High Voltage Engineering

HIGH VOLTAGE ENGINEERING

CRC Press is an imprint of the

Taylor & Francis Group, an informa business

Boca Raton London New York

HIGH VOLTAGE ENGINEERING

FAROUK A.M. RIZK

Life Fellow IEEE

Lightning Electrotechnologies Inc

GIAO N. TRINH

Life Fellow IEEE

Consultant

CRC Press

Taylor & Francis Group

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Version Date: 20140210

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v

Contents

Preface ....................................................................................................................................................xix

Acknowledgments.................................................................................................................................. xxv

Authors.................................................................................................................................................xxvii

1. Power System Overvoltages............................................................................................................. 1

1.1 Introduction............................................................................................................................. 1

1.2 Lumped Circuits ..................................................................................................................... 2

1.3 Distributed Parameter Circuits............................................................................................... 4

1.3.1 Temporary Overvoltages........................................................................................... 4

1.3.1.1 Ferranti Effect........................................................................................... 4

1.3.1.2 Voltage Rise on Sound Phases.................................................................. 8

1.3.2 Transient Overvoltages on Transmission Lines...................................................... 10

1.3.2.1 Wave Equations...................................................................................... 10

1.3.2.2 Points of Discontinuity............................................................................11

1.3.2.3 Traveling Waves of General Form...........................................................14

1.3.2.4 Lattice Diagram.......................................................................................16

1.3.2.5 Energization of Open Line ......................................................................17

1.3.2.6 Three-Phase Lines...................................................................................17

1.3.3 Overvoltages due to Current Interruption............................................................... 19

1.3.3.1 Interruption of Small Inductive Currents............................................... 19

1.3.3.2 Interruption of Capacitive Current......................................................... 20

1.4 Electromagnetic Transient Program..................................................................................... 21

References........................................................................................................................................ 23

2. Electrostatic Field Calculation...................................................................................................... 25

2.1 Electromagnetism: Maxwell Equations................................................................................ 25

2.1.1 Fundamental Laws.................................................................................................. 25

2.1.2 Boundary Conditions.............................................................................................. 26

2.2 Electrostatics: Laplace Equation........................................................................................... 27

2.3 Analytical Solution of the Laplace Equation........................................................................ 28

2.3.1 Cartesian Coordinates............................................................................................. 29

2.3.1.1 Uniform Field ......................................................................................... 29

2.3.1.2 Uniform Field Electrodes....................................................................... 30

2.3.1.3 Uniform Field in the Presence of Composite Dielectrics....................... 35

2.3.2 Cylindrical Coordinates.......................................................................................... 36

2.3.2.1 Coaxial Cable ......................................................................................... 37

2.3.2.2 Cylindrical Field in the Presence of Composite Dielectrics.................. 38

2.3.3 Spherical Coordinates............................................................................................. 40

2.3.3.1 Spherical Field........................................................................................ 40

2.3.4 Spheroidal Coordinates........................................................................................... 42

2.3.4.1 Prolate Spheroidal Coordinates.............................................................. 42

2.3.4.2 Hyperboloidal Field................................................................................ 49

2.3.4.3 Oblate Spheroidal Metal Protrusion in a Uniform Field........................ 50

vi Contents

2.4 Methods of Transformation .................................................................................................. 53

2.4.1 Method of Images................................................................................................... 53

2.4.1.1 Images with Respect to a Ground Plane................................................. 53

2.4.1.2 Image with Respect to a Cylindrical Conductor.................................... 55

2.4.1.3 Sphere Gap ............................................................................................. 56

2.5 Numerical Solution Laplace Equation.................................................................................. 60

2.5.1 Field and Potential around Elementary Charges.................................................... 60

2.5.2 Method of Successive Images................................................................................. 62

2.5.2.1 Overhead Line ........................................................................................ 63

2.5.2.2 High-Voltage Cable................................................................................. 66

2.5.3 Method of Charge Simulation................................................................................. 69

2.5.3.1 Two-Dimensional Field .......................................................................... 69

2.5.3.2 Field in the Presence of Composite Dielectrics...................................... 70

2.5.3.3 Three-Dimensional Field: Representation of the Surface Charge

by Orthogonal Functions........................................................................ 70

2.5.3.4 Floating Electrode .................................................................................. 72

2.5.4 Method of Global Solution...................................................................................... 74

2.5.4.1 Method of Finite Differences................................................................. 74

2.5.4.2 Method of Finite Elements..................................................................... 75

References........................................................................................................................................ 79

3. Application of Statistical Analysis in High Voltage Engineering.............................................. 81

3.1 Introduction........................................................................................................................... 81

3.2 Characterization of a Set of Data under Specific Conditions............................................... 81

3.2.1 Global Statistical Parameters.................................................................................. 82

3.2.2 Experimental (Discrete) Distribution ..................................................................... 82

3.2.2.1 Experimental Distribution with a Small Amount of Data ..................... 82

3.2.2.2 Experimental Distribution with a Large Amount of Data ..................... 84

3.2.2.3 Correspondence with the Global Parameters......................................... 85

3.2.2.4 Other Characteristic Parameters............................................................ 85

3.2.3 Statistical Functions (Models) ................................................................................ 85

3.2.3.1 Discrete Distributions............................................................................. 85

3.2.3.2 Continuous Distributions........................................................................ 88

3.3 Estimation of the Population Distribution............................................................................ 94

3.3.1 Randomness Test .................................................................................................... 94

3.3.2 Using the Sample’s Statistic Parameters................................................................. 94

3.3.2.1 Sample Means......................................................................................... 95

3.3.2.2 Sample Variance..................................................................................... 95

3.3.3 Confidence Interval................................................................................................. 96

3.3.3.1 One-Sided Test ....................................................................................... 96

3.3.3.2 Two-Sided Test ....................................................................................... 97

3.3.4 Distribution Test...................................................................................................... 98

3.3.4.1 Chi-Square Test ...................................................................................... 98

3.3.4.2 Graphical Test......................................................................................... 98

3.3.4.3 Linear Regression Analysis.................................................................. 103

3.3.5 Adequacy Representation of a Statistical Model.................................................. 104

3.3.5.1 Extreme Value Distribution.................................................................. 107

3.3.5.2 Weibull Distribution ............................................................................. 108

3.3.5.3 Discussion............................................................................................. 109

3.3.6 Direct Extrapolation of Experimental Data...........................................................110

3.3.7 Verification of an Experimental Law.....................................................................110

3.4 Weak Link Statistics............................................................................................................112

Contents vii

3.5 Optimization of Experimental Data ....................................................................................112

3.5.1 Determination of the Component Distributions....................................................113

3.5.1.1 Audible Noise ........................................................................................113

3.5.1.2 Streamer Length ....................................................................................113

3.5.2 Improvement of Experimental Data ......................................................................114

3.5.2.1 Breakdown Probability of Elementary Volume ....................................116

3.6 Joint Probability...................................................................................................................117

3.6.1 Risk of Failure........................................................................................................117

3.6.2 V–t Breakdown Characteristic...............................................................................117

3.7 Verification of Characteristics or Behavior by Specific Tests.............................................118

3.7.1 Optimization of the Number of Test Samples .......................................................118

3.7.1.1 Minimum Required Number of Tests ...................................................118

3.7.2 Statistical Significance of Test Procedures............................................................118

3.7.2.1 Test with Impulse Voltage .....................................................................119

3.7.2.2 Practical Test Procedures..................................................................... 120

3.7.2.3 Test with AC Voltage............................................................................ 122

3.7.3 Computer Simulation of Test Procedures............................................................. 124

3.7.3.1 Hancox Test Procedures....................................................................... 125

3.7.3.2 Fryxell (or α–β) Test Procedures.......................................................... 126

3.7.3.3 Modified α–β Test Procedures ............................................................. 126

3.8 Conclusions......................................................................................................................... 127

References...................................................................................................................................... 127

4. Electrical Breakdown in Gases................................................................................................... 129

4.1 Introduction......................................................................................................................... 129

4.2 Gases Composed Uniquely of Neutral Molecules.............................................................. 130

4.2.1 General Laws and Definitions............................................................................... 130

4.2.1.1 Conservation of Energy........................................................................ 130

4.2.1.2 Conservation of Momentum................................................................. 130

4.2.1.3 Inelastic Collisions ................................................................................131

4.2.1.4 Hypothesis of Avogadro ........................................................................132

4.2.1.5 Law of Gay-Lussac................................................................................132

4.2.2 Distribution of Velocities of Gas Molecules..........................................................133

4.2.2.1 Distribution Function of the Velocities of Gas Molecules................... 134

4.2.2.2 Some Characteristic Values of the Velocity c of Gas Molecules

in Air and SF6 ........................................................................................135

4.2.3 Equal Partition of Energy ..................................................................................... 136

4.2.4 Mean Free Path ..................................................................................................... 137

4.2.4.1 Statistical Distribution of Free Paths.................................................... 137

4.2.4.2 Evaluation of the Mean Free Path ........................................................ 138

4.2.5 Diffusion in a Gas................................................................................................. 139

4.2.5.1 Number of Molecules Traversing a Unit Area per Second .................. 139

4.2.5.2 General Equation of Diffusion ............................................................. 140

4.2.5.3 Diffusion of a Gas in Another Gas........................................................141

4.3 Atomic Structure of the Elements .......................................................................................145

4.3.1 Bohr’s Atomic Model.............................................................................................145

4.3.2 Energy States of an Electron in an Atom ............................................................. 150

4.3.3 Exclusion Principle of Pauli.................................................................................. 150

4.3.4 Interpretation of the Periodic Table of Elements.................................................. 150

4.4 Excitation and Ionization of Atoms.....................................................................................151

4.4.1 Ionization by Electronic Collisions........................................................................152

4.4.2 Ionization by Ionic Collisions............................................................................... 154

viii Contents

4.4.3 Photoionization ......................................................................................................155

4.4.4 Thermal Ionization ............................................................................................... 156

4.4.5 Cumulative Ionization........................................................................................... 157

4.5 Ion Movement in an Electric Field ..................................................................................... 157

4.5.1 Ion Mobility .......................................................................................................... 157

4.5.2 Electron Mobility...................................................................................................161

4.5.3 Ions in a Gas Subjected to an Electric Field ..........................................................162

4.5.4 Electric Current Produced by the Movement of a Charged Particle .....................163

4.6 Deionization and Deexcitation............................................................................................ 164

4.6.1 Recombination .......................................................................................................165

4.6.2 Attachment............................................................................................................ 166

4.6.3 Deionization by Diffusion .................................................................................... 166

4.7 Sources of Free Electrons....................................................................................................167

4.8 Development of Electron Avalanches..................................................................................170

4.8.1 Townsend Discharge ..............................................................................................170

4.8.2 Ionization by Electron Collisions in the Gas Volume............................................171

4.8.2.1 Mechanism of Discharge by Electronic Collisions: Electron

Avalanche ..............................................................................................171

4.8.2.2 Townsend’s First Coefficient of Ionization, α........................................173

4.8.2.3 Practical Expressions of Townsend’s First Ionization

Coefficient ................................................................................174

4.8.3 Electronegative Gases............................................................................................175

4.9 Classical Theory of Gaseous Discharges ............................................................................176

4.9.1 Influence of Secondary Processes .........................................................................176

4.9.2 Regimes of Sustained and Self-Sustained Discharges ..........................................178

4.9.3 Onset Conditions of Self-Sustained Discharge......................................................179

4.9.3.1 Breakdown Voltage in Uniform Fields: Paschen’s Law ........................179

4.9.3.2 Streamer Criterion: Onset Condition in Nonuniform Fields................ 180

4.10 Examples of Self-Sustained Discharges..............................................................................181

4.10.1 Glow Discharges....................................................................................................182

4.10.1.1 Physical Mechanism of the Discharge ..................................................183

4.10.1.2 Electrical Characteristics ..................................................................... 184

4.10.2 Electric Arc............................................................................................................185

4.10.2.1 Physical Mechanism..............................................................................186

4.10.2.2 Arc Characteristics................................................................................186

4.11 Fundamentals of Corona Discharges in Atmospheric Air ..................................................187

4.11.1 Empirical Expressions of Onset and Breakdown of Practical Gap

Configurations........................................................................................................188

4.11.2 Active Ionization Processes and Source of Free Electrons ...................................188

4.11.3 Corona Discharges under Negative Polarity..........................................................189

4.11.3.1 Electron Avalanche and Space Charges................................................189

4.11.3.2 Negative Corona Modes ....................................................................... 192

4.11.4 Corona Discharges under Positive Polarity .......................................................... 199

4.11.4.1 Electron Avalanche and Ion Space Charge .......................................... 199

4.11.4.2 Modes of Positive Corona Discharges.................................................. 201

4.11.5 Corona Discharges under Alternating Voltage ..................................................... 208

4.11.6 Impact of Corona Discharges ............................................................................... 209

4.11.6.1 Main Effect of Corona Discharges on High-Voltage Testing............... 209

4.11.6.2 Main Effects of Corona Discharges on Overhead Lines.............................. 209

4.12 Electric Breakdown in Compressed Gases: Sulfur Hexafluoride........................................213

4.12.1 Sulfur Hexafluoride................................................................................................213

4.12.2 Ionization Processes and Source of Free Electrons...............................................214

4.12.3 Mixtures of SF6 and Neutral Gases .......................................................................215

Contents ix

4.12.4 Dielectric Withstand ..............................................................................................217

4.12.4.1 Uniform and Quasiuniform Fields ........................................................217

4.12.4.2 Leader Breakdown in Nonuniform Fields.............................................218

References...................................................................................................................................... 220

5. Breakdown Characteristics of Long Air Gaps.......................................................................... 223

5.1 Introduction......................................................................................................................... 223

5.2 Breakdown of Long Air Gaps with Fast Front Impulses.................................................... 224

5.2.1 Breakdown Mechanism ........................................................................................ 224

5.2.2 Standard Lightning Impulse Breakdown Voltage ................................................ 228

5.3 Air Gap Strength under Direct Voltage.............................................................................. 228

5.4 Positive Switching Surge Strength of Long Gaps............................................................... 230

5.4.1 System Overvoltages............................................................................................. 230

5.4.2 Air Gap Strength Data ...........................................................................................231

5.4.3 Modeling of Positive Critical Switching Impulse Breakdown ............................. 233

5.5 Air Gap Breakdown under Composite Stress..................................................................... 236

5.5.1 Experimental Results............................................................................................ 236

5.5.2 Modeling of Air Gap Breakdown under Composite Voltages.............................. 238

5.6 AC Breakdown of Long Air Gaps...................................................................................... 241

5.6.1 Breakdown Mechanism ........................................................................................ 241

5.6.2 AC Breakdown Test Procedures........................................................................... 241

5.6.3 AC Breakdown Test Data...................................................................................... 243

5.7 Altitude Effect on Air Gap Breakdown.............................................................................. 244

5.8 Humidity Effects on Air Gap Breakdown.......................................................................... 246

5.8.1 Effect of Humidity with Special Reference to Streamer Breakdown................... 247

5.8.2 Effect of Humidity on Switching Impulse Breakdown ........................................ 248

5.8.3 More Recent Approaches to Humidity Corrections............................................. 250

5.8.4 Modeling of Humidity Effects on Switching Impulse Breakdown ...................... 252

5.8.5 Comparison of Correction Factors........................................................................ 255

5.8.6 Further Application of Generalized Correction Approach................................... 256

References...................................................................................................................................... 257

6. Electric Breakdown in Liquids....................................................................................................261

6.1 Chemical Composition of Mineral Oil................................................................................261

6.2 Interest in Synthetic Oils .................................................................................................... 262

6.2.1 Required Properties for Synthetic Oils................................................................. 263

6.2.2 Principal Synthetic Oils Presently Available........................................................ 263

6.2.2.1 Aliphatic Hydrocarbons ....................................................................... 265

6.2.2.2 Silicone Oil........................................................................................... 265

6.2.2.3 Perfluorocarbons................................................................................... 266

6.2.2.4 Synthetic Esters.................................................................................... 266

6.3 Breakdown Mechanisms..................................................................................................... 266

6.3.1 Early Studies......................................................................................................... 266

6.3.1.1 Electrical Conduction and Strength of Pure Liquids ........................... 267

6.3.1.2 Conduction and Breakdown Processes................................................. 268

6.3.1.3 Breakdown of Commercial Liquids..................................................... 269

6.3.1.4 Breakdown of Liquid–Solid Dielectrics............................................... 270

6.3.2 Breakdown in Short Gaps..................................................................................... 271

6.3.2.1 Streamer Discharges in Oil .................................................................. 271

6.3.2.2 Formation of a Gaseous Cavity ............................................................ 273

6.3.3 Breakdown of Long Oil Gaps............................................................................... 276

6.3.3.1 Direct Breakdown................................................................................. 276

6.3.3.2 Breakdown by Discharges in Streamer Burst ...................................... 281

x Contents

6.4 Factors Affecting the Oil Insulation................................................................................... 284

6.4.1 Impurities.............................................................................................................. 284

6.4.2 Dissolved Gases and Hydrostatic Pressure........................................................... 284

6.4.3 Humidity ............................................................................................................... 285

6.4.4 Dissolved Metals................................................................................................... 285

6.4.5 Solid Particle Contamination................................................................................ 285

6.4.5.1 Particle Content .................................................................................... 286

6.4.5.2 Effect of Stressed Area and Volume .................................................... 286

6.4.6 Dielectric Interfaces.............................................................................................. 294

6.4.6.1 Incipient Fault....................................................................................... 294

6.4.6.2 Electrostatic Discharges....................................................................... 295

6.4.7 Aging and Decomposition By-Products of Oils................................................... 295

References...................................................................................................................................... 295

7. Electric Breakdown in Solid and Composite Materials........................................................... 299

7.1 Introduction......................................................................................................................... 299

7.1.1 Intrinsic Breakdowns............................................................................................ 299

7.1.1.1 Theory of Intrinsic Strength................................................................. 299

7.1.1.2 Measurement of Intrinsic Strength....................................................... 300

7.1.2 Initial Breakdown and Strength............................................................................ 301

7.1.3 Aging and Incipient Fault ..................................................................................... 301

7.1.3.1 Thermal Breakdown............................................................................. 302

7.1.3.2 Breakdown by Electrical Discharges ................................................... 303

7.1.3.3 Mechanical Aging ................................................................................ 304

7.1.3.4 Combined Stress................................................................................... 304

7.1.3.5 Chemical Deterioration ........................................................................ 305

7.1.3.6 Electrochemical Deterioration ............................................................. 305

7.1.4 Decomposition By-Products................................................................................. 306

7.1.5 Insulation Systems Reviewed ............................................................................... 306

7.2 Polymeric (PE and XLPE) Insulation................................................................................. 306

7.2.1 Physical–Chemical Properties of Insulating Materials........................................ 307

7.2.1.1 Natural Rubber ..................................................................................... 307

7.2.1.2 Ethylene–Propylene Rubber................................................................. 307

7.2.1.3 Butyl Rubber......................................................................................... 308

7.2.1.4 Silicone Rubber .................................................................................... 309

7.2.1.5 Neoprene and Polychloroprene............................................................. 309

7.2.1.6 Polyvinyl Chloride.................................................................................310

7.2.1.7 Polyethylene and Cross-Linked Polyethylene .......................................310

7.2.2 Dielectric Performance of New Samples...............................................................311

7.2.2.1 Initial Breakdown..................................................................................312

7.2.2.2 Factors Affecting Synthetic Polymer Insulation ...................................313

7.3 Paper–Oil Composite Insulation..........................................................................................316

7.3.1 Lapped Insulation ..................................................................................................316

7.3.1.1 Physical–Chemical Properties of Impregnated Paper–Oil Insulation...... 318

7.3.1.2 Improvement of Insulation Properties.................................................. 324

7.3.2 Dielectric Performances of New Samples............................................................ 325

7.3.2.1 Initial Strength...................................................................................... 326

7.3.2.2 Factors Affecting the Initial Strength .................................................. 327

7.4 Gas–Solid (SF6–Epoxy) Composite Insulation................................................................... 328

7.4.1 Gas (SF6) Insulation .............................................................................................. 329

7.4.1.1 Corona Onset Field............................................................................... 329

7.4.1.2 Limit Withstand Field............................................................................331

7.4.1.3 Voltage–Time Breakdown Characteristics............................................331

Contents xi

7.4.2 Solid (Epoxy) Insulation ........................................................................................335

7.4.2.1 Initial Breakdown Strength ...................................................................341

7.4.2.2 Voltage–Time Breakdown Characteristics............................................341

7.4.3 Factors Affecting SF6–Epoxy Insulation.............................................................. 344

References...................................................................................................................................... 349

8. Selection of Overhead Transmission Line Conductors.............................................................351

8.1 Development of Overhead Lines .........................................................................................351

8.1.1 AC Power Transmission Lines...............................................................................351

8.1.2 Bundle Conductor to Improve the Natural Transmission Capability

of AC Lines......................................................................................................... 352

8.1.3 Electrostatic Field Optimization of Conductor Bundle ........................................ 354

8.2 Average Height of Conductors............................................................................................ 356

8.2.1 Electric Field at Ground in the Vicinity of the HV Line...................................... 357

8.2.2 Magnetic Field at Ground in the Vicinity of the HV Line ................................... 360

8.3 Selection of Conductors...................................................................................................... 362

8.3.1 Corona Onset Conditions...................................................................................... 362

8.3.2 Energy Losses....................................................................................................... 363

8.3.2.1 Mechanism of Generating Energy Losses from Corona Discharges........363

8.3.2.2 Empirical Formulae for Evaluating Energy Losses............................. 364

8.3.2.3 Corona Loss Characteristics of Bundle Conductors ............................ 366

8.3.3 Electromagnetic Interference................................................................................ 366

8.3.3.1 Generation Mechanism of Interference from Corona Discharges....... 367

8.3.3.2 Interference to the Radio Reception..................................................... 370

8.3.3.3 Quantification of Electromagnetic Interference................................... 373

8.3.3.4 Measurement of Electromagnetic Interference .....................................375

8.3.3.5 Empirical Formulae for the Calculation of Interference from a Line.......379

8.3.3.6 Calculation of Electromagnetic Interference on a Single-Phase Line ....... 380

8.3.3.7 Calculation of Electromagnetic Interference from a Three-Phase Line.....385

8.3.3.8 Television Interference ......................................................................... 390

8.3.4 Audible Noise........................................................................................................ 393

8.3.4.1 Static and Acoustic Pressures............................................................... 394

8.3.4.2 Propagation of Acoustic Wave.............................................................. 394

8.3.4.3 Solution of the Wave Equation ............................................................. 397

8.3.4.4 Specific Acoustic Notions .................................................................... 400

8.3.4.5 Acoustical Characteristics of Corona Discharges................................ 401

8.3.4.6 Measurement of Audible Noise ............................................................ 406

8.3.4.7 Sound Meter ......................................................................................... 406

8.3.4.8 Methods of Calculation of Audible Noise ............................................ 408

8.3.5 Selection of Conductors.........................................................................................412

8.3.5.1 Evaluation of the Worst-Case Performances.........................................413

8.3.5.2 Long-Term Corona Performance...........................................................421

8.3.6 Emission of Polluting Effluents ............................................................................ 422

8.4 Selection of Conductors for HVDC Lines.......................................................................... 424

8.4.1 Average Conductor Height.................................................................................... 424

8.4.2 Selection of Conductors........................................................................................ 425

8.4.2.1 Corona Onset........................................................................................ 425

8.4.2.2 Generating Functions ........................................................................... 425

8.4.2.3 Corona Losses ...................................................................................... 425

8.4.2.4 Radio Interference .................................................................................431

8.4.2.5 Audible Noise ....................................................................................... 434

8.4.2.6 Experimental Evaluation of Corona Performance of Conductor......... 436

References...................................................................................................................................... 437

xii Contents

9. Lightning Incidence and Lightning Protection......................................................................... 439

9.1 Cloud Charging................................................................................................................... 439

9.2 Meteorological Data ........................................................................................................... 440

9.3 Lightning Detection and Location...................................................................................... 442

9.3.1 Flash Counters ...................................................................................................... 442

9.3.2 Lightning Location Systems................................................................................. 442

9.3.2.1 Direction Finders.................................................................................. 442

9.3.2.2 Time-of-Arrival (TOA) Method........................................................... 443

9.4 Lightning Flash Parameters................................................................................................ 444

9.4.1 Flash Classification ............................................................................................... 444

9.4.2 Return Stroke Current........................................................................................... 444

9.4.2.1 Statistical Distribution.......................................................................... 444

9.4.2.2 Current Waveform................................................................................ 444

9.4.3 Statistical Parameters............................................................................................ 447

9.5 Lightning Attachment......................................................................................................... 449

9.5.1 Negative Downward Flash.................................................................................... 449

9.5.2 Return Stroke ........................................................................................................ 450

9.5.2.1 General ................................................................................................. 450

9.5.2.2 Return Stroke Models........................................................................... 450

9.5.3 Lightning Attachment Models...............................................................................452

9.5.3.1 Electrogeometric Model........................................................................452

9.5.3.2 Eriksson and Dellera–Garbagnati Models............................................453

9.5.3.3 Rizk Model........................................................................................... 454

9.5.4 Shielding Failure................................................................................................... 459

9.5.5 Backflashover........................................................................................................ 459

9.5.5.1 Tower Top Potential.............................................................................. 461

9.5.5.2 Tower Surge Impedance ....................................................................... 463

9.5.5.3 Conductor Coupling ............................................................................. 465

9.5.5.4 Reflections from Adjacent Towers........................................................ 466

9.5.5.5 Tower Grounding.................................................................................. 466

9.5.5.6 Estimation of Backflashover Rate ........................................................ 467

9.6 Upward Flash...................................................................................................................... 467

9.7 Protective Measures............................................................................................................ 469

9.7.1 Lightning Rods and Masts.................................................................................... 469

9.7.2 Ground Wires........................................................................................................ 470

9.7.3 Improving Grounding ............................................................................................471

9.7.4 Line Arresters....................................................................................................... 472

9.7.5 Streamer Inhibition ............................................................................................... 473

References.......................................................................................................................................474

10. High-Voltage Insulators............................................................................................................... 479

10.1 Introduction......................................................................................................................... 479

10.2 Insulator Types and Materials ............................................................................................ 479

10.2.1 Insulator Types...................................................................................................... 479

10.2.2 Insulator Materials................................................................................................ 481

10.2.2.1 Porcelain ............................................................................................... 481

10.2.2.2 Glass ..................................................................................................... 482

10.2.2.3 Polymers............................................................................................... 482

10.3 Electrical Performance of High-Voltage Insulators............................................................ 484

10.3.1 Lightning Impulse Flashover................................................................................ 484

10.3.2 Switching Impulse Flashover................................................................................ 487

10.3.2.1 Comparison with Air Gaps................................................................... 487

10.3.2.2 Effect of Rain ....................................................................................... 487

Contents xiii

10.3.3 Pollution Flashover ............................................................................................... 490

10.3.3.1 Pollution Layer Buildup........................................................................ 490

10.3.3.2 Site Severity...........................................................................................491

10.3.3.3 Effect of Exposure Time ...................................................................... 492

10.3.3.4 Pollution Layer Pattern......................................................................... 494

10.3.3.5 Effect of Operating Voltage.................................................................. 495

10.3.3.6 Effect of Distance from Pollution Source ............................................ 495

10.3.3.7 Effect of Wind Speed ........................................................................... 496

10.3.3.8 Insulator Surface Wetting..................................................................... 498

10.3.3.9 Pollution Flashover Mechanism ........................................................... 501

10.3.4 Mechanical Requirements .....................................................................................517

10.4 Insulator Selection ...............................................................................................................519

10.4.1 Insulator Type and Material...................................................................................519

10.4.2 Insulator Profile..................................................................................................... 520

10.4.3 Design Approach................................................................................................... 520

10.4.3.1 Flowchart.............................................................................................. 520

10.4.3.2 Statistical Approach to Insulator Selection .......................................... 522

References...................................................................................................................................... 526

11. High-Voltage (Underground) Cables...........................................................................................531

11.1 Development of High-Voltage Cables..................................................................................531

11.1.1 Paper–Oil-Insulated Cables...................................................................................531

11.1.1.1 Pressurized Oil-Filled Paper-Impregnated Cables................................532

11.1.1.2 Mass-Impregnated Cables.................................................................... 534

11.1.2 Extruded Insulation Cables................................................................................... 534

11.1.3 Cables with Gas Insulation ....................................................................................535

11.1.3.1 Pressurized-Gas Cables.........................................................................535

11.1.3.2 Rigid Gas-Insulated Cables (Lines) ......................................................535

11.1.4 Future Trends in High-Voltage Cables.................................................................. 536

11.1.4.1 Forced Cooling ..................................................................................... 536

11.1.4.2 Synthetic Paper and Tape ......................................................................537

11.1.4.3 Pressure................................................................................................. 538

11.1.4.4 Compressed SF6-Insulated Cable ......................................................... 538

11.2 High-Voltage AC Cables and Accessories.......................................................................... 538

11.2.1 Cable Parameters ...................................................................................................539

11.2.2 Dimensioning of the Conductor............................................................................ 540

11.2.2.1 Energy Losses....................................................................................... 542

11.2.2.2 Thermal Dissipation ............................................................................. 545

11.2.3 Dimensioning of the Insulation Based on Limit Field (New Cable) .................... 547

11.2.3.1 Selection of the Withstand Voltage Level ............................................ 547

11.2.3.2 Determination of the Design Field, E0 ................................................. 548

11.2.3.3 Determination of the Insulation Thickness.......................................... 549

11.3 Aging and Incipient Fault ....................................................................................................551

11.3.1 Self-Contained Oil-Filled Cables ..........................................................................551

11.3.1.1 Thermal Aging ......................................................................................551

11.3.1.2 Electrical Aging.....................................................................................551

11.3.1.3 Environmental Aging ............................................................................553

11.3.2 Polymeric (PE and XLPE) Cables.........................................................................553

11.3.2.1 Thermal Aging ......................................................................................553

11.3.2.2 Electrical Aging.....................................................................................553

11.3.2.3 Environmental Aging ............................................................................558

11.3.2.4 Decomposition By-Products................................................................. 560

xiv Contents

11.3.3 Gas (SF6)-Insulated Cables (Lines)....................................................................... 560

11.3.3.1 Thermal and Mechanical Aging........................................................... 560

11.3.3.2 Electrical Aging.................................................................................... 560

11.3.3.3 Environmental Aging ........................................................................... 562

11.3.4 Experimental Evaluation of Life Function ........................................................... 562

11.3.4.1 Accelerated Aging Tests....................................................................... 562

11.3.4.2 Analysis of Data ................................................................................... 563

11.3.4.3 Optimization of Test Parameters.......................................................... 564

11.4 Gas-Insulated Substations................................................................................................... 565

11.4.1 Generation of Fast Transients ............................................................................... 565

11.4.2 Risk of Burn Through........................................................................................... 568

11.4.3 Special Considerations for Operating Gas-Insulated Equipment......................... 569

11.4.3.1 Temperature.......................................................................................... 569

11.4.3.2 Humidity............................................................................................... 569

11.5 Accessories ..........................................................................................................................571

11.5.1 Impregnated Paper–Oil Accessories .....................................................................571

11.5.1.1 Principal Types of Accessories .............................................................571

11.5.2 Extruded Insulation............................................................................................... 573

11.5.3 Gas (SF6) Insulation ...............................................................................................575

11.6 High-Voltage DC Cables and Accessories.......................................................................... 577

11.6.1 Dimensioning of Conductors................................................................................ 578

11.6.2 Dimensioning of the Insulation ............................................................................ 578

11.6.2.1 Field Distribution in Steady-State Regime........................................... 578

11.6.2.2 Field Distribution in Transient Conditions........................................... 579

11.6.2.3 Field Enhancement in Butt Gap ........................................................... 580

11.6.3 SF6-Insulated Cable ...............................................................................................581

11.6.4 Accessories............................................................................................................ 582

11.6.4.1 Impregnated Paper–Oil Insulation ....................................................... 582

11.6.4.2 Polymer and SF6 Insulation .................................................................. 582

11.6.4.3 DC Pollution ......................................................................................... 582

11.7 Maintenance Practices Consideration................................................................................. 583

11.7.1 Actual State of Insulation ..................................................................................... 583

11.7.2 End of Life ............................................................................................................ 583

References...................................................................................................................................... 584

12. Power Transformers .................................................................................................................... 587

12.1 Introduction......................................................................................................................... 587

12.2 Transformer Insulation ........................................................................................................591

12.2.1 Operating Stresses .................................................................................................591

12.2.2 Oil–Paper Insulation in Power Transformers ....................................................... 592

12.2.2.1 Winding Arrangement.......................................................................... 592

12.2.2.2 Transformer Insulation Characteristics................................................ 593

12.2.2.3 Physical–Chemical Properties of Oil-Impregnated Paper................... 595

12.2.2.4 Control of Humidity ............................................................................. 598

12.2.2.5 Control of Particle Contamination ....................................................... 600

12.2.3 SF6 Insulation........................................................................................................ 604

12.3 Considerations on the Dimensioning of Oil–Paper Insulation........................................... 606

12.3.1 Cumulative Stress ................................................................................................. 606

12.3.2 Breakdown Probability ......................................................................................... 607

12.3.3 Example of Assessment for Adequacy of a Test Cell ............................................610