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Transmission Line Reference Book
345 kV and Above/Second Edition
Prepared by
Project UHV Technical Resource Operation Large Transformer Division General Electric Co. Pittsfield, Massachusetts
Transmission Engineering Electric Utility Systems Engineering Department Energy Systems and Technology Division General Electric Co. Schenectady, New York
Electriq~Power Research Institute 3412 Hillview Avenue, Palo Alto, California
Copyright "'1982 by the Electric Power Research Institute, Inc. All rights reserved. First edition, 1975. Reprinted 1979. Second edition, 1982.
Notice
This report was prepared by General Electric Company as an account of work sponsored by the Electric Power Research Institute, Inc. (EPRI). Neither EPRI, members of EPRI, General Electric Company, nor any person acting on behalf of anyofthern: (a) makes any warranty, express or implied, with respect to the use of any information, apparatus, method, or process disclosed in this report or that such use may' not infringe privately owned rights; or (b) assumes any liabilities with respect to the use of, or for damages resulting from the use of, any information, apparatus, method, or process disclosed in this report.
Keywords
EHV-UHV Conductors Corona Audible Noise Electric Fields
Ordering Information
Requests for copies of this book should be directed to Research Reports Center (RRC), Box 50490, Palo Alto, CA 94303, (415) 965-4081. There is no charge for reports requested by EPRI member utilities and affiliates, contributing nonmembers, U.S. utility associations, U.S. government agencies (federal, state, and local), media, and foreign organizations with which EPRI has an information exchange agreement. On request, RRC will send a catalog of EPRI reports.
·--ii
Editor
J. J. LaForest
Editorial Committee
M.G. Comber L. E. Zaffanella
Authors
Chapter Project UHV: A Transmission Research Facility J. R. Doyle and L. E. Zaffanella
Chapter 2 EHV-UHV Transmission Systems F. J. Ellert, S. A. Miske, Jr., and C. J. Truax
Chapter 3 Electrical Characteristics of EHV-UHV Conductor Configurations and Circuits J. R. Doyle, J. J. LaForest, and T. S. Lauber (Rensselaer Polytechnic Institute)
Chapter 4 Corona Phenomena on AC Transmission Lines M. G. Comber, D. W. Deno, and L. E. Zaffanella
Chapter 5 Radio Noise M. G. Comber and R. J. Nigbor
Chapter 6 Audible Noise M. G. Comber, R. J. Nigbor, and L. E. Zaffanella
Chapter 7 Corona Loss M. G. Comber and L. E. Zaffanella
Chapter 8 Field Effects of Overhead Transmission Lines and Stations D. W. Deno and L. E. Zaffanella
Chapter 9 Insulation - Design Criteria J. D. Brown, F. A. Fisher, W. Neugebauer, and J. Panek
Chapter 10 Insulation for Power Frequency Voltage K. J. Lloyd and H. M. Schneider
Chapter 11 Insulation for Switching Surges K. J. Lloyd and L. E. Zaffanella
Chapter 12 Lightning Performance of Transmission Lines J. G. Anderson
Chapter 13 Planning and Electrical Design of Transmission Lines D. W. Deno, L. L. Garver, and J. J. LaForest
IV
Quick Reference Chart for Major Design Items
To facilitate the use of this book by experienced line designers, a portion of the contents of Chapter 13, Sections 13.9 and 13.8, is presented below for quick reference. Section 13.9 summarizes the main design topics covered by this Second Edition, and Section 13.8 summarizes general circulation performance items useful for design. Each topical summary directs the reader to specific design sections elsewhere in the book.
Design Topics: Line
Switching Surge Insulation Lightning Insulation Insulation for Contamination Ground Electric Field Magnetic Induction Audible Noise Radio Interference Television Interference Corona Loss Ground Wire Design (60 Hz)
VI
614 615 616 617 618 619 620 621 621 622
Design Topics: Station
Transient Voltage Insulation Insulation tor Contamination Corona Performance Corona Shields Ground Electric Field
Circuit Performance Items
Compensation Stability Line Loading Routing Transposition Transmission-Line Protection Power-Line Carrier Environmental Measurements Line Parameters
623 624 624 625 625
606 606 607 608 609 610 611 612 613
Contents
Forewor'd 2.6 Optimization of Transmission Systems 26 Long-Range Transmission Planning 26
Chapter 1 Project UHV: A Transmission Optimum Line Design 27 Research Facility 1
2.7 EHV Tower Geometries and Line Characteristics 30 1.1 Introduction 1
References 62 1.2 Description of Project UHV Facilities 2
900-kV Surge Arresters 3 Chapter 3 Electrical Characteristics of Precision Capacitor 3 EHV-UHV Conductor Configurations Single-Phase Cascade Operation 3 and Circuits 63 Switching Surge Operation 3 Three-Phase UHV Test Line 3 3.1 Introduction 63 Insulator Strings 6 3.2 Conductor Surface Gradients 63 Corona Testing Cage 6 Insulator Contamination Research 7 Gradient Terminology 63
Calculating Conductor Gradients 63 1.3 Instrumentation for Data Acquisition 8 Graphical Method - Single-Circuit Horizontal 64
Data Acquisition Computer 8 Graphical Method - Single-Circuit Vertical 75 Instrumentation Systems 8 Graphical Method - Single-Circuit Delta 75
Approximate Method for Single-Circuit Calculations 78 References 9 Graphical Method - Double-Circuit 87
Higher Phase Order 88 Chapter 2 EHV-UHV Transmission Systems 11 Distribution of Gradient in a Bundle 88
Asymmetrical Bundle Gradients 99 2.1 Introduction 11 Graphical Method -Toroidal Shielding Electrodes 100
Role of Transmission 11 3.3 Reactance and Resistance of General Transmission Design Criteria 11
Bundle Conductors 105 2.2 Load Growth and Transmission System Evolution 14 Introduction 105
Historical Load Growth 14 Types of Conductors and Conductor Materials 105 Forecast Load Growth 14 Inductive Reactance 105 AC Transmission Line Growth 14 Capacitive Reactance 123 Evolution of DC Transmission 16 Surge Impedance and Surge Impedance Loading 124
2.3 Resistance 124
Factors Affecting EHV-UHV Ground Wires 125 Transmission Growth 17 Equivalent Single Conductor 125 Load Growth 17 Transmission-Line Parameters 125 Generation Siting 17
3.4 Transmission-Line Unbalance 131 Fuel Costs and Availability 18 Reliability 18 Electrostatic Unbalance 131 Ecology 18 Single-Circuit Electromagnetic Unbalance 133 Government 18 Unbalance in Parallel Double-Circuit Untransposed Lines 136 Energy Centers 19 Summary 140
2.4 EHV-UHV Transmission System Characteristics 19 3.5 Induced Voltages on Parallel Lines 140
Stability Considerations 19 Electrostatic Induction on the De-energized Circuit 142 Series Compensation 20 Electromagnetic Induction on the De-energized Circuit 142 Shunt Compensation
,~
20 Power Transmission Capability 22 Appendix 3. 1 Calculation of Electric Fields 143
2.5 EHV-UHV Line Design - Principal Areas Appendix 3.2 Inductive Reactance of
to Be Considered 24 Bundled Conductors 145
Electrical 24 Appendix 3.3 Capacitive Reactance of Environmental 25 Bundled Conductors 146
vii
TRANSMISSION LINE REFERENCE BOOK 345 KV AND ABOVE
Appendix 3.4 Conductor Table Calculations 148 Antenna Systems 210
Appendix 3.5 Transmission-Line Parameters Measurement of Transmission-Line Noise 211
(>60Hz) 150 5.3 Design Considerations 211
Appendix 3.6 Unbalance Factor Equations 165 Characterization of Transmission-Line Radio Noise 212 Effect of Line Geometry and Conductor Surface
References 167 Conditions 212 Noise Tolerability Criteria 213
Chapter 4 Corona Phenomena on 5.4 Calculation of Transmission Line Rl 217 AC Transmission Lines 169 Generation and Propagation of Rl 217
4.1 Introduction 169 Rl Generation Data 222 Determination of Propagation Characteristics 225
4.2 Mechanism of Corona 169 Rl Design Curves 229 Gas Discharge Processes 169 Comparison of the Reference Book Rl Calculation
The Townsend Avalanche Process 170 Method with Measured Data 245 DC Corona Modes 170 Rl Statistics 247 AC Corona 175 5.5 Television Interference 248
4.3 Corona Loss Concept 175 TVI Calculation Procedure 249 Field Without Corona 175 Example Calculation 250
Field in the Presence of Corona - Corona Current 175 Comparison of Calculations with Measurements 250
Corona Loss in Fair Weather 176 5.6 Radio Noise from Substations 251
4.4 Effect of Surface and Atmospheric Conditions 180 Calculation of Rl from Substations 251
Fair-Weather Corona Sources 180 Rl Generation from Toroidal Grading Rings 252
Corona Due to Particles Near the Conductor 181 5.7 Additional Topics 253 Effect of Water on the Conductor 181 Effect of Air Density, Humidity, and Wind 181 Radio Noise of Insulator Strings 253
Effect of Surface Conditions 182 Ghosting and Blocking 253
Surface Treatment - Measurements and Results 185 Interference to Other than AM and TV Broadcast Services 253
4.5 Evaluation of Corona Effects from Single-Phase Appendix 5. 1 Rl Analysis for Single Conductor
and Three-Phase Tests 187 Above Ground 254
Measurement and Analysis Using Single-Phase Appendix 5.2 Transmission-Line Propagation in Test Facilities 187 Modal Quantities 256
Corona Generation and Surface Gradient 187 Generation Quantities 188 Appendix 5.3 Reference Method of Rl Analysis of Audible Noise-Generated Power 189 Three-Phase Transmission Lines 258 Radio Noise Generation Function 189 Measurement and Analysis Using Three-Phase Appendix 5.4 Attenuation Constants and Modal
Test Facilities 191 Transformation Matrices 261
4.6 Influence of Corona Currents on Switching-Surge References 264
Overvoltages 192 Project EHV Test Program 192 Chapter 6 Audible Noise 267 Project UHV Test Program 195
6.1 Introduction 267 4.7 Ozone 199
Introduction 199 6.2 Audible Noise Characteristics and Measurement 267
Ambient Concentration 199 Characteristics of Transmission-Line Noise 267 Acceptable Levels 199 Measures of Audible Noise 268 Measurements at Project UHV 200 Instrumentation 269 Ozone Measurements in Other Locations 202 Measurements 270 Calculations of Incremental Ozone Concentration 202 6.3 Design Considerations 270 Other Corona Products 203
Effect of Weather Conditions 270 References 203 Effect of Line Geometry and Conductor Surface
Conditions 271 Chapter 5 Radio Noise 205 Assessing the Impact of Transmission-Line Audible Noise 272
5.1 Introduction 205 6.4 Calculation of Transmission-Line Audible Noise 274
5.2 Radio Noise Measurement 205 Introduction 274 Generation and Propagation of AN 275
The Radie-No.ise Meter 206 AN Generation Data - Broad-Band Noise 278 Weighting Circuits 206 Calculation of Audible-Noise Levels -Meter Response - Bandwidth and Pulse Repetition Rate 208 Random Noise 281 Actual Band-Pass Characteristics 210 Influence of Tower, Sag, and Ground Wires 283
viii
CONTENTS
AN Design Curves 283 Vertical Component of the Electric Field 330 Effect of Rain Rate 284 Space Potential 330 Effect of Conductor-Surface Aging 299 Effect of Air Density 299 8.3 Calculation of Electric Fields 330
Comparison of the Reference Book AN Calculation General Method for Transmission Lines 330 Method with Measured Data 300 Lateral Profile of Electric Field at Ground Level 332
Bundle Geometry Optimizatjon 301 Maximum Electric Field at Ground - Generalized Curves 332 Generation of 120-Hz Hum 305 Effect of Changes in Line Geometry 333 Calculation of Audible Noise- 120-Hz Hum 306 Electric Field of Double-Circuit Lines 335 Audible Noise in Dry Conditions 307 Electric Field at Line Bends 338
Electric Field in Substations 338 6.5 Audible Noise from Corona in Substations 307
Audible-Noise Generation of Basic Electrode Shapes 308 8.4 Calculation of Magnetic Fields 341
Calculation of Audible-Noise Levels for a Substation 309 General Method for Transmission Lines 341 Example Calculation 342
6.6 Techniques of Audible-Noise Reduction 310 8.5 Measurement of Electric Fields 343
6.7 Correlation Between Audible Noise, Techniques for the Measurements of the Unperturbed
Radio Noise, and Corona Loss 312 Electric Field 343 Audible Noise [dB (A)] Versus Radio Noise 312 Measurements of the Electric Field on a Boundary Surface 346 Audible-Noise Hum Versus Corona Loss 314 Measurement of the Space Potential 346
Appendix 6. 1 Ambient Noise During Rain 314 8.6 Measurements of Magnetic Fields 347
Appendix 6.2 Sound Attenuation of Structures 314 8.7 Comparison Between HV Transmission-Line and
Appendix 6.3 Adjustment of Measured Noise Levels to Common Environment Electric and
Account for Ambient Noise Intrusions 315 Magnetic Fields 347
References 317 8.8 Electric-Field Induction In Objects 348
Introduction 348
Chapter 7 Corona Loss 319 Transmission-Line Induced Currents 348 Currents Induced on a Sphere Above Ground 348
7.1 Introduction 319 Current Induced on a Round-Topped Hemisphere on a
7.2 Corona Loss in Fair Weather 319 Ground Plane 349
Current Induced on a Cylinder Above Ground 349
7.3 Corona Loss in Foul Weather 320 Current Induced on a Half-Cylinder on a Ground Plane 349
Corona Loss in Rain 320 Methods for Approximate Calculation of Current Induced
on Objects Close to the Ground 349 Corona Loss in Fog, Snow, and Frost 322 Currents Induced in Large Objects 350 Results with the Three-Phase UHV Test Line 323 Currents Induced in TV and FM Antennas 352
7.4 Evaluation of Corona Loss 324 Induced Current Summary Tables 354
324 Accuracy Expected in Calculating Induced Currents 354
Corona Loss Weather Model Examples of Electric Induction Calculation 357 Adjustment for Precipitation Within a Given Climate 325 Single-Phase vs Three-Phase Induction 358
7.5 Heavy-Rain Corona Loss for Electric Induction Calculation with lmpeda,nce to Ground 359
Base Case Geometries 325 Statistical Impedance with Vehicles 360 Example Calculations 362
7.6 Example of Corona Loss Computations 327 8.9 Magnetic Induction on Objects 363
7.7 Comparison of Corona Losses with Impedance Matrix with Ground Return 364 Resistance Losses 327 Shield Wire Currents 364
References 328 Induction in Conductive Objects Parallel to the Line 364
8.10 Electric-Field Induction in People 365 Chapter 8 Field Effects of Overhead Transmission
Inducted Currents and Their Distribution 365 Lines and Stations 329 Electric Field Exposure Monitors 369
8.1 Introduction 329 Exposure Measurements Within Field Ranges 370 Currents Induced by Spark Discharges 372
8.2 Electric and Magnetic Fields: Definitions 329 Transient Currents Induced by Switching Transients 373
Phasors and Vectors 329 People Response to Short-Term Exposure to
Electric Field 329 Electric Fields 374
Magnetic Field 330 8.11 Biological Effects of Electric Fields Frequency
,_ 330
Harmonic Content 330 on People and Animals 379
Maximum Value of the Electric (Magnetic) Field 330 8.12 Magnetic Field Induction in People 379 Unperturbed Field 330 Single-Phase and Three-Phase Fields 330 8.13 Biological Effects of Magnetic Fields Uniform Field 330 on People and Animals 380
IX
TRANSMISSION LINE REFERENCE BOOK 345 KV AND ABOVE
8.14 Fuel Ignition 381 Transient Network Analyzers 437
Introduction 381 Digital Models 437
Fuel Ignition Induced by Spark Discharge 381 TNA Compared with Digital Programs 439
Corona-Induced Fuel Ignition 383 Aids to Calculation of Transients 441
Flashovers Caused by Fires 384 9.5 Methods of Controlling Overvoltages 441
8.15 Trees and Poles in High-Intensity Electric Fields 386 Introduction 441
Introduction 386 Resistor Insertion 441
Dead Tree-Tip Burning 388 Breaker Timing Control 442
Pole Fire with Grounded Hardware 389 System Modification 442
Pole Fire Without Grounded Hardware 389 Switching Restrictions 443
Mechanism Causing Wood Fires 392 Line Discharge Resistors 443
Live Tree-Tip Corona Damage 392 Surge Arresters 443
8.16 Corona from Grounded Objects 392 9.6 Weather Considerations 444
Introduction 392 9.7 Insulation Dielectric Strength 445 Measuring Techniques 392 Withstand Voltage 445 Space Potential as the Independent Variable 393 Types of Insulation 448 Corona Current and Corona Power 394 Corona Onset 394 9.8 Statistical Properties of Withstand Voltage 448 Radio Noise 396 Audible Noise 396 9.9 Stress vs Strength 449
Ozone 396 Appendix 9.1 Resonant Voltages on Parallel, Conclusions 397
Reactor-Compensated Lines 452 8.17 Shielding Methods 397
Appendix 9.2 ABCD Method of Analysis 455 Introduction 397 Shielding by a Horizontal Grid of Grounded Wires 397 Appendix 9.3 Electrostatic Method of Analysis for Design Procedure 399 Resonant Voltages 456 Shielding by a Vertical Grid of Grounded Wires 399 Shielding by Meshes of Grounded Wires 403 Appendix 9.4 Probability of Overvoltage Occurrence 458
Natural Shields -Trees and Houses 403 References 460 Underbuilt Lower-Voltage Lines 405
Appendix 8. 1 Calculation of Maximum Field 409 Chapter 10 Insulation for Power Frequency Voltage 463
Appendix 8.2 Measurements of Electric Field with a 10.1 Introduction 463 Free-Body Meter 410 Contamination Flashover on Transmission Systems 463
Appendix 8.3 Air Model Facility 411 Research in the Field of Contamination Flashover 463
Appendix 8.4 Transmission-Line Electric Induction 10.2 Survey of the Contamination Performance
Calculation with Matrices 413 of Power Transmission Systems 464
Spot and Area Contamination 464 Appendix 8.5 Magnetic Induction with Resistive Types of Contaminants and Weather Conditions 465
Ground Return 415 Countermeasures 465
References 417 10.3 Contamination Test Methods 466
Introduction 466
Chapter 9 Insulation-Design Criteria 421 Outline of Test Methods 467 Comparison of Test Methods 468
9.1 Introduction 421 10.4 Research at Project UHV 468
9.2 Voltage Stress on Insulation 421 Introduction 468 Introduction 421 Insulators Tested 469 System Voltage 422 Power Sources for Testing 469 Overvoltage 422 Influence of the Parameters of the Test Circuit 469
Factors that Affect Wetting Mechanisms 472 9.3 Characteristics of Overvoltages 424 Investigation of Natural Wetting Conditions 473
Temporary Overvoltages 424 Wetting Method and Contaminants Used at Project UHV 473 Switching Overvoltages 428 Flashover Probability of Contaminated Insulators 474 Switching of Reactive Circuits - Observed Phenomena 430 Performance of Various Types of Insulators in Fault Occurrence and Fault Clearing 433 Short Strings 475 Other Switching Operations 434 Performance of Insulators in Long Strings 477 Recovery Voltage Across Breakers 435 Contamination Tests with Natural and Artificial Wetting Lightnin~ervoltages 435 Conditions 478
9.4 Nonlinearity of Flashover Strength with Insulator Length 479
Methods of Analysis 436 Comparison of Electrical Strength for Different String Introduction 436 Orientations 481
X
CONTENTS
Double Strings with Close Spacing 483 11.9 Comparison of Fundamental Gaps 524 Phase-to-Phase Insulators 483 Semiconducting Glaze Insulators 484 11.10 Correction of Switching-Surge Flashover Data to
Ice-Flashover Performance 485 Standard Conditions 525 Corona on Long Insulator Strings 488 11. 11 Effects of Geometry on Switching-Surge
10.5 Mechanism of Contamination Flashover 489 Flashover Strength: Corrections to Base Case
Introduction 489 Conditions 525 Flashover Mechanism of Single Insulator Units 489 Tower Window Height 525 Flashover Mechanism of Long Insulator Strings 492 Size and Shape of Electrodes 526 Discussion 493 Tower Width 526
Rectangular Window 527 10.6 Insulation Design 493 Insulator Strings 527
Insulator Design for Clean Areas 493 Effect of Rain on Clean Insulation 493 11.12 Effects of Waveshape on Switching-Surge
Full-Scale UHV Tests in Artificial Rain 494 Flashover Strength: Corrections to Base Case Insulation Design for Contamination: Prediction of Conditions 527
Contamination Conditions 495 11.13 Effects of Atmospheric Conditions on Design for Contaminated Conditions 497
Switching-Surge Flashover Strength: Corrections
I Appendix 10.1 Meteorological Corrections for to Standard Conditions 528
Power-Frequency Tests 498 Effects of Humidity 528
f References 499 Effects of Relative Air Density 529 Effects of Rain 530
'! ;j Chapter 11 Insulation for Switching Surges 503 11.14 Standard Deviation 531
t 11. 1 Introduction 503 11.15 Design Procedures 531 ·i l 11.2 Principal Variables in Switching-Surge Flashover 503 Appendix 11. 1 Computation of Swing Angle ,, ~ Waveshape 504 Distribution 535 1 Polarity 505
Geometric Influence on Switching-Surge Strength 505 Appendix 11.2 Testing Methods for Critical Flashover Meteorological Influence on Switching-Surge Strength 505 Voltage ( V50.;.) and Standard Statistical Fluctuations in Switching Impulse Strength 505 Deviation {u) 538
11.3 Flashover Mechanism 506 Appendix 11.3 Models for Calculation of Switching-
11.4 Switching Impulse Flashover Testing Technique 506 Surge Strength 539
Principal Data Variables 509 References 542 Organization of Data 509
11.5 Switching-Surge Flashover Strength of Simple Chapter 12, Lightning Performance of Transmission
Lines 545 Airgaps 509 Rod-Plane and Vertical Rod-Rod Gaps 509 12.1 Introduction 545
Horizontal Rod-Rod Gaps 510 12.2 Problems of Accuracy 545 Sphere-Plane Gaps 511
11.6 Switching-Surge Flashover Strength of Line 12.3 Terminology 546
Insulation 512 12.4 Lightning Flash Parameters 546
Tower Window Gap 512 Keraunic Levels and lsokeraunic Maps 546 Outside Phase Tower Gap 512 Number of Flashes to Earth 547 Insulator Strings 512 Interception of Flashes by the Line 547 Conductor to Tower Leg 515 Lightning Flashes to Shield Wires and Towers 548 Conductor to Grounded Objects at Midspan 515 Flashes to Tall Structures 549 Angled Line to Tower 516 Probability Distribution of Stroke Amplitudes 549 Anomalous Flashovers 516 Stroke Waveshape Parameters Influencing Flashover 549
11.7 Composite Waveshapes 550
Switching-Surge Flashover Strength of Station Front and Tail Constants 551 Insulation 516 Horizontal Insulator Strings 516 12.5 Circuit Elements Involved in Computation of
Station Post Insulators 516 Flashover Performance 552
11.8 Phase-to-Phase Switching-SurgEt~Strength 517 Reducing Bundle Conductors to Equivalent Single
Conductors 553 Introduction 517 Finding Effective Radii of Shield Wires and Phase Results of Phase-to-Phase Switching-Impulse Tests 519 Conductors with Corona Present 554 Phase-to-Phase Insulation Stress 520 Reduction of Shield Wire Surge Impedances to Design Procedure for Phase-to-Phase Distances 522 Equivalent Single Wire Surge Impedances 554 Examples 523 Computation of Tower Surge Impedances 555
;j XI
-~ II
TRANSMISSION LINE REFERENCE BOOK 345 KV AND ABOVE
Determination of Coupling Factors for Phase Conductors 556
Selection of Footing Resistance 556 Effects of a Statistical Distribution of Footing Resistance
Values 560
12.6 Response of a Transmission Tower to a Lightning Flash 560
Computation of Tower Top Voltage 560 Computation of Crossarm Voltages 561 Computation of Insulator Surge Voltages 562 Penetration of Insulator Voltage into the Volt-Time Curve 563 Reflections from Adjacent Towers 564 Effects of Power-Frequency Voltage 566
12.7 Shielding Failures of Transmission Lines 567
The Electrogeometric Theory 567 Attainment of Effective Shielding 568 Shielding Failure Rate Computation 569
12.8 Lightning Performance of UHV Lines 570
12.9 Equivalent R-L Circuits of Transmission Towers 570
12.10 A Simplified Two-Point Method for Computation of Lightning Performance of Transmission Lines 573
Appendix 12. 1 Reduction of Bundles to Equivalent Single Conductors 586
Appendix 12.2 Computation of the Effective Diameter of a Conductor at High Voltage 586
Appendix 12.3 Surge Impedance of Shield Wires and Voltages Coupled to the Phase Conductors 587
Appendix 12.4 Derivation of the Fundamental Travelling Wave Equation for Tower Top Voltage 589
Appendix 12.5 Travelling Wave Equations for the Voltage at the Crossarm or at Any Point on the Tower 591
Appendix 12.6 Power-Frequency Voltage Effects 592
Appendix 12.7 Tower Damping and the Equivalent R-L Circuit 593
References 596
Chapter 13 Planning and Electrical Design of Transmission Lines 599
13.1 Introduction 599
13.2 Conceptual Planning 599
13.3 Preliminary Planning 601
13.4 Primary Decisions 602
13.5 Planning Summary 604
13.6 Additional Reading on Planning 605
13.7 Licenses and Approvals 605
13.8 Generai·Gircuit Performance and Application Items 605
Compensation 606
xii
Stability (Steady State) Line Loading Routing Transpositions Transmission-Line Protection Power-Line Carrier Environmental Measurements Line Parameters
13.9 Line and Station Performance and Application
606 607 608 609 610 611 612 613
Items 614
Insulation for Switching Surges 614 Insulation for Lightning 615 Insulation for Contamination 616 Ground Electric Field 617 Magnetic Induction 618 Audible Noise (AN) 619 Radio Interference (RI) 620 Television Interference (TV!) 621 Corona Loss 621 Ground Wire Design (60 Hz) 622 Transient Voltage Insulation (Station) 623 Insulation for Contamination (Station) 624 Corona Performance (Station) 624 Corona Shields (Station) 625 Ground Electric Field (Near Stations) 625
