
References
309
11 HVD C Transmission
Systems and
FACTS Devices
311
11.1 Introduction
311
of HVDC
11.2
History
11.3
Features and Drawbacks
Applications
11.4 Converters
314
11.4.1
Rectifiers
316
11.4.2
Inverters
327
11.5 HVDC Links 11.5.1 11.5.2 11.5.3
11.6
311 313
Configurations Operation and Control Filters and Capacitor Banks
329 329
331 334
11.5.4 Back-to-Back Converter Stations
334
FACTS
335
11.6.1
336
Thyristor-Controlled Controllers
11.6.2 Converter-Based Controllers
338
ix
X
Electrical Design of Overhead Power Transmission Lines
Chapter
Problems
340
References
341
12 Corona and Electric Field Effects of Transmission Lines
343
12.1
343
Introduction
12.2 Corona Characteristics 12.3 Calculation of Corona
344
Inception
on
Single Conductors
345
12.4 Calculation of Surface Gradient
on
Bundle Conductors
351
12.5 Power Loss
355
12.6
357
Electromagnetic Interference 12.6.1
Radio Interference
359
12.6.2 Television Interference
12.6.3 Interference with Radio
360
Digital
Systems
362
12.7 Audible Noise
362
12.8 Corona Wind and Vibration Effects
364
12.9 Corona
364
Testing
12.10 Evolution of EHV and UHV Transmission
366
Systems
Problems
367
References
367
Chapter 13 Lightning Performance of Transmission Lines 13.1
13.2
369
Introduction
Lightning
369
Characteristics
13.3 Statistics of
Lightning
369
Stroke
Peak Currents
13.4
Interception
372
of Flashes
by
Transmission
Lines 13.5
376
Lightning
Protection
379
Concepts
13.6 Overhead Ground wire
Shielding
of
Transmission Lines
382
13.6.1
Overhead Groundwire Conductors
13.6.2
Computation of Shielding Failure Rate
13.6.3
Computation
Shielding
Failure
Mitigation
390 of Shielding
Failure Flashover Rate 13.7
384 385
of
Flashover Rate 13.6.4 Arrester
...
391
Grounding
of ing Structures
395
13.7.1
and Touch Potentials
395
Step
13.7.2 Three-Terminal Earth Resistance
Testing: Fall of Potential Method
397
Contents
13.7.3 Three-Terminal Earth Resistance
Testing: Oblique Method 13.7.4 Relation between Soil Resistivity
399 400
and Resistance 13.8
Computation
of Back-Flashover Rate
13.8.1 Calculation of Coupled on
403
Voltage 404
Insulated Phases
13.8.2 Calculation of
Voltage Rise from 405
Tower Inductance Rise from
13.8.3 Calculation of Tower
Voltage Footing Impedance
406
13.8.4 Calculation of Back-Flashover Rate
Chapter
...
409
Problems
411
References
412
14 Coordination of Transmission-Line
Insulation
415
14.1
415
Introduction
14.2 Statistical Distributions for Insulation Coordination
416
14.2.1 Classification of a Distribution of Data
416
14.2.2 The Normal Distribution for
Flashover of a
Single
Insulator
419
14.2.3 The Normal Distribution for Flashover of
Any of Several 422
Insulators in Parallel 14.2.4 The
Log-Normal
Distribution
423
14.2.5 The Weibull Distribution
426
14.2.6 The Gumbel Distribution
428
14.3 Statistical
Electrical
Properties Strength
of 429
14.3.1 The Flashover Process in Air 14.3.2
Switching Impulse
Strength
across
429
Flashover 431
Air Gaps
System Voltage Flashover Strength across Air Gaps Lightning Impulse Flashover Strength across Insulators
14.3.3 Power 14.3.4
14.3.5 The AC Flashover Process
435 436
across a
Wet, Polluted Insulator Surface
438
14.3.6 The AC Flashover Process across an
Iced, 14.4 Statistical
Polluted Insulator Surface
Properties
443
of Electrical and
Environmental Stresses
445
14.4.1
445
Switching Surge 14.4.2 Lightning Surge
447
xi
Electrical
Design of Overhead Power Transmission Lines 14.4.3 Insulator Surface Contamination 14.4.4
14.5
451
Precipitation Conductivity
452
14.4.5 Climate Factors
452
Insulation Coordination
453
14.5.1
Deterministic Method: Insulator
Leakage
Distance in Polluted Areas
...
453
14.5.2 Statistical Method with One Stress Variable: 14.5.3
456
Switching Surge
Deterministic/Statistical Method for Two Variables: Wind
Swing, 459
Switching Surge 14.5.4 Statistical Method for Two
Uncorrelated Variables: Ground Resistance and
Lightning
Peak Current
464
14.5.5 Statistical Method for Three
Uncorrelated Variables: Insulator
Pollution,
Ice
Conductivity,
and Ice
Accretion Thickness
:er
15
468
Problems
470
References
471
Ampacity 15.1
of Overhead Line Conductors
473
Introduction
473
15.2 Conductor Materials for Overhead Transmission Lines
474
15.3 Stranded Conductors for Transmission Lines
475
15.4 Cross-Sections of ACSR Conductors
477
15.5 DC Resistance of ACSR Conductors
481
15.6 AC Resistance of ACSR Conductors
482
15.7 Mechanical
Properties
of
ACSR Conductors 15.8
Sag-Tension
15.9 Effect of
15.10 15.11
485
Behavior in
a
Single Span and Tension
Temperature Sag Sag-Tension Behavior in Multiple Spans The Line Condition Survey and Line Rating on
492 ...
495 498 504
15.12 Calculation of Ampacity
506
15.13 Conductors for
512
Improved Ampacity
Problems
513
References
515
List of Index
Symbols
and Abbreviations
517 527
Mc Graw Hill New York Lisbon
Chicago
London Milan
Seoul
Madrid
San Francisco Mexico
New Delhi
Singapore Sydney
City
San Juan Toronto
Contents Preface
xiii
Acknowledgments Chapter
1
xv
Introduction
1
1.1
1
1.2
History of Electric Power Systems Organization of Modern Electric Power
2
Systems
1.3 Modern Transmission 1.4 1.5
Components
System Alternatives
...
of Overhead Transmission Lines
6
of the Book
8
Organization 1.5.1 The Learning Objective Initiative 1.5.2
8
Links to Industrial Resources and Standards
1.5.3
9
Level of Treatment
9
1: Introduction
1.5.4
Chapter
1.5.5
Chapter 2:
AC Circuits and
10
Sequence
Circuits of Power Networks
1.5.6 1.5.7
Chapter 3:
Matrix Methods in
AC Power
System Analysis
10 11
Chapter 4: Overhead Transmission Line Parameters
1.5.8
11
Chapter 5: Modeling of 11
Transmission Lines 1.5.9
6: AC Power-Flow
Chapter Analysis Using Iterative Methods 1.5.10 Chapter 7: Symmetrical Faults 1.5.11 Chapter 8: Unsymmetrical Faults 1.5.12
Chapter 9:
11 12
12
Control of Voltage and
Power Flow
12
1.5.13
Chapter 10: Stability in AC Networks
1.5.14
Chapter 11: HVDC
1.5.15
Chapter Chapter
1.5.16
Transmission
12: AC-Corona Effects 13
Lightning
Chapter Chapter
12 12 13
13
14: Transmission Line
Insulation and Coordination 1.5.18
..
Performance
of Transmission Lines 1.5.17
3
15:
Ampacity
13
of
Overhead Line Conductors
14
V
yj
Electrical
Chapter
2
Design of Overhead Power Transmission
AC Circuits and
Sequence
Circuits of
Power Networks 2.1
Introduction
2.2
Single-Phase
2.3
2.4
15 15 Circuits
Power in
Single-Phase Circuits
2.2.2
Complex
Power
2.3.1
Balanced Three-Phase Circuits
22
2.3.2
Unbalanced Three-Phase Circuits
27
Single-Line Diagram Per-Unit
3
and Per-Phase
Presentation
33
Representation
35
Definition
35
Advantages
of Per-Unit Presentation
...
36
Symmetrical Sequence Impedance of Power
Chapter
19 22
2.5.2
2.7
15
Three-Phase Circuits
2.5.1
2.6
15
2.2.1
Equivalent Circuit 2.5
Lines
System Components Load
39
2.6.1
Symmetrical
2.6.2
Synchronous
2.6.3
Power Transformers
46
2.6.4
Transmission Lines
49
39
Impedances
Generators
44
Sequence Networks
50
Problems
52
References
53
Matrix Methods in AC Power
System
Analysis 3.1 3.2
55
Introduction
Representation
55 of Generators
and
Impedances Analysis and Bus-ittance Matrix, Ybus Loop Analysis and Bus-Impedance
55
3.3 Bus 3.4
Matrix, '
3.5
56
Z.
60
bus
Node Elimination
3.6 Thevenin's
by Kron Reduction
63
Equivalent Impedance and
Elements of Z.
Matrix
64
^>us
3.7
3.8
Modifications of Z. ^>U5
Algorithm
for Direct Construction of
Problems
Chapter
4
70 73
Zbus
79
References
80
Overhead Transmission Line Parameters
81
4.1
Introduction
81
4.2
Resistance
81
4.2.1
DC Resistance
82
4.2.2
Alternating-Current (AC) Resistance
4.3
...
83
Inductance
84
4.3.1
88
Two-Wire Solid-Conductor Line
Contents
4.3.2
Composite
Conductor
Using 90
Geometric Mean Radius 4.3.3
Three-Phase Lines with Conductor
4.3.4
4.4
93
Three-Phase Lines with Conductor
Equal
Spacing Unequal
94
Spacing Groups of Conductors
4.3.5
Lines with
4.3.6
Double-Circuit Lines
4.3.7
Earth Return
96 98 101
101
Capacitance 4.4.1
Two-Wire Solid-Conductor Line
4.4.2
Three-Phase Lines with
103
Equal
Conductor Spacing Conductor
Unequal 105
Spacing
4.4.4
Bundled Conductor
4.4.5
Transmission Lines with Neutral
4.4.6
Chapter 5
104
Three-Phase Lines with
4.4.3
Using
106
GMR
Conductor and Earth Return
107
Double-Circuit Lines
115
Problems
116
References
117
Modeling of Transmission
119
Lines
119
5.1
Introduction
5.2
Transmission Line Representation
as a
119
Two-Port Network
121
5.3 Short Transmission Lines 5.4 5.5
Long 5.5.2 5.5.3
Chapter
6
130
Transmission Lines
5.5.1
5.6
126
Medium Transmission Lines
Exponential Hyperbolic
130
Form
133
Form
140
n-Circuit
Equivalent through a Transmission
Power Flow
Line
....
141
5.6.1
Maximum Power Flow
141
5.6.2
Surge-Impedance Loading
143
5.6.3
Ferranti Effect
146
5.6.4
Transmission Line
148
Loadability
Problems
151
References
152
AC Power-Flow
Analysis Using
Iterative
Methods
153
6.1
Introduction
153
6.2
Power-Flow Problem
153 156
6.3 The Gauss-Seidel Method 6.4 6.5
The
168
Method
Newton-Raphson Decoupled Newton-Raphson
Power Flow
....
179
vii
vijj
Electrical Design of Overhead Power Transmission Lines
6.6
Fast
Decoupled Newton-Raphson
Power Flow
181
Problems
184
References
Chapter
7
185
Symmetrical
Faults
187
7.1
Introduction
187
7.2
Fault in
a
188
7.3
Fault in
an
7.4
Series R-L Circuit Unloaded Transmission
Line with
a
Fault in
Loaded Transmission Line
with
a
7.5.2
Single Synchronous
Machine
Single Synchronous Machine
7.5 Fault in 7.5.1
a
a
Network
Fault Calculation
Using Synchronous
Machine Internal
Voltage Using the Thevenin
Equivalent Circuit
Chapter
8
Using Impedance Matrix Zbus
the Bus
208
Problems
217
References
218
Unsymmetrical Faults
219
8.1
219
Introduction
Types of Unsymmetrical Faults 8.3 Fault Calculation Using Interconnection of
Sequence
Networks
219
221
8.3.1
Single
8.3.2
Line-to-Line (L-L) Fault
8.3.3
Double Line-to-Ground (L-L-G)
Line-to-Ground (L-G) Fault
Fault 8.3.4
9
203
206
Fault Calculation
8.2
Chapter
200
203
Fault Calculation
7.5.3
193
224
230 233
Open-Conductor
Fault
236
Problems
240
References
241
Control of
Voltage and Power Flow
9.1
Introduction
9.2
Generation and
243
Absorption
of Reactive
Power
243
9.2.1
Loads
9.2.2
Overhead Transmission Lines
9.2.3
Underground
9.2.4
Power Transformers
244
Cables
9.2.5
Capacitor
9.2.6
Shunt Reactors
9.2.7
243
Banks
Machines
244 244 244 244 244
Series
Synchronous Compensation
244
9.3 9.4
Shunt
Compensation
251
9.4.1
Shunt
251
Capacitors
246
Contents
9.4.2 9.5
Shunt Reactors
254
Voltage Control Methods 9.5.1
256
Generator's Excitation Control
9.5.2
9.5.3
System Injection of Reactive Power Tap-Changing and Regulating
256
Transformers
259
Problems
266
References
Chapter
10
Stability
267
in AC Networks
10.1
Introduction
10.2
of
Dynamics
269 269
a Synchronous Swing Equation Steady-State Stability
Machine
and 10.3
270 276
10.4 Transient Stability 10.4.1
Equal-Area
280 Criterion
10.4.2 Numerical Solution of 10.5
282
Swing Equation
301
Stability Improvement Techniques
307
10.5.1
High-Speed Reclosing Single Pole Operation of Circuit
307
Breakers
307
Increasing Steady-State Stability Limit
307
10.5.2
10.5.3
10.5.4 Fast Fault
Clearing
10.5.5 Fast Excitation
10.5.6
Chapter
257
Systems
307 307
FastValving
307
10.5.7 HVDC Links
308
Problems
308
References
309
11 HVD C Transmission
Systems and
FACTS Devices
311
11.1 Introduction
311
of HVDC
11.2
History
11.3
Features and Drawbacks
Applications
11.4 Converters
314
11.4.1
Rectifiers
316
11.4.2
Inverters
327
11.5 HVDC Links 11.5.1 11.5.2 11.5.3
11.6
311 313
Configurations Operation and Control Filters and Capacitor Banks
329 329
331 334
11.5.4 Back-to-Back Converter Stations
334
FACTS
335
11.6.1
336
Thyristor-Controlled Controllers
11.6.2 Converter-Based Controllers
338
ix
X
Electrical Design of Overhead Power Transmission Lines
Chapter
Problems
340
References
341
12 Corona and Electric Field Effects of Transmission Lines
343
12.1
343
Introduction
12.2 Corona Characteristics 12.3 Calculation of Corona
344
Inception
on
Single Conductors
345
12.4 Calculation of Surface Gradient
on
Bundle Conductors
351
12.5 Power Loss
355
12.6
357
Electromagnetic Interference 12.6.1
Radio Interference
359
12.6.2 Television Interference
12.6.3 Interference with Radio
360
Digital
Systems
362
12.7 Audible Noise
362
12.8 Corona Wind and Vibration Effects
364
12.9 Corona
364
Testing
12.10 Evolution of EHV and UHV Transmission
366
Systems
Problems
367
References
367
Chapter 13 Lightning Performance of Transmission Lines 13.1
13.2
369
Introduction
Lightning
369
Characteristics
13.3 Statistics of
Lightning
369
Stroke
Peak Currents
13.4
Interception
372
of Flashes
by
Transmission
Lines 13.5
376
Lightning
Protection
379
Concepts
13.6 Overhead Ground wire
Shielding
of
Transmission Lines
382
13.6.1
Overhead Groundwire Conductors
13.6.2
Computation of Shielding Failure Rate
13.6.3
Computation
Shielding
Failure
Mitigation
390 of Shielding
Failure Flashover Rate 13.7
384 385
of
Flashover Rate 13.6.4 Arrester
...
391
Grounding
of ing Structures
395
13.7.1
and Touch Potentials
395
Step
13.7.2 Three-Terminal Earth Resistance
Testing: Fall of Potential Method
397
Contents
13.7.3 Three-Terminal Earth Resistance
Testing: Oblique Method 13.7.4 Relation between Soil Resistivity
399 400
and Resistance 13.8
Computation
of Back-Flashover Rate
13.8.1 Calculation of Coupled on
403
Voltage 404
Insulated Phases
13.8.2 Calculation of
Voltage Rise from 405
Tower Inductance Rise from
13.8.3 Calculation of Tower
Voltage Footing Impedance
406
13.8.4 Calculation of Back-Flashover Rate
Chapter
...
409
Problems
411
References
412
14 Coordination of Transmission-Line
Insulation
415
14.1
415
Introduction
14.2 Statistical Distributions for Insulation Coordination
416
14.2.1 Classification of a Distribution of Data
416
14.2.2 The Normal Distribution for
Flashover of a
Single
Insulator
419
14.2.3 The Normal Distribution for Flashover of
Any of Several 422
Insulators in Parallel 14.2.4 The
Log-Normal
Distribution
423
14.2.5 The Weibull Distribution
426
14.2.6 The Gumbel Distribution
428
14.3 Statistical
Electrical
Properties Strength
of 429
14.3.1 The Flashover Process in Air 14.3.2
Switching Impulse
Strength
across
429
Flashover 431
Air Gaps
System Voltage Flashover Strength across Air Gaps Lightning Impulse Flashover Strength across Insulators
14.3.3 Power 14.3.4
14.3.5 The AC Flashover Process
435 436
across a
Wet, Polluted Insulator Surface
438
14.3.6 The AC Flashover Process across an
Iced, 14.4 Statistical
Polluted Insulator Surface
Properties
443
of Electrical and
Environmental Stresses
445
14.4.1
445
Switching Surge 14.4.2 Lightning Surge
447
xi
Electrical
Design of Overhead Power Transmission Lines 14.4.3 Insulator Surface Contamination 14.4.4
14.5
451
Precipitation Conductivity
452
14.4.5 Climate Factors
452
Insulation Coordination
453
14.5.1
Deterministic Method: Insulator
Leakage
Distance in Polluted Areas
...
453
14.5.2 Statistical Method with One Stress Variable: 14.5.3
456
Switching Surge
Deterministic/Statistical Method for Two Variables: Wind
Swing, 459
Switching Surge 14.5.4 Statistical Method for Two
Uncorrelated Variables: Ground Resistance and
Lightning
Peak Current
464
14.5.5 Statistical Method for Three
Uncorrelated Variables: Insulator
Pollution,
Ice
Conductivity,
and Ice
Accretion Thickness
:er
15
468
Problems
470
References
471
Ampacity 15.1
of Overhead Line Conductors
473
Introduction
473
15.2 Conductor Materials for Overhead Transmission Lines
474
15.3 Stranded Conductors for Transmission Lines
475
15.4 Cross-Sections of ACSR Conductors
477
15.5 DC Resistance of ACSR Conductors
481
15.6 AC Resistance of ACSR Conductors
482
15.7 Mechanical
Properties
of
ACSR Conductors 15.8
Sag-Tension
15.9 Effect of
15.10 15.11
485
Behavior in
a
Single Span and Tension
Temperature Sag Sag-Tension Behavior in Multiple Spans The Line Condition Survey and Line Rating on
492 ...
495 498 504
15.12 Calculation of Ampacity
506
15.13 Conductors for
512
Improved Ampacity
Problems
513
References
515
List of Index
Symbols
and Abbreviations
517 527
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