Electrical Design of Overhead power Transmission lines

8/18/2019 Electrical Design of Overhead power Transmission lines

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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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yj Electrical Design of Overhead Power Transmission Lines

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


6.2 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


7.2 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


8.2 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


9.2 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



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


13.2 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


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


14.2 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


15.2 Conductor Materials for Overhead


15.3 Stranded Conductors for


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

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Electrical Design of Overhead power Transmission lines