High Voltage Engineering

804 Pages·2014·76.81 MB·English

by  Farouk A.M. Rizk

HIGH VOLTAGE ENGINEERING

HIGH VOLTAGE ENGINEERING

FAROUK A.M. RIZK
L i f e F e l l o w I E E E
L i g h t n i n g E l e c t r o t e c h n o l o g i e s I n c
GIAO N. TRINH
L i f e F e l l o w I E E E
C o n s u l t a n t
Boca Raton London New York
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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
v
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 SF ........................................................................................135
6
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 SF and Neutral Gases .......................................................................215
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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