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 SanJuan

(2)

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 OverheadTransmission Lines 6

1.5

_Organization

of theBook 8

1.5.1 The

_Learning

_Objective

Initiative 8

1.5.2 LinkstoIndustrialResourcesand

Standards 9

1.5.3 LevelofTreatment 9

1.5.4

_Chapter

1: Introduction 10

1.5.5

_Chapter

2: AC Circuits and

_Sequence

Circuitsof Power Networks 10

1.5.6

_Chapter

3: Matrix Methodsin

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

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yj

Electrical

_Design

of Overhead Power

Transmission

Lines

Chapter

2 AC Circuitsand

_Sequence

Circuits of

Power Networks 15

2.1 Introduction 15

2.2

_Single-Phase

Circuits 15

2.2.1 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

ofPer-Unit Presentation ... 36

2.6

_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 MethodsinAC Power

_System

Analysis

55

3.1 Introduction 55

3.2

_{Representation}

of Generators

and

_Impedances

55

3.3 Bus

_Analysis

andBus-Admittance

Matrix,

_Ybus

56

3.4

_{Loop Analysis}

and

_{Bus-Impedance}

Matrix,

' Z._bus 60

3.5 NodeElimination

_by

Kron Reduction 63

3.6 Thevenin's

_{Equivalent Impedance}

and

Elements ofZ. Matrix 64 ^>us

3.7 Modifications of Z._^>U5 70

3.8

_Algorithm

for Direct Construction of

_Zbus

73

Problems 79

References 80

Chapter

4 Overhead TransmissionLine Parameters 81 4.1 Introduction 81

4.2 Resistance 81

4.2.1 DC Resistance 82 4.2.2

_{Alternating-Current}

(AC) Resistance 83

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Contents

_vii

4.3.2

_Composite

Conductor

_Using

Geometric Mean Radius 90 4.3.3 Three-Phase Lineswith

_Equal

Conductor

_Spacing

93

4.3.4 Three-Phase Lines with

_Unequal

Conductor

_Spacing

94

4.3.5 Lineswith

_Groups

of Conductors 96

4.3.6 Double-CircuitLines 98

4.3.7 Earth Return 101

4.4

_Capacitance

101

4.4.1 Two-WireSolid-Conductor Line 103

4.4.2 Three-Phase Lines with

_Equal

Conductor

_Spacing

104 4.4.3 Three-PhaseLines with

_Unequal

Conductor

_Spacing

105

4.4.4 Bundled Conductor

_Using

GMR 106

4.4.5 Transmission Lineswith 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-PortNetwork 119

5.3 Short Transmission Lines 121

5.4 Medium TransmissionLines 126

5.5

_Long

5.5.1

_Exponential

Form 130

5.5.2

_Hyperbolic

Form 133

5.5.3

_Equivalent

n-Circuit 140

5.6 Power Flow

_through

aTransmissionLine .... 141

5.6.1 Maximum Power Flow 141

5.6.2

_{Surge-Impedance}

_Loading

143

5.6.3 Ferranti Effect 146

5.6.4 TransmissionLine

_Loadability

148

Problems 151 References 152

Chapter

6 AC Power-Flow

_Analysis

_Using

Iterative

Methods 153

6.2 Power-FlowProblem 153

6.3 The Gauss-Seidel Method 156

6.4 The

_{Newton-Raphson}

Method 168

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vijj

Electrical

Design

of Overhead Power Transmission Lines

6.6 Fast

_Decoupled

_{Newton-Raphson}

Power Flow 181 Problems 184 References 185

Chapter

7

_Symmetrical

Faults 187

7.2 Faultin aSeries R-L Circuit 188

7.3 Fault inanUnloaded Transmission

Line witha

Single Synchronous

Machine 193

7.4 FaultinaLoaded Transmission Line

with a

_{Single Synchronous}

Machine 200 7.5 Fault inaNetwork 203

7.5.1 Fault Calculation

_{Using Synchronous}

Machine Internal

_Voltage

203

_Using

the Thevenin

Equivalent

Circuit 206

_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

9.2 Generationand

_Absorption

of Reactive

Power 243

9.2.1 Loads 244

9.2.2 OverheadTransmission 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

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ix

9.4.2 ShuntReactors 254

9.5

_Voltage

Control Methods 256

9.5.1 Generator'sExcitation

Control

_System

256

9.5.2

_Injection

of Reactive Power 257

9.5.3

_Tap-Changing

and

_Regulating

Transformers 259

Problems 266

References 267

Chapter

10

_Stability

in AC Networks 269

10.2

_Dynamics

ofa

Synchronous

Machine

and

_{Swing Equation}

270

10.3

_Steady-State

_Stability

276

10.4 Transient

_Stability

280 10.4.1

_Equal-Area

Criterion 282

10.4.2 NumericalSolution of

_{Swing Equation}

301

10.5

_{Stability Improvement}

_Techniques

307

10.5.1

_{High-Speed Reclosing}

307

10.5.2

_Single

Pole

_Operation

ofCircuit

Breakers 307

10.5.3

_{Increasing Steady-State}

Stability

Limit 307

10.5.4 Fast Fault

_Clearing

307

10.5.5 FastExcitation

_Systems

307

10.5.6

_FastValving

307

10.5.7 HVDC Links 308

Problems 308

References 309

Chapter

11 HVD C Transmission

_Systems

and

FACTS Devices 311

11.1 Introduction 311 11.2

_History

of HVDC

_Applications

311

11.3 Features and Drawbacks 313

11.4 Converters 314

11.4.1 Rectifiers 316

11.4.2 Inverters 327

11.5 HVDC Links 329

11.5.1

_{Configurations}

329

11.5.2

_Operation

and

Control

331

11.5.3 Filters and

_Capacitor

Banks 334

11.5.4 Back-to-Back Converter Stations 334

11.6 FACTS 335

11.6.1

_{Thyristor-Controlled}

Controllers 336 11.6.2 Converter-Based Controllers 338

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X Electrical

Design

of

Overhead

Power Transmission Lines

Problems 340

References 341

Chapter

12 Corona and Electric Field Effects of

12.1 Introduction 343 12.2 Corona Characteristics 344 12.3 Calculation of Corona

_Inception

on

Single

Conductors 345

12.4 Calculation of Surface Gradienton

Bundle Conductors 351

12.5 Power Loss 355

12.6

_{Electromagnetic}

Interference 357

12.6.1 Radio Interference 359

12.6.2 Television Interference 360

12.6.3 Interference with

_Digital

Radio

_Systems

362 12.7 AudibleNoise 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

Transmission Lines 382 13.6.1 OverheadGroundwireConductors ... 384

13.6.2

_Computation

of

_Shielding

Failure Rate 385 13.6.3

_Computation

of

_Shielding

Failure

Flashover Rate 390 13.6.4 Arrester

_Mitigation

of

_Shielding

FailureFlashover Rate 391

13.7

_Grounding

of

_Supporting

Structures 395 13.7.1

_Step

and Touch Potentials 395 13.7.2 Three-Terminal EarthResistance

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Contents

xi

13.7.3 Three-Terminal Earth Resistance

Testing: Oblique

Method 399

13.7.4 Relation between Soil

_Resistivity

andResistance 400

13.8

_Computation

ofBack-Flashover Rate 403 13.8.1 Calculation of

_{Coupled Voltage}

onInsulated Phases 404 13.8.2 Calculationof

_Voltage

Rise from

Tower Inductance 405

13.8.3 Calculation of

_Voltage

Risefrom

Tower

_Footing

_Impedance

406

13.8.4 Calculationof Back-Flashover Rate ... 409

Problems 411

References 412

Chapter

14 Coordination of Transmission-Line

Insulation 415

14.2 StatisticalDistributionsfor Insulation

Coordination 416

14.2.1 Classification ofaDistributionof Data 416

14.2.2 The NormalDistribution for

Flashoverofa

Single

Insulator 419

14.2.3 The Normal Distributionfor Flashoverof

_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 FlashoverProcessin Air 429 14.3.2

_{Switching Impulse}

Flashover

Strength

acrossAir

Gaps

431 14.3.3 Power

_System

_Voltage

Flashover

Strength

acrossAir

Gaps

435

14.3.4

_{Lightning Impulse}

Flashover

Strength

acrossInsulators 436 14.3.5 The AC FlashoverProcessacross a

Wet,

Polluted Insulator Surface 438

14.3.6 TheAC Flashover Processacross an

Iced,

PollutedInsulator Surface 443 14.4 Statistical

_Properties

of Electrical and

Environmental Stresses 445

14.4.1

_{Switching Surge}

445

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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 ClimateFactors 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 Statistical Method forTwo

Uncorrelated Variables:

Ground Resistance and

_Lightning

Peak Current 464 14.5.5 Statistical MethodforThree

Uncorrelated Variables: Insulator

Pollution,

Ice

_{Conductivity,}

andIce

Accretion Thickness 468 Problems 470 References 471

:er15

Ampacity

of OverheadLineConductors 473

15.2 Conductor Materials forOverhead

15.3 Stranded Conductors for

TransmissionLines 475 15.4 Cross-SectionsofACSR 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

Behaviorin a

Single Span

492

15.9 Effectof

_Temperature

on

Sag

and Tension ... 495

15.10

_Sag-Tension

Behavior in

_{Multiple Spans}

498

15.11 The Line Condition

_Survey

and 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