electrical design of overhead power transmission lines
TRANSCRIPT
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Electrical Design of
Overhead Power
Transmission Lines
Masoud Farzaneh
Shahab Farokhi
William A. Chisholm
Mc
Graw
Hill
New York Chicago San Francisco
Lisbon London Madrid Mexico City
Milan New Delhi San Juan
Seoul Singapore Sydney Toronto
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Contents
Preface xiii
Acknowledgments xv
Chapter 1 Introduction 1
1.1 History of Electric Power Systems 1
1.2 Organization of Modern Electric
Power Systems 2
1.3 Modern Transmission System Alternatives ... 3
1.4 Components of Overhead Transmission Lines 6
1.5 Organization of the Book 8
1.5.1 The Learning Objective Initiative 8
1.5.2 Links to Industrial Resources and
Standards 9
1.5.3 Level of Treatment 9
1.5.4 Chapter 1: Introduction 101.5.5 Chapter 2: AC Circuits and Sequence
Circuits of Power Networks 10
1.5.6 Chapter 3: Matrix Methods in
AC Power System Analysis 11
1.5.7 Chapter 4: Overhead Transmission
Line Parameters 11
1.5.8 Chapter 5: Modeling of
Transmission Lines 11
1.5.9 Chapter 6: AC Power-Flow Analysis
Using Iterative Methods 11
1.5.10 Chapter 7: Symmetrical Faults 12
1.5.11 Chapter 8: Unsymmetrical Faults 12
1.5.12 Chapter 9: Control of Voltage and
Power Flow 12
1.5.13 Chapter 10: Stability in AC Networks .. 12
1.5.14 Chapter 11: HVDC Transmission 12
1.5.15 Chapter 12: AC-Corona Effects 13
1.5.16 Chapter 13 Lightning Performance
of Transmission Lines 13
1.5.17 Chapter 14: Transmission Line
Insulation and Coordination 13
1.5.18 Chapter 15: Ampacity of
Overhead Line Conductors 14
V
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Chapter 2 AC Circuits and Sequence Circuits of
Power Networks 15
2.1 Introduction 15
2.2 Single-Phase Circuits 152.2.1 Power in Single-Phase Circuits 15
2.2.2 Complex Power 19
2.3 Three-Phase Circuits 22
2.3.1 Balanced Three-Phase Circuits 22
2.3.2 Unbalanced Three-Phase Circuits 27
2.4 Single-Line Diagram and Per-Phase
Equivalent Circuit Presentation 33
2.5 Per-Unit
Representation 35
2.5.1 Definition 35
2.5.2 Advantages of Per-Unit Presentation ... 362.6 Symmetrical Sequence Impedance of
Power System Components 39
2.6.1 Symmetrical Load Impedances 39
2.6.2 Synchronous Generators 44
2.6.3 Power Transformers 46
2.6.4 Transmission Lines 49
2.7 Sequence Networks 50
Problems 52
References 53
Chapter 3 Matrix Methods in AC Power System
Analysis 55
3.1 Introduction 55
3.2 Representation of Generators
and Impedances 55
3.3 Bus Analysis and Bus-Admittance
Matrix, Ybus 56
3.4 Loop Analysis and Bus-ImpedanceMatrix, Z. 60' bus
3.5 Node Elimination by Kron Reduction 63
3.6 Thevenin's Equivalent Impedance and
Elements of Z. Matrix 64^>us
3.7 Modifications of Z. 70^>U5
3.8 Algorithm for Direct Construction of Zbus 73Problems 79
References 80
Chapter 4 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 ... 83
4.3 Inductance 84
4.3.1 Two-Wire Solid-Conductor Line 88
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Contents vii
4.3.2 Composite Conductor UsingGeometric Mean Radius 90
4.3.3 Three-Phase Lines with EqualConductor Spacing 93
4.3.4 Three-Phase Lines with Unequal
Conductor Spacing 94
4.3.5 Lines with Groups of Conductors 96
4.3.6 Double-Circuit Lines 98
4.3.7 Earth Return 101
4.4 Capacitance 101
4.4.1 Two-Wire Solid-Conductor Line 103
4.4.2 Three-Phase Lines with EqualConductor Spacing 104
4.4.3 Three-Phase Lines with UnequalConductor Spacing 105
4.4.4 Bundled Conductor Using GMR 106
4.4.5 Transmission Lines with Neutral
Conductor and Earth Return 107
4.4.6 Double-Circuit Lines 115
Problems 116
References 117
Chapter 5 Modeling of Transmission Lines 119
5.1 Introduction 119
5.2 Transmission Line Representation as a
Two-Port Network 119
5.3 Short Transmission Lines 121
5.4 Medium Transmission Lines 126
5.5 Long Transmission Lines 130
5.5.1 Exponential Form 130
5.5.2 Hyperbolic Form 133
5.5.3 Equivalent n-Circuit 140
5.6 Power Flow through a Transmission 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 Loadability 148
Problems 151
References 152
Chapter 6 AC Power-Flow Analysis Using Iterative
Methods 153
6.1 Introduction 153
6.2 Power-Flow Problem 153
6.3 The Gauss-Seidel Method 156
6.4 The Newton-Raphson Method 168
6.5 Decoupled Newton-Raphson Power Flow
.... 179
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6.6 Fast Decoupled Newton-RaphsonPower Flow 181
Problems 184
References 185
Chapter 7 Symmetrical Faults 187
7.1 Introduction 187
7.2 Fault in a Series R-L Circuit 188
7.3 Fault in an Unloaded Transmission
Line with a Single Synchronous Machine 193
7.4 Fault in a Loaded Transmission Line
with a Single Synchronous Machine 200
7.5 Fault in a Network 2037.5.1 Fault Calculation Using Synchronous
Machine Internal Voltage 203
7.5.2 Fault Calculation Using the Thevenin
Equivalent Circuit 206
7.5.3 Fault Calculation Using the Bus
Impedance Matrix Zbus 208
Problems 217
References 218
Chapter 8 Unsymmetrical Faults 219
8.1 Introduction 219
8.2 Types of Unsymmetrical Faults 219
8.3 Fault Calculation Using Interconnection of
Sequence Networks 221
8.3.1 Single Line-to-Ground (L-G) Fault 224
8.3.2 Line-to-Line (L-L) Fault 230
8.3.3 Double Line-to-Ground (L-L-G)
Fault 233
8.3.4 Open-Conductor Fault 236
Problems 240
References 241
Chapter 9 Control of Voltage and Power Flow 243
9.1 Introduction 243
9.2 Generation and Absorption of Reactive
Power 243
9.2.1 Loads 244
9.2.2 Overhead Transmission Lines 244
9.2.3 Underground Cables 244
9.2.4 Power Transformers 244
9.2.5 Capacitor Banks 244
9.2.6 Shunt Reactors 244
9.2.7 Synchronous Machines 244
9.3 Series Compensation 246
9.4 Shunt Compensation 2519.4.1 Shunt Capacitors 251
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X Electrical Design of Overhead Power Transmission Lines
Problems 340
References 341
Chapter 12 Corona and Electric Field Effects of
Transmission Lines 343
12.1 Introduction 343
12.2 Corona Characteristics 344
12.3 Calculation of Corona Inception on
Single Conductors 345
12.4 Calculation of Surface Gradient on
Bundle Conductors 351
12.5 Power Loss 355
12.6 Electromagnetic Interference 35712.6.1 Radio Interference 359
12.6.2 Television Interference 360
12.6.3 Interference with Digital
Radio Systems 362
12.7 Audible Noise 362
12.8 Corona Wind and Vibration Effects 364
12.9 Corona Testing 364
12.10 Evolution of EHV and UHV
Transmission Systems 366
Problems 367
References 367
Chapter 13 Lightning Performance of Transmission
Lines 369
13.1 Introduction 369
13.2 Lightning Characteristics 369
13.3 Statistics of Lightning Stroke
Peak Currents 372
13.4 Interception of Flashes by Transmission
Lines 376
13.5 Lightning Protection Concepts 379
13.6 Overhead Ground wire Shielding of
Transmission Lines 382
13.6.1 Overhead Groundwire Conductors ...
384
13.6.2 Computation ofShielding
Failure Rate 385
13.6.3 Computation of Shielding Failure
Flashover Rate 390
13.6.4 Arrester Mitigation ofShieldingFailure Flashover Rate 391
13.7 Grounding ofSupporting Structures 395
13.7.1 Step and Touch Potentials 395
13.7.2 Three-Terminal Earth Resistance
Testing: Fall of Potential Method 397
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Contents xi
13.7.3 Three-Terminal Earth Resistance
Testing: Oblique Method 399
13.7.4 Relation between Soil Resistivity
and Resistance 400
13.8 Computation of Back-Flashover Rate 403
13.8.1 Calculation of Coupled Voltage
on Insulated Phases 404
13.8.2 Calculation of Voltage Rise from
Tower Inductance 405
13.8.3 Calculation of Voltage Rise from
Tower Footing Impedance 406
13.8.4 Calculation of Back-Flashover Rate ... 409
Problems 411
References 412
Chapter 14 Coordination of Transmission-Line
Insulation 415
14.1 Introduction 415
14.2 Statistical Distributions for Insulation
Coordination 416
14.2.1 Classification ofa 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
Insulators in Parallel 422
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 Properties of
Electrical Strength 429
14.3.1 The Flashover Process in Air 429
14.3.2 Switching Impulse Flashover
Strength across Air Gaps 431
14.3.3 Power System Voltage Flashover
Strength across Air Gaps 435
14.3.4 Lightning Impulse Flashover
Strength across Insulators 436
14.3.5 The AC Flashover Process across a
Wet, Polluted Insulator Surface 438
14.3.6 The AC Flashover Process across an
Iced, Polluted Insulator Surface 443
14.4 Statistical Properties of Electrical and
Environmental Stresses 445
14.4.1 Switching Surge 445
14.4.2 Lightning Surge 447
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Electrical Design of Overhead Power Transmission Lines
14.4.3 Insulator Surface Contamination 451
14.4.4 Precipitation Conductivity 452
14.4.5 Climate Factors 452
14.5 Insulation Coordination 453
14.5.1 Deterministic Method: Insulator
Leakage Distance in Polluted Areas ... 453
14.5.2 Statistical Method with One Stress
Variable: Switching Surge 456
14.5.3 Deterministic/Statistical Method
for Two Variables: Wind Swing,
Switching Surge 459
14.5.4 StatisticalMethod
forTwo
Uncorrelated Variables:
Ground Resistance and LightningPeak Current 464
14.5.5 Statistical Method for Three
Uncorrelated Variables: Insulator
Pollution, Ice Conductivity, and Ice
Accretion Thickness 468
Problems 470
References 471
:er 15 Ampacity of Overhead Line Conductors 473
15.1 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 485
15.8 Sag-Tension Behavior in a Single Span 492
15.9 Effect of Temperature on Sag and Tension ... 495
15.10 Sag-Tension Behavior in Multiple Spans 498
15.11 The Line Condition Surveyand Line Rating 504
15.12 Calculation of Ampacity 506
15.13 Conductors for Improved Ampacity 512
Problems 513
References 515
List of Symbols and Abbreviations 517
Index 527