Electrical Design of Overhead power Transmission lines

Electrical Design of Overhead Power Transmission Lines Masoud Farzaneh Shahab Farokhi William A. Chisholm

Mc Graw Hill New York Lisbon

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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-Admittance 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 Supporting 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