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
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
ii
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.
iii
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
To my parents and my beloved wife WANG Yue for all their love.
v
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.
I 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.
I 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.
I 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. I am grateful for her deep love, her joy,
invaluable support and encouragement throughout the last five years.
I 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 ..................................Born – 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 Electrical Insulation and Dielectric
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.
viii
3.
E. P. Casale, W. Que and S. A. Sebo, “Distribution of salt 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. 437440.
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. 441444.
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.
L. Wang, X. Liang, Z. Guan, 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 of Dielectric Materials, June 2000, Vol.
1, 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
cm,” Proceedings of the Electrical Insulation Conference and Electrical
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. Objectives 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 methods ........................................................................ 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
xi
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 nonceramic 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
xii
5.3.
5.4.
5.5.
5.6.
Experiments in the OSU fog chamber...........................................................110
Model setup ..................................................................................................112
Insulator models under rain conditions .........................................................113
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.
6.2.
6.3.
6.4.
Calibration test ..............................................................................................136
Verification test .............................................................................................138
Error analysis.................................................................................................141
Summary .......................................................................................................141
7. Design considerations .............................................................................................142
7.1.
7.2.
7.3.
7.4.
7.5.
7.6.
Model setup ...................................................................................................143
Effects of the distance between the first shed and the end fitting .................144
Effects of the shed spacing............................................................................145
Effects of the shed profile .............................................................................146
Effects of the position of the corona ring......................................................147
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
xiii
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
Hydrophobicity 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 µl 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 Laboratory ............................. 111
5.2
Geometry and dimensions of a four-shed non-ceramic insulator ................ 112
5.3
Case RHC1 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 HC1 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 RHC1-3 ........................ 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 FHC1 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 FHC1, (c) Case FHC2,
(d) Case FHC3 ............................................................................................. 132
5.22
Electric field strength magnitude along the insulation distance at the surface of the
sheath for Cases FHC1-FHC3 ..................................................................... 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 distribution along the insulator measured by 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.1
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
xxiii
CHAPTER 1
INTRODUCTION
1.1
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 flashovers. 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 been 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 been
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
hydrophobicity 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 probability of dry band
formation, which leads to higher flashover voltage.
However, polymer materials have weaker bonds 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 hydrophobicity on the surface of the polymer weather sheds will
be temporarily or permanently lost, which will worsen the pollution performance of nonceramic 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 nonceramic 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 mechanical or electrical failure of nonceramic insulators.
3
•
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
hydrophobicity 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.
4
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
5
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 bounded 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:
6
•
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.
7
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 nonceramic 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 fourshed 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 hydrophobicity
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
hydrophobicity classification (HC) 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 nonceramic 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
B
C
D
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 (FRP) rod. The
FRP 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 E-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 (ECR) 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 (EPDM), ethylene-propylene rubber
(EPR) 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 hydrophobicity 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
hydrophobicity 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 hydrophobicity − Water droplets related corona discharges age
the polymer material around the droplets and reduce the hydrophobicity by
rotation or breaking of the polymer chains. The filaments are joined together
due to the reduction of hydrophobicity, which leads to irregular shape
formations in the wet region.
8. Dry band formation − The areas of the surface with the highest power
dissipation dry first. As dry bands are insulating areas, the surface discharge
activities continue within the dry band region until the band 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 Pockels sensor is one
of the probes, which is used for electric field strength measurement.
Hidaka [11, 12] published comprehensive reviews related to the Pockels sensor
for electric field strength measurement. In his papers, he described the structure of the
Pockels 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 Pockels 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 Pockels 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 (FDM).
18
A comprehensive reference book related to numerical electric field analysis
methods is authored by 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 FDM.
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 be calculated so that their
integrated effect satisfies the boundary conditions. The potential due to unknown surface
charges can be 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 be 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 FDM.
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 by Integrated Engineering Software Company [55]. It
combines the efficiency of the BEM with a powerful user interface. It can be used for the
calculation of the distribution of the static and the quasi-static electric field. It can be 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 been 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 be evaluated.
Flux3D, a fully integrated finite element based CAD package, has been developed
by 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 by 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 be solved by 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 be 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, φ, are maintained.
2. On the dielectric-dielectric boundaries, the condition for the normal
component of the electric flux density, Dn, 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 ε. There may exist a finite, impressed volume source, which
has volume charge density ρv or a surface source, which has surface charge density σs in
24
the space. From Maxwell’s equations, it is known that at every ordinary point in the
medium whose physical properties are continuous:
r
∇×E = 0
(2.1)
r
∇ ⋅ D = ρv
(2.2)
r
It is convenient to introduce an electric polarization vector P defined by
r r
r (ε − ε 0 ) r
P = D − ε0E =
D
ε
(2.3)
where ε0 is the permittivity of vacuum. By invoking Eq. (2.1), Eq. (2.2) can be written as
r 1
r
r
1
∇ ⋅ E = (∇ ⋅ D − ∇ ⋅ P ) = ( ρ v + ρ ev )
ε0
ε0
r ε −ε
ρ ev = −∇ ⋅ P = 0
ρv
ε
where
(2.4)
(2.5)
ρev is called the equivalent volume charge density.
At the interface of dielectric materials, the electric flux density is subject to the
boundary condition
r
r r
n ⋅ ( D1 − D2 ) = σ s
(2.6)
r
where unit vector n points from medium (2) into medium (1). By using Eq. (2.3) in Eq.
(2.6),
r
r r
r r
1
1
n ⋅ ( E1 − E 2 ) = [σ s − n ⋅ ( P1 − P2 )] = (σ s + σ es )
ε0
ε0
(2.7)
r r r
where σ es = − n ⋅ ( P1 − P2 ) is the equivalent surface charge density.
From Eqs. (2.4) and (2.7), it can be concluded that the effects of a dielectric body
in the electric field can be completely accounted for by 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
r
E = −∇φ
(2.8)
Substitution of Eq. (2.8) into Eq. (2.4) yields modified Poisson’s equation
∇ 2φ = −
1
( ρ v + ρ ev )
ε0
(2.9)
Thus, the potential φ 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 φ of the observation point r can be determined by Eq. (2.10):
φ (r ) = ∫
v
ρ v + ρ ev 1
σ + σ es 1
( )dv + ∫ s
( )ds
4πε 0
rv
4πε 0 rs
s
(2.10)
where rs, rv are the radial distances from the point of the source to the observation point;
ρv and σs are the impressed volume and surface charge density of the source,
respectively; ρev and σes are the equivalent volume and surface charge density of the
source, respectively.
Usually the impressed volume and surface charge densities, ρv and σs, are given
in practice. The equivalent volume charge density, ρev, in a homogeneous medium can be
26
obtained from Eq. (2.5). However, the equivalent surface charge density, σes, must be
determined by the specified boundary conditions. The most commonly used boundary
conditions are:
(1) Interface condition:
If σs is the boundary surface charge density on the dielectric-dielectric
boundary, then the boundary condition at any point i on the interface of two
dielectrics can be written as
ε1 (
∂φ
∂φ
)1 − ε 2 ( ) 2 = σ s
∂n
∂n
(2.12)
where ε1, ε2 is the permittivity of dielectric 1, 2 respectively.
(2) Dirichlet condition:
φ i = f (i )
(2.13)
on the surface of a conductor where f(i) is a known function.
(3) Neumann condition:
∂φ
∂n
i
= f (i )
(2.14)
at the interface of a conductor and a dielectric where f(i) is a known function.
By discretizing the boundary into non-separated, non-overlapping subregions,
called “boundary elements”, Eq. (2.10) become:
φ ( p) =
1
4πε
n
 m ρ vi + ρ evi
σ sj + σ esj 
dv
ds 
+
∑ ∫
∑
∫
rip
r jp
j =1 S
 i =1 V

where
•
φ(p) is the point p on the electrode surface with known potential.
27
(2.15)
•
rip and rjp are the radial distances from the point on the boundary of the source to the
point p.
•
ρesi and σesj 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 SF6 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
the BEM to calculate the 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 the electric field and potential distribution along
non-ceramic insulators. The Coulomb electric field analysis software was used. The
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
contaminated conditions
under
wet
and
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 (STRI), which was developed by
Hornfeldt [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 µS/cm). A resistive electric
field distribution may be obtained at and below 85 kV at values of 1.6 mm/min and 50
µS/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 distribution
agreed reasonably with the calculated capacitive electric field distribution 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 distribution 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 [Ω/m] and the thickness of the contaminant layer
[m] are treated as a single parameter, ρs, which is called surface resistivity. They found
that for ρs≥1011 Ω, the field is capacitive, while for ρs≤108 Ω, it is resistive. For
31
intermediate values of ρs, 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 thermal 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 10-4 m. The influence of surface
conductivity was also investigated. When the surface conductivity was in the range of
10-11 to 10-7 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 10-10 to 10-8 S, the electric field was of resistive-capacitive type. When it
exceeded 10-8 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 band 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 2cm×25cm with different sizes of water droplets from 50
mm3 to 900 mm3. 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 nonceramic 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 be 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 be 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 be 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 distribution 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 both healthy and defective non-ceramic insulators along
a longitudinal path about 40mm from 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 by 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 be 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 Steinbigler [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 but 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 nonceramic 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 nonceramic 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 flat 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
CHAPTER 3
FUNDAMENTAL STUDIES
In Chapter 2, a survey was presented on the study of the EFVD along nonceramic insulators and several issues were pointed out. Recently, various issues about 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 be 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 be 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 be 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 by 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 both 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 by 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
D
39
22
25
C
94
Ground end
154
B
16
A
Line end
460
812
Figure 3.1: Simplified geometry and dimensions of the non-ceramic insulators to be
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 by 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
(a)
(b)
(c)
(d)
(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
24
24
22
150
22
26
24
150
20
18
18
12
10
250
300
12
10
350
8
8
6
400
450
500
550
600
650
700
0
0
8
900
950 850 750
6
2
0
-2
-4
0 1 2 3 4 5
(a)
12
300
350
4
14
250
10
8
4
2
0
-2
-4
400
450
500
550
600
650
900 800
0
950850 75
700
0 1 2 3 4 5
(b)
200
16
14
14
24
20
18
200
150
22
20
16
24
22
20
200
150
26
22
20
16
26
6
4
2
0
-2
-4
18
200
18
300
350
400
450
500
550
600
650
0
70
0 00
90 8 0
950 850 75
0 1 2 3 4 5
(c)
14
12
10
8
6
4
2
250
-4
14
12
300
10
350
8
400
450
500
550
600
650
0
-2
200
16
16
250
150
900800
950 50 750
8
700
0 1 2 3 4 5
(d)
6
4
2
0
-2
-4
250
300
350
400
450
500
550
600
650
0
70
900800
950850 750
0 1 2 3 4 5
(e)
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.
Voltage (V)
1000
Insulator with 12 sheds for Case (e)
Insulator with 4 sheds for Case (d)
900
800
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
Electric field strength (kVp/mm)
number of weather sheds (for example, 2) at the each end of the insulator.
0.026
0.024
0.022
0.02
0.018
0.016
0.014
0.012
0.01
0.008
0.006
0.004
0.002
0
Insulator with 12 sheds for Case (e)
Insulator with 4 sheds for Case (d)
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 ´ 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) 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.
26
24
150
26
26
24
24
22
22
20
20
18
200
18
16
14
12
10
8
6
4
2
0
-2
-4
16
250
14
12
300
350
400
450
500
550
600
650
0
70
900800
950850 750
0 1 2 3 4 5
(a) Full insulator
with no conductor
10
8
6
4
2
-4
350
20
18
400
400
16
14
450
12
500
10
550
8
600
6
650
700
750
0
-2
22
350
4
2
800
900
950 850
0 1 2 3 4 5
(b) Full insulator
with conductor
0
-2
-4
450
500
550
600
650
700
750
800
85
0
950900
0 1 2 3 4 5
(c) Simplified insulator
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
distribution 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
Electric field strength (kVp/mm)
line end, but increases the electric field strength near the ground end.
0.026
Insulator with the conductor and grounded supporting structure
Insulator without the conductor and grounded supporting structure
0.024
0.022
0.02
0.018
0.016
0.014
0.012
0.01
0.008
0.006
0.004
0.002
0
0
10
20
30
40
50
60
70
80
90
100
Insulation distance (%)
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.
Electric field strength (kVp/mm)
3.10, which again shows the similarity between the two functions.
0.018
Full insulator with the conductor and grounded supporting structure
Simplified insulator with conductor and grounded supporting structure
0.016
0.014
0.012
0.01
0.008
0.006
0.004
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, θ. The contact angle θ 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
θ
Figure 3.11: Definition of contact angle.
The second method is called the hydrophobicity classification (HC) method,
which has been developed by the Swedish Transmission Research Institute (STRI). The
HC method was introduced by Gubanski and Hartings 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, HC1 to HC7. The criteria for the different classes are
given in Table 3.1.
HC
Description
1
Only discrete droplets are formed. θ≈80°or larger for the majority of droplets.
2
Only discrete droplets are formed. 50° < θ < 80° for the majority of droplets.
3
Only discrete droplets are formed. 20° < θ < 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 < 2cm2. Together they cover < 90% of the test area.
5
Some completely wetted areas > 2cm2, 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 (HC) [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.
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. The 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 µl, the
applied E-field values for corona onset were found between 0.56 and 0.44 kV/mm for
SiR material with 88° contact angle. The applied E-field required for corona onset
56
decreased with increasing water drop size from 10 to 80 µl and remained the same
between 80 to 100 µl.
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 µl, the measured average
corona onset E-field remained between 0.86 and 0.96 kV/mm.
Lopes, Jayaram and Cherney [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 kVrms/cm and 4.2 kVrms/cm
for a single water droplet with volume of 30 and 80 µl, 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 µl.
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 the polymer material. The combination of the high
discharge temperature and the plasma chemistry of the water vapor and air are
responsible for the loss of hydrophobicity. 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 µl 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 µl water droplet
located on a SiR sheet and a PGF (a kind of polymer material) sheet during a half cycle
(between ωt=0 and π) of the AC field.
Figure 3.13: Behavior of 10 µl 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 nonceramic 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 droplet
Pendant droplet
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 flat 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 × 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.
100 V
0.5cm
Z
Y
X
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 (cm)
1
0.5
-1
-5
-4
-3
-2
-1
0
1
2
3
5
10
15
20
25
30
35
40
45
50
55
65
60
-0.5
95
90
85
80
75
70
0
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
-4
-3
-2
-1
0
1
2
3
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)
37
3
37..6
37 .9
37
38.5
0.7
40
39.7
39.4
39.1
38
.8
0.8
38
.2
0.6
-0.2
-0.1
38.5
.8
38
0.3
-0.3
.1
39 4
39.
39.7
40
0.4
0
38
.2
37.
9
37.6
37.3
37
0.5
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
62
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
15
12
9
6
3
0
0.3
0.2
0.1
0
Y (cm) -0.1-0.2
-0.3
-0.3
-0.2
-0.1
0.1
0
0.2
0.3
Electric field strength (V/cm)
Electric field strength (V/cm)
field strength vector or its components at any point on the surface of the water droplet.
33
30
27
24
21
18
15
12
9
6
3
0
0.3
0.2 0.1
Y (cm)
X (cm)
9
6
3
0.1
0
Y (cm) -0.1-0.2
-0.3
-0.3
-0.2
-0.1
(c) Z component
0
0.1
X (cm)
0.2
0.3
Electric field strength (V/cm)
Electric field strength (V/cm)
12
0.2
-0.2
-0.3
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
X (cm)
(b) Y component
(a) X component
0
0.3
0 -0.1
33
30
27
24
21
18
15
12
9
6
3
0
0.3
0.2 0.1
0.2 0.3
0.1
0
0
-0.1
Y (cm) -0.1 -0.2
-0.2
X
(cm)
-0.3 -0.3
(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.
0.5 cm
10 cm
100 V
Z
Y
X
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
47
0.5
40
41
0
39
38
-0.5
-1
-5
3
31 2
-4
-3
37
46
42
36
-2
35
45
44
34
-1
0
1
43
33
2
3
4
32 1
3
5
Y (cm)
Figure 3.21: Equipotential contours and electric field lines for shed region simulation.
Em (V/cm)
15
10
5
0
-5
-4
-3
-2
-1
0
1
2
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)
0.8
0.7
0.6
45 .5 45 .3
45 .1 44 .9
.5
44 .7 4.34
44
.9
44 .1 43
.7
3
4
43 .5
43 .3
0.5
43 .1
42 .9
0.4
0.3
-0.3
42 .7
-0.2
-0.1
42 .5
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
10
8
6
4
2
0
0.3
0.2
0.1
0
Y (cm) -0.1
-0.2
-0.3
-0.3
-0.2
-0.1
0
0.2
0.1
0.3
Electric field strength (V/cm)
Electric field strength (V/cm)
12
12
10
8
6
4
2
0
0.3
0.1
0.2
0.1
Y (cm)
X (cm)
Electric field strength (V/cm)
Electric field strength (V/cm)
0.2
0.1
0
Y (cm) -0.1
-0.2
-0.3
-0.3
-0.2
-0.1
-0.2
-0.3
0.3
0
-0.1 X (cm)
-0.2
-0.3
(b) Y component
(a) X component
30
27
24
21
18
15
12
9
6
3
0
0.3
0
0.2
-0.1
0
0.1
0.2
30
27
24
21
18
15
12
9
6
3
0
0.3
0.3
0.2
0.1
Y (cm) 0-0.1
-0.2
-0.3
X (cm)
(c) Z component
-0.3 -0.2
-0.1
0
0.1
0.2
0.3
X (cm)
(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 be 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 be seen
from Fig. 3.25 that the water droplet with larger contact angle causes more distortion in
68
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.
.5
38
.9
0.8
0.5
0.2
0.3
-0.2
37.3
0.1
0.2
0.3
0.8
40
39.7
39
.4
0.3
0.3
-0.2
-0.1
0
37
36.7
36.4
37.9
0.1
37.6
37.3
38.2
38.5
37
.9
37
.6
37.3
37
36.7
36.4
0.2
38.5
38.8
38.5
39.1
39.7
39.4
36.1
38.2
0.1
39.1
0
38.8
-0.1
0.4
39.4
39.7
40
-0.2
37.9
0.5
.2
38
39.4
39.7
40
.1
39
38
.8
.8
38
.5
38
0.5
.1
39
36.4
36.7
37
37.3
37.6
40
36.1
36.4
36.7
37
37.3
37.6
38.2
37.9
0.7
0.6
0.6
0.3
-0.1
(b) 90 degrees
0.8
0.4
0
37
0.3
(a) 120 degrees
0.7
37.
9
37.6
37
.
37 6
.3
37
36.7
36.4
0.1
38
.2
38.2
0
0.4
.1
39
-0.1
.9
4
39.
39.7
40
38.5
.4
39 .7
39 0
4
-0.2
37
.8
38
39 38.8
.1
38.5
0.5
0.3
38.5
0.6
0.6
0.4
38
.2
37
0.7
0.7
3
37.
.6
37
.9
37
40
39.7
39.4
40
39 .
39 7
39 .4
.1
38
.8
37
38.5
0.8
.2
4
36. .7
36
37 3
.
37 .6
37
38
39.1
38
.8
0.9
0.2
0.3
(d) 30 degrees
(c) 60 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
Maximum electric field
strength, V/cm
120
90
60
30
38.4
32.9
25.9
20.1
Electric field enhancement factor
Table 3.2: The electric field enhancement factors on the surface of the water droplet with
different contact angles.
4
3.8
3.6
3.4
3.2
3
2.8
2.6
2.4
2.2
2
1.8
20
40
60
80
100
120
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 µl. 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
Electric field enhancement factor
more significant than that on the shed region.
4.5
4
3.5
3
2.5
2
1
2
3
4
5
6
7
8
9
Diameter of water droplet (mm)
Electric field enhancement factor
Figure 3.27: The electric field enhancement factor for a water droplet of different
diameter on the sheath region.
3
2.9
2.8
2.7
2.6
2.5
1
2
3
4
5
6
7
8
9
Diameter of 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)
1
.2
.6
0.8
36.2
36.6
37
4
37. 8
.
37
.2
38
.6
38
39
.4
39
.8
40
39
42.6
42.2
41.8
41.4
41
Z (cm)
40
0.9
0.9
0.8
0.7
0.6
0.6
40.2
0.7
-0.3
-0.2
-0.1
0.4
39
38
.6
38
37..2
8
37.4
.2
.8
39
-0.4
3
0
0.1
0.2
0.3
6
43.
43.2
46.4
46
45.6
45.2
44.8
44.4
44
43.6
43.2
43.2
0.5
9.4
40
0.3
-0.5
41
.4
41
.8
41
2
42.
42.6 43
0.4
40.6
0.5
46.4
46
45.6
45.2
44.8
44.4
44
43.6
46.4
46
45.6
45.2
44.8
44.4
44
0.4
0.3
-0.5
0.5
Z (cm)
42.8
42.8
42.8
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
Y (cm)
(b) Merged water droplet on the shed
(a) Tilted water droplet on the sheath
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
Electric field enhancement factor
between the two water droplets.
5.6
5.4
5.2
5
4.8
4.6
4.4
1
2
3
4
5
6
7
8
9
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 µs/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 µs/cm to 2500 µs/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 nonceramic 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 0.50.7 kVrms/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 nonceramic 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 nonceramic 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 foursubconductor 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 fullscale 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 foursubconductor 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.
5.8
2.2
13
16.3
Units: cm
9
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.
4.9
6.35
3
3.8
Units: cm
30
43
(b) Ground end corona ring
(a) Line 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.
(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 Vstring yoke plate are shown in Fig. 4.4. The thickness of the yoke plate for foursubconductor 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 subconductor diameter for four-subconductor
45.7
7 12.4
bundles is 2.96 cm. The number of the elements used for each subconductor is 560.
45.7
(b) Element configuration
(a) Dimensions (cm)
Figure 4.4: Dimensions and element configuration of the yoke plate for foursubconductor bundles.
The dimensions and element configuration of the six-subconductor V-string yoke
plate is shown in Fig. 4.5. The thickness of the yoke plate is 2.54 cm. The subconductor
33
12.6
33
35.2
diameter for the six-subconductor bundle is 2.7 cm.
38.1
19
(b) Element configuration
(a) Dimensions (cm)
Figure 4.5: Dimensions and element configuration of the yoke plate for six-subconductor
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
518
945
613
790
1250
2035
1441
50°
Figure 4.6: Geometry and dimensions of 765 kV power line tower with foursubconductor bundles.
The two ground wires are ignored in the calculations. The ground plane is
modeled with a 50 m × 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 × 50 m large plane with zero potential. The number of the elements
594
183
used for the tower is 600 and for the ground plane, it is 225.
Units: cm
534
50°
1408
3200
3901
716
Figure 4.7: Geometry and dimensions of a 765 kV power line tower with sixsubconductor 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 nonceramic 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:
•
Vleft = - 0.5× Vcenter= - 0.5*624.6= - 312.3 kV,
•
Vcenter= 765 × 2 / 3 =624.6 kV (i.e., maximum value of the line-to-ground voltage)
•
Vright= - 0.5× 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
436
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
2950
3250
2925
10
3200
5
15
3150
2900
20
3100
25
2875
95
30
3050
35
3000
90
85
2850
80
75
70
40
90 80
85
75
2800
60
65
95
2800
70
2850
2825
50 5
5 0
6
2900
0
50
100
65
45
2950
150
200
250
300
350
0
25
50
75
100
400
(a) Full view of one of the insulator
(Simplified model)
(b) Enlarged area around the line end
Figure 4.11: Per cent equipotential contours for a 765 kV tower with four-subconductor
bundles under three phase energization.
88
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.
Voltage (kVmax)
700
600
500
400
300
200
100
0
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
Electric field strength magnitude (kVmax/mm)
region.
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
10
20
30
40
50
60
70
80
90
100
Insulation distance (%)
Electric field strength magnitude (kVmax/mm)
Figure 4.13: Electric field strength magnitude along the per cent insulation distance at the
surface of the insulator sheath with four-subconductor bundles.
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
2
4
6
8
10
12
Insulation distance (%)
Figure 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
The electric field strength distribution along the insulation distance near the
Electric field strength magnitude (kVmax/mm)
ground end fitting is also shown in Fig. 4.15.
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
88
90
92
94
96
98
100
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.
2915
2910
i
h
2905
e
f
c
2900
b
a
g
d
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
Electric field strength magnitude (kVmax/mm)
insulator near the line-end fitting is shown in Fig. 4.17.
1.8
1.7
1.6
a
1.5
1.4
1.3
c
b
1.2
e
h
f
i
1.1
1
0.9
g
0.8
d
0.7
0.6
0.5
0.4
0.3
0.2
0
5
10
15
20
25
30
35
40
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
3600
20
3550
10
3350
5
3325
25
3500
30
3300
35
3450
40
3400
3275
45
50
3350
55
3300
95
3250
85
80
5
7
80
75
70
70
3200
95
3225
65
90
85
60
90
3250
3150
15
0
3200
100
200
300
0
25
50
75
100
400
(a) Full view of one of the insulators
(Simplified model)
(b) Enlarged area around the line end
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
Voltage (kVmax)
600
500
400
300
200
100
0
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
Electric field strength magnitude (kVmax/mm)
strength at the triple junction point is 1.162 kVmax/mm.
1.4
1.2
Figure 16: Electric field strength magnitude along the insulation distance at the surface of
1
the insulator
sheath with a six-subconductor bundle.
0.8
The electric field strength distribution near the line end fitting is shown in Fig. 17.
0.6
0.4
0.2
0
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 distributions along the insulation
Electric field strength magnitude (kVmax/mm)
distance near the line and ground end fittings are shown in Figs. 4.21 and 4.22.
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
2
4
6
8
10
12
Insulation distance (%)
Electric field strength magnitude (kVmax/mm)
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.
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
88
90
92
94
96
98
100
Insulation distance (%)
Figure 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
4.4
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-subconductor 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
Case F
Case S
Voltage (kVmax)
600
500
400
300
200
100
0
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
Electric field strength magnitude (kVmax/mm)
Figs. 4.24 and 4.25, respectively.
1.6
Case F
Case S
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
2
4
6
8
10
12
Insulation distance (%)
Electric field strength magnitude (kVmax/mm)
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.
0.8
Case F
Case S
0.6
0.4
0.2
0
88
90
92
94
96
98
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 kVmax/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 the 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: Vleft = - 312.3 kV, Vcenter=624.6 kV,Vright= - 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
3300
3250
3250
10
3200
10
15
5
20
3150
3150
20
3100
30
30
3050
35
35
3000
45
70
95
100
150
200
250
300
350
2800
400
0
75
50
2950
2950
2925
2925
2900
2900
100
150
200
250
300
350
400
2875
90
85
80
2850
75
65
65
2825
75
70
70
2850
90
95
95
2875
85
50
2850
80
0
55
60
65
2900
85 90
80
70
90 80
85
75
2850
50
65
95
45
2950
50 5
5 0
6
2900
40
3000
40
2950
2800
25
3100
25
3050
5
3200
15
60
60
2825
2800
0
25
50
75
2800
100
0
25
50
75
100
(b) Three phase
(a) Single 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
Voltage (kVmax)
700
Three phase energization
Single phase energization
600
500
400
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
Electric field strength magnitude (kVmax/mm)
1.6
Three phase energization
Single phase energization
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
2
4
6
8
10
12
Insulation distance (%)
Electric field strength magnitude (kVmax/mm)
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
1.4
1.2
Three phase energization
Single phase energization
1
0.8
0.6
0.4
0.2
0
88
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
kVmax/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. However, naturally it influences the voltage
103
distribution near the ground end significantly. The grounded tower body reduces the
electric field strength near the ground end of the insulator.
Distance units: cm
3300
3300
3250
3250
15
20
3200
25
3150
10
5
10
15
3200
20
3150
30
25
3100
3100
35
30
40
3050
3050
35
45
3000
55
50
2850
65
2850
50
95
75
0
55
60
65
2900
100
150
200
250
300
350
2800
400
(a) Without tower
0
85 90
80
70
95
85
80
70
90
45
2950
60
2900
40
3000
50
2950
2800
5
75
50
100
150
200
250
300
350
400
(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 body is an important part of the calculation
model. The tower body 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 foursubconductor bundles are shown in Fig. 4.31.
Distance units: cm
3300
3300
3250
3250
3200
3200
10
15
20
3150
3150
5
25
3100
3100
30
10
3050
3050
35
15
3000
20
25
30
3
2950 4540 5
50
40
3000
45
2950
50
2900
2850
2850
55
60
65
95
55
60
95
65
70
0
50
100
150
200
250
300
350
400
(a) Without four-subconductor bundles
2800
0
85 90
80
70
9
2900 0
2800
5
75
50
100
150
200
250
300
350
400
(b) With four-subconductor bundles
Figure 4.31: Equipotential contours for the 765 kV tower without and with the foursubconductor bundles.
105
It can be seen from Fig.4.31 that there are “shielding” effects of foursubconductor bundles. If the four-subconductor bundles are ignored in the calculation
model, the EFVD along the insulator is significantly different from the EFVD along the
insulator with four-subconductor 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 sixsubconductor 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 FIELD 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
hydrophobicity properties of the weather sheds will temporarily or permanently lost
during its service life. That might worsen the wet and contamination performance of nonceramic 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 kVrms/mm [51], water
droplet corona discharges may occur. The discharges usually occur between water
107
droplets and destroy the hydrophobicity 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 been 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 nonceramic 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 hydrophobicity
classification method developed by STRI to characterize the hydrophobicity of the
108
insulator surface. This method is also adopted in this research work to describe the
hydrophobicity of the surface of non-ceramic insulators.
Research studies show that the pollution performance of non-ceramic insulators is
jointly determined by the surface hydrophobicity 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 hydrophobicity distribution along the surface of nonceramic 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 hydrophobicity of HC 2~4,
while the bottom surface hydrophobicity 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 hydrophobicity 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 9.5m3. 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 by a
pump.
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 hydrophobicity 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 be 250 µs/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 1kVp.
Ground end
15
48
2.2
Units: cm
4
3
2
1
Z
Y
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 HC1 to HC6 are studied. They are named as Case RHC1 – Case
RHC6.
For Case RHC1, 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 RHC4, 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. About 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
be able 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.
(b) Case RHC1 rain calculation model.
(a) Case RHC1 photo.
Figure 5.3: Case RHC1 water droplet distribution on the surface of a non-ceramic
insulator and the calculation model used for study.
Voltage (V)
Y (cm)
800
5
780
760
740
640
650
4
720
660
700
680
67
0
68
0
690
3
660
640
2
1
X (cm)
790
2
1
3
4
5
0
1
2
3
780
77
0
5
4
0
Y (cm)
0
1
2
0 20 30
0 71 7 7 740 0
70
75
0
76
620
0
3
4
5
X (cm)
(a) Case RHC1 voltage distribution on
the top surface of the first shed.
(b) Case RHC1equipotential contours
on the top surface of the first shed.
Figure 5.4: Voltage distribution and equipotential contours on the surface of the first shed
on a wet non-ceramic insulator with HC1 hydrophobicity.
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)
5
780
760
740
640
65
0
4
720
660
670
700
3
680
680
690
660
0
70
640
2
620
0
760
770
1
2
X (cm)
72
0
73
0
740
1
71
0
75
0
3
4
5
0
1
2
3
4
5
Y (cm)
0
0
1
2
3
4
5
X (cm)
(a) Case RHC2 voltage distribution
on the top surface of the first shed.
(b) Case RHC2 equipotential contours
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
(a) Case RHC3 photo.
(b) Case RHC3 rain calculation model.
Figure 5.7: Case RHC3 water droplet distribution on the surface of a non-ceramic
insulator and the calculation model used for the study.
Y (cm)
Voltage (V)
5
6 10
4
6 20
6 30
6 60
3
64
0
65
0
66
0
67
0
2
68
0 90
6
0
7 0 10
7
1
73
X (cm)
0
0
1
72
0
2
0
3
4
5
X (cm)
Y (cm)
(b) Case RHC3 equipotential contours
on the top surface of the first shed.
(a) Case RHC3 voltage distribution on
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
5
720
700
4
680
63
0
64
0
660
3
640
65
0
620
2
0
1
2
3
4
5
Y (cm)
0
0
1
2
3
630
5
650
4
690
680
720
700
0
71
670
1
3
710
720 0
73
2
X (cm)
700
1
670
680
690
66
0
0
4
5
X (cm)
(a) Case RHC4 voltage distribution
on the top surface of the first shed.
(b) Case RHC4 equipotential contours
on the top surface of 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 HC4 hydrophobicity.
118
(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)
5
700
580
680
4
590
610
600
660
650
640
2
1
0
4
5
0
1
2
3
5
4
Y (cm)
0
1
2
580
670
3
630
590
600
610
620
640
66
0
2
650
X (cm)
66
0
67
0
600
560
0
1
0
60
600
580
59
0
630
3
620
58
0
620
640
3
4
5
X (cm)
(b) Case RHC5 equipotential contours
on the top surface of the first shed.
(a) Case RHC5 voltage distribution
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
(b) Case RHC6 rain calculation model.
(a) Case RHC6 photo.
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
680
4
654
660
3
640
652
65
2
0
650
X (cm)
650
1
3
4
5
0
1
2
3
4
5
0
654
1
2
2
652
620
65
4
0
1
2
3
4
5
X (cm)
Y (cm)
(a) Case RHC6 voltage distribution
on the top surface of the first shed.
(b) Case RHC6 equipotential contours
on the top surface of 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 RHC5). 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 RCH3 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.
Dry Case
(kV/mm)
Triple junction point
Top of the first shed
Under the first shed
0.028
0.017
0.026
Case
RHC1
E. F.
0.9
2.4
0.9
Case
RHC2
E. F.
1.0
2.3
1.0
Case
RHC3
E. F.
1.2
2.1
1.1
Case
RHC4
E. F.
1.4
3.7
1.2
Case
RHC5
E. F.
1.8
4
1.6
Case
RHC6
E. F.
1.7
1.4
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 RHC1-6, 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
9
8
350
400
7
6
450
500
550
600
650
5
4
3
2
0
300
9
8
350
8
7
400
7
6
450
6
3
2
1
95
0
85 90
0 0
80
0
0
75
-3
0
1 2
3 4
-3
5
-4
0
(a) Dry Case
1
2
3
13
11
-3
4
5
-4
0
6
4
3
2
3
2
2
3
0
0
70
4
-1
5
9
250
8
300
-2
-3
950
0
1
2
3
4
3
2
1
-2
-3
(e) Case RCH4
-4
4
5
(d) Case RCH3
50
12
100
11
150
200
250
300
350
6
400
450
500
550
600
5
4
3
2
1
0
-1
5
2 3
7
400
450
500
550
600
650
5
4
1
8
0
-1
0
9
350
6
0
75
0
0
0
9 80
850
-4
0
75
10
7
0
0
85
13
10
0
-3
14
200
11
70
-2
15
150
12
1
-4
4
50
100
13
450
500
550
600
650
5
400
450
500
550
600
650
5
(c) Case RCH2
14
350
400
7
1
15
300
8
350
6
800
900
0
950850 75
-2
250
9
7
1
-1
200
10
400
0
150
12
300
1
50
100
14
8
450
500
550
600
650
(b) Case RCH1
15
350
2
900
850
950
-2
200
250
3
800
150
11
9
4
750
0
12
10
300
5
500
550
600
650
700
-1
-2
-4
9
4
-1
250
10
5
70
0
1
200
11
250
10
300
12
100
70
0
250
10
200
13
0
11
100
150
65 0
12
200
11
13
0
12
150
90
0
80
13
150
50
14
-1
70
13
15
50
14
0
1
85
2
4
5
(f) Case RCH5
-4
70
0
95 0 0 5 0
85 7
-3
0
3
0 0
90 80
-2
0 9
00
80
0
0
100
15
50
100
14
75
14
95
0
15
50
95
15
0
1
2
3
4
(g) Case RCH6
Figure 5.15: Equipotential contours for (a) dry Case (b)-(g) Cases RHC1-RHC6.
123
5
Fig. 5.15 (b) shows the voltage distribution for Case RHC1. 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
RHC1-3.
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 RHC1-3.
Fig. 5.15 (g) shows the voltage distribution 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 HC1-2, the EFVD
along the insulator under rain condition is nearly the same as along the dry and clean
insulator.
125
Electric field strength magnitude ( kVmax/mm)
0.035
Dry case
Case RHC1
Case RHC2
Case RHC3
0.03
0.025
0.02
0.015
0.01
0.005
0
0
10
20
30
40
50
60
70
80
90
100
Insulation distance (%)
Electric field strength magnitude ( kVmax/mm)
Figure 5.16: Electric field strength magnitude along the insulation distance at the surface
of the sheath for Dry Case and Cases RHC1-3.
0.04
Dry case
Case RHC4
Case RHC5
Case RHC6
0.035
0.03
0.025
0.02
0.015
0.01
0.005
0
0
10
20
30
40
50
60
70
80
90
100
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 nonceramic 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 FHC1, Case
FHC2, and Case FHC3.
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.
Top of the shed
Under the shed
Sheath region
Case FHC1
Case FHC2
Case HC3
HC1
HC1
No water
HC2
HC2
HC1
HC3
HC3
HC1
Table 5.3: Hydrophobicity of polymer insulator in different regions.
Case FHC1 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.
(b) Case FHC1 with HC1 underside
surface and dry sheath.
(a) Case FHC1 with HC1 top surface.
(C) Case FHC1 calculation model.
Figure 5.18: Case FHC1 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.
(a) Case FHC2 with HC2 top surface.
(b) Case FHC2 with HC2 underside surface
and HC1 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.
(b) Case FHC3 with HC3 underside surface
and HC 1 sheath surface.
(a) Case FHC3 with HC3 top surface.
(C) Case FHC3 calculation model.
Figure 5.20: Case FHC3 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 FHC1. 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 FHC2. 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.
250
10
350
400
7
6
5
4
3
2
1
0
-1
-3
0
1 2
11
300
9
8
350
8
400
450
7
400
450
7
500
550
600
650
5
0
70
1
3
2
6
3
-3
-4
-1
0 1
2 3
3
2
1
0
90000
950 8
850750
-2
-3
4 5
-4
(b) Case FHC1
500
550
600
650
4
1
-1
-2
5
650
2
300
350
400
450
6
500
550
600
4
0
70
0
100
150
200
250
10
9
350
4
(a) Dry case
250
10
7
5
5
11
8
450
500
550
600
650
3 4
200
12
300
6
0
0 80
90
0
0 50 75
95 8
-2
250
9
300
8
200
13
0
9
11
150
12
0
1
2
-1
9 00
-2
0 50
85 7
3
70
0
70
10
12
200
50
14
0
11
13
15
0
80
12
150
50
100
4
0
13
150
14
90
100
13
15
50
100
85
14
0
14
-4
15
50
95
15
-3
5
(c) Case FHC2
-4
0
9 50
1 2
3
0
800
75
0
4
5
(d) Case FHC3
Figure 5.21: Equipotential contours for (a) Dry case, (b) Case FHC1, (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.
Triple junction point
Top of the first shed
Under the first shed
Sheath region
Dry Case
(kV/mm)
0.028
0.017
0.026
0.013
Case FHC1
E. F.
0.9
2.4
1.9
1.0
Case FHC2
E. F.
2.4
2.1
2.0
3.6
Case FHC3
E. F.
2.4
3.2
2.1
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.
Electric field strength magnitude ( kVmax/mm)
0.03
0.027
Dry case
Case FHC1
Case FHC2
Case FHC3
0.024
0.021
0.018
0.015
0.012
0.009
0.006
0.003
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 FHC1 and FHC2. 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
HC1-6 surface conditions and three insulator models under fog conditions with HC1-3
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 .
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
(kVrms)
Insulator tester
reading, T
1.6
4
6
8
10
12
14
16
18
20
14
40
60
81
104
122
145
164
187
208
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 Vrms = 0.0952 ´ T + 0.255.
Applied voltage (kVrms)
25
20
15
10
5
0
0
50
100
150
200
250
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.
Figure 6.3 Calculation model for the sphere gap.
In this calculation model, the upper sphere was energized at 1 kVrms and the lower
one was grounded. The ground plane was modeled as a 10 m ´ 10 m large plane with
zero potential. The calculated electric field strength in the middle of the sphere gap was 4
kVrms/m.
Therefore, the relationship between the electric field strength magnitude and the
insulator tester readings is:
E = 4 ´ (0.0952 ´ T + 0.255) = 0.3808 ´ 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.
82
59
225
Units: cm
23
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.
Electric field strength (kVrms/m)
35
30
25
20
15
10
5
90
100
110
120
130
140
150
Distance above the ground (cm)
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 ´ 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 be 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. The 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
1kVp.
Units: cm
13.7 2.2
48
Ground end
D
9.4
Line 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 3cm. The electric field strength
distribution along the per cent insulation distance at the surface of the insulator sheath is
Electric field strength magnitude (kVmax/mm)
shown in Fig. 7.2. The triple junction point is at 0% of the insulation distance.
0.025
D=1cm
D=2cm
D=3cm
0.02
0.015
0.01
0.005
0
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
Electric field strength magnitude (kVmax/mm)
these two cases.
0.03
Four sheds
Three sheds
0.025
0.02
0.015
0.01
0.005
0
0
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.
R 0.5 cm
R 2 cm
(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
Electric field strength magnitude (kVmax/mm)
0.03
0.5 cm radius
2 cm radius
0.025
0.02
0.015
0.01
0.005
0
0
10
20
30
40
50
60
70
80
90
100
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 by 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 distribution 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
Units: cm
6.3
Dc
from 3.8 cm to 10.8 cm.
43
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
Electric field strength magnitude (kVmax/mm)
line end fitting is shown in Fig. 7.8.
1.6
1.55
1.5
1.45
1.4
1.35
1.3
1.25
1.2
1.15
3
4
5
6
7
8
9
10
11
Distance Dc between the corona ring and the end fittings (cm)
Electric field strength magnitude (kVmax/mm)
Figure 7.7: Maximum electric field magnitude at the triple junction point as a function of
the corona ring position.
1.6
Dc=3.8 cm
Dc=5.8 cm
Dc=10.8 cm
1.4
1.2
1
0.8
0.6
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 nonceramic 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 the 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 have 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, the 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:
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 nonceramic 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 GHz 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.1 shows the number of elements used, the symmetry and periodicity
conditions used for the study, and the computation time.
Models
Figure 3.2 (e)
Figure 4.8
Figure 5.20
Elements
used
8811
19645
12956
Symmetry
plane
XZ, YZ
XZ
Periodicity
(degrees)
10
Computation
time (hours)
2
9
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 cases 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.1. The upper electrode is
grounded and the lower electrode is energized. The applied voltage is 1 kV.
0 kV
13.8 cm
Z
Y
X
1 kV
100 cm
Figure B.1: 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
5.6
5.5
B
602
5.4
5.3
605
5.2
608
611
5.1
5
620
617
614
599
596
590
593
C
A
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
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