ELECTRIC FIELD AND VOLTAGE DISTRIBUTIONS ALONG NON-CERAMIC INSULATORS
DISSERTATION
Presented in Partial Fulfillment of the Requirements for
the Degree Doctor of Philosophy in the Graduate
School of The Ohio State University
By
Weiguo Que, M.S.
* * * *
The Ohio State University
2002
Dissertation Committee: Approved by Professor Stephen A. Sebo, Adviser
Professor Donald G. Kasten Adviser Professor Longya Xu Department of Electrical Engineering UMI Number: 3081955
UMI UMI Microform 3081955 Copyright 2003 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code.
ProQuest Information and Learning Company 300 North Zeeb Road PC Box 1346 Ann Arbor, Ml 48106-1346 ABSTRACT
High voltage insulators are essential for the reliable performance of electric power
systems. All insulators, regardless of their material, are exposed to various electrical, mechanical and environmental stresses. The electrical stresses are the consequences of regular voltages and overvoltages. The mechanical stresses are related to the presence of various loads, e.g., the weight of conductors and hardware, wind load, ice load, etc. The environmental stresses of prime importance are the many forms of precipitation, UV radiation, and pollution. Since an increasing number of non-ceramic insulators are employed by electric utility companies for their new or updated power transmission lines, the analysis of their performance is relevant.
The performance of these high voltage non-ceramic insulators is important for both dry and wet conditions. Long-term problems with them are related to the degradation of polymer materials used for the insulator, corona phenomena on the insulator surface, and pollution flashover. Most of these problems are related to the electric field distribution along the insulators.
The dissertation research topic is the investigation of electric field and voltage distributions (EFVD) in the vicinity of non-ceramic insulators. A three-dimensional
11 electric field analysis software package, Coulomb, based on the boundary element method, has been obtained and employed for the calculations.
Main contributions of the dissertation research to the state of the art are as follows:
1. Principles of the full and simplified models as well as the calculation models
of dry and clean non-ceramic high voltage insulators have been developed for
the purpose of accurate calculations together with efficient calculation times.
The modeling and its procedures are illustrated in detail by practical
examples.
2. Models of the high voltage insulators alone are not sufficient. The detailed
modeling of several more major components have been found essential. These
major components are the power line tower, the three phase conductors, all
conductor hardware, and corona rings. The effects of all these components on
the EFVD along dry and clean insulators are analyzed and discussed.
3. A simple model with a flat polymer insulating sheet between two electrodes
and a water droplet on it has been used to simulate the behavior of a water
droplet on the shed and on the sheath region, respectively, of a non-ceramic
insulator. Basic studies related to the effects of the changes in water droplet
contact angle, size of droplet, shape of droplet, distance between adjacent
droplets, and conductivity of water have been described in terms of the
electric field strength enhancement, always referred to an appropriate base
case.
Ill 4. Several models of a four-shed non-ceramic insulator exposed to rain or fog
conditions have been initiated, following observations during and after aging
tests in a high voltage fog chamber. The calculation models of nine examples
have been developed. The electric field and voltage distribution along wet
insulators have been calculated and analyzed.
5. Selected calculations on dry and clean insulators using Coulomb software
package have been verified with an electric field strength meter. The
correspondence of calculations and high voltage measurements has been
reasonably good.
6. Several research issues applied to various practical insulator design aspects
have been investigated and discussed, such as the effect of the distance
between the first shed and the end fitting, the shed spacing, the shed profile
and the position of the corona ring on the EFVD along polymer insulators.
The research described in the dissertation is directly applicable to the field of high voltage insulator design and development.
IV
ACKNOWLEDGMENTS
First and foremost, I express my sincere appreciation to Professor Stephen A.
Sebo for guiding me through the most important five years in my life at The Ohio State
University. I appreciate his invaluable guidance, insightful discussions, patience, and generous support throughout my studies.
1 would also like to thank Professors Donald G. Kasten and Longya Xu for their kindness of participating in my dissertation committee and for all their constructive advice.
The generous support of Mr. Craig Armstrong, General Manager, Integrated
Engineering Software was invaluable for this research. The use of Coulomb, an excellent
software package of his company, Integrated, has made the dissertation research possible, as well as has made the completion time possible within a reasonable time.
1 also wish to thank Dr. Tiebin Zhao (The Ohio Brass Co.), who provided several polymer insulator samples used for this study. In addition, his technical advice and experience were indispensable for this research.
1 sincerely thank Mr. Robert Hill and Mr. David Crutcher (MacLean Power
Systems) for their technical support by providing information and important examples related to 765 kV insulators and hardware.
VI I am also grateful for the help of Mr. Ozkan Altay, my colleague, for spending his valuable time in order to conduct some of the experiments with me.
My deepest love and gratitude go to my wife WANG Yue, who has shared the excitements and difficulties in my life with me. 1 am grateful for her deep love, her joy, invaluable support and encouragement throughout the last five years.
1 also owe special thanks to my parents, for the education and love I received from them, and for their full support over the years.
VII VITA
March 12, 1971 ...... Bom-Harbin, Heilongjiang, China
1994...... B.S.E.E Tsinghua University, Beijing, China
1997 ...... M.S.E.E Tsinghua University, Beijing, China
1997 -2002 ...... Graduate Research Associate, Department of
Electrical Engineering, The Ohio State University
PUBLICATIONS
Research Publications:
1. W. Que, and S. A. Sebo, “Typical cases of electric field and voltage distribution calculations along polymer insulators under various wet surface conditions,” Proceedings of the 2002 Conference on Eleetrical Insulation and Dieleetric Phenomena, October 2002, pp. 840-843.
2. W. Que, E. P. Casale and S. A. Sebo, “Voltage-current phase angle measurements during aging tests of polymer insulators,” Proceedings of the 2002 Conference on Electrical Insulation and Dielectric Phenomena, October 2002, pp. 367-370.
vm 3. E. P. Casale, W. Que and S. A. Sebo, “Distribution of sait contamination in the course of fog chamber tests of polymer insulators,” Proceedings of the 2002 Conference on Electrical Insulation and Dielectric Phenomena, October 2002, pp. 359-362.
4. W. Que, and S. A. Sebo, “Electric field and potential distributions along dry and clean non-ceramic insulators,” Proceedings of the Electrical Insulation Conference and Electrical Manufacturing & Coil Winding Conference, October 2001, pp. 437- 440.
5. W. Que, and S. A. Sebo, “Electric field and potential distribution along non-ceramic insulators with water droplets,” Proceedings of the Electrical Insulation Conference and Electrical Manufacturing & Coil Winding Conference, October 2001, pp. 441- 444.
6. W. Que, and S. A. Sebo, “Electric field distribution in air for various energized and grounded electrode configurations,” Proceedings of the 2000 Conference on Electrical Insulation and Dielectric Phenomena, October 2000, pp. 498-501.
7. E. Wang, X. Eiang, Z. G nan, and W. Que, “Research on 500 kV phase to phase composite spacer for compact lines,” Proceedings of the 6th International Conference on Properties and Applications o f Dielectric Materials, June 2000, Vol. l,pp. 346-349.
8. S. A. Sebo, C. M. Pawlak, D. Oswiencinski, and W. Que, “Effects of humidity correction on the AC sparkover voltage characteristics of rod-rod gaps in air up to 30 /fWHwAafk)» .EThcZticfrZ Manufacturing & Coil Winding Conference, October 1999, pp. 327-330.
IX 9. S. A. Sebo, J. Kahler, S. Hutchins, C. Meyers, D. Oswiencinski, A. Eusebio and W. Que, “Effects of the insulating cylinders (guards) in various gaps - the study of AC breakdown voltages,” Proceedings of the 11th International Symposium on High Voltage Engineering, August 1999, Vol. 3, pp. 63-66. 10. S. A. Sebo, J. Kahler, S. Hutchins, C. Meyers, D. Oswiencinski, A. Eusebio and W. Que, “Effects of the insulating sheets (barriers) in various gaps - the study of AC breakdown voltages and barrior factors,” Proceedings of the 11th International Symposium on High Voltage Engineering, August 1999, Vol. 3, pp. 144-147.
11. C. M. Pawlak, D. Oswiencinski, W. Que and S. A. Sebo, “Influence of rod electrode orientation on power frequency AC sparkover voltages of small air gaps,” Proceedings of the 30th Annual North American Power Symposium, October 1998, pp. 347-352.
12. C. M. Pawlak, D. Oswiencinski, W. Que and S. A. Sebo, “Humidity correction procedure and their effects on AC sparkover voltage characteristics of small air gaps,” Proceedings of the 30th Annual North American Power Symposium, October 1998, pp. 364-369.
FIELDS OF STUDY
Major Field: Electrical Engineering Minor Field: Circuits and Electronics Minor Field: Mathematics
X TABLE OF CONTENTS
Abstract ...... ii
Dedication ...... v
Acknowledgments ...... vi
Vita...... viii
List of tables ...... xiv
List of figures ...... xv
Chapters:
1. Introduction ...... 1 1.1. Overview ...... 1 1.2. Necessity for electric field strength distribution study along non-ceramic insulators ...... 3 1.3. Methods used for the study ...... 5 1.4. Description of existing problems ...... 6 1.5. Obj ectives and main contributions ...... 7 1.6. Organization of dissertation ...... 9 2. Review of literature ...... 11 2.1. Structure of non-ceramic insulators ...... 12 2.2. Flashover mechanism of non-ceramic insulators ...... 14 2.3. Methods used for the electric field and voltage distribution study along insulators ...... 16 2.3.1. Experimental m ethods ...... 16 2.3.2. Numerical electric field analysis methods ...... 18 2.4. Software used for study and boundary element method ...... 21 2.4.1. Software used for study ...... 21 2.4.2. Boundary element method ...... 24 2.5. Electric field and voltage distribution study along insulators ...... 28
x i 2.5.1. EFVD study along insulators under dry and clean conditions ...... 28 2.5.2. EFVD study along insulators under wet and contaminated conditions ...... 30 2.5.3. Fault detection by electric field strength measurements...... 34 2.5.4. Design considerations for non-ceramic insulators ...... 37 2.6. Summary and tasks of the dissertation ...... 39 3. Fundamental studies ...... 42 3.1. Simplification of the non-ceramic insulator model ...... 43 3.2. Effects of conductor and ground supporting structure ...... 49 3.3. Some basic features of water droplets on a non-ceramic insulator surface.... 53 3.3.1. Hydrophobicity of non-ceramic insulators ...... 53 3.3.2. Water droplet corona and dynamic behavior on the surface of non- ceramic insulators ...... 56 3.4. Flat SIR sheet with a water droplet ...... 59 3.4.1. Sheath region simulation ...... 60 3.4.2. Shed region simulation ...... 64 3.5. Effects of water droplet contact angle, size, shape, distance, and conductivity ...... 68 3.5.1. Effect of water droplet contact angle ...... 68 3.5.2. Effect of water droplet size ...... 70 3.5.3. Effect of water droplet shape ...... 72 3.5.4. Effect of the distance between adjacent water droplets ...... 74 3.5.5. Effect of water droplet conductivity ...... 75 3.6. Summary...... 75 4. Electric field and voltage distributions along non-ceramic insulators under dry and clean conditions ...... 77 4.1. Introduction ...... 77 4.2. Model of insulator, tower and additional components ...... 79 4.2.1. Modeling of a non-ceramic insulator and corona rings ...... 79 4.2.2. Modeling of line end hardware and conductors ...... 81 4.2.3. Modeling of tower and ground plane ...... 83 4.3. Voltage and electric field distributions along a non-ceramic insulator ...... 87 4.4. Comparisons between four and six subconductor bundles ...... 96 4.5. Effects of the tower configuration and other components ...... 98 4.5.1. Effects of other two phases of the three phase system ...... 99 4.5.2. Effects of tower configuration ...... 103 4.5.3. Effects of conductor bundles ...... 105 4.6. Summary...... 106 5. Electric field strength and voltage distributions along a non-ceramic insulator under various wet conditions ...... 107 5.1. Introduction ...... 107 5.2. Hydrophobicity status of non-ceramic insulators ...... 108
x ii 5.3. Experiments in the OSU fog chamber ...... 110 5.4. Model setup ...... 112 5.5. Insulator models under rain conditions ...... 113 5.6. Analysis of enhancement factors and electric field and voltage distributions for an insulator under rain conditions ...... 121 5.7. Insulator models under fog conditions ...... 127 5.8. Analysis of enhancement factors and electric field and voltage distributions for an insulator under fog conditions ...... 131 5.9. Summary...... 134 6. Verification tests for dry insulator ...... 135 6.1. Calibration te st ...... 136 6.2. Verification test ...... 138 6.3. Error analysis ...... 141 6.4. Summary...... 141 7. Design considerations ...... 142 7.1. Model setup ...... 143 7.2. Effects of the distance between the first shed and the end fitting ...... 144 7.3. Effects of the shed spacing ...... 145 7.4. Effects of the shed profile ...... 146 7.5. Effects of the position of the corona ring ...... 147 7.6. Summary...... 149 8. Conclusions and future work ...... 150 8.1. Conclusions ...... 150 8.2. Suggested future work ...... 153 Appendices:
A. Brief review of Coulomb Software ...... 154
B. Basic two-shed insulator model ...... 158
Bibliography ...... 160
X lll LIST OF TABLES
Table ...... Page
3.1 Criteria for the hydrophobicity classification (HC) [44] ...... 54
3.2 The electric field enhancement factors on the surface of the water
droplet with different contact angles ...... 70
5.1 ffydrophobicity status of the insulator after 2 and 7 years of service[54]... 110
5.2 Electric field enhancement factor (E. F.) for Cases RHC1-RHC6 at different
locations ...... 122
5.3 Hydrophobicity of polymer insulator in different regions ...... 127
5.4 Electric field enhancement factor (E. F.) for Cases FHC1-FHC6 at different
locations ...... 132
6.1 Insulator readings under various applied voltages ...... 137
A. 1 Sample computation time and related parameters ...... 157
XIV LIST OF FIGURES
Figure...... Page
2.1 Simplified structure of non-ceramic insulators ...... 12
2.2 Insulator tester ...... 35
3.1 Simplified geometry and dimensions of the non-ceramic insulator to
be modeled ...... 44
3.2 Four simplified insulator models and a “full” insulator model used for
calculation ...... 45
3.3 Element configuration on the 34.5 kV non-ceramic insulator model ...... 45
3.4 Equipotential contours around the five computation models ...... 46
3.5 Voltage magnitude along the insulation distance at the surface of
the sheath for Cases (d) and (e) ...... 47
3.6 Electric field strength magnitude along the insulation distance at the sheath
surface for the “full” insulator, Case (e), and the simplified insulator model,
Case (d )...... 48
3.7 Insulator model with grounded support structure and line conductor ...... 49
3.8 Equipotential contours around three computation models ...... 50
XV 3.9 Electric field strength magnitude along the insulation distance at the sheath
surface of the insulator with and without the conductor and the grounded
supporting structure ...... 51
3.10 Electric field strength magnitude along the insulation distance at the sheath
surface for the “full” insulator and the simplified insulator model with the
conductor and grounded supporting structure ...... 52
3.11 Definition of contact angle...... 54
3.12 Typical examples of surfaces with HC from 1 to 6. HC 7 represent the
completely wet surface ...... 55
3.13 Behavior of 10 |^1 water droplet located on a SIR sheet [50] ...... 58
3.14 Three types of water droplets on a vertical suspension insulator ...... 59
3.15 Experimental setup for the sheath region simulation ...... 60
3.16 Equipotential contours and electric field lines for sheath region simulation. 61
3.17 Electric field distribution along the SIR sheet surface for sheath region
simulation ...... 61
3.18 Equipotential contours and electric field lines around a water droplet on
the sheath surface ...... 62
3.19 Vector components and the magnitude of the electric field strength on the
surface of the water droplet on the sheath surface ...... 63
3.20 Experimental setup for the shed region simulation ...... 64
3.21 Equipotential contours and electric field lines for the shed region simulation..
...... 65
XVI 3.22 Electric field distribution along the SIR sheet surface for the shed region
simulation ...... 65
3.23 Equipotential contours and electric field lines around a water droplet on
the shed surface ...... 66
3.24 Vector components and the magnitude of the electric field strength on
the surface of the water droplet on the shed surface ...... 67
3.25 Equipotential contours and electric field lines around a water droplet on
the sheath surface with different contact angles ...... 69
3.26 Electric field enhancement factor for a water droplet with different
contact angles on the sheath region ...... 70
3.27 Electric field enhancement factor for a water droplet of different
diameters on the sheath region ...... 71
3.28 Electric field enhancement factor for a water droplet of different
diameters on the shed region ...... 71
3.29 Water droplet shapes on the sheath and shed region ...... 72
3.30 Equipotential contours around a water droplets with different shapes on
the sheath and shed region ...... 73
3.31 Effect of the distance between water droplets on electric field enhancement
on the sheath and shed region ...... 74
4.1 Simplified geometry and dimensions of the 765 kV non-ceramic insulator
model with 10 weather sheds at the line and ground end ...... 80
4.2 Dimensions and positions of the line and ground end corona rings ...... 80
4.3 Element configuration on the insulator and the corona ring surface ...... 81 xvii 4.4 Dimensions and element configuration of the yoke plate for
four-subconductor bundles ...... 82
4.5 Dimensions and element configuration of the yoke plate for
six-subconductor bundles ...... 82
4.6 Geometry and dimensions of a 765 kV power line tower with
four-subconductor bundles ...... 83
4.7 Geometry and dimensions of a 765 kV power line tower with
six-subconductor bundles ...... 84
4.8 Entire view of a 765 kV power line tower with four-subconductor bundles. 85
4.9 Entire view of a 765 kV power line tower with six-subconductor bundles .. 86
4.10 Calculation path along the sheath surface of the insulator ...... 88
4.11 Per cent equipotential contour for a 765 kV tower with four-subconductor
Bundles under three phase energization ...... 88
4.12 Voltage distribution along the per cent insulation distance at the surface
of the insulator sheath with four-subconductor bundles ...... 89
4.13 Electric field strength magnitude along the per cent insulation distance
at the surface of the insulator sheath with four-subconductor bundles 90
4.14 Electric field strength magnitude along the per cent insulation distance
at the surface of the insulator sheath with four-subconductor bundles near
the line end ...... 90
4.15 Electric field strength magnitude along the per cent insulation distance at the
surface of the insulator sheath with four-subconductor bundles near
the ground end ...... 91 xviii 4.16 Leakage path at the surface of the insulator sheath and weather sheds 91
4.17 Electric field strength magnitude along the leakage path at the surface of the
insulator ...... 92
4.18 Per cent equipotential contours for a 765 kV tower with six-subconductor
bundles under three phase energization ...... 93
4.19 Voltage distribution along the per cent insulation distance at the surface
of the insulator sheath with six-subconductor bundles ...... 94
4.20 Electric field strength magnitude along the per cent insulation distance
at the surface of the insulator sheath with six-subconductor bundles 94
4.21 Electric field strength magnitude along the per cent insulation distance at the
surface of the insulator sheath with six-subconductor bundles near
the line end ...... 95
4.22 Electric field strength magnitude along the per cent insulation distance at the
surface of the insulator sheath with six-subconductor bundles near
the ground end ...... 95
4.23 Voltage distribution along the per cent insulation distance at the surface
of the insulator sheath for Cases F and S ...... 96
4.24 Electric field strength magnitude along the per cent insulation distance at
the surface of the insulation sheath near the line end for Cases F and S 97
4.25 Electric field strength magnitude along the per cent insulation distance at
the surface of the insulation sheath near the ground end for Cases F and S.. 97
4.26 Equipotential contours for a 765 kV tower with four-subconductor
bundles under (a) single phase and (b) three phase energization ...... 100 xix 4.27 Voltage distribution along the per cent insulation distance at the
surface of the insulator sheath under single and three phase energization ..101
4.28 Electric field strength magnitude along the per cent insulation distance at
the surface of the insulator sheath near the line end under single and
three phase energization ...... 102
4.29 Electric field strength magnitude along the per cent insulation distance at
the surface of the insulator sheath near the ground end under single and
three phase energization ...... 102
4.30 Equipotential contours for the four-subconductor bundles without and
with the 765 kV tower under three phase energization ...... 104
4.31 Equipotential contours for the 765 kV tower without and
with the four-subconductor bundles ...... 105
5.1 The fog chamber in the OSU High Voltage Eaboratory ...... I l l
5.2 Geometry and dimensions of a four-shed non-ceramic insulator ...... 112
5.3 Case RHCl water droplet distribution on the surface of a non-ceramic
insulator and the calculation model used for study ...... 115
5.4 Voltage distribution and equipotential contours on the surface of the first
shed on a wet non-ceramic insulator with HCl hydrophobicity ...... 115
5.5 Case RHC2 water droplet distribution on the surface of a non-ceramic
insulator and the calculation model used for study ...... 116
5.6 Voltage distribution and equipotential contours on the surface of the first
shed on a wet non-ceramic insulator with HC2 hydrophobicity ...... 116
XX 5.7 Case RHC3 water droplet distribution on the surface of a non-ceramic
insulator and the calculation model used for study ...... 117
5.8 Voltage distribution and equipotential contours on the surface of the first
shed on a wet non-ceramic insulator with HC3 hydrophobicity ...... 117
5.9 Case RHC4 water droplet distribution on the surface of a non-ceramic
insulator and the calculation model used for study ...... 118
5.10 Voltage distribution and equipotential contours on the surface of the first
shed on a wet non-ceramic insulator with HC4 hydrophobicity ...... 118
5.11 Case RHC5 water droplet distribution on the surface of a non-ceramic
insulator and the calculation model used for study ...... 119
5.12 Voltage distribution and equipotential contours on the surface of the first
shed on a wet non-ceramic insulator with HC5 hydrophobicity ...... 119
5.13 Case RHC6 water droplet distribution on the surface of a non-ceramic
insulator and the calculation model used for study ...... 120
5.14 Voltage distribution and equipotential contours on the surface of the first
shed on a wet non-ceramic insulator with HC6 hydrophobicity ...... 120
5.15 Equipotential contours for (a) dry Case and (b)-(g) Cases RHC1-RHC6 ... 123
5.16 Electric field strength magnitude along the insulation distance at
the surface of the sheath for Dry Case and Cases RHCl-3 ...... 126
5.17 Electric field strength magnitude along the insulation distance at the surface of the
sheath for Dry Case and Cases RHC4-6 ...... 126
5.18 Case FHCl water droplet distribution on the surface of a non-ceramic insulator
and the calculation model ...... 128 xxi 5.19 Case FHC2 water droplet distribution on the surface of a non-ceramic insulator
and the calculation model ...... 129
5.20 Case FHC3 water droplet distribution on the surface of a non-ceramic insulator
and the calculation model ...... 130
5.21 Equipotential contours for (a) Dry Case, (b) Case FFICI, (c) Case FF1C2,
(d) Case FHC3 ...... 132
5.22 Electric field strength magnitude along the insulation distance at the surface of the
sheath for Cases FFICI-FFIC3 ...... 133
6.1 Calibration test setup ...... 136
6.2 Relationship between the applied voltage and the insulator tester
readings (T) ...... 137
6.3 Calculation model for the sphere gap ...... 138
6.4 Verification test setup and dimensions of the grounded supporting
structure...... 139
6.5 Electric field distrihution along the insulator measured hy the insulator
tester (*) and calculated by the simulation model (-) ...... 140
7.1 Geometry and dimensions of a four-shed insulator ...... 143
7.2 Electric field strength magnitude along the per cent insulation distance
at the surface of the insulator sheath with different D ...... 144
7.3 Electric field strength magnitude along the per cent insulation distance
at the surface of the insulator sheath with two different shed spacings 145
7.4 Two shed profiles with different sheath/shed transition rounding radius.... 146
xxii 7.5 Electric field strength magnitude along the per cent insulation distance
at the surface of the insulation sheath with different sheath/shed
rounding radius values...... 147
7.6 Dimensions and positions of the line end corona ring ...... 147
7.7 Maximum electric field magnitude at the triple junction point as
a function of the corona ring position ...... 148
7.8 Electric field strength magnitude along the insulation distance at the
surface of the insulator sheath with the corona ring at different locations ..148
A.l The screen view of Coulomb software ...... 155
B. 1 Two-shed insulator between two parallel electrodes ...... 158
B.2 Equipotential contours around the shed edge of a two-shed insulator 159
XXlll CHAPTER 1
INTRODUCTION
I.l Overview
The reliability of the power networks and apparatus is very important for the performance of an electric power system. In recent years, extra high voltage power lines have been widely used to transmit the electric energy from the power stations to the end users. Insulators are among the key devices of the electric power transmission systems.
They are used to support, separate or contain conductors at high voltage. The insulators need to withstand not only regular voltages and overvoltages, such as lightning and
switching events, but also various environmental stresses such as rain, snow and pollution.
Pollution flashover is one of the main problems that endanger the reliability of an electric power system. The presence of contamination on the insulator surface, combined with highly humid and wet conditions such as fog, dew or rain, is particularly responsible for many insulator pollution ftashovers. With higher and higher voltages, the problem of insulator pollution flashover increases and the penalties increase sharply due to direct and
1 indirect lost revenue and the damage to the equipment. Therefore, more and more attention must be paid to improve the pollution performance of insulators.
Both porcelain and glass insulators have been used for over a hundred years.
Although these materials have heen proven themselves to resist environmental aging, the pollution performance of these insulators is poor due to the hydrophilic surface of porcelain and glass materials. During recent decades, polymer insulators have heen introduced and widely used due to their better pollution performance. Currently, in the
United States, polymer insulators represent approximately 60-70% of all new high voltage insulator sales [1]. Insulators made of polymer materials are often called composite or non-ceramic insulators.
Non-ceramic insulators offer several advantages over porcelain insulators. They have excellent hydrophobic surface property under wet conditions, high mechanical
strength to weight ratio, resistance against vandalism, saving on labor, and reduced maintenance costs [2]. A non-ceramic insulator consists of a core fiberglass rod, two metal end fittings, and polymer weather sheds, which are shaped and spaced over the fiberglass rod to protect the rod and to provide the required leakage distance. One of the parameters strongly affecting the long-term performance of non-ceramic insulators is the hydrophohicity of the weather shed surface. On a hydrophobic surface, water forms water beads, so the conductive contamination dissolved within the water beads is discontinuous. This reduces the leakage current and the prohability of dry band formation, which leads to higher flashover voltage.
However, polymer materials have weaker honds than porcelain so they are more
susceptible to chemical changes under multiple stresses encountered in service. These
2 stresses include the electric stresses due to the operating voltage, corona, arc, and environmental stresses due to contamination, ultraviolet (UV) rays, and heat cycling.
Under these stresses, the hydrophohicity on the surface of the polymer weather sheds will be temporarily or permanently lost, which will worsen the pollution performance of non- ceramic insulators.
The main disadvantages of non-ceramic insulators are: (1) they are subject to chemical changes, (2) they suffer from erosion and tracking, (3) their life expectancy is difficult to evaluate, (4) faulty insulators are difficult to detect [2].
1.2 Necessity for electric field strength distribution study along non-ceramic insulators
The electric field distribution of non-ceramic insulator is different compared to porcelain insulators. Generally the electric field distribution of a non-ceramic long insulator is more nonlinear than that of a porcelain insulator. The reason is that there are no intermediate metal parts for a non-ceramic insulator.
The electric field strength on non-ceramic insulators and associate hardware need to be controlled for three reasons:
• To prevent significant discharge activity on the surface material of non-
ceramic insulators under both dry and wet conditions which may result in the
degradation of the pollution performance of non-ceramic insulators.
• To avoid the internal discharge activity inside the fiberglass rod and the sheath
rubber material that could result in mecbanical or electrical failure of non-
ceramic insulators. • To prevent corona activity from the metal hardware or the non-ceramic
insulator, which may cause radio interference and acoustic emissions.
When non-ceramic insulators are installed on a three phase power line, the conductors, the hardware, the tower configuration and the presence of the other two phases of the three phase system can influence the electric field strength in the vicinity of the non-ceramic insulators. Therefore, it is important to study these effects from a practical standpoint. To control the electric field strength in the vicinity of non-ceramic insulators, the end fitting shape of non-ceramic insulators need to be carefully designed.
If necessary, a grading ring needs to be added.
The pollution flashover mechanism of non-ceramic insulators has been studied and published by various researchers [3, 4, 5]. According to a recent study [6], the pollution flashover voltage of non-ceramic insulators is determined not only by the hydrophohicity but also by the pollution severity. When the contaminated layer of the insulator becomes moist or wet under rain and fog conditions, the contaminated layer becomes conducting. The presence of the water droplets on the surface of a non-ceramic insulator causes electric field enhancement. Intensification of the electric field strength on the non-ceramic insulator surface could trigger the surface discharges, which may ultimately lead to an undesirable surface flashover. The thorough study of the electric field strength enhancement due to water droplets on the surface of non-ceramic insulators under various wet conditions is important for the in-depth understanding of the discharge process and the pollution flashover initiation mechanism on non-ceramic insulators. In addition, users often have some concerns about the aging of non-ceramic insulators. Their preference is to obtain simple diagnostic tools in order to evaluate the
state of insulators and to replace the defective insulators in time. Visible problems can be found relatively easily by visual inspection. However, the non-visible defects inside the insulators are also very dangerous. They usually occur between the fiberglass rod and the
sheath material covering the rod that might become separated from the rod. The discharges may occur inside and carbonize the rod. The carbonization of the rod not only reduces the insulating length of the insulator but also weakens the rod mechanically.
Since the electric field strength in the vicinity of a non-ceramic insulator decreases considerably in front of an internally shorted or defective insulator, the electric field
strength measurement method permits the detection of this kind of non-visible defect if the right type of instrument is available [7, 8].
1.3 Methods used for the study
Two kinds of methods have been used to study the electric field strength distribution along non-ceramic insulators. These methods can be classified as experimental methods and numerical analysis methods.
For experimental methods, capacitive probes, flux meters, dipole antennas and electro-optical quartz sensors can be used as electric field strength measuring devices to
study the electric field strength distribution along non-ceramic insulators under dry or wet conditions. A commercial available insulator tester designed by Positron Power Division can be used for the on-line measurement of the electric field strength distribution along non-ceramic insulators, at some distance from the insulator.
For numerical analysis methods, they can be used to calculate the electric field and voltage distribution (EFVD) along non-ceramic insulators. According to Maxwell’s equations, all electromagnetic field problems can be expressed by partial differential equations, which are subject to the associated boundary conditions. By using Green’s function, the partial differential equations can be transformed into integral equations.
There are two different kinds of numerical analysis methods, using either differential equations or integral equations. The former is known as the “field” approach or domain method, and the second is known as the source distribution technique or boundary method. The domain methods include the finite difference method (FDM) and finite element method (FEM), which apply mainly for domains with hounded boundaries. The boundary method include the charge simulation method (CSM), and the boundary element method (BEM) which apply for domains with open boundaries and have no restrictions in regards the geometry of the domain. Since the research task is related to domains having open boundaries, the boundary element method is adopted for the study in this dissertation.
1.4 Description of existing problems
Although the EFVD along the non-ceramic insulators has been widely studied for a long time, the results of these studies cannot be applied directly to the real power line insulators. The limitations of the previous studies are: • The analysis of the EFVD along non-ceramic insulators usually assumes
single phase energization. However, a real power line means three phase
energization, and the presence of the other two phases may have some
influence on the EFVD along a non-ceramic insulator.
• Corona from water droplets has been demonstrated to play an important role
in the aging of the non-ceramic insulator [9]. The knowledge of the
relationship between the contact angle, size, shape and distribution of water
droplets on the non-ceramic insulator surface and the electric field strength
enhancement around the surface of water droplets is still rather limited.
• The flashover usually happens during fog and light rain conditions. Water
droplets on the surface of non-ceramic insulators will change the EFVD along
the insulators. The relationship between the wet status of the insulator surface
and the EHVD along non-ceramic insulators under wet conditions is still not
known completely.
1.5 Objectives and main contributions
The general objective of this research is to study the electric field and voltage distribution along non-ceramic insulators, first, under dry and clean conditions and then,
under various wet conditions. A commercially available software [55] (Coulomb of
Integrated Engineering Software) based on the BEM is employed for the modeling and the calculation for the non-ceramic insulators under different surface conditions. The specific objectives and the main contributions of the research can be summarized as follows:
1. Develop the model of a non-ceramic insulator with clean and dry surface. The
geometry and dimensions of typical non-ceramic insulators have been used for
modeling purposes. To reduce the calculation time for long non-ceramic
insulators, several simplified insulator models have been developed in order to
decide which geometry can be simplified without significantly impacting on
the accuracy of the EFVD calculation results in the vicinity of the non-
ceramic insulators. Discussion of this contribution is in Section 3.1. Practical
examples are discussed in Section 4.2.1.
2. Develop the models of two typical 765 kV power line tower with four or six
subconductor bundles and non-ceramic insulators under three phase
energization to simulate actual conditions. A simplified insulator model has
been used for this case. The effects of the presence of the other two phases of
the three phase system on the EFVD along the center phase insulators have
been investigated. The effects of tower configuration and conductor bundles
have also been studied. Practical examples are discussed in Sections 4.2, 4.3,
and 4.4.
3. Develop a simple model of a flat silicon rubber sheet with a discrete water
droplet on the upper side. This model has been used to simulate the water
droplet on the shed and on the sheath region of a non-ceramic insulator. The
relationships between the contact angle, size, shape, distance between adjacent
droplets and conductivity of the water and the electric field strength
8 enhancement on the surface of water droplets have been studied. Discussions
of this contribution are in Sections 3.3, 3.4 and 3.5.
4. Develop a four-shed insulator model with discrete water droplets only on the
top of each shed to simulate the insulator under rain conditions. Discussions
can be found in Chapter 5, especially in Sections 5.5 and 5.6. Develop a four-
shed insulator model with discrete water droplets on the top of each shed, on
the downside of each shed, and on each sheath region of the insulator as well
to simulate the insulator under fog conditions. Discussions of this contribution
are in Section 5.7 and 5.8. The relationships between the hydrophohicity
status of the non-ceramic insulator and the EFVD along the insulator have
been analyzed.
5. Verify the calculation results on a dry and clean non-ceramic insulator by
using an electric field strength tester. Description of the measurements are in
Chapter 6.
6. Study some important items for the non-ceramic insulator design, such as the
distance between the first shed and the line end fitting, shed spacing, shed
profile and the position of the corona ring. Results are discussed in Chapter 7.
1.6 Organization of dissertation
The rest of this dissertation is organized as follows. In Chapter 2, the structure and the flashover mechanism of non-ceramic insulators are introduced first. Then, several experimental methods and numerical calculation methods used to study the EFVD along
9 the non-ceramic insulator are reviewed. A brief description of the BEM method and the
Coulomb software [55] are given. The related research works on the EFVD study along insulators are summarized.
In Chapter 3, the simplified model of the non-ceramic insulator is determined for the study of the EFVD along the insulator. Some basic features related to the electric field enhancement due to the existence of water droplets are investigated.
In Chapter 4, the EFVD along a 765 kV non-ceramic insulator installed on two typical 765 kV power line tower with four or six sub-conductor bundles under dry and clean conditions are studied. The effects of the other two (side) phases of the three phase
system, the tower configuration, and the conductor bundles are analyzed.
In Chapter 5, the EFVD along a four-shed non-ceramic insulator under various wet surface conditions are studied. The cases analyzed are based on several stages of the hydrophohicity classification (FlC) recommended by the Swedish Transmission Research
Institute (STRI). Electric field enhancement factors on the surface of water droplets are calculated.
In Chapter 6, the electric field distribution along a non-ceramic insulator is measured with an insulator tester. The axial component of the electric field strength is measured and compared to the calculation results.
In Chapter 7, some important items of the non-ceramic insulator design are discussed. In Chapter 8, the conclusions are summarized and future work is suggested. In
Appendix A, Coulomb software package is described. In Appendix B, a two-shed insulator model is set up and the equipotential contours around the shed are shown.
10 CHAPTER 2
REVIEW OF LITERATURE
In this chapter, several issues related to non-ceramic insulator research will be discussed. First, the structure of non-ceramic insulators will be introduced. Second, the flashover mechanism of non-ceramic insulators will be described in detail. There are many differences between the flashover mechanism of ceramic and non-ceramic insulators. The simultaneous existence of contamination layer and water droplets on the
surface of weather sheds changes the electric field distribution along non-ceramic insulators and plays an important role during the discharge process.
Third, to study the electric field distribution along non-ceramic insulators under various conditions, two kinds of methods can be used. They can be classified as experimental methods and numerical analysis methods. A brief description of each method and an introduction of the software package Coulomb, employed for the calculation in this research will be given.
At the end of this chapter, research studies related to the EFVD along non- ceramic insulators will also be reviewed. These research studies can be divided into four different groups:
11 1. EFVD study along non-ceramic insulators under dry and clean conditions.
2. EFVD study along non-ceramic insulators under wet and contaminated
conditions.
3. Fault detection for non-ceramic insulators using the electric field
measurement method.
4. Design considerations for non-ceramic insulator from the electric field
strength distribution viewpoint.
2.1 Structure of non-ceramic insulators
Non-ceramic insulators have three main components, which are shown in Fig. 2.1.
The design of each component needs to be optimized to yield satisfactory electrical and mechanical performance over the lifetime of non-ceramic insulators.
A V B ^ c ^ D
IZZI (ZZI
Figure 2.1: Simplified structure of non-ceramic insulators: A: fiberglass rod; B: polymer sheath; C: polymeric weather sheds; D: metal end fitting.
At the center of the insulator is a fiberglass reinforced polymer (FRF) rod. The
FRF rod is reinforced with either polyester, vinyl ester or epoxy resin to provide the appropriate mechanical strength [2]. Epoxy resins offer better electrical properties than polyester resins, which are applied in some cases in order to reduce costs. Glass fibers are
12 made of alkali-borosilicate glasses (E-glass), which is a low alkali, lime-alumina borosilicate glass. The FRP rod has the dual burden of being the main insulating part and of being the main load-bearing part as well.
Brittle fracture is a mechanical failure for the FRP rod of the non-ceramic insulator, which leads to catastrophic breakage under loads as low as 10 to 15 percent of their design strength. The mechanism involved is stress corrosion of the F-glass fibers, and can occur when the rod becomes exposed to acids in the environment. To avoid brittle fracture, chemical resistant alkali-aluminosilicate glass fibers (FCR) should be
used, which are able to withstand acid attacks.
The metal end fittings are typically forged steel, ductile cast iron, malleable iron or aluminum and are selected for mechanical strength. The end fittings are usually crimped or swaged to the FRP rod. This method has been proven suitable to supply the most dependable and economical solution for attaching the end fittings to the FRP rod
[1]. The shape of the end fittings is also an important factor to limit the production of corona discharges. Corona discharges cause polymeric materials to become brittle, and it may even crack, leading to failure of the insulator by exposing the fiberglass rod to the ambient moisture [10].
The polymeric weather sheds and sheath are shaped and spaced over the FRP rod to prevent the rod from damage and to provide the required leakage distance. Therefore, the materials for sheds and sheath are required to have excellent aging resistance under multiple environmental stresses. The possible materials of the weather sheds include epoxy resins, ethylene-propylene diene monomer (FPDM), ethylene-propylene rubber
(FPR) and silicone rubber (SiR).
13 The long-term performance of most of these materials in clean environments has been successful; however, in polluted environments their long-term performance has been less satisfactory. But SiR is an exception. The reason for the superior pollution performance of SiR is its ability to transfer the hydrophobic characteristic to the pollution layer on the surface at heavily polluted sites. No other polymeric material shows this property. The mechanism for this phenomenon is that the low molecular weight (LMW) compounds in the silicone rubber migrate to the surface of the pollution layer and form a thin film. Due to this coating effect, the pollution layer behaves like a SiR surface and becomes hydrophobic, which causes the water to bead up rather than to form a continuous film.
2.2 Flashover mechanism of non-ceramic insulators
A flashover is a disruptive discharge over the surface of a solid insulation in a gas or liquid. The flashover mechanism of ceramic and glass insulators has been studied and well understood. For an EPDM insulator, the surface of weather shed becomes hydrophilic after a short period of exposure to a polluted environment. Thus the flashover mechanism of an EPDM insulator is similar to that of a ceramic insulator due to the hydrophilic surface. The flashover mechanism of a SiR insulator is different compared to a ceramic insulator due to the hydrophohicity transfer behavior to pollution layers.
The contamination flashover is a multi-step process [3, 4, 5] for a SiR insulator.
The basic steps in the common flashover process are:
14 1. Contamination build-up - The wind drives dust and/or other conductive
contaminants onto the surface of the insulators. Insulators are usually covered
by a uniform pollution layer.
2. Diffusion of LMW chains - Diffusion (it occurs naturally) drives the LMW
polymer chains out of the weather shed material. The top of the pollution layer
is covered by a thin layer formed by LMW polymer chains, which assure the
hydrophohicity of the surface.
3. Wetting of the surface - Dew, fog, and light rain deposit the water droplets on
the hydrophobic surface of the insulator. Salt from the pollutant dissolves in
the water droplets that become conductive. The residual dry surface pollution
is slowly wetted by the droplet migration. This forms a high resistance
conductive layer and changes the leakage current from capacitive to resistive.
4. Ohmic heating - The leakage current flows through a high resistive layer on
the surface of the insulator. Since the electrolyte has a negative thermal
coefficient, the surface resistance will decrease slowly and the leakage current
will increase due to ohmic heating. At the same time, drying and loss of
moisture increase the surface resistance. The two opposing phenomena reach
equilibrium at a lower value of leakage current.
5. Electric field effect on a hydrophobic surface - The continuous wetting
increases the droplet density and reduces the distances among the droplets.
The applied electric field flattens and elongates the droplets. If the distance is
small, the neighboring droplets coalesce and filaments are formed.
15 6. Spot discharges - Filaments reduce the distance between the electrodes,
increasing the electric field strength between the adjacent filaments. Corona
discharges can occur if the electric field strength is sufficiently large.
7. Reduction of hydrophohicity - Water droplets related corona discharges age
the polymer material around the droplets and reduce the hydrophohicity by
rotation or breaking of the polymer chains. The filaments are joined together
due to the reduction of hydrophohicity, which leads to irregular shape
formations in the wet region.
8. Dry hand formation - The areas of the surface with the highest power
dissipation dry first. As dry hands are insulating areas, the surface discharge
activities continue within the dry hand region until the hand grows to a
sufficient length to withstand the applied voltage. The resultant discharge
activities cause surface erosion.
9. Flashover occurrence - Increase of the length of the filament and formation of
wet areas finally short the insulator by a conductive electrolytic path. This
conductive water surface provides a path for the arc, which travels on the
surface of the electrolyte layer and causes the flashover.
2.3 Methods used for the electric field and voltage distribution study along insulators 2.3.1 Experimental methods
In order to obtain measurements of the electric field strength distribution along an
insulator, several kinds of devices were designed and used in laboratory and field tests. 16 Initially capacitive probes, flux meters and dipole antennas were used as the electric field
strength measuring devices. They typically had conductive electrodes, connecting cables, and measurement circuits. The metal connection caused considerable distortion of the electric field when the measurement point was above the ground plane.
The systems used presently to measure the electric field strength have been designed differently. The signal is transmitted by means of an optical fiber from the probe at high potential to a receiving unit at ground. The optical fiber link may introduce only a small distortion of the electric field distribution. The size of the probe could be made very small in order to avoid the electric field distortion. The Pockets sensor is one of the probes, which is used for electric field strength measurement.
Hidaka [11, 12] published comprehensive reviews related to the Pockets sensor for electric field strength measurement. In his papers, he described the structure of the
Pockets sensor in detail. The electric field strength measuring system consists of a coherent light source, an electro-optic material, polarizing plates, optical devices such as a quarter-wave plate for adjusting a phase shift, and a photo-detector. The main advantages of the Pockets sensors are:
• they directly measure the electric field strength
• they respond to changes in electric field strength in a wide range of
frequencies from dc to GHz
• the electric field strength distortion by a Pockets sensor is very small.
R. Parraud [13] published a comparative study of different electric field strength measurement methods. The sensors used were:
• ac potential meters 17 • capacitive spherical sensors with optical data link [14]
• electro-optical quartz cubic sensors.
The results showed that:
• The method using ac potential meters is not a good choice. Although the
measured potentials are within ±10% of the calculated values, the meter
shows significant differences compared to the correct results due to the
influence of the measuring probe on the potential distribution.
• The method with capacitive spherical sensors shows a good correlation in the
region between the electrodes. However, there is a significant difference near
the electrode connected to the ground.
• The electro-optical method is a good choice. The measurement results of the
electric field strength are very close to the calculated results between the two
electrodes, except significant differences close to the electrodes, which can be
attributed to the distortion of the field by the measuring probe.
2.3.2 Numerical electric field analysis methods
There are several numerical analysis methods that are often used for the calculation of the electric field strength distribution along insulators. They are:
• charge simulation method (CSM)
• boundary element method (BEM)
• finite element method (FEM)
• finite difference method (EDM).
18 A comprehensive reference book related to numerical electric field analysis methods is authored hy Zhou [15]. The numerical electric field analysis methods can be divided into two categories: the boundary methods and the domain methods. The boundary methods include the CSM and the BEM. The domain methods include the FEM and the EDM.
The basic concept of the CSM is to replace the distributed charge of conductors and the polarization charges on the dielectric interfaces by a large number of fictitious discrete charges. The magnitudes of these charges have to he calculated so that their integrated effect satisfies the boundary conditions. The potential due to unknown surface charges can he approximated by three forms of concentrated fictitious charge arrangements - line, ring and point charges [16]. These charges can be placed at appropriate positions, which are usually inside the conductor surfaces. An adequate combination of the three forms of charges can he made to simulate almost any practical electrode system.
The CSM method can be used to solve open boundary problems and is easily applied for three-dimensional electric field problems without axial symmetry. A major problem of CSM is the difficult and subjective placement of simulation charges. The other disadvantage is that it is difficult or impossible to calculate the electric field
strength near very thin electrodes because the fictitious charges approximating the field must be usually inside the electrodes.
The BEM is based on the boundary integral equation and the principle of weighted residuals, where the fundamental solution is chosen as the weighting function.
There are two kinds of BEM. One is called indirect BEM, the other is called direct BEM.
19 In the indirect BEM, the potential is not solved directly. An equivalent source, which would sustain the field, is found by forcing it to satisfy prescribed boundary conditions under a free space Green function that relates the location and effect of the
source to any point on the boundary. Once the source is determined, the potential or derivatives of the potential can be calculated at any point.
The surface charge simulation method (SCSM) is one type of the indirect BEM.
In 3-D problems, the surfaces of the electrodes or the interfacial boundaries are discretized by planar triangle elements, curved triangle elements, or any other curved
surface. After the boundary is discretized and the approximate function of the charge distribution is chosen, a great number of integral expressions has to be evaluated. Then the values of the surface charges can be solved from matrix equations. Compared to
CSM, due to the flexibility of the approximate function of the surface charge, SCSM is more suitable for problems with complex geometry.
In the direct BEM, the value of the function such as the potential and its normal derivative along the boundary are assumed to be unknown. The integral equations are discretized along boundaries and interfaces using the Galerkin method. Setting the proper boundary conditions to the given nodes, a set of linear algebraic equations is obtained.
The solutions of these equations result in the boundary value of the potential and its normal derivatives. The field strength of most interest on the boundary is computed directly from the matrix equations.
The FEM is a numerical method of solving Maxwell’s equations in the differential form. The basic feature of the FEM is to divide the entire problem space, including the surrounding region, into a number of non-separated, non-overlapping
20 subregions, called “finite elements”. This process is called meshing. These finite elements can take a number of shapes, but generally triangles are used for 2-D analysis and tetrahedra for 3-D analysis. Each element geometry is expressed by polynomials with nodal values as coefficients. The electric potential within each element is a linear interpolation of the potentials at its vertices. By using the weighted residual approach, the partial differential equations are reduced to a sparse, symmetric and positive definite matrix equation. Since the shape and the size of the elements are arbitrary, it is a flexible method that is well suited to problems with complicated geometry. The FEM analysis is effective for small problems that are closed bounded. If the problems are too large, a large number of finite elements are required, and the calculation becomes intensive.
The FDM is an approximate method for solving partial differential equations. It replaces a continuous field problem by a discretized field with finite regular node. This method utilizes a truncated Taylor series expansion in each coordinate direction, and applied at a set of finite discretization points to approximate the partial derivatives of the unknown function. The partial differential equations are transformed into a set of algebraic equations. The FDM is suitable for obtaining an approximate solution within a regular domain. If a region contains different materials and complex shapes, the FEM is better than the EDM.
2.4 Software used for study and boundary element method 2.4.1 Software used for study
The goal of this research is to analyze the electric field and voltage distribution in the vicinity of non-ceramic insulators in relevant cases by using an appropriate tool,
21 which is an electric field analysis software for the solution of three-dimensional (3-D) problems. There are several commercial software packages available for the computation of the electromagnetic fields. Coulomb, ANSYS/Emag, Maxwell 3D and Flux3D are the most popular ones.
Coulomb has been designed hy Integrated Engineering Software Company [55]. It combines the efficiency of the BEM with a powerful user interface. It can he used for the calculation of the distribution of the static and the quasi-static electric field. It can he used to calculate the electric field strength and voltage values at any location throughout the entire model domain. The detailed features of Coulomb are described in Appendix A.
ANSYS/Emag has been developed by ANSYS, Inc. It can be used for static, transient, and harmonic low frequency and electromagnetic field calculations. It can
simulate electrostatics, circuits, and current conduction, as well as charged-particle tracing in both electrostatic and magnetostatic fields. This software is based on the FEM.
Maxwell 3D, a 3D structure electromagnetic field simulator, has heen designed by
Ansoft Corporation. The Maxwell 3D Field Simulator includes three analysis capabilities: electric fields, magnetostatic, and AC magnetic problems. The Electric Field module accurately solves electric fields and voltage levels in systems with conductors, charges and dielectrics. Electric stress levels, voltage maps, regions of dielectric stress and capacitance can also he evaluated.
Flux3D, a fully integrated finite element based CAD package, has heen developed hy Magsoft Corporation. Flux3D solves electromagnetic and thermal problems for 3D geometry. Flux3D can handle static and steady state problems in closed or open boundary domains.
22 It has been observed by researchers that the analysis of the electric field distribution by integral methods such as BEM is more convenient than hy differential techniques such as FEM [17]. A BEM-type software (Coulomb) have several advantages over an FEM-type software (ANSYS/Emag):
• In BEM models, it uses only 2D surface elements on the surface, which are
the interfaces of regions with different materials or surfaces with boundary
conditions. This can greatly simplify the modeling process.
• Results are more accurate due to the smoothness of the integral operator.
• Its analysis of open boundary problems is superior to that of the FEM. The
analysis of unbounded structures can he solved hy BEM without any
additional effort because the exterior field is calculated the same way as the
interior field. For open boundary problems, artificial boundaries, which are far
away from the real structure, must he used for FEM.
Therefore, Coulomb is particularly appealing for high voltage application models.
In the proposed research work. Coulomb is used for the study of the EFVD along the non-ceramic insulators under different surface conditions.
In Coulomb software, there are several basic steps to develop the non-ceramic insulator model in order to calculate the electric field and voltage distribution along the insulators:
• Setting up model units
• Creating the geometry
• Assigning physical properties
• Assigning voltages to boundaries 23 • Assigning boundary elements to the boundaries
• Solving the problem and analysis.
2.4.2 Boundary element method
Coulomb is based on the BEM numerical analysis method. In the BEM numerical analysis method [17], the electrode and dielectric boundaries are discretized into several boundary elements and a suitable distribution function is introduced for the equivalent
surface charges along the discrete boundary elements. Then the electric field in the region of interest is considered to be caused by the equivalent surface charges along the boundary elements. The equivalent surface charges are determined by solving a system of integral equations, which are obtained by satisfying the following boundary conditions:
1. On the conductor surfaces with known potential, the prescribed values of the
potential function, 0, are maintained.
2. On the dielectric-dielectric boundaries, the condition for the normal
component of the electric flux density, D„, is maintained.
Details of the BEM can be found in [15] and [18]. In [19], there is a brief introduction to the BEM.
Consider a bounded, linear, isotropic and homogenous dielectric material body, which is embedded in free space. The material medium is bounded by surface S, and characterized by permittivity e. There may exist a finite, impressed volume source, which has volume charge density Pv or a surface source, which has surface charge density <7, in
24 the space. From Maxwell’s equations, it is known that at every ordinary point in the medium whose physical properties are continuous:
xJF = () (2.1)
= (2 2)
It is convenient to introduce an electric polarization vector P defined by
F = D - e ,Ê = D (2.3) £ where Eq is the permittivity of vacuum. By invoking Eq. (2.1), Eq. (2.2) can be written as
V.^ = ±(V.^_V.f) = l( p + P ^ ) (2.4) ^0 ^0 where p^=S/-P = ^— - p , (2.5) e
Pev is called the equivalent volume charge density.
At the interface of dielectric materials, the electric flux density is subject to the boundary condition
n-{b^-bp) = a^ (2.6) where unit vector n points from medium (2) into medium (1). By using Eq. (2.3) in Eq.
(2.6),
M . (Æ, - ) = — [(T, - » . (^ - ^ )] = — (a , + (T,, ) (2.7) ^0 ^0 where =-n-{P^ -.^ )is the equivalent surface charge density.
From Eqs. (2.4) and (2.7), it can he concluded that the effects of a dielectric body in the electric field can he completely accounted for hy the distribution of the equivalent
25 volume charges in the dielectric body and the equivalent surface charges on the interface of adjacent dielectric bodies.
Since the electric field strength E is conservative, there exists a scalar potential
such that
^ (2.8 )
Substitution of Eq. (2.8) into Eq. (2.4) yields modified Poisson’s equation
= (2.9) ^0
Thus, the potential (j) at any point can be calculated by using Green’s theorem and solving
Poisson’s equation.
For a continuously distributed surface or volume source in free space, the electric
field strength at an observation point has a component in the direction connecting the
source point and the observation point. If the potential of an arbitrary reference is set to zero at infinity and the medium in the problem domain is linear and isotropic, then the potential (j) of the observation point r can be determined by Eq. (2.10):
0(r)= rfii±Au(l)^y+ (l)ùk (2.10) J 4ÆEo ^ J 4ÆEo r. where r,, are the radial distances from the point of the source to the observation point;
Pv and Os are the impressed volume and surface charge density of the source, respectively; Pe,, and (Jes are the equivalent volume and surface charge density of the
source, respectively.
Usually the impressed volume and surface charge densities, Pv and Oi, are given in practice. The equivalent volume charge density, p^, in a homogeneous medium can be
2 6 obtained from Eq. (2.5). However, the equivalent surface charge density, Oes, must be
determined by the specified boundary conditions. The most commonly used boundary
conditions are:
(1) Interface condition:
If (7s is the boundary surface charge density on the dielectric-dielectric
boundary, then the boundary condition at any point / on the interface of two
dielectrics can be written as
Gi(^)i-e2(%2=(T, (2.12) an dn
where £i, £2 is the permittivity of dielectric 1, 2 respectively.
(2) Dirichlet condition:
^ 1 3 )
on the surface of a conductor where f(i) is a known function.
(3) Neumann condition:
|^ |,= /( 0 (2 14) dn
at the interface of a conductor and a dielectric where/(z) is a known function.
By discretizing the boundary into non-separated, non-overlapping subregions,
called “boundary elements”, Eq. (2.10) become:
1 (2 15) 4ke ' = 1 ('■ ip .7=1 5 jp
where
• (f)(p) is the point p on the electrode surface with known potential.
27 • Tip and rjp are the radial distances from the point on the boundary of the source to the
point p.
• Pesi and Oesj are the equivalent volume and surface charge density at the element,
respectively.
By solving the system of equations, the unknown values of charge density can be determined. Once the sources are determined, the potential and electric field strength in the problem domain can also be determined.
2.5 Electric field strength and voltage distribution study along insulators
2.5.1 EFVD study along insulators under dry and clean conditions
Misaki, Tsuboi, Itaka and Hara [20, 21] computed the electric field strength distribution to optimize the insulator design. Using the SCSM method, each curved
surface was divided into many curved surface elements. The use of the curved surface elements made it easy to approximate the insulator contour. The correction of the insulator contour could be performed smoothly for optimum insulator design. A concentric sphere model and a coaxial cylinder model were chosen to examine the accuracy of this method. This method was used to determine the optimum design of epoxy pole spacers in SFg gas insulated cables.
Kaana-Nkusi, Alexander and Hackam [22] calculated the voltage and electric field distribution along a post-type insulator shed. The system was modeled with 146 ring charges, with 30 charges modeling each electrode. Several criteria were applied in order 28 to evaluate the quality of the calculation results, which included the potential error, the potential discrepancy, the normal electric flux density and the tangential electric field
strength discrepancies. The calculation results showed that the maximum values of the electric field strength along the surface increased with higher dielectric permittivity of the insulating material. Decreasing the radius of curvature of the insulator shed increased both the normal and tangential components of the electric field strength.
Gutfleisch, Singer, Forger and Gomollon [23] described a new algorithm based on tbe BEM to calculate tbe electric field strength. The potential formulas of the different types of surface elements, such as rectangular, triangular, cylindrical, spherical, conical, toroidal, were presented in this paper. The accuracy of the results could be checked by computing the potential and electric field strength at the contour points or at test points at given contours. Two application examples were given in their paper. One was a disc insulator of a three-phase GIS, the other one was a transformer.
Zhao and Comber [19] studied tbe electric field and potential distribution along non-ceramic insulators. The Coulomb electric field analysis software was used. Tbe insulator, tower and conductors were considered in the calculation model. Results
showed that the conductor length has significant “shielding” effect on the insulators; the maximum electric field strength decreases when the length of the conductor increases; and the tower structure in the vicinity of the insulator and the diameter and the location of the grading ring are important in determining the maximum electric field strength along an insulator.
29 2.5.2 EFVD study along insulators under wet and contaminated conditions
Hartings [24] introduced several experimental techniques to study the discharge phenomena on the surface of outdoor insulators. He used a two-dimensional ac probe available at Swedish Transmission Research Institute (STRl), which was developed by
Homfeldt [25]. Two electro-optic voltmeters were placed inside a sphere (diameter:
50mm), which was divided into four galvanically separated quarters. The electro-optic voltmeters modified the polarization of appropriate light beams, which were converted to voltages. Hartings [26, 27] also conducted a series of experiments to study the ac behavior of hydrophilic and hydrophobic post insulators during rain. The radial and axial components of the electric field strength along an insulator under dry and rain conditions were measured.
Under dry and clean conditions, no corona activity was observed at 50 kV. At 85 kV, discharge activity was observed at the HV flange. The effect of corona activity there is to extend the boundary of the HV flange. Under rainy condition, for a hydrophilic insulator, a capacitive electric field distribution was obtained only in the case of moderate rain intensity (0.4 mm/min) and low rain conductivity (50 pS/cm). A resistive electric field distribution may be obtained at and below 85 kV at values of 1.6 mm/min and 50 pS/cm. For a hydrophobic insulator, a capacitive electric field distribution was observed during all the test environmental conditions. At 50 kV, the electric field distribution during rain was similar to that at dry conditions.
Hartings [26] also theoretically analyzed the effect of rain on the electric field distribution along non-ceramic insulators. He used a two-dimensional, cylindrically 30 symmetrical FEM program to perform the capacitive field calculations. Under dry conditions and in case of corona activity, the measured electric field distribution agreed well with the calculated capacitive distributions if the corona activity is considered in the model. During rain and no corona conditions, the measured electric field distrihution agreed reasonably with the calculated capacitive electric field distrihution if the water layer on the upper surface was included in the model. During rain and corona conditions, it was difficult to calculate the electric field distrihution due to the unknown potential of the corona activity, if it is not located at the electrode.
Eklund and Hartings [28] studied the electric field distribution along composite and ceramic insulators during pollution tests using the same probe described in [24]. The probe was placed about 0.2 m away from the insulator to avoid discharge activities. Axial and radial electric field strength components were obtained for porcelain insulators,
RTV-coated insulators, and composite insulators. On hydrophilic porcelain insulators, the increase of the axial electric field strength was accompanied by an increase of leakage currents up to several hundred mA. On hydrophobic composite insulators, the axial electric field strength increased as the amount of pollution built up on the insulator
surface.
Chakravorti and Mukherjee [29] developed an algorithm based on the CSM for calculating the power frequency and impulse electric field distributions around a HV insulator either with uniform or non-uniform surface pollution. The product of the electric resistivity of the contaminant [Q/m] and the thickness of the contaminant layer
[m] are treated as a single parameter, Ps, which is called surface resistivity. They found that for ps>10" Q, the field is capacitive, while for ps<10^ ^2, it is resistive. For 31 intermediate values of ps, the field is capacitive-resistive. The highest electric field
strength for the resistive field is nearly twice the corresponding value for the capacitive field and these stresses occur near the tip of the uppermost shed.
For non-uniform surface pollution, excessively high dielectric stresses occurred at the junction of two different surface resistivities. Partial pollution of the insulator surface near the electrodes caused higher dielectric stresses than uniform pollution. Also the effect of dry bands was studied. The wider the dry band, the lower are the stresses at the edges of the dry band. The location of a dry band does not have a strong influence on the electric field strength at the edges.
Xu and McGrath [30] studied the electric field strength and fherrnal field distribution of a 15 kV silicone rubber insulator under contaminated surface conditions
using FEM. A 6-node triangular element, which has three extra or secondary nodes at the center of each side of the triangle, was employed. The contamination of the insulator was treated as an insulator covered uniformly with a conductive layer. The product of the electric conductivity of the contaminant [S/m] and the thickness of the contaminant layer
[m] was treated as a single parameter, which was called surface conductivity. The thickness of the contaminant layer was fixed as ICf^ m. The influence of surface conductivity was also investigated. When the surface conductivity was in the range of
10"" to 10"^ S, the potential distribution along the surface of the insulator was primarily determined by the distribution of stray capacitance. When the surface conductivity was between 10"^** to 10"^ S, the electric field was of resistive-capacitive type. When it exceeded 10"* S, the potential distribution was completely resistive.
32 Ahmed, Singer and Mukherjee [31] developed a numerical method for the computation of the electric potential and electric field distribution on the surface of polluted insulators. The method was based on the surface charge simulation and discrete charge simulation techniques. The effects of the dry hand and wet pollution were taken into account. In order to produce a capacitive-resistive field, the value of the wet pollution surface conductance should be greater than 0.01 nS and less than 10 nS.
Chakravorti and Steinbigler [32] calculated the capacitive-resistive field of HV porcelain and capacitor bushings. The boundary element method was used for electric field strength computations in two axi-symmetric bushing configurations including four dielectrics with transformer oil, porcelain, air, and bakelite tube. Effects of uniform and non-uniform distributions of surface resistivity and volume resistivity of different dielectric media were studied in detail. The dielectric stresses in the critical zone, where the distance between the live central conductor and the grounded metal tank is at a minimum, were calculated. The results showed that the volume resistivity of the dielectric medium had a significant effect on the stresses in the critical zone. The magnitudes and locations of the maximum dielectric stress were also determined. The
uniform surface pollution did increase the dielectric stress near the tip of the uppermost
shed, but the worst dielectric stress occurred for non-uniform surface pollution.
El-Kishky and Gorur [33] used a modified charge simulation method for calculating the electric potential and field distribution along ac HV outdoor insulators.
Accurate modeling of a non-ceramic insulator could be achieved with a significant reduction in the number of charges used in this method. They [34] also studied the electric field and energy distribution on wet insulating surfaces. The insulator wet surface
33 model is a rectangular strip of 2cmx25cm with different sizes of water droplets from 50 mm^ to 900 mm^. The relationships between the maximum electric field strength and the
size, shape, spacing and location of the droplets were studied. As the size of the water droplets increased, the maximum electric field strength was reduced. As the water droplets were spaced further apart, the maximum electric field strength was reduced. The droplets near the HV electrode were subjected to severe electric field intensification.
In another paper, El-Kishky and Gorur [35] also presented an approach for electric field strength computation on an insulating surface in the presence of discrete water droplets. The calculation method was based on the charge simulation technique, which was modified to handle long insulator chains. The accuracy of the method was established by internal error checks in the computation. Spherical and ellipsoidal shapes of water droplets were considered. Significant field intensification was observed at the triple junction of the insulator, air, and water droplet. The electric field intensification increased with the decreasing value of water resistivity. The shape of the water droplets was also an important factor that influenced the field intensification.
2.5.3 Fault detection by electric field strength measurements
Many electric power utilities routinely install and replace non-ceramic insulators on overhead transmission lines using live working procedures. An essential requirement for ensuring worker safety is to confirm the electrical and mechanical integrity of non- ceramic insulator prior to performing live work. Non-ceramic insulators may have some hidden or internal faults due to the manufacturing process, or due to the joint electric and
34 environmental stresses. One critical defect is the puncture or severe degradation of the
sheath, since this type of defect allows ingress of moisture into the FRP rod of the insulator that may cause flashover or brittle fracture. Live line maintenance work needs
some simple and economical test methods to detect the faults on the insulators. These defects need to he categorized and analyzed in terms of their likelihood to cause catastrophic failure during live work.
Vaillancourt, Bellerive, St-Jean and Jean [36] developed a new live line tester as
shown in Fig. 2.2 for porcelain suspension insulators. The insulator tester consists of a
specially designed electric field strength probe. The probe is transversally mounted on a plastic sled that can he moved along an insulator string by means of a hot stick. The value of the electric field strength measured at the edge of each insulator shed is automatically recorded by a data logging unit. At the same time, an insulator counting circuit automatically keeps track of the probe position along the string. Data interpretation is done later, using a personal computer. A defective insulator appears as a dip on the plot of the electric field strength vs. probe position along the insulator string. Field tests were performed on some insulators of a 315-kV line and four faulty insulators were found by this method. The new device proved to he a very efficient way to test whether there are internal short-circuits of insulators of long insulator strings.
Figure 2.2: Insulator tester [36].
35 Spangenberg and Riquel [37] summarized and evaluated measurement techniques in order to detect internal defects in non-ceramic insulators. The electric field strength measurements were carried out with a probe mounted on a carriage attached to a dielectric rod. The results showed that the presence of an insulator defect results in a potentially significant distortion of the electric field. The limitations of this method are:
• The length of the defective place, compared to the total length of the insulator,
needs to be sufficiently long to produce a distortion of the field distribution
curve.
• The measurement must be conducted on dry insulators.
• The probe must be in close contact with the insulator.
Vaillancourt, Carignan and Jean [7] did some modifications to redesign the tester in [36] for its use on composite insulators. Since composite insulators usually have a much smaller diameter than that of porcelain insulators, the new probe size became much
smaller. An optical sensor was used. The shed counting circuit was also redesigned to allow the counting of a large number of thin sheds. Laboratory experiments were designed to put various conductive and semi-conductive materials into the sheds of the insulator. The test results showed that this method worked well. During field tests, insulators damaged internally were located successfully by this method.
Chen, Li, Liang and Wang [38] used the electric field mapping method to detect conductive internal defects of a 110 kV composite insulator. The tests were taken under dry and clean condition, wet condition, and polluted condition. The test data showed that
under dry and clean conditions, tracking defects extending over one or two sheds can be easily detected at the HV end of the insulator. Experiments conducted on polluted and 36 wet insulators showed that the electric field distrihution is strongly distorted. The author concluded that in fair weather, at 82% humidity or less, the electric field strength mapping method is efficient for inspection.
Gela and Mitchell [39] initiated a research project to analyze the performance of non-ceramic insulators from the live line working viewpoint. The electric field strength calculations were performed for hoth healthy and defective non-ceramic insulators along a longitudinal path ahout 40mm tfom the tips of the weather sheds. The path corresponds to the location of the electric field tester. The theoretically predicted behavior of the electric field profile along the non-ceramic insulator with a defect was confirmed experimentally using the commercially available tester. The presence of a moist contamination layer on the non-ceramic insulator distorted the electric field strength profiles.
2.5.4 Design considerations for non-ceramic insulators
There are various concepts employed in insulator design to limit the leakage current and electric field strength near the surface of the weather shed which are responsible for tracking, erosion and flashover. These include:
• creating an aerodynamic weather shed profile for natural cleaning of the
contaminants hy wind and rain;
• increasing the leakage path to limit the magnitude of the leakage current;
• providing a protected leakage path to establish dry bands of sufficient number.
37 One of the most important details of composite insulator design is the design of the triple junction, i.e., the junction of the housing, air and metal end fittings. The electric field strength near this junction must he controlled in such a way that partial discharges at the metal flange are prevented.
Sokolija and Kapetanovic [40] discussed three issues related to the non-ceramic insulator design. They studied the electric field strength in the vicinity of three types of the metal end fittings and pointed out that the point with the highest electric field strength on the electrode should be away from the triple junction point. They also mentioned that many insulator designs are created in such a way that the lowest shed is very close to the metal end fitting to enable the discharge activities reaching the shed region.
Chakravorti and Steinhigler [17] studied the relationship between the shape of a porcelain post-type insulator and the maximum electric field strength around it with or without pollution. The position of the maximum electric field strength is near the top triple junction region. The parameters studied in their work are the slope angle of the insulator weather shed, the shed radius, the core radius, the axial height, and the electrode radius. Their findings were as follows:
• The higher slope angle does not yield notable reduction in the maximum
electric field strength.
• Increasing the shed radius from 6 cm to 10 cm significantly lowers the
maximum electric field strength.
• The increase of the core radius has little effect on the maximum electric field
strength reduction.
• The higher the axial height, the lower the maximum electric field strength. 38 • For a given insulator shape, increasing the electrode radius increases the
maximum electric field strength in clean conditions hut reduces the maximum
electric field strength in the presence of surface pollution.
Gorur, Cherney and Hackam [41] used fog chamber experiments to evaluate the polymer insulator shed profile designs. Six insulator profiles were evaluated with the
same end fitting design and same leakage distance to surface area ratio. These experiments showed that the protected leakage path provided by the weather sheds plays a major role in the tracking and erosion performance of polymer insulators. For values of the electric field strength between 30 and 40 V/mm on the surface of a polymer insulator, tracking and erosion failure can be expected to occur.
2.6 Summary and tasks of the dissertation
The literature reviews shows that the EFVD along dry and clean ceramic or non- ceramic insulators has been studied extensively by several researchers. The effect of uniform and non-uniform pollution on the surface of the ceramic insulators has also been
studied.
The analysis of the EFVD along non-ceramic insulators usually assumes single phase energization. However, a real power line means three phase energization. The presence of the other two phases may have some influence on the EFVD along a non- ceramic insulator and need to be studied.
The performance of non-ceramic insulators under polluted and wet conditions is quite different and more complex than that of the ceramic insulators. There are only a few
39 experimental studies related to the EFVD along non-ceramic insulators when there are water droplets on the surface of the insulator weather shed. The relationship between the hydrophobicity status of the non-ceramic insulator under rain and fog conditions and the
EFVD along the insulator is still unknown.
The design of non-ceramic insulators and corona rings should also be considered to limit the maximum electric field strength near the triple junction area.
Based on the literature review, there are six categories of the tasks for this dissertation.
The first group of tasks consists of the simplification of the insulator model in order to reduce calculation time with the least influence on the EFVD calculation along the insulators.
The second group of tasks consists of the model development for the 765 kV non- ceramic insulator, suspension tower, live end hardware, grading rings, and conductors.
The study of the EFVD along the 765 kV non-ceramic insulator under dry and clean condition, and the study of the effects of the other two phases (side phase) of the three phase system, conductors, tower configuration are also included.
The third group of tasks consists of the model development of a fiat silicon rubber
sheet with discrete water droplets on the upper shed and the study of the basic electric field enhancement around the surface of a water droplet.
The fourth group of tasks consists of the development for a four-shed non-ceramic insulator model under various wet surface conditions, the study of the EFVD along a four-shed non-ceramic insulator, and the study of the electric field enhancement on the water droplet surface.
40 The fifth group of tasks consists of the experimental study for the electric field distribution measurements along non-ceramic insulators using an insulator tester for the verification of the calculation results by the experiment results.
The sixth group of tasks consists of the design consideration for non-ceramic insulators, such as the distance between the first shed and the electrode, the shed spacing, the position of the corona ring.
41 CHAPTERS
FUNDAMENTAL STUDIES
In Chapter 2, a survey was presented on the study of the EFVD along non- ceramic insulators and several issues were pointed out. Recently, various issues ahout the
EFVD study along 765 kV non-ceramic insulators and water droplet related corona have received considerable attention. The two primary tasks of this chapter are:
1. Determine which simplification models of non-ceramic insulators can he used
to study the EFVD along the insulators without losing much accuracy.
2. Investigate some basic features related to the electric field enhancement factor
due to the existence of water droplets on a non-ceramic insulator.
For the first task, several simplified models are investigated to determine the best method for modeling non-ceramic insulators and the approximations necessary to get valid results without requiring excessive computation time.
For the second task, a flat silicone rubber (SiR) sheet with water droplets is used to examine the electric field enhancement factor due to the existence of water droplets with different contact angle, size, shape, and conductivity.
42 3.1 Simplification of the non-ceramic insulator model
There are various kinds of non-ceramic insulators. One of the typical 34.5 kV non-ceramic insulators has 12 weather sheds, and its length is about 0.8 m. For comparison purposes, a typical 765 kV non-ceramic insulator has 103 weather sheds, and its length is 4.7 m. To get accurate results, much more elements have to he used for a 765 kV non-ceramic insulator than for a 34.5 kV non-ceramic insulator. When using the boundary element method to calculate the EFVD along non-ceramic insulators, the more elements are used, the more computation time is needed. In order to reduce the calculation time when analyzing long insulators, some simplifications of the non-ceramic insulator model are necessary.
A non-ceramic insulator has four main components. They are the fiberglass rod, polymer sheath on the rod, polymer weather sheds, and two metal end fittings. To decide which component of the insulator can he simplified with the least influence on the accuracy of the calculation results on the EFVD along the non-ceramic insulators, a 34.5 kV non-ceramic power line insulator shown hy Fig 3.1 is employed for the study.
The detailed geometric dimensions of a 34.5 kV insulator are shown in Fig. 3.1.
The insulator is equipped with metal fittings at hoth line and ground ends. The insulator is made of silicone rubber with a relative permittivity of 4.3 and fiberglass reinforced polymer (FRP) rod with a relative permittivity of 7.2. There are 12 weather sheds on the housing. The insulator is surrounded hy air with a relative permittivity of 1.0. The top metal end fitting is taken as the ground electrode and the bottom electrode is connected to
43 a steady voltage source of 1 kV for the purpose of calculations. The insulator is positioned vertically, but it is shown in Fig. 3.1 horizontally for convenience.
Units: mm
Ground end Line end
a
154 460
812
Figure 3.1: Simplified geometry and dimensions of the non-ceramic insulators to he modeled. A: metal end fitting; B: fiber glass rod; C: polymer material weather sheds; D: polymer material sheath.
Four simplified computation models are used for the step hy step comparison process. In addition, a three dimensional “full” insulator model is set up as a reference to
study the effects of the four simplified computation models of the non-ceramic insulator on the EFVD along the insulator.
These five calculation models are shown in Fig. 3.2:
(a) two electrodes only
(b) two electrodes and the fiberglass rod
(c) two electrodes, rod and sheath on the rod without weather sheds
(d) two electrodes, rod, sheath, two weather sheds at the each end of the insulator
(e) the “full” 34.5 kV insulator.
44 I
r (a) (c) (e) Figure 3.2: Four simplified insulator models and a “full” insulator model used for calculation.
As an example to show the element configuration, the “full” insulator model has
12553 four-sided elements applied to the surface of boundaries and the interfaces of different media. The element configuration on the surface of the insulator is partially
shown in Fig. 3.3.
Figure 3.3: Element configuration on the 34.5 kV non-ceramic insulator model. 45 The equipotential contours around the five computation models are shown in Fig.
3.4. As a reminder, the bottom electrode is energized, the top electrode is grounded. The energizing voltage is 1000 V. The insulation distance between two electrodes is 46 cm.
26- 26 26 26
24- 24 24 - 150- 24 150 158 -
-1 5 0 - 2 2- 22 150- 2 2 - 22
20 20 2 0 - 20
18 - 18 18 200-- 18 - 200.
16^ 16 16- 16 - 200--
14- 14 250 14 14 -
- 250- 12
1 0 -
450 450 450 6 " 400- 6 450 "" ."-450 "500 -
4 ^ - - 500 - 4 550 - - - 550 550
2 -_ ^ _ 600 2 650 650 0 - 0 '"''7 0 6 ' |700
■2 9 0 0 ' ■2 9:^ / 95^850750 ' 75O, ■4 ■4
1 2 3 4 5 0 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
(a) (b) (c) (d) (G)
Figure 3.4: Equipotential contours around the five computational models.
Each number shown along the perimeters of the four contour plots means centimeters. Case (a), no solid insulating material between the electrodes, shows that about 20% of the insulation distance sustain about 70% of the applied voltage. The presence of the fiberglass rod slightly changes the voltage distribution, see Case (b). The 46 distribution of the equipotential contours for Case (c), with the sheath on the rod, is very close to Case (e), however, the presence of the weather sheds changes somewhat the equipotential contours. If more accurate results of the voltage distribution are needed near the line and ground end area, the simplified insulator model with two weather sheds at each end of the insulator. Case (d) can be used. Comparing Cases (d) and (e), the voltage distribution in the vicinity of the two weather sheds is very similar to each other. The positions of the equipotential lines for Cases (d) and (e) are very close to each other along the sheath surface of the insulator. To see the comparison more clearly, the voltage distribution for Cases (d) and (e) along the paths (shown as the dashed line in Figs. 3 (d) and (e) ) are shown in Fig. 3.5. Comparing Cases (d) and (e), the maximum difference between the voltages at the same point along the sheath surface of the insulator is only
1.2% of the applied voltage. This indicates that the simplification introduced by Case (d) is acceptable for the calculation of the voltage distribution of the “full” insulator. Case
(e), along the sheath surface.
1000 900 ------Insulator with 12 sheds for Case (e) > 800 ------Insulator with 4 sheds for Case (d) & 700 ^ 600 \ > 500 400 300 200 100 0 0 10 20 30 40 50 60 70 80 90 100 Insulation distance (%)
Figure 3.5: Voltage magnitude along the insulation distance at the surface of the sheath for Cases (d) and (e).
47 The electric field strength magnitudes for Cases (d) and (e) along the paths defined on the surface of the sheath are also calculated for comparison, which is shown in
Fig. 3.6. The dips in the electric field strength plot of the insulator modeled with weather
sheds are due to the calculation path passing through the weather shed material, which has a relative permittivity of 4.3. The electric field strength in the vicinity of the two weather sheds at each end of the insulator is same for Cases (d) and (e). There is a slight change in the electric field strength distribution near the other 8 weather sheds shown by
Case (e). However, the electric field strength outside the weather sheds region still has a good correspondence in Cases (d) and (e). The maximum electric field strength for Case
(d) is 0.0256 kVp/mm, and for Case (e) is 0.0256 kVp/mm. They are the same, which means that the electric field distribution of the insulator with the “full” number of weather sheds can be estimated through the simplified insulator model with a small number of weather sheds (for example, 2) at the each end of the insulator.
^ 0.026 a 0.024 Insulator with 12 sheds for Case (e) ^ 0.022 Insulator with 4 sheds for Case (d) â 0.02 Æ 0.018 % 0.016 g 0.014 ^ 0.012 13 0.01 ^ 0.008 •a 0.006 Cl W 0.002 0 10 20 30 40 50 60 70 80 90 100 Insulation distance (%
Figure 3.6: Electric field strength magnitude along the insulation distance at the sheath surface for the “full” insulator. Case (e), and the simplified insulator model. Case (d). 48 3.2 Effects of conductor and ground supporting structure
When a suspension non-ceramic insulator is put in service, the tower window that is at ground potential, and the conductors that are energized will have some effects on the electric field distribution in the vicinity of the insulator. The effects of the grounded
supporting structure and the power line conductor on the EFVD near the insulator are
studied by adding a 3m long, 1.74 cm diameter single conductor section just below the insulator. The insulator is suspended from the middle of a 1.6 m x 0.4 m grounded
supporting structure. The “full” insulator. Case (e), and the simplified insulator model,
Case (d), are both used for the calculation for comparison purpose. The two insulator models with the conductor and the grounded supporting structure are shown in Fig. 3.7.
A
(a) Full insulator model (b) Simplified insulator model
Figure 3.7: Insulator model with grounded supporting structure and line conductor.
49 The equipotential contours around the “full” insulator model and the simplified insulator model together with the conductor and the grounded supporting structure are
shown in Fig. 3.8.
.. 1.-. __ 26 26
d 5 8 - 24 24
22 22 350- 20 20
18 18
16 16
-250 14 14 -450-
12 12 " 386. — 10 10 550- 550- _ " -400 8 8 450 6 6 - 500 -650 7 00 550 4 4 700 600 750 2 ^ ^ 65[ ..... A 0 n r ' goOgoo ; ■2 950 05%50 755 / ; ; 1' ; ' -4 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 (a) Full insulator (b) Full insulator (c) Simplified insulator with no conductor with conductor with conductor
Figure 3.8 Equipotential contours around three computation models.
For the insulator without the conductor and the grounded supporting structure,
20% of the insulation distance sustain about 65% of the applied voltage. For the insulator with the grounded supporting structure and conductor, it can be seen that now 20% of the 50 insulation distance sustain about 47% of the applied voltage. Comparing the voltage distrihution between the “full” insulator model and the simplified insulator model, both with the conductor and the grounded supporting structure, they are still very similar to each other.
The electric field strength distributions along the sheath surface of the insulator, with and without the conductor and the grounded supporting structure, are shown in Fig.
3.9. The maximum value of the electric field strength at the line end of the insulator with the presence of the 3m long conductor section is 0.018 kVp/mm and at the ground end is
0.006 kVp/mm at 1000 V energizing voltage. The maximum value of the electric field
strength at the line end of the insulator without the conductor is 0.0256 kVp/mm and at the ground end is 0.003 kVp/mm. It is obvious that the existence of the conductor at the line end and the grounded supporting structure reduces the electric field strength at the line end, but increases the electric field strength near the ground end.
0.026 0.024 Insulator with the conductor and grounded supporting structure Ih. 0.022 Insulator without the conductor and grounded supporting structure 0.02 à 1 0.018 W) o.oif I I" g 0.014 1 \ ^ 0.012
Figure 3.9: Electric field strength magnitude along the insulation distance at the sheath surface of the insulator with and without the conductor and the grounded supporting structure.
51 The electric field strength magnitudes along the sheath surface for the “full” insulator and the simplified insulator, which is with the conductor and the grounded
supporting structure, are also calculated for comparison. The results are shown in Fig.
3.10, which again shows the similarity between the two functions.
0.018
0.016 -Full insulator with the conductor and grounded supporting structure -Simplified insulator with conductor and grounded supporting structure 0.014
0.012
t 0.01
0.008 « o 0.006 'B y 0.004 w 0.002
0 0 10 20 30 40 50 60 70 80 90 100 Insulation distance (%)
Figure 3.10: Electric field strength magnitude along the insulation distance at the sheath surface for the “full” insulator and the simplified insulator model with the conductor and grounded supporting structure.
The conclusion is drawn that the simplified insulator model with only a small number of weather sheds, which is shown in Fig. 3.2 (d), can be used to calculate the electric field and voltage distribution along the “full” insulator in service with no
significant influence on the accuracy.
52 3.3 Some basic features of water droplets on a non-ceramic insulator surface
3.3.1 Hydrophobicity of non-ceramic insulators
The excellent pollution performance of non-ceramic insulators is due to the good hydrophobic surface property of weather sheds under wet and contaminated conditions.
During the service life of an insulator, the combined effects of electric and environmental
stresses accelerate the aging of the non-ceramic insulators. Consequently, the hydrophobicity properties of non-ceramic weather sheds will be temporarily or permanently lost.
Hydrophobicity describes the wettability of a surface. There are two methods that are usually used to describe the hydrophobicity of a non-ceramic insulator surface. One is called the single drop method and the other is called the hydrophobicity classification method. The classical method, which is usually used in laboratories to characterize the hydrophobicity of a surface, is the single drop method [42]. A single water drop is put on the surface that needs to be examined. A tangent line is drawn on the water drop’s surface at the triple point of water/solid/air. The angle formed by this tangent line and the base line of the water drop is called static contact angle, 6. The contact angle 0 is shown in
Fig. 3.11, which is used to characterize the hydrophobicity of a surface. Contact angles are measured in degrees. “Low” is below about 20° and “high” is 90° or above. Low angles mean wettable surface. The contact angle can be determined by using a goniometer or projecting the water drop onto an angle net. This technique is relatively
simple and gives good indication of the surface hydrophobicity status.
53 ////////////
Figure 3.11: Definition of contact angle.
The second method is called the hydrophobicity classification (FTC) method, which has been developed by the Swedish Transmission Research Institute (STRI). The
HC method was introduced by Gubanski and Flartings in [43]. The only equipment needed is a common spray bottle. The spraying shall continue for 20-30 seconds from a distance of 20+10 cm. The wetting appearance of a surface sprayed with water is identified with one of seven classes, HCl to HC7. The criteria for the different classes are given in Table 3.1.
HC Description
1 Only discrete droplets are formed. 0~8O°or larger for the majority of droplets.
2 Only discrete droplets are formed. 50° < 0 < 80° for the majority of droplets.
3 Only discrete droplets are formed. 20° < 0 < 50° for the majority of droplets. Usually they are no longer circular. 4 Both discrete droplets and wetted traces from the water runnels are observed. Completely wetted areas < 2cm^. Together they cover < 90% of the test area. 5 Some completely wetted areas > 2cm^, which cover < 90% of the test area. 6 Wetted areas cover > 90%, i.e. small unwetted areas are still observed. 7 Continuous water film over the whole tested area.
Table 3.1: Criteria for the hydrophobicity classification (TIC) [43].
54 Each HC class corresponds to a characteristic wetting pattern, which is described by a reference picture shown in Fig. 3.12. Apart from the different contact angles, the
size and shape of the water droplets are also different for different HC classes. i f f
s-r.
..
2 A :# # HC*
ÿ'-'-1
Figure 3.12: Typical examples of surfaces with HC from 1 to 6. HC7 represents the completely wet surface [43].
This method is very simple for the practical evaluation of the hydrophobicity of insulators in service. Since many researchers have used this method to characterize the hydrophobicity of the insulator surface, the wet insulator models with water droplets on their surface in this research work will also be described using this method. 55 3.3.2 Water droplet corona and dynamic behavior on the surface of non-ceramic insulators
Water droplets increase the electric field strength at the insulator surface because of their high permittivity. Surface corona discharges from water droplets accelerate the aging of the polymer material of the insulator shed and destroy the hydrophobicity locally, causing the water to spread and the adjacent water drops to coalesce. The loss of hydrophobicity leads to the formation of a wet region, introducing a partial short circuit along the surface of the insulator. This reduces the resistance that limits the current and provides a path for an arc [5].
The corona discharge phenomena from water droplets have received considerable attention and are investigated in recent publications.
Phillips, Childs and Schneider [9, 44] studied the corona onset level for a water droplet on the sheath region and the shed region of a non-ceramic insulator by small scale experiments. Tbe surface electric field strength was calculated by the potential difference between the electrodes without any water droplets on the sheath region. This electric field
strength is referred to as applied E-field.
For the sheath region, a single water drop was put at the center of the sheath region of the insulator section. The electric field is increased at the interface between the water drop, air, and insulating material. For water drops with volumes of 10 to 100 |il, the applied F-field values for corona onset were found between 0.56 and 0.44 kV/mm for
SIR material with 88° contact angle. The applied F-field required for corona onset
56 decreased with increasing water drop size from 10 to 80 |ll and remained the same between 80 to 100 |al.
For the shed region, a single water drop was put on the surface of a non-ceramic insulator shed. For water drops with volumes of 65 to 125 |il, the measured average corona onset E-field remained between 0.86 and 0.96 kV/mm.
Lopes, Jayaram and Chemey [45] studied the partial discharge from water droplets on a silicone rubber insulating surface. They found that the measured average corona onset applied electric field strength values were 5.2 kV,ms/cm and 4.2 kVrms/cm for a single water droplet with volume of 30 and 80 |ll, respectively. Considering that the corona takes place when the local electric field strength around the water droplet reaches the critical ionization value in air 20.4 kVrms/cm for the existing ambient conditions, the average field enhancement factors were 3.9 to 4.8 for one droplet with the volume changing from 30 to 80 |xl.
Discharges between water droplets were carefully studied by Blackmore and
Birtwhistle [46]. They found that discharges between water drop electrodes produced the localized loss of the hydrophobicity of tbe polymer material. Tbe combination of the high discharge temperature and the plasma chemistry of the water vapor and air are responsible for tbe loss of bydropbobicity. The rate of hydrophobicity loss was found to be dependent on water droplet conductivity and contact angle. At higher conductivity and lower contact angle, a longer time has been observed until the hydrophobicity of a polymer material was lost.
57 The behavior of water droplets on the surface of the hydrophobic insulating
surface under low frequency ac electric field was also investigated by several researchers.
Keim and Koenig [47, 48] studied the behavior of a single water droplet of different volumes under applied ac electric field stress. They found that the water droplets were oscillating with an up and down movement. Very active drops varied their contact angle up to a difference of 30 degrees.
Krivda and Birtwhistle [49] observed that when a 40 |il water drop was deposited on the surface under 0.68 kVrms/mm electric field strength, a significant deformation of water drop was viewed, which elongated and contracted in the direction of the electric field. The diameter of the water drop in the voltage peak positions changed from 6.4 mm in the positive half-cycle to 4.3 mm in the negative half-cycle.
Yamada, Sugimoto and Higashiyama [50] experimentally studied the resonance phenomena of a single water droplet located on a hydrophobic sheet under ac electric field. Fig. 3.13 shows the time variation of the deformation of a 10 |il water droplet located on a SIR sheet and a PGF (a kind of polymer material) sheet during a half cycle
(between co(=0 and %) of the AC field.
1
Figure 3.13: Behavior of 10 pi water droplet located on a SIR and a PGF sheet [50].
58 3.4 Flat SIR sheet with a water droplet
The presence of water droplets changes the EFVD on the surface of a non- ceramic insulator. Different distributions of water droplets on the surface of the non- ceramic insulator lead to different electric field and voltage distributions. Before calculating the EFVD along the non-ceramic insulator model with water droplets, some
simple cases should be studied as a preliminary step.
Assuming a vertical suspension insulator, there are sessile water droplets on the weather sheds, clinging water droplets on the vertical surface of the polymer sheath of the insulator and pendant water droplets under the sheds as shown in Fig. 3.14. The surface of the insulator shed is close to parallel to the equipotential lines. The surface of the
sheath is close to perpendicular to the equipotential lines.
Sheath region
Sessile dronlet Pendant dronlet Clinging droplet Shed region
Figure 3.14: Three types of water droplets on a vertical suspension insulator.
As the first step, two simple models have been set up to study the basic features of the electric field distribution around water droplets. In both models, a fiat hydrophobic
silicone rubber sheet with one discrete water droplet between two electrodes is used to
study the electric field enhancement in the vicinity of water droplets. One electrode is energized (e.g., 100 Volts), the other one is grounded. The software used assumes a
59 “remote” ground as well. It is equivalent to conducting an experiment in a high voltage laboratory with the floor, ceiling and walls grounded.
In order to represent the sheath region, two electrodes are considered together with a single SIR sheet between them, which are shown in Fig. 3.15. In order to represent the shed region, the SiR sheet is positioned parallel between the two electrodes, which are
shown in Fig. 3.20. The effects of the contact angle, size, shape and conductivity, of a water droplet on the electric field enhancement are to be studied using these two models.
3.4.1 Sheath region simulation
In order to represent the sheath region of an insulator, two electrodes are assumed together with a single SiR sheet. The size of the SiR sheet is 10 cm x 10 cm and it is 0.5 cm thick. The relative permittivity of the SiR material used in the calculation is 4.3. The two electrodes are positioned at 10 cm distance from each other. The position of the SiR
sheet is shown in Fig. 3.15; the SiR sheet is between the two electrodes as a spacer to
simulate the sheath region. The energized electrode is on the left side and the grounded electrode is on the right side. The applied voltage is 100 V, which means the average electric field strength is 100/10=10 V/cm. The x, y, z directions are defined as shown in
Fig. 3.15.
Z A IT) 100 V d
X T 10 cm
Figure 3.15: Experimental setup for the sheath region simulation.
60 A water droplet of hemispherical shape is assumed at the midway of the electrode
spacing. The diameter of the water droplet is 4mm and its height is 2 mm. The relative permittivity of the water droplet is 80 and its conductivity is assumed to be zero.
For the sheath region simulation, Fig. 3.16 shows the equipotential contours with a single water droplet at the center on the surface. The electric field distribution along the
surface of the sheet is also calculated and shown in Fig. 3.17. The electric field strength is intensified at the interface between the water droplet, air, and insulating sheet to 32.9
V/cm. Z tcm t 1
0.5
0
-0.5 ^ LQ ~ O - O C3 U) O If) TO - -iri ^ _ CO “00— C4 -1 Î -4 -3 -2 -1 0 1 2 3 4 5 Y (cm )
Figure 3.16: Equipotential contours and electric field lines for sheath region simulation.
Em (V /cm ) 35
30 -
25 20 - 15 -
10
5 0 -5 -2 4 5 Y (cm )
Figure 3.17: Electric field distribution along the SIR sheet surface for sheath region simulation.
61 The enlarged view of the equipotential contours and electric field lines around the water droplet positioned on a SiR sheet simulating the sheath region is shown in Fig.
3.18. Continuous lines represent the equipotential contours; dashed lines are used for the electric field lines. It can be seen from Fig. 3.18 that the presence of the water droplet causes a considerable distortion in the configuration of the equipotential contours and the electric field lines in the vicinity of the water droplet. For the sheath region simulation, the electric field strength is significantly increased at the interface of the water droplet, air, and the insulating sheet.
Z (cm ) O.i
0.7
0.6
0.5
0.4 AS--*
0.3------:------^ -0.3 -0.2 -0.1 0.1 0.2 0.3 Y (cm )
Figure 3.18: Equipotential contours and electric field lines around a water droplet on the sheath surface.
The electric field strength vector changes its magnitude and direction along the
surface of the water droplet. To follow its changes, several quantities can be monitored, for example, the x, y, or z components of the electric field strength vector, or the magnitude of the electric field strength vector. The x, y, z, components and the magnitude of the electric field strength on the surface of the water droplet on the sheath region are
6 2 shown in Fig. 3.19 (a), (b), (c), (d), respectively. Each point on the surface of the water droplet is described by its three coordinates (x, y, z). In fact, a fourth dimension would be needed to show the distribution of the magnitude of the electric field strength. In order to be able to show the electric field strength distribution on the surface of the water droplets
using a 3D graph, the surface point is represented by its (x,y) coordinates only. In other words, all points on the surface of the water droplet are represented by their projection in the (x,y) plane. Then the z dimension can be used to show the magnitudes of the electric field strength vector or its components at any point on the surface of the water droplet.
>
. a 2 7 % 2 4 S 21 J n 1 8
1.1, . i.i,' Ü 6 'S 3
0 .3 0 .3 0.2 Ü-1 0.2 0.1 0.1 0.2 0 .3 Y ( c m ) - 0 1-02 u n 1 Y (cm) -0.2 -0.2"°'' X(cm) - 0 .3 _o .3 - 0 2 X (cm) - 0 .3 - 0 .3
(a) X component (b) Y component
s I ^ 3 3 > > 3 0 ^27 2 4 a 21 a 1 8 VD 1 5 3 12 1 ! s 0.2 'S ^ 0.2 o 0 0.2 ^ 0 .3 0.2 0.2 0 .3 Ü-1 0.1 - 0.1 Y ( c m ) - 0 1 - _0 2 0.2 - 0 .3 - 0 .3 -0.2 X (cm)
(c) Z component (d) Total electric field strength Figure 3.19: Vector components and the magnitude of the electric field strength on the surface of the water droplet on the sheath surface. 63 For a water droplet in the sheath region, the maximum value of the electric field
strength, at 100 V applied voltage, is 32.9 V/cm on the surface of the water droplet, at the interface of the water droplet, air and insulating material. The electric field enhancement factor is 3.29, which is defined as the ratio of the maximum electric field strength at the tip of the water droplet and the applied field strength under dry conditions without the water droplet. The y component of the electric field strength vector is the dominant component, as expected.
3.4.2 Shed region simulation
In order to represent the shed region of an insulator, two electrodes are assumed together with a single SiR sheet. The two electrodes are positioned at 10 cm distance from each other. The SiR sheet is in a parallel position between the two electrodes for
simulating the weather shed region as shown in Fig. 3.20. The upper electrode is energized and the lower electrode is grounded. The applied voltage is 100 V, which means the average electric field strength is 100/10=10 V/cm. The x, y, z directions are defined as shown in Fig. 3.20.
100 V
o
Figure 3.20: Experimental setup for the shed region simulation. 64 A water droplet of hemispherical shape is assumed at the midway of the electrode
spacing. The diameter of the water droplet is 4mm and its height is 2 mm. The relative permittivity of the water is 80 and its conductivity is assumed to be zero.
For the shed region simulation, Fig. 3.21 shows the equipotential contours with a
single water droplet at the center on the surface. The electric field distribution along the
surface of the sheet is also calculated and shown in Fig. 3.22. The electric field strength has been enhanced at the top of the water droplet. The reason for the change of the magnitude of the electric field strength in Fig. 3.22 is a result of the measurement line passing through the water which has a relative permittivity of 80.
Z (cm ) 1 4?— 4 : - -/ir'O --- -AA 0.5 41 % 0 IT + — — 4 IT? Î -0.5 136 -3 5 34- -1 T3 4 5 Y (cm )
Figure 3.21: Equipotential contours and electric field lines for shed region simulation.
Em (V /cm )
15
10
-5 -3 -2 -1 3 4 5 Y (cm )
Figure 3.22: Electric field distribution along the SiR sheet surface for shed region simulation.
65 The enlarged view of the equipotential contours and electric field lines around the water droplet positioned on a SiR sheet simulating the shed region is shown in Fig. 3.23.
Continuous lines represent the equipotential contours; dashed lines are used for the electric field lines. It can be seen from Fig. 3.23 that the presence of the water droplet causes a considerable distortion in the configuration of the equipotential contours and the electric field lines in the vicinity of the water droplet. For the shed region simulation, the electric field strength is enhanced at the top of the water droplet.
Z (cm )
451.57 '46 .3' rC
0.7
I4 4 A 43'^ I I I
0.5 ■ 4M
0.4 -f- & 7 - .4 ..^7 .. J--', '-ry 0.3 ' ' - 0.3 - 0.2 - 0.1 0 0.1 0.2 0.3
Y (cm )
Figure 3.23: Equipotential contours and electric field lines around a water droplet on the shed surface.
The X , y, z, components and the magnitude of the electric field strength on the
surface of the water droplet on the sheath region are shown in Fig. 3.24 (a), (b), (c), (d), respectively. Similarly to the sheath region simulation, all points on the surface of the
water droplet are represented by their projection in the (x,y) plane. Then the z dimension
can be used to show the magnitudes of the electric field strength vector or its components
at any point on the surface of the water droplet.
66 .XVf:;..
...... 0.3 0.2 0.1 Y (cm) .n i - 0 0.2 0.3 X (cm) - 0.2 X (cm ) Yk:m) -0.3 -0-3
(a) X component (b) Y component
g > 30 3 0 ...... 27 ■ s 2 7 g ) 2 4 . ... 24 21 21 § .. 18 . ^ 18 .. I 15 2 ^2 12 I 9 6 I 3 I : 0 0.3 I %2 0.2 0.1 0.3 0.2 Y (cm ) i Y (cm) -0.2 - 0.2 -0.2 X (c m ) '-0.3 -0.3 -0.3 X (cm)
(c) Z component (d) Total electric field strength
Figure 3.24: Vector components and the magnitude of the electric field strength on the surface of the water droplet on the shed surface.
For a water droplet in the shed region, the maximum value of the electric field
strength, at 100 V applied voltage, is 27.6 V/cm on the top of the water droplet. The electric field enhancement factor is 2.76. The z component of the electric field strength vector is the dominant component, as expected.
67 3.5 Effects of water droplet contact angle, size, shape, distance, and conductivity
3.5.1 Effect of water droplet contact angle
For a water droplet on the sheath region, the highest electric field strength is at the interface between the water droplet, air, and insulating sheet. It is of practical interest to know the electric field enhancement at various contact angles of the water droplet. For a water droplet on the shed region, the highest electric field is at the top of the water droplet, not the junction between the water droplet and insulating sheet. The effect of the contact angle is not significant. So only the water droplet on the sheath region is considered.
Under different hydrophobicity stages of the SiR sheet surface, the contact angle of the water droplet varies. Four typical values of the contact angle are considered for comparison purposes, which are 120, 90, 60, and 30 degrees. To avoid the effect on the electric field enhancement due to varying the water droplet size, the contact area between the water droplet and the SiR sheet for these four cases is kept constant. The contact area in this study is defined as a circle with 4mm diameter. The relative permittivity of the water droplet is 80 and its conductivity is assumed to he zero.
The enlarged views of the equipotential contours and electric field lines around the water droplet for these four cases are shown in Fig. 3.25. The water droplet is positioned on a SiR sheet simulating the sheath region. Continuous lines represent the equipotential contours; dashed lines are used for the electric field lines. It can he seen from Fig. 3.25 that the water droplet with larger contact angle causes more distortion in the configuration of the equipotential contours. The maximum values of the electric field
strength on the surface of the water droplet with different contact angles are given in
Table 3.2. The relationship between the electric field enhancement factor and the contact angle is shown in Fig. 3.26.
0,9
0.8 0,8
0.7 0,7
I 0,6 0.6
0,5 0.5
0,4 0.4
0,3 0.3 - 0.2 - 0.1 0 0.1 0.2 0.3 -0.2 - 0.1 0 0.1 0.2 0.3
(a) 120 degrees (b) 90 degrees
0,8
0,7
0,6 -
0,5
CD _ _ ^ _ CSJ
0,4 - T-
0,3 -0.2 -0.1 0.2 0.3
(c) 60 degrees (d) 30 degrees
Figure 3.25: Equipotential contours and electric field lines around a water droplet on the sheath surface with different contact angles.
69 Contact angle, degrees 120 90 60 30 Maximum electric field 38A 329 2 5 ^ 20.1 strength, V/cm
Table 3.2: The electric field enhancement factors on the surface of the water droplet with different contact angles.
I 0O 1 8
w 40 60 80 100
Contact angle of water droplet (degrees)
Figure 3.26: The electric field enhancement factor for a water droplet with different contact angles on the sheath region.
The results show that the electric field enhancement factor increases as the contact angle increases. The relationship between them is almost linear. Although in reality, the
shape of the water droplet on the vertical sheath region may not be spherical, the results can still be used to estimate the electric field enhancement for the water droplet with
same advancing contact angle. The reason is described in detail in section 3.5.3.
3.5.2 Effect of water droplet size
The effects of the electric field strength enhancement due to various water droplet
sizes are also investigated. The shape of a typical water droplet is hemispherical. The
70 diameters of typical water droplets in this study are between 2 to 8 mm. It means that the volume of water droplet is between 2 to 134 |il. The electric field enhancement factors are studied for a water droplet with different diameters on the sheath region and on the
shed region. The results are shown in Figs. 3.27 and 3.28. It is clear that the larger the water droplet, the higher the electric field enhancement. For the water droplet on the
sheath region, the effect of the size of water droplet on the electric field enhancement is more significant than that on the shed region.
ë 4.5
g S
i g 3 (U C 2.5
Diameter of water droplet (mm)
Figure 3.27: The electric field enhancement factor for a water droplet of different diameter on the sheath region.
i . . % « Z6 o 2.5 W 1
Diameter o f water droplet (mm)
Figure 3.28: The electric field enhancement factor for a water droplet of different diameter on the shed region.
71 3.5.3 Effect of water droplet shape
Based on the laboratory observations and studies of several other researchers, the
shape of a water droplet is not always hemispherical and it changes under different conditions. To study the shape effects of water droplets, two pictures of the different
shapes of water droplets are shown in Fig. 3.29.
(a) Water droplets on the sheath region (b) Water droplets on the shed region
Figure 3.29: Water droplet shape on the sheath and the shed region.
The larger the water droplet, the more chance exists that it may change its shape.
Two typical shapes of water droplets are considered with the same base width of 8mm on the sheath region. The first water droplet shape shows the water droplet on the sheath region (pointed by an arrow in Fig. 3.29 (a)). The second water droplet shape represents the shape of two water droplets merged together on the shed region (pointed by an arrow in Fig. 3.29 (b)).
72 The calculation results are shown in Fig. 3.30. It should be rotated to the left by
90° to see the true position of the distorted water droplet on the vertical sheath. The maximum electric field strength for Case (a) is at the interface of the water droplet, air and insulating material. The electric field enhancement factor is 4.13 for Case (a).
Considering that the electric field enhancement factor for the water droplet (8mm diameter) on the sheath with hemispherical shape is 4.41, the effects of the shape difference are not significant.
The maximum electric field strength for Case (b) is at the top surface of the water droplet. The electric field enhancement factor is 2.55 for Case (b). Considering that the electric field enhancement factor for the water droplet (4mm diameter) on the sheath with hemispherical shape is 2.76, the effects of the shape difference are not significant.
Y (cm )
Z (cm )
46.4 -4 6 ;
0.7
0.6 4 3 .2
0.5 0.5
0.4 0.4 42.1
0.3 -0.5 -0.4 - 0.3 - 0.2 - 0.1 0 0.1 0.2 0.3 0.4 0.5 - 0.5 -0.4 - 0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Z (cm ) Y (cm )
(a) Tilted water droplet on the sheath (b) Merged water droplet on the shed
Figure 3.30: Equipotential contours around a water droplet with different shapes on the sheath and shed region.
73 3.5.4 Effect of the distance between adjacent water droplets
For the water droplets on the sheath region, the effect of the electric field enhancement due to multiple water droplets is also studied with a pair of 8mm diameter, hemispherical shape water droplets. The distance between them has been varies from
2mm to 8 mm. Fig. 3.31 shows the electric field enhancement factor vs. the distance between the two water droplets.
^ 5.4
5.2
5
4.8
4.6 I1) w 4.4 1 23456789
Distance between water droplets (mm)
Figure 3.31: Effect of the distance between water droplets on the electric field enhancement for sheath region simulation.
It can be seen that the closer the water droplets, the higher the electric field enhancement. When the distance between the two water droplets is 8mm, the electric field enhancement factor is about 4.6, which is very close to the electric field enhancement factor for a single water droplet, 4.4. Therefore, the influence of the other water droplet can be ignored if the distance between the two water droplets is larger than the diameter of the water droplet.
74 3.5.5 Effect of water droplet conductivity
The conductivity of water droplets also influences the electric field enhancement.
If the relative permittivity and the conductivity of the water droplet are both considered, the electric field enhancement factor on the surface of the are modified. A water droplet with hemispherical shape and 4 mm diameter is used to illustrate the effects of the water droplet conductivity. The relative permittivity remains 80. One typical value of the conductivity are considered for comparison purposes, which is 250 |is/cm. The electric field enhancement factor changes from 3.29 to 3.55 for the water droplet on the sheath region and from 2.76 to 3.17 for the water droplet on the shed region. Increasing the conductivity from 250 |xs/cm to 2500 jas/cm, there is no change on the electric field enhancement factor.
3.6 Summary
In this chapter, the first three objectives of the dissertation research have been addressed.
The first objective was to find possible simplifications of an insulator model without significantly compromising the accuracy of the calculation results. The
simplified insulator model with only a small number of weather shed at each end is proved to be an accurate model to calculate the electric field and voltage distribution along the “full” insulator in service.
75 The second objective, the effects of conductor and ground supporting structure have also been analyzed. The conductor section at the line end reduces the electric field
strength at the line end, but increases the electric field near the ground end.
The third objective was to study the basic electric field enhancement feature of the water droplet on the sheath and on the shed region.
For a water droplet on the sheath region, the maximum electric field strength on the surface of the water droplet is at the junction point of the water droplet, air and insulating material. The larger the contact angle and the size of the water droplet, the higher the electric field enhancement. The closer the water droplets, the higher the electric field enhancement.
For a water droplet on the shed region, the maximum electric field strength is on the top of the water droplet. The larger the size, the higher the electric field enhancement.
The shape and conductivity of the water droplet have some effects on the electric field enhancement for a water droplet on sheath or shed region. The influence is not
significant.
76 CHAPTER 4
ELECTRIC FIELD AND VOLTAGE DISTRIBUTION ALONG NON-CERAMIC INSULATORS UNDER DRY AND CLEAN CONDITIONS
4.1 Introduction
High electric field strength may cause corona around non-ceramic insulators, which may result in corona cutting, deterioration and aging of polymer materials of non- ceramic insulators. Therefore, control of the electric field strength around non-ceramic insulators is an important aspect for the design of non-ceramic insulators and their associate grading devices. Several studies recommend that the maximum electric field
strength should not exceed 2.28 kV/mm at any point on the surface of a non-ceramic insulator in order to prevent dry corona on the insulator surface. Also the typical electric field strength threshold value for water droplet triggered corona are in the range of 0.5-
0.7 kVrins/mm [51]. This value is the electric field strength on the surface of the insulator under dry condition without any water droplets.
Understanding the electric field strength distribution in the vicinity of a non- ceramic insulator is very important for the design and development of non-ceramic insulators. One of the most important details of non-ceramic insulator design is the design of the triple junction point: sheath, air and metal end fittings [40]. The electric field 77 strength near this junction should be limited to a value less than the corona onset electric field strength.
When non-ceramic insulators are installed on a power line, the tower geometry, live-end hardware and conductors in the vicinity of the insulators will have some effects on the electric field distribution around the insulators. Depending on the voltage level, the magnitude of the electric field strength on the surface of the insulator may exceed the corona onset values. Grading rings should be used to redistribute the electric field distribution and reduce the maximum value of the electric field strength. Consequently, to consider all these effects, a three-dimensional calculation model must be set up in the
Coulomb software in order to evaluate the EFVD near and along a non-ceramic insulator.
In the United States, 765 kV non-ceramic insulators are in the design and development stage. The utility companies are now considering using 765 kV non-ceramic insulators to replace ceramic insulators without changing the tower configuration and line-end hardware and using six-subconductor bundles to replace four-subconductor bundles.
This chapter describes the research related to the EFVD along the 765 kV non- ceramic insulators when they are installed on a 765 kV tower under three phase energization. The effects of the tower configuration and other components to the EFVD are also analyzed.
There are two typical of 765 kV tower configurations. One is considered for four-
subconductor bundles and the other is considered for six-subconductor bundles. The
simplified geometry and major dimensions of the two 765 kV power line towers and conductor bundles are identified in Sections 4.2.2 and 4.2.3. 78 Since the center phase insulator is inside the tower window and that is the worst case, the EFVD along the center phase non-ceramic insulator is of most interest.
Therefore, for the center phase, the non-ceramic insulators, conductor bundles, line and ground end hardware, and corona rings are included in the calculation model. For the other two (i.e., outer) phases, only the conductor bundles are simulated and the other components are ignored.
The basic geometry of the 765 kV non-ceramic insulator, grading rings, line and ground end hardware, ground plane and tower configuration are described in detail
separately in the following sections.
4.2 Model of insulator, tower and additional components
4.2.1 Modeling of a non-ceramic insulator and corona rings
It is of practical interest to know the electric field strength distribution for a full-
scale insulator during field conditions under three phase energization. A typical 765 kV non-ceramic insulator is used for this study, which is designed for both four-
subconductor and six-subconductor bundles. The insulators are fitted with corona rings at both line and ground ends.
The detailed geometric dimensions of the 765 kV insulator are shown in Fig. 4.1.
The insulator is made of silicon rubber with a relative permittivity of 4.0 and an FRP rod with a relative permittivity of 5.5. There are 51 large and 52 small weather sheds on an actual 765 kV insulator. The insulator is equipped with metal fittings at both line and ground ends.
79 Based on the previous study in Chapter 3, the calculation model for this full scale insulator can be simplified with only a small number of weather sheds (for example, 10) at each end of the insulator to calculate the electric field and voltage distribution. The
simplified insulator model is shown in Fig. 4.1.
Units: cm
17 < 436 > 470 Figure 4.1: Simplified geometry and dimensions of the 765 kV non-ceramic insulator model with 10 weather sheds at the line end and ground end. In order to reduce the electric field strength in the triple junction region of the insulator, a 17-inch corona ring is applied at the line end of the insulator and a 12-inch corona ring is applied at the ground end. The dimensions and positions of the two corona rings are shown in Fig. 4.2. Units: cm (a) Line end corona ring (b) Ground end corona ring Figure 4.2: Dimensions and positions of the line end and ground end corona rings. 80 The insulator model has 12000 elements applied to the surface of boundaries and the interfaces of the different media. For the line end corona ring, the number of the elements used is 2377. For the ground end corona ring, the number of elements used is 832. The element configurations on the surface of the insulator and the corona ring at the line end and the ground end are shown in Fig. 4.3. I (a) Element configuration at the line end (b) Element configuration at the ground end Figure 4.3: Element configuration on the insulator and the corona ring surface. 4.2.2 Modeling of line end hardware and conductors When the insulator is installed on a 765 kV tower, yoke plates are needed to attach the subconductor bundle to the insulators. Two types of yoke plates are used in practice for four-subconductor and six-subconductor bundles. The dimensions and element configuration of a four-subconductor bundle V- string yoke plate are shown in Fig. 4.4. The thickness of the yoke plate for four- subconductor bundles is 1.9 cm. The bundle conductors have been modeled as smooth conductors, positioned parallel to the ground. As mentioned in [19], the length of the conductor bundles modeled should at least 8 times the insulator length for accurate results. The length of each 81 conductor considered here is 60m. The subeonduetor diameter for four-suhconductor bundles is 2.96 cm. The number of the elements used for each subeonduetor is 560. m s (a) Dimensions (cm) (b) Element configuration Figure 4.4: Dimensions and element configuration of the yoke plate for four- subeonduetor bundles. The dimensions and element configuration of the six-subeonduetor V-string yoke plate is shown in Fig. 4.5. The thickness of the yoke plate is 2.54 cm. The suheonduetor diameter for the six-subeonduetor bundle is 2.7 cm. m m 3 8 .1 (a) Dimensions (cm) (b) Element configuration Figure 4.5: Dimensions and element configuration of the yoke plate for six-subeonduetor bundles. 82 4.2.3 Modeling of tower and ground plane The simplified geometry and major dimensions of a typical 765 kV power line tower with four-subconductor bundles are shown in Fig. 4.6. The angle between the center phase insulator and the symmetry line of the tower is 50°, as marked on Fig. 4.6. Units: cm 945 00 sen m Figure 4.6: Geometry and dimensions of 765 kV power line tower with four- subconductor bundles. The two ground wires are ignored in the calculations. The ground plane is modeled with a 50 m x 50 m large plane with zero potential. The number of the elements used for the tower is 800 and for the ground plane are 100. The simplified geometry and major dimensions of a typical 765 kV power line tower with six-subconductor bundles are shown in Fig. 4.7. The angle between the center phase insulator and the symmetry line of the tower is also 50°, as marked on Fig. 4.7. 83 The two ground wires are also ignored in the calculations. The ground plane is modeled with a 50 m x 50 m large plane with zero potential. The number of the elements used for the tower is 600 and for the ground plane, it is 225. Units: cm 1408 Figure 4.7: Geometry and dimensions of a 765 kV power line tower with six- subconductor bundles. The view of the entire 765 kV power line tower with four-subconductor bundles, the non-ceramic insulator, end fittings, and hardware is shown three-dimensionally in Fig. 4.8. The entire view for the 765 kV power line tower with six-subconductor bundles is shown in Fig. 4.9. The center phase inside the tower window is enlarged for a clearer view; see Figs. 4.8 (b) and 4.9 (b). 84 (a) View of the entire tower with four-subconductor bundles. (b) View of the insulators of the center phase with four-subconductor bundles. Figure 4.8: Entire view of a 765 kV power line tower with four-subconductor bundles. 85 (a) View of the entire tower with six-subconductor bundles. (b) View of the insulators of the center phase with six-subconductor bundles. Figure 4.9: Entire view of a 765 kV power line tower with six-subconductor bundles. 86 4.3 Voltage and electric field distributions along a non- ceramic insulator The electric field and voltage distributions along the 765 kV non-ceramic insulator of the center phase have been studied on two typical power line towers with four and six-subconductor bundles. The instantaneous voltages applied to the three phase conductor system for the worst case when there is maximum voltage across the center phase insulator are: • Vicft~ - 0.5x Vccntcr” " 0.5*624.6— - 312.3 kV, • Vccntcr^ 765 X V2 / =624.6 kV (i.e., maximum value of the line-to-ground voltage) • Vright= - 0.5x Vcenter= ‘ 0.5*624.6= - 312.3 kV. There are some basic principles for showing the calculation results: • In the following paragraphs, the voltages are expressed either in kVmax or in per cent values, referred to 624.6 kVmax , which is the actual applied voltage on the center phase insulator. • The electric field strength is always expressed in kVmax/mm units. • The insulation distances used in the figures are expressed either in cm units or in per cent values, referred to 436 cm as shown in Fig. 4.10. • The calculation path on the surface of the insulator sheath is identified as a straight dashed line as shown in Fig. 4.10 (not along the leakage path). 87 Figure 4.10: Calculation path along the sheath surface of the insulator. The resulting per cent equipotential contours inside the tower window for a 765 kV non-ceramic insulator with four-subconductor bundles are shown in Fig. 4.11. Distance units: cm 3300 3250 3200 3150 2900 : 3100 2875 - 3050 3000 i 2950 2900 2850 25 50 75 100 - 85 2W00 0 50 100 150 200 250 300 350 400 (a) Full view of one of the insulator (b) Enlarged area around the line end (Simplified model) Figure 4.11: Per cent equipotential contours for a 765 kV tower with four-subconductor bundles under three phase energization. It can be seen that the line end equipotential contours are greatly influenced by the line-end hardware and the line-end corona ring and are nearly parallel to the shed surface. The ten weather sheds near the line end sustain about 35% of the applied voltage. The ten weather sheds near the ground end sustain about 12% of the applied voltage. Fig. 4.12 shows the actual voltage distribution in the worst case along the per cent insulation distance at the surface of the insulator sheath with four-subconductor bundles. The non-linear property of the voltage distribution along the non-ceramic insulator is clearly shown. 700 6 0 0 500 I0 4 0 0 1o 300 > 200 100 0 10 20 30 40 50 60 70 80 90 100 Insulation distance (%) Figure 4.12: Voltage distribution along the per cent insulation distance at the surface of the insulator sheath with four-subconductor bundles. The electric field strength magnitude along the path defined on the surface of the insulator sheath is shown in Fig. 4.13. The maximum value of the electric field strength at the triple junction point is 1.586 kVmax/mm. For a clearer view, the electric field strength distribution along the insulation distance near the line-end fitting is shown in Fig. 4.14. The discontinuities in the 89 magnitude of the electric field strength in Fig. 4.13 and 4.14 are the result of the calculation path, shown in Fig. 4.10, passing through the shed material, which has a relative permittivity of 4.0. It can be seen that electric field strength is much higher at the junction region between the sheath and the shed than that at the middle part of the sheath region. 1.6 I 1.4 > 1.2 -a 0.8 f 0.6 g 0.4 0.2 « 10 20 30 40 50 60 70 80 90 100 Insulation distance (%) Figure 4.13: Electric field strength magnitude along the per cent insulation distance at the surface of the insulator sheath with four-subconductor bundles. a 1.4 > I I 2 4 6 Insulation distance (%) Figure 4.14: Electric field strength magnitude along the per cent insulation distance at the surface of the insulator sheath with four- sub conductor bundles near the line end. 90 The electric field strength distribution along the insulation distance near the ground end fitting is also shown in Fig. 4.15. I 0.8 0.7 è 0.6 "OCD S 0.5 0.4 .a! % 03 0.2 ? 0.1 0 90 92 94 96 98 100 üj Insulation distance (%) Figure 4.15: Electric field strength magnitude along the per cent insulation distance at the surface of the insulator sheath with four sub-conductor bundles near the ground end. It is also of practical interest to know the electric field strength along the leakage path on the surface of the insulator, which is the path along a-b-c-d-e-f-g-h-i in Fig. 4.16. 2910 - 2905 2900 - 2895 2890 30 35 40 45 50 55 Figure 4.16: Leakage path at the surface of the insulator (a-b-c-d-e-f-g-h-i). 91 The electric field strength distribution along the leakage path on the surface of the insulator near the line-end fitting is shown in Fig. 4.17. I 1.8 1.7 - 1.6 r > , a 1.5 1.4 J 1.3 - h i I 1.2 I ® 1.1 1 I 1 0.9 0.8 - /" 0.7 ^ ' 0.6 - 1 0.5 - 1 ; ' 0.4 I 0.3 ii' 0.2 5 10 15 20 25 30 35 Leakage distance from the line end fittings (cm) Figure 4.17: Electric field strength magnitude along the leakage path at the surface of the insulator. The result shows that the electric field strength on the sheath region is higher than that on the shed region, especially at the junction region between the sheath and the shed. The electric field strength on the top of the shed is very close to the electric field strength on the down side of the shed. The maximum electric field strength on the shed surface is close to the very edge of the shed. It is interesting that the electric field strength near the shed edge (point d, g) suddenly drops. The equipotential lines are close to parallel to the surface of the weather shed. The rounded shed edge “presses out” the equipotential lines to the side of the shed edge. The electric field strength is only enhanced at the up and down side of the shed edge, but it is much lower at the center of the shed edge. There is a more detailed explanation in Appendix B. 92 The resulting per cent equipotential contours inside the tower window for a 765 kV non-ceramic insulator with six-subconductor bundles are shown in Fig. 4.18. Distance units: cm 3650 4b/S 3 3 5 0 3600 3550 3 3 2 5 3500 3300 3450 3 2 7 5 ----.... k ". 4b . 3 2 5 0 3300 '\^o \ \ \ U i / / 3250 ' fW / ; 3225 &0 %■: / i : 1Û 3200 3 2 0 0 3150 2 5 50 7 5 100 0 100 200 300 400 (a) Full view of one of the insulators (b) Enlarged area around the line end (Simplified model) Figure 4.18: Per cent equipotential contours for a 765 kV tower with six-subconductor bundles under three phase energization. It can be seen that the ten weather sheds near the line end sustain about 33% of the applied voltage and the ten weather sheds near the ground end sustain about 14% of the applied voltage. Due to the larger size of the six-subconductor bundles, the density of the equipotential lines at the line end is less than that of the four-subconductor bundles. The larger the line end hardware size, the better “shielding” effect it has to the insulator. Fig. 4.19 shows the actual voltage distribution in the worst case along the per cent insulation distance at the surface of the insulator sheath with six-subconductor bundles. 93 700 - 600 - 500 > 400 (11 tJ) 300 - o > 200 - 100 - 0 - 10 20 30 40 50 60 70 80 90 100 Insulation distance (%) Figure 4.19: Voltage distribution along the per cent insulation distance at the surface of the insulator sheath with six-subconductor bundles. The electric field strength magnitude along the paths defined on the surface of the insulator sheath is shown in Figure 4.20. The maximum value of the electric field strength at the triple junction point is 1.162 kVmax/mm. ? CD 3 1- I0.8 - # 0 6 V 1 3 0.4 I .a 0.2 QJ S 0- 10 20 30 40 50 60 70 80 90 100 Insulation distance (%) Figure 4.20: Electric field strength magnitude along the per cent insulation distance at the surface of the insulator sheath with six-subconductor bundles. 94 For a clearer view, the electric field strength distrihutions along the insulation distance near the line and ground end fittings are shown in Figs. 4.21 and 4.22. § 1.4 1.2 s I 0.6 0.4 % « o 0.2 W 4 6 8 10 12 Insulation distance (%) Figure 4.21: Electric field strength magnitude along the per cent insulation distance at the surface of the insulator sheath with six-subconductor bundles near the line end. I 0.8 0.7 a 0.6 "OCD S 0.5 I 0.4 0.3 t 0.2 ? 0.1 0 — 88 90 92 94 96 98 100 w Insulation distance (%) Figure 4.22: Electric field strength magnitude along the per cent insulation distance at the surface of the insulator sheath with six-suhconductor bundles near the ground end. 95 4.4 Comparisons between four and six subconductor bundles In Section 4.3, the EFVD along the same non-ceramic insulators installed on two typical 765 kV towers with four or six subconductor bundle are calculated. It is interesting to compare the EFVD along the insulators for these two cases. To make the analysis easier, the 765 kV tower with four- sub conductor bundles is named as Case F and with six-subconductor bundles as Case S. The actual voltage distributions in the worst case along the per cent insulation distance at the surface of the insulator sheaths for these two cases are shown together in Fig. 4.23. 700 C ase F 600 - C ase S 500 I(D 400 I 300 > 2 0 0 - 100 - 0 - 10 20 30 40 50 60 70 80 90 100 Insulation distance (%) Figure 4.23: Voltage distribution along the per cent insulation distance at the surface of the insulator sheath for Cases F and S. It can be seen that the voltage distribution along the insulator for Case S is more uniform than that of Case F. Since it is closer to a straight line, the voltage sustained by 10 line-end sheds is 35% for Case F and is 33% for Case S. The voltage sustained by 10 ground-end sheds is 12% for Case F and 14% for Case S. 96 The electric field strength magnitudes near the line and ground ends along the paths defined on the surface of the insulator sheaths for these two cases are shown in Figs. 4.24 and 4.25, respectively. 1.6 ------C ase F ^ 1.4 ------C ase S 1 ^ 1^ "O 1 Ia 0.8 ' 1 1 1 uq &6 j ! 0.4 1 «o 0.2 Üj 2 4 6 8 10 12 Insulation distance (%) Figure 4.24: Electric field strength magnitude along the per cent insulation distance at the surface of the insulator sheath near the line end for Cases F and S. C ase F > C ase S o 100 Insulation distance Figure 4.25: Electric field strength magnitude along the per cent insulation distance at the surface of the insulator sheath near the ground end for Cases F and S. 97 It is shown clearly that the electric field strength on the sheath surface of the insulator for Case S is lower than that of Case F at the line end and higher than that of Case F at the ground end. The maximum electric field strength at the triple junction point at the line end is 1.586 kVmax/mm for Case F and 1.162 kVmax/mm for Case S. The reason for that is the much larger bundle diameter and line end hardware size for Case S. It has better “shielding” effects on the line end fittings. The maximum electric field strength at the triple junction point at the ground-end is 0.437 kVrnax/mm for Case F and 0.576 kVmax/mm for Case S. It can be seen that the electric field distribution along the insulator for Case S is more uniform than that of Case F. 4.5 Effects of the tower configuration and other components When evaluating the EFVD along a non-ceramic insulator in service, it is not just the non-ceramic insulator alone that is of concern. The tower, line- and ground-end fittings, corona rings and the three phase conductor bundles are also part of tbe geometry. They should also be included in the calculation model. Therefore, the calculation model is very complex and it is very time-consuming to solve it. It is of practical interest to know the effects of these components and whether some of the components can be omitted without a significant impact on the accuracy of the estimates of the EFVD along the non-ceramic insulators. The 765 kV tower with four-subconductor bundles is selected for this study as an example. 98 4.5.1 Effects of other two phases of the three phase system Due to the large phase spacing and the grounded tower structure, the inclusion of the other two phase conductors in the calculation model should not significantly effect the EFVD along the center phase insulator. The effects of the other two phases of the three phase system have been investigated for the 765 kV tower with four-subconductor bundles. The center phase conductor is inside the tower window. In order to evaluate the effects of the three phase energization, two cases have been considered. In the first case, only the center phase conductor bundles inside the tower window are included in the calculation model. The instantaneous applied voltage is 624.6 kV, which is the maximum value of the line-to-ground voltage. In the second case, the other two phase conductor bundles are also included in the calculation model and the instantaneous voltages applied to the three phase conductor system are: Vkft^ - 312.3 kV, Vccntcr^624.6 kV,Vrighr - 312.3 kV. The resulting equipotential contours for a 765 kV tower with four-subconductor bundles are shown in Fig. 4.26. It can be seen from Fig. 4.26 that there are slight differences between Cases (a) and (b). For example, the 10 per cent equipotential line is closer to the ground end of the insulator for single phase energization than the three phase energization. The equipotential contours between 95% and 80%, i.e., close to the conductor bundles, are very similar for Case (a) and Case (b). 99 Distance units: cm 3300 I 3300 ------,----- 3250- 3250 - 3200- 3200 - 20 3150 3150 25 3 1 0 0 : 3100 30 3050 3050 - X' 35 3000 % 3000 29501 ■ » 2950 29001 2900 «%' , 4 I, 2850l 2850 :,, 85 ' ' i\ 2800- 2800 0 50 100 \ 150 200 250 300 350 400 50 100 200 250 300 350 (a) Single phase (b) Three phase Figure 4.26: Equipotential contours for a 765 tower with four-subconductor bundles under (a) single phase and (b) three phase energization. The actual voltage distribution in the worst case along the percent insulation distance at the surface of the insulator sheath with four-subconductor bundles for single phase and three phase energization are shown in Fig. 4.27. 100 70 0 1 ------Three phase energization ^ 600 Single phase energization 500 u ^ 400 o > 300 200 100 0 0 10 20 30 40 50 60 70 80 90 100 Insulation distance (%) Figure 4.27: Voltage distribution along the per cent insulation distance at the surface of the insulator sheath under single and three phase energization. It can be seen that the voltage distribution at the ground end and the middle part of the insulator is changed by the presence of the other two phases. The voltage distribution at the line end does not change as much as at the middle part of the insulator. The reason is that the line end of the insulator is of course much closer to its conductors, the hardware, and the corona ring there than to the other two phases. The largest difference between the two curves is about 2% of the applied voltage. The electric field strength distributions along the surface of the insulator sheath near the line and ground end fittings are shown in Fig. 4.28 and 4.29, respectively. 101 1.6 1 Three phase energization g 1.4 > Single phase energization 1.2 QJ "O 1 ia 0.8 % 0.6 1 0.4 1 0.2 ■1o üj 0 4 6 10 12 Insulation distance (% Figure 4.28: Electric field strength magnitude along the per cent insulation distance at the surface of the insulator sheath near the line end under single and three phase energization. 1.6 I 1.4 Three phase energization Single phase energization a 1.2 "OCD S 1 ! 0.8 I 0.6 0.4 ? 0.2 0 w 90 92 94 96 98 100 Insulation distance (%) Figure 4.29: Electric field strength magnitude along the per cent insulation distance at the surface of the insulator sheath near the ground end under single and three phase energization. 102 The maximum electric field strength at the triple junction point is 1.547 kVinax/mm under single phase energization and 1.586 kVmax/mm for three phase energization. The effects of the presence of the other two phases of the three phase system on the voltage distribution is very small and can be ignored. The effects of the presence of the other two phases of the three phase system on the electric field is that the electric field strength under three phase energization near the line end is higher than that of single phase energization and is lower near the ground end. The conclusion can be drawn that for a 765 kV tower with four-subconductor bundles, there is no significant difference between the EFVD along a non-ceramic insulator under single phase energization and under three phase energization. 4.5.2 Effects of tower configuration The effects of the 765 kV tower configuration with four-subconductor bundles have also been studied. In order to evaluate the effects of the tower configuration, two cases have been considered. In the first case, the 765 kV tower is removed from the calculation model shown in Fig. 4.8. The second case is the same calculation model shown in Fig. 4.8. The resulting equipotential contours for the four-subconductor bundles without and with a 765 kV tower under three phase energization are shown in Fig. 4.30. The figure shows that the existence of the 765 tower at zero potential has only a minor effect on the voltage distribution near the line end. Flowever, naturally it influences the voltage 103 distribution near the ground end significantly. The grounded tower hody reduces the electric field strength near the ground end of the insulator. Distance units: cm 3 3 0 0 3300 3250 3 2 5 0 h 3200 — ...... 3 2 0 0 _____ 2 0 # . 3 1 5 0 : 3 1 5 0 ...... _ " 2 5 '' \ 3 1 0 0 - % 3 1 0 0 % 3 0 5 0 % 3 0 5 0 - 35 3 0 0 0 3 0 0 0 : ^ \ : : Tr 2950 2950 2 9 0 0 : / V 2 9 0 0 2850 2850 1 1 1 1 : ! / ' I - V , / : : 2 8 0 0 2800 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 (a) Without tower (b) With tower Figure 4.30: Equipotential contours for the four-subconductor bundles without and with the 765 kV tower under three phase energization. The results show that the tower hody is an important part of the calculation model. The tower hody cannot be ignored and it has significant influence on the EFVD along the insulator near the ground end. 104 4.5.3 Effects of conductor bundles The effects of the four-subconductor bundles to the EFVD along the non-ceramic insulator have also been studied. In order to evaluate the effects of the four-subconductor bundles, two cases have been considered. In the first case, the four-subconductor bundles attached to the line-end hardware are removed from the calculation model shown in Fig. 4.8. The line end hardware and the metal end fitting are energized to 624.6 kVmax- The second case is the same calculation model as shown in Fig. 4.8. The equipotential contours for the 765 kV tower without and with four- subconductor bundles are shown in Fig. 4.31. Distance units: cm 3300 3300 I I I . I „ 3250 3250 % 15 3200 3200 - 20 3150 3150- 25 3100 3100 30, 3050 3050 : 35 3000 3000 2950 2950 2900-56 2900 2850 2850 '^7 2800 2800 t 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 (a) Without four-subconductor bundles (b) With four-subconductor bundles Figure 4.31: Equipotential contours for the 765 kV tower without and with the four- subconductor bundles. 105 It can be seen from Fig.4.31 that there are “shielding” effects of four- subconduetor bundles. If the four-subconduetor bundles are ignored in the calculation model, the EFVD along the insulator is significantly different from the EFVD along the insulator with four-subeonduetor bundles, which means that this is not an acceptable model. 4.6 Summary In this chapter, the voltage and electric field distribution along the non-ceramic insulators have been calculated for two practical cases. One is with four-subconductor bundles and the other one is with six-subconductor bundles. The maximum values of the electric field strength at the triple junction point have been calculated for these two cases. For four-subconductor bundles, the maximum value is 1.586 kVmax/mm. For six- subconductor bundles, the maximum value is 1.162 kVmax/mm. There is only a slight difference between the EFVD along a non-ceramic insulator under single phase energization and under three phase energization. The conductor bundles and the tower body should be included in the calculation model in order to get the accurate results. 106 CHAPTER 5 ELECTRIC EIELD STRENGTH AND VOLTAGE DISTRIBUTIONS ALONG A NON-CERAMIC INSULATOR UNDER VARIOUS WET CONDITIONS 5.1 Introduction The excellent pollution performance of non-ceramic insulators is due to the good hydrophobic surface property of weather sheds under wet and contaminated conditions. However, the combined effects of electric and environmental stresses, such as the energizing voltage, corona and arcing, also contamination, ultraviolet rays, heat cycling, etc., can cause the accelerated aging of non-ceramic insulators during the service life of an insulator. Consequently, due to the weak bonds of polymer materials, the hydrophohicity properties of the weather sheds will temporarily or permanently lost during its service life. That might worsen the wet and contamination performance of non- ceramic insulators. Under rain and fog conditions, the presence of water droplets intensifies the electric field strength on the surface of a non-ceramic insulator. If the magnitude of the surface electric field strength exceeds a threshold value, 0.5-0.7 kVnns/mm [51], water droplet corona discharges may occur. The discharges usually occur between water 107 droplets and destroy the hydrophohicity of the polymer material surface. The high temperature of such discharges also thermally degrades the insulator surface. As a consequence, the surface corona discharges from water droplets accelerate the aging of the polymer material, cause surface damage due to tracking and erosion, and increase the risk of the flashover of the non-ceramic insulator. The pollution flashover phenomena of non-ceramic insulators have heen studied and described by various researchers [52]. The flashover of a clean non-ceramic insulator during rain conditions shows that a discharge bridges the weather sheds and the leakage distance along the surface of the insulators is not used efficiently. The flashover of non- ceramic insulators with artificial contamination in clean fog tests shows that the discharges on a fully contaminated insulator follow the leakage path along the surface of the insulator. For partially contaminated insulators, the discharges in the contaminated section follow the leakage path along the surface of the insulator in the contaminated part. However, an arc may also develop and it may bridge the weather sheds along the clean section of the insulator, which is a high resistance region. Therefore, the study of the electric field strength and voltage distribution along non-ceramic insulators is important for the in-depth understanding of the aging process and the pollution flashover initiation mechanism for non-ceramic insulators. 5.2 Hydrophobicity status of non-ceramic insulators As mentioned in Section 3.3.1, many researchers have used the hydrophohicity classification method developed by STRl to characterize the hydrophohicity of the 108 insulator surface. This method is also adopted in this research work to describe the hydrophohicity of the surface of non-ceramic insulators. Research studies show that the pollution performance of non-ceramic insulators is jointly determined hy the surface hydrophohicity status and pollution severity [6]. When non-ceramic insulators are operating in heavy or medium pollution environment for a long time, the change of hydrophobicity and the build-up of a pollution layer directly affect the pollution performance of non-ceramic insulators. To evaluate the performance of non-ceramic insulators in the field, the information of the surface hydrophobicity status need to be investigated. Wang, Liang, and Guan [53] conducted a system investigation aiming at the inspection and evaluation on the hydrophohicity distribution along the surface of non- ceramic insulators. They found that in general, the hydrophobicity distribution on the upper surface of the weather sheds always presented hydrophobicity better than that of the lower surface. In many cases, the top surface showed a hydrophohicity of HC 2-4, while the bottom surface hydrophohicity approached HC 5-6. Due to the high electric field strength around the line end fittings, the weather sheds near the line end are always less hydrophobic. The surface of the sheath, especially at the triple junction areas, is also vulnerable to hydrophobicity loss. Obviously, the electric field plays an essential role on the initiation of hydrophobicity loss. Seifert and Besold [54] reported their service experience of the SiR insulators under tropical climate conditions in Malaysia. The hydrophohicity of the insulators was checked after 2 and 7 years of service by the HC method. They also found that the top sides of the weather shed showed better hydrophobicity than the other parts of the 109 insulator. Four or five sheds near the line end insulator showed less hydrophobicity due to more pollution in that region. Their investigation results are shown in Table 5.1: Suspension insulator Tension insulator 2 years 7 years 2 years 7 years Shed top side 1 1 1 1 Shed bottom side 2 3 2 2 Sheath region 4 4 3 3 Table 5.1: Hydrophobicity status (HC numbers) of the insulator after 2 and 7years of service [54]. 5.3 Experiments in the OSU fog chamber One of the objectives of this research is to study the EFVD along non-ceramic insulators under various wet conditions and to study the electric field enhancement factors on the surface of water droplets. Appropriate experiments should be done in order to decide the size, shape and number of droplets and their distribution at the various hydrophobicity conditions of non-ceramic insulators. A series of aging experiments on non-ceramic insulators was performed in the fog chamber at The Ohio State University High Voltage Laboratory. The fog chamber was constructed in 1995. Fig. 5.1 shows the view of the fog chamber. The fog chamber is transparent and is made of polycarbonate sheets. The dimensions of the chamber are 1.72m wide x 2.44m long x 1.83m high. The volume of the chamber is 9.5m^. The high voltage bushing is mounted on one of the end walls of the 110 chamber. A detachable access door is located at the side across from the bushing. Four nozzles are used to generate the fog inside the chamber. Both a water pump and an air compressor are used to apply water and pressurized air simultaneously to the nozzles. A drainage system collects the water and returns it to a container for recycling purpose hy a pump. ? 11#'^: - v n -I Figure 5.1: The fog chamber in the OSU High Voltage Laboratory. Two types of non-ceramic insulators were used for the experiments. One type was made of SiR and the other one was made of EPDM. The insulators under the aging tests were suspended vertically inside the chamber with their ground ends upwards. The insulators were subjected to a continuous electric stress and simultaneous but intermittent salt fog using a 6-hour fog on, 6-hour fog off duty cycle. No artificial solid or liquid contaminants were used. The aging test lasted for about one week. Different hydrophobicity status conditions of the polymer surface of the insulator were observed. In order to avoid drying effects, the typical hydrophohicity status of the insulator surface 111 was recorded using a Canon digital camera at the beginning of the fog off period. The calculation models of the insulator under wet conditions are based on these photos. 5.4 Model setup A short insulator with only four sheds is considered for the following calculations in order to reduce calculation time. The simplified geometry and dimensions of the polymer insulator to be modeled are shown in Fig. 5.2. The sheds are numbered 1-4 from the line end to the ground end. The weather sheds are made of silicon rubber with a relative permittivity of 4.3. The relative permittivity of the fiberglass rod is 7.2. The conductivity of the water droplets is assumed to he 250 ps/cm. The number of the elements used for each case is about 12,000. The applied voltage on the line end of the insulator is assumed to be IkVn. Ground end Units: cm 00 Y 1< 9.4 X Line end Figure 5.2: Geometry and dimensions of a four-shed non-ceramic insulator. Three types of models are used for simulating specific weather conditions. The first one is the base case, which is a dry and clean insulator model. 112 The second one is the insulator model under rain conditions. Due to the “shielding” effects of the weather shed, one assumption is made that there are only water droplets on the top of each weather sheds. The surface of the vertical sheath and the undersides of the sheds remain dry. The third one is the insulator model under fog conditions. There are water droplets not only on the top of each weather sheds but also on the downside of each shed. Some models may also have water droplets on each sheath region of the insulator as well. 5.5 Insulator models under rain conditions Under rain conditions, the water droplets are usually on the top surface of the weather sheds. The surface of the vertical sheath and the undersides of the weather sheds are dry. Six typical cases of non-ceramic insulators under rain conditions with the surface hydrophobicity from HCl to HC6 are studied. They are named as Case RHCl - Case RHC6. For Case RHCl, only a 10 degree segment of the shed surfaces is modeled. This segment is used 36 times to represent the entire circumference of a shed. There are five medium size water droplets and 10 small size water droplets per segment. The shape of all water droplets is hemispherical, with a diameter of 2mm for medium size water droplets and 1mm for small size water droplets. For Case RHC2, only a 10 degree segment of the shed surfaces is modeled. This segment is used 36 times to represent the entire circumference of a shed. There are four 113 large size water droplets and one medium size water droplets per segment. The shape of all water droplets is hemispherical, with a diameter of 4mm for large size water droplets and 3mm for medium size water droplets. For Case RHC3, only a 90 degree segment of the shed surfaces is modeled. This segment is used 4 times to represent the entire circumference of a shed. The shape of some water droplets is no longer hemispherical, which have a length of 6mm. For Case RFIC4, only a 36 degree segment of the shed surfaces is modeled. This segment is used 10 times to represent the entire circumference of a shed. There is a water runnel on the surface of the insulator. For Case RHC5, only a 90 degree segment of the shed surfaces is modeled. This segment is used 4 times to represent the entire circumference of a shed. Several water runnels are merged together on the surface of the insulator. For Case RHC6, only a 90 degree segment of the shed surfaces is modeled. This segment is used 4 times to represent the entire circumference of a shed. Ahout 90% of the surface of the insulator are covered by water film. For the calculations illustrated by Figs. 5.4, 5.6, 5.8, 5.10, 5.12, 5.14 (a) and (b), each point on the surface of the shed is described by the (x, y, z) coordinates of its location. In fact, a fourth dimension is needed to show the voltage distribution. In order to he ahle to show the voltage distribution on the surface of the shed using a 3D-type view, the surface point is represented by its (x, y) coordinates only. The voltage distribution for each case with water droplets on the surface of the shed closest to the line end (1st shed) is shown in the figure. The equipotential contours on the shed projected in the (X, Y) 114 plane are also shown in these figures. The numbers indicated in the graph show the voltage in volts. The applied voltage on the line end is assumed to be 1 kVp. (a) Case RHCl photo. (b) Case RHCl rain calculation model. Figure 5.3: Case RHCl water droplet distribution on the surface of a non-ceramic insulator and the calculation model used for study. Voltage (V) 800, Y (cm ) 5 780. 760. B40 740. Y _ 720. % 700. % 680. 660. % 640. 62 0 . ' % - X (cm ) : ■■ ■ ' i . J 1 ■■;Y, '■ ■■ ■■ Y (cm ) 1 1 2 3 4 5 X (cm ) (a) Case RHCl voltage distribution on (b) Case RHC1 equipotential contours the top surface of the first shed. on the top surface o f the first shed. Figure 5.4: Voltage distrihution and equipotential contours on the surface of the first shed on a wet non-ceramic insulator with HCl hydrophohicity. 115 (a) Case RHC2 photo. (b) Case RHC2 rain calculation model. Figure 5.5: Case RHC2 water droplet distribution on the surface of a non-ceramic insulator and the calculation model used for the study. Y (cm ) Voltage (V) 780 . 780 . 740 720 700 880^ 880 . 840 . 620^ 0 X (cm ) 3 Y (cm ) X (cm ) (a) Case RHC2 voltage distribution (b) Case RHC2 equipotential contours on the top surface of the first shed. on the top surface of the first shed. Figure 5.6: Voltage distribution and equipotential contours on the surface of the first shed on a wet non-ceramic insulator with HC2 hydrophobicity. 116 ■ ■ ''I (a) Case RHC3 photo. (b) Case RHC3 rain calculation model. Figure 5.7: Case RFLC3 water droplet distribution on the surface of a non-ceramic insulator and the calculation model used for the study. Voltage (V) Y (cm ) 5 7 4 0 , ...... 7 2 0 , 6 l 0 - 7 0 0 , _ . - y 6 2 0 6 8 0 , _ _ 6 3 0 6 6 0 , 6 6 0 ^ - , 6 4 0 , 6 2 0 , % f f > 6 0 0 , 0 \ 1 1 1 ■ X (cm ) 1 ■■ 1 1 ■ i 4 5 X (cm ) Y (cm ) (b) Case RHC3 equipotential contours (a) Case RHC3 voltage distribution on on the top surface of the first shed. the top surface of the first shed. Figure 5.8: Case RHC3 voltage distribution and equipotential contours on the surface of the first shed on a wet non-ceramic insulator with HC3 hydrophobicity. 117 (a) Case RHC4 photo. (b) Case RHC4 rain calculation model. Figure 5.9: Case RHC4 water droplet distribution on the surface of a non-ceramic insulator and the calculation model used for the study. Voltage (V) Y (cm ) 740. 5i------720 700 680 660 640 % 620 0 X (cm ) 2 3 2 3 4 5 Y (cm ) X (cm ) (a) Case RHC4 voltage distribution (b) Case RHC4 equipotential contours on the top surface of the first shed. on the top surface o f the first shed. Figure 5.10: Voltage distribution and equipotential contours on the surface of the first shed on a wet non-ceramic insulator with ffC4 hydrophobicity. 118 T ■>rst ~- ) -. n :,ü% i ;vS ei (a) Case RHC5 photo. (b) Case RHC5 rain calculation model. Figure 5.11: Case RHC5 water droplet distribution on the surface of a non-ceramic insulator and the calculation model used for the study. Voltage (V) Y (cm ) 700 680 660 640 620 I ; 11 _ 600 ClV'I 580 - 560 0 1 X (cm ) 0 12 3 4 X (cm ) Y (cm ) (a) Case RHC5 voltage distribution (b) Case RHC5 equipotential contours on the top surface of the first shed. on the top surface of the first shed. Figure 5.12: Voltage distribution and equipotential contours on the surface of the first shed on a wet non-ceramic insulator with HC5 hydrophobicity. 119 a. ' mKMTF mil' * m we (a) Case RHC6 photo. (b) Case RHC6 rain calculation model. Figure 5.13: Case RHC6 water droplet distribution on the surface of a non-ceramic insulator and the calculation model used for the study. Y (cm ) Voltage (V) 5 4 ...... --654 % % 620 0 — 650 X (cm ) 0 1 2 3 4 5 Y (cm ) X (cm ) (a) Case RHC6 voltage distribution (b) Case RHC6 equipotential contours on the top surface of the first shed. on the top surface o f the first shed. Figure 5.14: Voltage distribution and equipotential contours on the surface of the first shed on a wet non-ceramic insulator with HC6 hydrophobicity. 120 5.6 Analysis of enhancement factors and electric field and voltage distributions for an insulator under rain conditions The voltage distributions on the shed closest to the line end (first shed) with water droplets on the top surface are shown in Figs. 5.4, 5.6, 5.8, 5.10, 5.12, 5.14 (a) and (b). The resulting distribution of the voltage is due to the different shape and size of water droplets. From these results, it can be seen that if the diameter of the water droplet is smaller than 2mm, the effect of the water droplet to the voltage distribution can be ignored. That is the reason why many small size water droplets in the photo are not included in the calculation model. The larger the water droplet size, the bigger its effect is on the voltage distribution along the top surface of the shed. The voltage distribution is significantly distorted by the merged water runnels (Case RFfC5). The existence of the merged water runnels increases the voltage difference between the neighboring water droplets and itself. If the electric field strength between them exceeds the threshold value, 0.5-0.7 kVrms/mm, water droplet corona discharges may occur between water droplets, and that may destroy the hydrophobicity of the shed material. Without water droplets, the highest electric field strength on the top of the first shed is 0.017 kVp/mm at 1 kVp. For example, the highest electric field strength on the surface of the water droplets on the first shed for Case RCF13 is 0.035 kVp/mm at 1 kVp. This clearly shows that the presence of the water droplets enhances the electric field strength on the shed by a factor of about 2.1. 121 The electric field enhancement factors on the surface of water droplets on the shed at various locations of the non-ceramic insulator for Cases RCH1-RCH6 are summarized in Table 5.2. The sheath region is between the first shed and the second shed. D ry C ase C ase C ase Case C ase C ase C ase (k V /m m ) R H C l R H C 2 RHC3 R H C 4 RHC5 R H C 6 E. F. E. F. E.F. E.F. E.F. E.F. Triple junction point &028 0.9 1.0 1.2 1.4 1.8 1.7 Top of the first shed 0.017 2.4 2.3 2.1 3.7 4 1.4 Under the first shed C026 0.9 1.0 1.1 1.2 1.6 1.4 Table 5.2: Electric field enhancement factors (E. F.) for Cases RCH1-RCH6 at various locations. The equipotential contours along a dry and clean non-ceramic insulator are also calculated and then compared to those of wet insulators, such as Cases RHC 1-6, in order to visualize the different overall voltage distributions of the six models. The calculation results are summarized in Fig. 5.15. Each number shown along the perimeters of the seven contour plots means centimeters. The numbers indicated in the graph show the voltage in volts. Fig. 5.15(a) shows the base case, the non-uniform voltage distribution along a dry and clean insulator. Comparison of the density of the equipotential lines in Figs 15 (b)-(g) to those of the base case can be used to study the overall distribution of the electric field for the cases with water droplets. The 200, 400, 600, 800 equipotential lines are drawn with a darker line for the purpose of comparison. 122 15- 15- ^8 ^ ,50 14- 14' - t o o .. 400 13' 13 = -1-50...... 1 2 - 1 2 - -450- 200 11 - 250 11 200 -2 5 0 _ 10 = 10 300 9- 9- 250 - 300 - ... 350 8 -350... 300 40CL 7 7- ^400 __ 350- - 4 5 0 6 6 ' 450 - 5 5 500 500 450 - r 550 . 41 -^_550 4- 500 600 C . . 65Ô-- 3- Geo ^ 3- 2- 650' 2 = 1 : 1 ' 0- 0 -1 'k?Y -1 - -2 -2- -3 -3- -4 -4 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 (a) Dry Case (b) Case RCH1 (c) Case RCH2 1 5 ^ 15 15 50- rO' 50 ^"^^.100 14 400 14 13- - - 13 13 150------|150 ...... ' 12 12 - 12 100 11 200 11 — ------: 11 150 10- 10 10 250=:-:-::= 9- 9 ' 250 ==:;::::;y 9 '200%: 300 .. 250.... 8 - 8 300... 8 300- 7 350 350 6 - 6 6 '450: 5 - .. 5 5 '400-: 450 4 - 4 4 450 500 - 500 3 :: -'GOO^XÇ 3 — 550 3 —.550 : - - 650 ■' ' 3 00 2- 2 - % 2 1 1 - 650 1 0- 0 0 § -1 -1 -1 -2 -2 ^ 1 -2 -3 -3 -3 -4 1 'I.-' i;' : : -4 r i ; ; ; r ' -4 0 1 2 3 4 : 0 1 2 3 4 5 0 1 2 3 4 5 (e) Case RCH4 (f) Case RCH5 (g) Case RCH6 Figure 5.15: Equipotential contours for (a) dry Case (b)-(g) Cases RHC1-RHC6. 123 Fig. 5.15 (b) shows the voltage distribution for Case RHCl. The positions of the 800, 600, 400, 200 equipotential lines are slightly higher than in the dry case. The electric field strength at the triple junction point is lower than in the dry case. As a result of small size water droplets on the top surface of the insulator shed, the overall electric field strength is a little more uniform than in the dry case. Of course, the local electric field strength enhance factor in the vicinity of each water droplet is enhanced to a ratio about 2.4. Fig. 5.15 (c) shows the voltage distribution for Case RHC2. The positions of the 800, 600, 400, 200 equipotential lines are almost the same as in the dry case. The electric field strength at the triple junction point is also almost the same as in the dry case. The local electric field strength enhancement factor in the vicinity of each water droplet is 2.3. Fig. 5.15 (d) shows the voltage distribution for Case RHC3. The positions of the 400, 200 equipotential lines are significant lower than in the dry case. The electric field strength enhancement factor at the triple junction point is 1.2. The local electric field strength enhancement factor in the vicinity of each water droplet is about 2.1. Fig. 5.15 (e) shows the voltage distribution for Case RHC4. The positions of the 800, 600 equipotential lines are slightly lower than in the dry case. The electric field strength enhancement factor at the triple junction point is 1.4. Due to the existence of the long water runnels on the top surface of the insulator, the local electric field strength enhancement factor in the vicinity of a water runnel is about 3.7, much higher than Cases RHC 1-3. Fig. 5.15 (f) shows the voltage distribution for Case RHC5. The positions of the 800, 600, 400 equipotential lines are significantly lower than in the dry case. Due to the 124 existence of the large complete wet areas on the top surface of the insulator, the electric field strength enhancement factor at the triple junction point is 1.8. The local electric field strength enhancement factor in the vicinity of wet areas is about 4, much higher than Cases RHCl-3. Fig. 5.15 (g) shows the voltage distrihution for Case RHC6. The positions of the 800, 600, 400, 200 equipotential lines are significantly lower than in the dry case. Due to the existence of the 90 % complete wet area on the top surface of the insulator, the electric field strength enhancement factor at the triple junction point is 1.7. The local electric field strength enhancement factor in the vicinity of the wet area is about 1.4. The electric field strength magnitude along the sheath surface of the insulator under rain conditions is also calculated. The calculation path (the dashed line shown in Fig. 5.15 (a)) is 4mm away from the surface of the sheath and starts from the point 0.2 mm above the line end metal fitting. To show the results more clearly, the magnitude of the electric field strength in the air along the surface of the sheath for Case (a) - (g) is shown in two figures. Fig. 5.16 shows the result for Case (a)-(d). Fig. 5.17 shows the result for Case (a) and Cases (e)- (g). The horizontal quantity is the insulation distance along the sheath surface, in percent. It is evident from the analysis of the results in Fig. 5.16 that the worse the hydrophobicity of the insulator surface, the more distortion it causes to the EFVD distribution along the insulators. If the hydrophobicity of the insulator surface is between HCl-2, the EFVD along the insulator under rain condition is nearly the same as along the dry and clean insulator. 125 0.0 3 5 D ry case ^ oœ3 C ase R H C 1 ÜKCRHC2 0 . 0 2 5 ÜMCRHC3 S) 0.02 a 0 . 0 1 5 '-y 2O 0.01 Iw O ■£ % 0 . 0 0 5 M 10 20 30 40 50 60 7 0 8 0 9 0 1 0 0 Insulation distance (%) Figure 5.16: Electric field strength magnitude along the insulation distance at the surface of the sheath for Dry Case and Cases RHC 1-3. 0.04 D ry case 1 ÜKCRHC4 0.03 ÜKCRHC5 C ase R H C 6 2 0.025 h I I — 1 0.015 2 0.01 , 0.005 w 0 10 20 30 40 50 60 70 80 90 to o Insulation distance (%) Figure 5.17: Electric field strength magnitude along the insulation distance at the surface of the sheath for Dry Case and Cases RHC4-6. 126 5.7 Insulator models under fog conditions Under fog conditions, the water droplets not only stay on the top surface of the weather sheds but also attach to the undersides of the weather sheds. Sometimes, there are some small water droplets on the sheath region of the insulator. On the vertical sheath region, the size of water droplets is much less than on the shed region because a large water droplet cannot cling itself to the sheath surface. Three typical cases of the non- ceramic insulator under different wetting conditions in the fog chamber are illustrated by the photographs shown in Figs. 5.18, 5.19, 5.20. They are named as Case FHCl, Case FFIC2, and Case FFIC3. The number of elements used for each case is about 12,000. The diameter of the water droplets used for the calculations is about 2-5 mm. The wetting conditions of the three cases are summarized in Table 5.3, in terms of the HC stages. Case FHCl Case FHC2 Case HC3 Top of the shed HCl HC2 HC3 Under the shed HCl HC2 HC3 Sheath region No water H C l H C l Table 5.3: Hydrophobicity of polymer insulator in different regions. Case FHCl represents a SIR insulator under early wetting status in the fog chamber as shown in Figs. 5.18 (a) and (b). There are small size water droplets on both the top and the underside of the shed. There is no water droplets on the sheath region of the insulator. The model used for the Coulomb software to calculate the electric field and voltage distribution is shown in Fig. 5.18 (c). To reduce the calculation time, only a 10 127 degree segment of the shed surface is modeled, and that segment is used 36 times to represent the entire circumference of a shed. m £ - If. 4 ■- (a) Case FHCl with HCl top surface. (b) Case FHCl with HCl underside surface and dry sheath. (C) Case FHCl calculation model. Figure 5.18: Case FHCl water droplet distribution on the surface of a non-ceramic insulator and the calculation model. Case FHC2 represents a SIR insulator under advanced wetting status, which are shown in Figs. 5.19 (a) and (b). There are medium size water droplets on top of each shed, on the underside of each shed, and small water droplets on each sheath region of the insulator as well. The model (as cross-section) used for the calculations is shown in Fig. 128 5.19 (c). To reduce the calculation time, only a 10 degree segment of the shed surface is modeled. That segment is used then 36 times to represent the entire circumference of a shed. mm (a) Case FHC2 with HC2 top surface. (b) Case FHC2 with ttC2 underside surface and FtCl sheath surface. (C) Case FHC2 calculation model. Figure 5.19: Case FHC2 water droplet distribution on the surface of a non-ceramic insulator and the calculation model. Case FHC3 represents a SIR insulator under more advanced wetting status, which are shown in Figs. 5.20 (a) and (b). There are large water droplets on top of each shed, on the underside of each shed, and small water droplets on each sheath region of the 129 insulator. The model (as cross-section) used for the calculations is shown in Fig. 5.20 (c). To reduce the calculation time, only a 10 degree segment of the shed surface is modeled. That segment is used then 36 times to represent the entire circumference of a shed. TP f IS (a) Case FHC3 with HC3 top surface. (b) Case FHC3 with HC3 underside surface and HC 1 sheath surface. \îir' I (C ) Case FHC3 calculation model. Figure 5.20: Case FF1C3 water droplet distribution on the surface of a non-ceramic insulator and the calculation model used for the study. 130 5.8 Analysis of enhancement factors and electric field and voltage distribution for an insulator under fog conditions The equipotential contours along a dry and clean non-ceramic insulator are also calculated and then compared to those of the insulators under fog conditions, such as Cases FHC1-FHC3, in order to visualize the different overall voltage distributions of the four models. The calculation results are summarized in Fig. 5.21. Each number shown along the perimeters of the four contour plots means centimeters. The numbers indicated in the graph show the voltage in volts. Fig. 5.21(a) shows the base case, the non-uniform voltage distribution along a dry and clean insulator. Comparison of the density of the equipotential lines in Figs. 5.21 (b)- (d) to those of in the base case can be used to study the overall distribution of the electric field for the cases with water droplets. Fig. 5.21(b) shows the voltage distribution for Case FFICI. The water droplets are on the topside and on the underside of the weather sheds. The electric field strength (0.0256 kVp/mm) at the triple junction area is lower than in the dry and clean case (0.028 kVp/mm). So the electric field enhancement factor is 0.0256/0.028=0.9. Fig. 5.21(c) shows the voltage distribution for Case FFIC2. The water droplets are on the topside and on the underside of the weather sheds. The electric field strength (0.067 kVp/mm) at the surface of the water at the triple junction area is higher than in the dry and clean case (0.028 kVp/mm). So the electric field enhancement factor is 0.067/0.028=2.4. 131 Fig. 5.21(d) shows the voltage distribution for Case FHC3. The hydrophobicity on the top and down surface are different compared to Case FHC2. The presence of the water droplets makes the voltage distribution along the entire insulator more uniform. 15 15 15 14 14 14 100 13 13 150 13 100 -150 -450— 12 12 ■ m r 12 11 11 250 10 250 10 10 9 9 300 9 300 300 350 8 8 8 350 7 7 7 450 6 6 6 5 450 5 500 5 500 500 .550 4 450 4 4 3 3 3 650 650 2 2 2 0 0 0 ■1 1 ■2 2 -2 3 3 ■3 -4 -4 4 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 (a) Dry case (b) Case FHCl (c) Case FHC2 (d) Case FHC3 Figure 5.21: Equipotential contours for (a) Dry case, (b) Case FHCl, (c) Case FHC2, (d) Case FHC3. The electric field enhancement factors on the surface of water droplet or the shed at different locations of the non-ceramic insulator for Cases FHC1-FHC3 are summarized in Table 5.4. D ry C ase C ase F H C l C ase FH C 2 C ase FH C 3 (kV /m m ) E. F. E. F. E. F. Triple junction point 0.028 0.9 2 .4 2.4 Top of the first shed 0.017 2.4 2.1 3.2 Under the first shed 0TG6 1.9 2 .0 2.1 Sheath region 0 013 1.0 3.6 4.3 Table 5.4: Electric field enhancements factor (E. F.) for Cases FHC1-FHC3 at various locations. 132 The magnitude of the electric field strength along the sheath surface of the insulator under fog conditions are shown in Fig. 5.22. The calculation path is 4mm away from the surface of the sheath and starts from the point 0.2 mm above the line end metal fitting. The horizontal quantity is the insulation distance along the sheath surface, in percent. 0.03- 0.027 : D ry case C ase F H C l 0.024 - > C ase FH C 2 0.021 - Case FHC3 0.018 - 2 0.015 0.012 § 0.009 0.006 0.003 W 0 0 10 20 30 40 50 60 70 80 90 100 Insulation distance (%) Figure 5.22: Electric field strength magnitude along the insulation distance at the surface of the sheath for Dry Case and Cases FHC1-FHC3. The electric field distribution along the sheath surface of the insulator is pretty close for Case FFICI and FF1C2. There is a significant difference between Dry Case and Case FHC3. The overall electric field strength is more uniform for Case FHC3 than the Dry Case. 133 5.9 Summary A four-shed insulator model has been used for the study to reduce the calculation time. The models developed for the calculations are based on photographs of insulators undergoing aging tests in a fog chamber. Six insulator models under rain conditions with HCl-6 surface conditions and three insulator models under fog conditions with HCl-3 surface conditions have been developed. The electric field and voltage distributions along non-ceramic insulators under various wet conditions have been calculated and analyzed. Electric field and equipotential lines and electric field enhancement factors on the surface of water droplets have also been presented. . 134 Chapter 6 VERIFICATION TESTS FOR DRY INSULATOR In order to verify the dry calculation results by experimental results, a series of experiments were conducted in the High Voltage Laboratory of The Ohio State University by using a Positron insulator tester to study the electric field strength distribution along a dry non-ceramic insulator. The insulator tester measures the AC electric field along insulators. The tester has two parallel dielectrically separated plates that sense the electric field strength between them. The probe measures and records the electric field strength along the insulator when the actuator is pushed. The information collected from the reading is stored in the memory and can be downloaded to a PC for graphical display. The insulator tester had to be calibrated before the verification tests. For that purpose, a 34.5 kV SiR insulator was suspended from a grounded supporting structure. A 1 meter long conductor was connected to the line end of the insulator. The vertical component of the electric field strength distribution along the insulator was measured using the insulator tester. The calculation results of the simulation were compared with the measurement results. 135 6.1 Calibration test The insulator tester needed to be calibrated before the verification tests. The vertical sphere gap, asymmetrically energized, was used for the calibration tests. The spheres were aligned and positioned vertically. The diameter of each one of the two sphere electrodes is 35.5 cm. The distance between the two spheres was 20 cm. The center of the upper sphere was 200 cm above the ground plane. The Positron insulator tester was put in the middle of the sphere gap. The upper sphere was energized, and the other one was grounded. The high voltage sphere was energized from a 25-kVA 240 V/250kV transformer via a current-limiting resistor and high voltage bus. The high voltage output of the transformer was controlled using a variable ratio autotransformer on the low voltage side of the transformer. A 40000:1 ratio capacitive voltage divider was connected to the high voltage bus for measurement purposes. The calibration test setup is shown in Fig. 6.1, which also shows how to download the data from the insulator tester to the PC . m # V,' -V» -'IK## Figure 6.1 : Calibration test setup. 136 By keeping the position of the insulator tester constant, the applied voltage on the upper sphere was raised from 1.6 kVrms to 20 kVrms- The readings of the insulator tester are shown in Table 6.1. Applied voltage 1.6 4 6 8 10 12 14 16 18 20 (kVrms) Insulator tester 14 40 60 81 104 122 145 164 187 208 reading, T Table 6.1 Insulator readings under various applied voltages. Fig. 6.2 shows the relationship between the applied voltages and the insulator tester readings (simplified as T). The line is the least square trend line fit for these values. The equation for the trend line is = 0.0952 x T + 0.255. 25 E 20 > QJ 15 o > -a & 10 < 50 100 150 200 2 5 0 T Figure 6.2 Relationship between the applied voltage and the insulator tester readings (T). 137 The electric field strength in the middle of the two spheres was calculated using the Coulomb software. The calculation model of the sphere gap in Coulomb is shown in Fig. 6.3. SESfea Figure 6.3 Calculation model for the sphere gap. In this calculation model, the upper sphere was energized at 1 kVims and the lower one was grounded. The ground plane was modeled as a 10 m x 10 m large plane with zero potential. The calculated electric field strength in the middle of the sphere gap was 4 kV rms/na. Therefore, the relationship between the electric field strength magnitude and the insulator tester readings is: Æ = 4 X (0.0952 X T + 0.255) = 0.3808 x T +1.02 (kVrms/m) 6.2 Verification test In order to verify the calculation results, the Positron insulator tester was used to measure the electric field distribution along a dry SiR insulator. The 34.5 kV insulator, which is shown in Fig. 3.1, was used for the verification tests. 138 The insulator was tested in its vertical position. The tower window was simulated by a grounded supporting structure. A 1 meter long conductor with 2.3 cm diameter is connected to the line end of the insulator. The experiment setup and dimensions of the grounded supporting structure are shown in Fig. 6.4. - • • A i r . . . - f f r , ITJ tgELpak# ^ IT ï-Î T è -A . . ’ v ,^ * ^ U nits: cm 160 Figure 6.4: Verification test setup and dimensions of the grounded supporting structure. 139 The insulator tester was attached to a horizontal hot stick, which was supported by an insulating stand. The height of the hot stick above the ground plane could be adjusted easily. The insulator tester was moved along a vertical line, which was about 18.5 cm away from the center line of the insulator tested. The angle between the hot stick and the conductor was 35 degrees (angle in the horizontal plane). The applied voltage on the conductor was 30 kVrms- The insulator tester was moved from 141 cm (55.5 inch) to 93 cm (36.5 inch) above ground by 2.54 cm (1 inch) steps. The vertical component of the electric field strength along the insulator was measured. The measurement and simulation results are shown in Fig. 6.5. Reasonably good agreement between measurement and calculation results is demonstrated. 3 5 ------s "s 30 ------& 1 " ------ 2 20 I o 15 I a 10 5 90 100 110 120 130 140 150 Distance above the ground (em) Figure 6.5: Electric field distribution along a dry insulator measured by the insulator tester (*) and calculated by the simulation models (-). 140 6.3 Error analysis Although Fig. 6.5 shows reasonably good correlation between the measurement and calculation results, there is still a small difference between them. There are several factors that may affect the accuracy of the measurement results: • The insulator tester has two parallel dielectrically separated plates that sense the electric field strength between them. The distance between the two plates was 4 cm. The size of the plate is about 18 cm x 3.5 cm. The spatial resolution of the insulator tester is not good enough, since it measures the average surrounding electric field strength. Since the spatial resolution is not sufficient for the measurement of small differences, the instrument could not he used for the verification of “wet surface” calculations. • Since the probe only measures and records the electric field strength when the actuator is pulled back, the pulling force may slightly change the position of the insulator tester. • The hot stick metal mounting and the two metal plates of the insulator tester may slightly distort the electric field distribution. 6.4 Summary Good agreement between the measurement and calculation results has been observed. It shows that the calculation results using the Coulomb software package are good and accurate. 141 CHAPTER 7 DESIGN CONSIDERATIONS Non-ceramic insulators are used worldwide. There is a large variety of designs of non-ceramic insulators available on the market. The electric field distribution is a key concern of the insulator design. The electric field distribution along a non-ceramic insulator is more non-linear than that of a ceramic insulator due to the lack of the intermediate metal parts. There are many different design parameters of a non-ceramic insulator, such as the shed profile, that can be varied. Tbe dimensions and position of the corona rings can also be changed. In this chapter, for illustration purpose, only some of the design parameters are selected and studied using a four-shed insulator model to illustrate the influence on the electric field distribution along the insulators. The most critical area of the insulator design is the sheath region between the live line end and the first shed. The end fittings of non-ceramic insulators are made of metal of high electrical conductivity. When there are water droplets and pollution at the joint between the end fitting and the housing material (it is called triple junction point), partial arcs may occur. The movement of the partial arcs, which start at the triple junction point, 142 to the point of the highest electric field strength (at the surface of the electrode away from the triple junction point) causes the instability of the partial arcs. From the instability model of partial arcs, it is most useful to design the joint of the housing and end fitting in such a way that instability of the arcs would be avoided at this joint. The objective of this chapter is to study the influence of some important design parameters on the electrical field strength distribution along non-ceramic insulators. 7.1 Model setup A short insulator with only four sheds is considered for the following calculations in order to reduce calculation time. The simplified geometry and dimensions of the polymer insulator to be modeled are shown in Fig. 7.1. The weather sheds are made of silicon rubber with a relative permittivity of 4.3. The relative permittivity of the fiberglass rod is 7.2. The applied voltage on the line end of the insulator is assumed to be IkVp. U nits: cm G round end □ N . JML JiiL TT00 Jh L > D I! - 1 9.4 □ L ine end Figure 7.1 : Geometry and dimensions of a four-shed insulator. 143 7.2 Effects of the distance between the first shed and the end fitting Based on the experience of many calculation examples, the distance D (as shown in Fig. 7.1) between the first shed and the line end fitting is a very important parameter. The distance between them usually varies from 1cm to 3 cm. The electric field strength distribution along the per cent insulation distance at the surface of the insulator sheath is shown in Fig. 7.2. The triple junction point is at 0% of the insulation distance. 0.025 a D = lc m 0.02 D = 2 cm D = 3 cm "O3 I 0.015 I 0.01 « 0.005 Ü 0 Üj 0 10 20 30 40 50 60 70 80 90 100 Insulation distance (%) Figure 7.2: Electric field strength magnitude along the per cent insulation distance at the surface of the insulator sheath with different distance D. Fig. 7.2 clearly shows that the larger the distance D, the lower the electric field strength at the triple junction point. The electric field strength magnitude practically everywhere else along the sheath region at the same point also decreases when D distance is larger. 144 7.3 Effects of the shed spacing The shed spacing is another parameter need to be studied. Two shed spacings are used here for the purpose of comparison. By keeping the distance between the two end fittings constant, one insulator has four sheds with 4 cm shed spacing and the other one has three sheds with 6 cm shed spacing. The electric field strength distribution along the per cent insulation distance at the surface of the insulator sheath is shown in Fig. 7.3 for these two cases. 0.03 Four sheds 0.025 s ------Three sheds CD 1 73 1 S 0.02 1 I 0.015 ' s 0.01 \ 1 0.005 / 1 \ 1 ' ' 1 / I1) w 10 20 30 40 50 60 70 80 90 100 Insulation distance (%) Figure 7.3: Electric field strength magnitude along the per cent insulation distance at the surface of the insulator sheath with two different shed spacings. The electric field strength profiles along the surface of the insulator sheath for these two cases are very close to each other. The influence of the shed spacing on the electric field distribution along the insulator under dry and clean conditions can be ignored. But the shed spacing has important effects on the insulator performance under wet and contaminated conditions, which should be determined by experiment conditions. The typical shed spacing used in the industry is about 3-5 cm. 145 7.4 Effects of the shed profile There are many designs for the shed profile of a non-ceramic insulator. The shed profile is a parameter that needs to be studied. The shed profile should be aerodynamic in shape. Based on the previous study in Section 4.3, the electric field strength is significantly higher in the sheath/shed transition area than in adjacent areas. The influence of the rounding radius of the sheath/shed transition area on the electric field distribution along the insulators is of interest. Two typical values are used for the purpose of comparison. One radius is 0.5 cm and the other is 2 cm. I R 0.5 cm R 2 cm I 9 _____ (a) Case 1 (b) Case 2 Figure 7.4: Two shed profiles with different sheath/shed transition rounding radius. The electric field strength distribution along the per cent insulation distance at the surface of the insulator sheath is shown in Fig. 7.5 for these two cases. Due to the shorter sheath region length, the electric field strength on the sheath region for the insulator (at the same location in terms of insulation distance) with larger rounding radius is higher than that with smaller rounding radius. 146 g 0 . 0 3 1 0.5 cm radius a 0 . 0 2 5 2 cm radius ^ 0.02 5 0 ^ 0 . 0 1 5 üû 0.01 \ I : g I 0 . 0 0 5 ! 10 20 30 40 50 60 70 8 0 9 0 100 M Insulation distance (%) Figure 7.5: Electric field strength magnitude along the per cent insulation distance at the surface of the insulator sheath with different sheath/shed rounding radius values. 7.5 Effects of the position of the corona ring Since the dimension of the corona ring has been designed hy the manufacturer, the only variable that can be adjusted is the position of the corona ring. To investigate the effects of the corona ring position on the electric field distrihution in the vicinity of the line end fitting of a insulator, the 765 kV tower with four-subconductor bundles model is used. The dimensions and positions of the line end corona rings are shown in Fig. 7.6. The height of the corona ring above the line end fitting is defined as Dc, which varies from 3.8 cm to 10.8 cm. U nits: cm Figure 7.6: Dimensions and positions of the line end corona ring. 147 The maximum electric field strength at the triple junction point is shown in Fig. 7.7. The electric field strength magnitude distribution along the sheath surface near the line end fitting is shown in Fig. 7.8. 1.6 1.55 1.5 1 .4 1.35 1.3 1 .25 1.2 1.15 4 5 6 7 8 9 10 Distance Dc between the corona ring and the end fittings (em) Figure 7.7: Maximum electric field magnitude at the triple junction point as a function of the corona ring position. D c= 3 .8 cm 1.4 D c= 5 .8 cm D c= 1 0 .8 cm -o I a 0.8 o 0.4 0.2 0 5 10 15 20 25 Insulation distance from end fitting (cm) Figure 7.8: Electric field strength magnitude along the insulation distance at the surface of the insulator sheath with the corona ring at different locations. 148 The position of the corona ring is very important to control the electric field strength distribution in the vicinity of the line end fittings. As the corona ring is moved from the line end toward the ground end in the range investigated, the maximum electric field strength is reduced. But the dry arcing distance between the line end and the ground end is also reduced as the corona ring is moved toward the ground end. 7.6 Summary Based on a four-shed insulator model, the effects of the distance between the first shed and the end fitting, shed spacing, and shed profile are studied. The results indicate that the larger the distance between the first shed and the end fitting, the lower the electric field strength at the triple junction point. The influence of the shed spacing to the electric field distribution along a non-ceramic insulator under dry and clean condition can be ignored. The effect of the position of a corona ring is also investigated by using a 765 kV insulator with four- subconductor bundles. As the corona ring is moved from the line end to the ground end, the maximum electric field strength at the triple junction point is reduced. 149 CHAPTER 8 CONCLUSIONS AND FUTURE WORK 8.1 Conclusions As discussed in Chapter 2, the electric field and voltage distribution (EFVD) along non-ceramic insulators has be studied previously experimentally and numerically. Hardly any research has been done to study the EFVD along non-ceramic insulators energized by a three phase voltage system. Although some experimental studies have been done to measure the axial electric field strength from a certain distance along the insulator, the knowledge of the electric field strength enhancement due to the water droplets on the surface of the insulator under various wet conditions is very limited. The main contributions of this dissertation research on the EFVD along non- ceramic insulators under various surface conditions are as follows: 1. The full, detailed model of a dry and clean non-ceramic insulator with 12 weather sheds has been developed for the base case calculations. Simplified insulator models of the same insulator have also been set up in order to decide which components of the insulator can be omitted, but accurate calculation 150 results still can be obtained with efficient calculation times (see Section 3.1 for discussions, and Section 4.2.1 for a practical example). 2. In order to obtain a detailed electric field analysis along and around dry and clean non-ceramic insulators, the effects of the conductor and the grounded supporting structure have been analyzed (see Section 3.2 for discussions, and Sections 4.2.2 and 4.2.3 for practical examples). 3. A simple model of a flat polymer insulating sheet between two electrodes and a water droplet on it has been developed and used to study tbe electric field enhancement of a water droplet on the shed and on the sheath region, respectively, of a non-ceramic insulator (see Sections 3.3 and 3.4). 4. The effects of changes in water droplet contact angle, size of water droplets, shape of water droplets, distances between adjacent water droplets, and conductivity of water bave been described in terms of an electric field strength enhancement factor, always referring to an appropriate base case (see Section 3.5). 5. A detailed example of the application of 765 kV non-ceramic insulator electric field and voltage distribution research has been described in Section 4.2. The voltage and electric field distributions have been calculated in Section 4.3 for two practical cases, one for four- and the other one with six subconductor bundles. The maximum values of the electric field strength at the so-called triple junction point have been calculated for these two cases. For four subconductors, tbe maximum value is 1.586 kV/mm, for six subconductors, it is 1.162 kV/mm (see Section 4.3). 151 6. An innovative plot of the electric field strength along the leakage path on the surface of all sheds and sheath sections along a section of a 765 kV polymer insulator has been developed (see Figures 4.16 and 4.17). 7. Effects of the 765 kV tower configuration, the other two (side) phases of the three phase system, and the conductor bundles have been analyzed (see Section 4.4). 8. Several models of a four-shed polymer insulator exposed to rain or fog conditions have been developed, following observations during and after aging tests in a high voltage fog chamber. The calculation models of 9 examples have been developed. The electric field and voltage distribution along the insulator under various wet conditions have been calculated and analyzed in detail (see Chapter 5). 9. Selected calculations on dry and clean insulators using the software package Coulomb have been verified with an electric field strength meter. The correspondence of calculations and high voltage measurements has been reasonably good (see Chapter 6). 10. Several research issues applied to the practical insulator design aspects have been investigated and discussed, such as the distance between the first shed and the end fitting, the shed spacing, shed profile, and the position of the corona ring (see Chapter 7). 152 8.2 Suggested future work To further study the electric field distribution along non-ceramic insulators, a list of topics is given as follows: 1. Optimization of specific non-ceramic insulator designs for wet conditions. 2. Effect of the water droplet shape distortion of water droplets on the EFVD along non-ceramic insulators when the non-ceramic insulator is energized. 153 APPENDIX A BRIEF REVIEW OF COULOMB SOFTWARE Coulomb is a software package written by Integrated Engineering Software Company. It is a powerful three-dimensional electrostatic and quasi-static simulation software, which combines the efficiency of the boundary element method technology with an easy-to-use user interface. Coulomb is especially suited for applications where the design requires a large open field analysis and exact modeling of the boundaries. The advanced technical features of Coulomb are: • Intuitive and structured interface • Static electric field and electrical conduction analysis • Electrostatic force, torque, and capacitance calculations • A variety of display forms for plotting vector field quantities including, graphs, contour plots, color maps, streamline plots • Data exportable to formatted files for other software packages • Batch functions allow unattended solution of multiple files • High quality graphics for preparation of reports and presentations 154 The typical screen view of Coulomb software package is shown below: r:\ViA)'Mile*''. H4# ...... I ] Linear -1 i iP .11^__ ^ É jGlobal iMj;tfsurface éJIIcopv Axis&t:jcm < i r f | jl| f h f f e m ii'4" JAih'MWA'. ffiHiL ,fy 1 1 3 Æ&ghd COULOMB (1: , ' 4 Figure A. 1 : The desktop of Coulomb software. In Coulomb software, there are several basic steps to develop the non-ceramic insulator model in order to calculate the electric field and voltage distributions along non- ceramic insulators: 1. Setting up model units 2. Creating the geometry 3. Assigning physical properties 4. Assigning voltages to boundaries 5. Assigning boundary elements to the boundaries 6. Solving the problem and analysis. 155 Before entering any of the geometry of the calculation model, the units have to be set up. Coulomb uses the International System (SI) units as default. To perform the calculation of the EFVD along a non-ceramic insulator, a geometric model of the insulator needs to be developed. The geometric modeler of Coulomb is used for this purpose. The files from many of the most popular commercial CAD packages can also be imported directly. Once the geometric model has been built, physical properties (such as boundary conditions, materials, sources, etc.) are then assigned. Coulomb provides users with the capability of entering their own material data. After the physical properties have been assigned, the model is discretized and the solution is calculated by the field solver. Boundary elements are required on surfaces that separate regions containing different materials; surfaces that are assigned some type of potential boundary condition; or in situations where a surface charge has been assigned. Coulomb can also be set to perform multiple unattended analyses by running the program in parametric or batch mode. It can perform phasor simulations to calculate steady state field solutions that result from sinusoidal sources. An AMD Athlon 1.3 GFlz computer was used for the research study is with 700 MB RAM and a 60 GB hard drive (7200 RPM, Ultra ATA/133 interface). The computation time depends on the number of elements and symmetry and periodicity conditions. By using symmetry and periodicity conditions, the size of the calculation model and computation time can be reduced. Coulomb allows to define symmetry about any of the three principle Cartesian planes: X=0 (YZ plane), Y=0 (ZX plane) and Z=0 (XY plane). A model is periodic when 156 a basic unit is repeated in a pattern to form the entire model. Periodicity can be angular or linear, depending on whether the design is repeated in a pattern around an axis or in a straight line. Table A.l shows the number of elements used, the symmetry and periodicity conditions used for the study, and the computation time. Models Elements Symmetry Periodicity Computation used plane (degrees) time (hours) Figure 3.2 (e) 8811 XZ, YZ 2 Figure 4.8 19645 XZ 9 Figure 5.20 12956 10 27 Table A. 1 : Sample computation time and related parameters. The limitation of Coulomb V5.2 software is that the number of the segments which is used for the geometry of the calculation model should be less than 4000. The largest number of the segments used in any eases of this dissertation was about 2600. That is one of the reasons why a four-shed insulator is chosen to study the EFVD along an insulator under various wet conditions. 157 APPENDIX B BASIC TWO-SHED INSULATOR MODEL In Chapter 4.3, the electric field strength along the leakage path on the surface of the insulator near the line-end fitting has been calculated. The result shows that the electric field strength near the edge of the shed suddenly drops. To explain this phenomena, a two-shed insulator model has been developed. Since the equipotential lines are close to parallel to the surface of the weather shed, the two-shed model is in a parallel position between the two electrodes as shown in Fig. B.l. The upper electrode is grounded and the lower electrode is energized. The applied voltage is 1 kV. OkV ^ A Y X 1 kV 100 cm Figure B.l: Two-shed insulator between two parallel electrodes. 158 The equipotential contours around the edge of the lower shed are shown in Fig. B.2. Z (cm ) 5.8 5.7 590- -593 5.5 596 599 5.4 602 5.3 - 605 5.2 608 611 4.9 4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8 7 Y (cm ) Figure B.2: Equipotential contours around the shed edge of a two-shed insulator. Figure B.2 clearly shows that the rounded edge of the shed (AB section) “presses out” the equipotential lines to the side of the shed edge. The electric field strength is only enhanced at the up and down sides of the shed edge, e.g., at points A and B, but it is much lower at the center of the shed edge, at point C. 159 BIBLIOGRAPHY [1] T. Zhao, and R. A. Bemstorf, “Aging Tests of Polymeric Housing Materials for Non-Ceramic Insulators,” IEEE Electrical Insulation Magazine, Vol. 14, No. 2, 1998, pp. 26-33. [2] R. Hackam, “Outdoor HV Composite Polymeric Insulators,” IEEE Transaetions on Dielectrics and Electrical Insulation, Vol. 6, No. 5, October 1999, pp. 557-585. [3] G. G. Karady, M. Shah, and R. L. Brown, “Flashover Mechanism of Silicone Rubber Insulators Used for Outdoor Insulation - 1,” IEEE Transactions on Power Delivei-y, Vol. 10, No. 4, October 1995, pp. 1965-1971. [4] J. Mackevich, and M. Shah, “Polymer Outdoor Insulating Materials Part I: Comparison of Porcelain and Polymer Electrical Insulation,” IEEE Electrical Insulation Magazine, Vol. 13, No. 3, May/June 1997, pp. 5-12. [5] G. G. Karady, “Flashover Mechanism of Non-ceramic Insulators,” IEEE Transaetions on Dielectries and Electrieal Insulation, Vol. 6, No. 5, October 1999, pp.718-723. [6] X. Liang, S. Wang, J. Fan, and Z. Guan, “Development of Composite Insulators in China,” IEEE Transactions on Dielectrics and Electrical. Insulation, Vol. 6, No. 5, October 1999, pp. 586-594. [7] G. H. Vaillancourt, S. Carignan, and C. Jean, “Experience with the Detection of Faulty Composite Insulators on High-Voltage Power Lines by the Electric Field Measurement Method,” IEEE Transactions on Power Delivery, Vol. 13, No. 2, April 1998, pp. 661-666. [8] D. H. Shaffner, D. L. Ruff, and G. H. Vaillancourt, “Experience with a Composite Insulator Testing Instrument Based on the Electric Field Method,” Proeeedings of the 9th International Conference on Operation and Live-Line Maintenance, 2000 IEEE ESMO, pp. 318-327. [9] A. J. Philips, D. J. Childs, and H. M. Schneider, “Water Drop Corona Effects on Full-Scale 500 kV Non-Ceramic Insulators,” IEEE Transaetions on Power Delivery, Vol. 14, No.l, Jan. 1999, pp. 258-265. 160 [10] E. A. Cherney, “Non-Ceramic Insulators - a Simple Design that Requires Careful Analysis,” IEEE Electrical Insulation Magazine, Vol. 12, No. 3, May/June 1996, pp. 7-15. [11] K. Hidaka, “Progress in Japan of Space Charge Field Measurement in Gaseous Dielectrics Using a Pockels Sensor,” IEEE Electrical Insulation Magazine, Vol. 12, No. 1, January 1996, pp. 17-28. [12] K. Hidaka, “Electric Field and Voltage Measurement by Using Electro-Optic Sensor,” Proceedings of the Eleventh International Symposium on HV Engineering, London, August 1999, Vol. 2, pp. 1-14. [13] R. Parraud, “Comparative Electric Field Calculation and Measurements on High Voltage Insulators,” Report of CIGRE WG 22.03, Electra, No. 141, April 1992, pp. 68-77. [14] K. Feser, and W. Pfaff, “A Potential Free Spherical Sensor for the Measurement of Transient Electric Fields,” IEEE Transactions on Power Apparatus and Systems, Vol. 103, No. 10, Oct. 1984, pp. 2904-2911. [15] P. B. Zhou, Numerical Analysis of Electromagnetic Fields. Spinger-Verlag, Berlin, 1993 [16] M. J. Khan, and P. H. Alexander, “Charge Simulation Modeling of Practical Insulator Geometries,” IEEE Transactions on Electrical Insulation, Vol. El-17, No. 4, August 1982, pp. 325-332. [17] S. Chakravorti, and H. Steinbigler, “Boundary-Element Studies on Insulator Shape and Electric Field around HV Insulators with or without Pollution,” IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 7, No. 2, April 2000, pp. 169-176. [18] Y. B. Yildir, K. M. Prasad, and D. Zheng, “Computer-Aided Design in Electromagnetic Systems: Boundary Element Method and Applications,” Control and Dynamic Systems, Vol. 59, 1993, pp. 167-221. [19] T. Zhao, and M. G. Comher, “Calculation of Electric Field and Potential Distrihution along Non-Ceramic Insulators Considering the Effects of Conductors and Transmission Towers,” IEEE Transactions on Power Delivery, Vol. 15, No. 1, January 2000, pp. 313-318. [20] T. Misaki, H. Tsuhoi, K. Itaka, and T. Hara, “Computation of Three Dimensional Electric Field Problems hy a Surface Charge Method and Its Application to Optimum Insulator Design,” IEEE Transactions on Power Apparatus and Systems, Vol. 101, No. 3, March 1982, pp. 627-634. 161 [21] T. Misaki, H. Tsuboi, K. Itaka, and T. Hara, “Optimization of Three-dimensional Electrode Contour Based on Surface Charge Method and Its Application to Insulation Design,” IEEE Transactions on Power Apparatus and Systems, Vol. 102, No. 6, June 1983, pp. 1687-1692. [22] S. Kaana-Nkusi, P. H. Alexander, and R. Hackam, “Potential and Electric Field Distributions at a High Voltage Insulator Shed,” IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 23, No. 2, April 1988, pp. 307-318. [23] F. Gutfleisch, H. Singer, K. Forger, and J. A. Gomollon, “Calculation of High- Voltage Fields by Means of the Boundary Element Method,” IEEE Transactions on Power Delivery, Vol. 9, No. 2, April 1994, pp. 743-749. [24] R. Hartings, “Modem Experimental Techniques to Study the Discharge Phenomena on Outdoor Insulators,” Proceedings of the Seventh International Symposium on HV Engineering, Dresden, August 1991, Paper No. 72.10. [25] S. P. Hornfeldt, “DC-Probes for Electric Field Distribution Measurement,” IEEE Transactions on Power Delivery, Vol. 6, No. 2, April 1991, pp. 524-529. [26] R. Hartings, “The AC-Behavior of Hydrophilic and Hydrophobic Post Insulators During Rain,” IEEE Transactions on Power Delivery, Vol. 9, No. 3, July 1994, pp. 1584-1592. [27] R. Hartings, “Electric Fields Along a Post Insulator: AC-Measurements and Calculations,” ÆEA Transactions on Power Delivery, Vol. 9, No. 2, April 1994, pp. 912-918. [28] A. Eklund, and R. Hartings, “Electric Field Measurements on Composite and Ceramic Insulators During Pollution Testing,” Proceedings of CIRED 97, June 1997, lEE Conference Publication No. 438. [29] S. Chakravorti, and P. K. Mukherjee, “Power Frequency and Impulse Field Calculation Around a HV Insulator with Uniform or Non-uniform Surface Pollution,” IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 28, No. 1, Febmary 1993, pp. 43-53. [30] G. Xu, and P. B. McGrath, “Electrical and Thermal Analysis of Polymer Insulator under Contaminated Surface Conditions,” IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 3, No. 2, April 1996, pp. 289-298. [31] A. Ahmed, H. Singer, and P. K. Mukherjee, “A Numerical Model Using Surface Charges for the Calculation of Electric Fields and Leakage Currents on Polluted Insulator Surfaces,” Annual ReporA o f the 1998 IEEE CEIDP, Atlanta, October, 1998, pp. 116-119. 162 [32] S. Chakravorti, and H. Steinbigler, “Capacitive-Resistive Field Calculation on HV Bushings Using the Boundary-Element Method,” IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 5, No. 2, April 1998, pp. 237-244. [33] H. El-Kishky, and R. S. Gorur, “Electric Potential and Field Computation Along AC HV Insulators,” IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 1, No. 6, December 1994, pp. 982-990. [34] H. El-Kishky, and R. S. Gorur, “Electric Field and Energy Computation on Wet Insulating Surfaces,” IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 3, No. 4, August 1996, pp. 587-593. [35] H. El-Kishky, and R. S. Gorur, “Electric Field Computation on an Insulating Surface with Discrete Water Droplets,” IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 3, No. 3, June 1996, pp. 450-456. [36] G. H. Vaillancourt, J. P. Bellerive, M. St-Jean, and C. Jean, “New Live Line Tester For Porcelain Suspension Insulators on High-Voltage Power Lines,” IEEE Transactions on Power Delivery, Vol. 9, January 1994, pp. 208-219. [37] E. Spangenberg, and G. Riquel, “In Service Diagnostic of Composite Insulators, EDF’s Test Results,” Proceedings of the Tenth International Symposium on HV Engineering, Montreal, August 1997, Vol. 4, pp. 139-142. [38] Y. Chen, C. Ei, X. Liang, and S. Wang, “The Influence of Water and Pollution on Diagnosing Defective Composite Insulators by Electric Field Mapping,” Proceedings o f the Eleventh International Symposium on HV Engineering, London, August 1999, Vol. 3, pp. 197-200. [39] G. Gela, and D. Mitchell, “Assessing the Electrical and Mechanical Integrity of Composite Insulators Prior to Live Working,” Proceedings of IEEE 9th Operation and Live-Line Maintenance, 2000, pp. 339 -343. [40] K. Sokolija, and M. Kapetanovic, “About Some Important Items of Composite Insulators Design,” Proceedings of the Eleventh International Symposium on HV Engineering, London, August 1999, Vol. 4, pp. 284-287. [41] R. S. Gorur, E. A. Cherney, and R. Hackam, “Polymer Insulator Profiles Evaluated in a Fog Chamber,” IEEE Transactions on Power Delivery, Vol. 5, No: 2, April 1990, pp. 1078-1085. [42] H. Janssen, and U. Stietzel, “Contact Angle Measurement on Clean and Polluted High Voltage Polymer Insulators,” Proceedings of the Tenth International Symposium on HV Engineering, Montreal, August 1997, Vol. 3, pp. 149-152. 163 [43] S. Gubanski, and R. Hartings, “Swedish Research on the Application of Composite Insulators in Outdoor Insulation,” IEEE Electrical Insulation Magazine, Vol. 11, No. 5, Oct. 1995, pp. 24-31. [44] J. Philips, D. J. Childs, and H. M. Schneider, “Aging of Non-ceramic Insulators due to Corona from Water Drops,” IEEE Transactions on Power Delivery, Vol: 14, No: 3, July 1999, pp. 1081 -1089. [45] 1. J. S. Lopes, S. H. Jayaram, and E. A. Cherney, “A Study of Partial Discharges from Water Droplets on a Silicone Rubber Insulating Surface,” IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 8, No. 2, April 2001, pp. 262-268. [46] P. Blackmore, and D. Birtwhistle, “Surface Discharges on Polymeric Insulator Shed Surfaces,” IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 4, No. 2, April 1997, pp. 210-217. [47] S. Keim, and D. Koenig, “The Performance of Electrically Stressed Droplets on Insulating Surfaces Observed with an Optical Measuring System,” 2000 Conference on Electrical Insulation and Dielectric Phenomena, October 2000, pp. 792-795. [48] S. Keim, and D. Koenig, “Tbe Dynamic Behaviour of Water Drops in an AC Field,” 2001 Annual Repor-t Conference on Electrical Insulation and Dielectric Phenomena, October 2001, pp. 613-616. [49] A. Krivda, and D. Birtwbistle, “Breakdown between Water Drops on Wet Polymer Surfaces,” 2001 Annual Report Conference on Electrical Insulation and Dielectric Phenomena, October 2001, pp. 572-580. [50] T. Yamada, T. Sugimoto, and Y. Higashiyama, “Resonance Phenomena of a Single Water Droplet Located on a Hydrophobic Sbeet under AC Electric Field,” Coriference Record o f the 2001 IEEE Industry Applications Coriference, Vol. 3, 2001, pp. 1530-1535. [51] V. M. Moreno, and R. S. Gorur, “Effect of Eong-term Corona on Non-ceramic Outdoor Insulator Housing Materials,” IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 8, No. 1, February 2001, pp. 117-128. [52] A. De Fa O, and R. S. Gorur, “Flashover of Contaminated Nonceramic Outdoor Insulators in a Wet Atmosphere,” IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 6, No. 6, December 1998, pp. 814-823. 164 [53] X. Liang, S. Wang, and Z. Guan, “Hydrophobicity Status of Silicone Rubber Insulators in the Field,” Proceedings of the 12th International Symposium on HV Engineering, Bangalore, August 2001, Vol. 3, pp. 703-706. [54] J. M. Seifert, and P. Resold, “Service Experience with Composite Insulators under Tropical Climatic Conditions in Malaysia,” 2001 CIGRE Symposium, Cairns, 2001. [55] “Coulomb 5.2 Users and Technical Manual,” Integrated Engineering Software, Winnipeg, Manitoba, Canada. 165