ELECTRIC FIELD AND POTENTIAL
AROUND WATER DROP ON OUTDOOR INSULATOR
1)
2)
Waluyo
1)
, Parouli M. Pakpahan
2)
, Suwarno
2)
Doctoral Student, School of Electrical Engineering and Informatics, ITB
Academic Staff, School of Electrical Engineering and Informatics, ITB
Jalan Ganesha No. 10 Bandung 40132 Indonesia e-mail : waluyo@students.itb.ac.id
Abstrak
Makalah ini memaparkan hasil komputasi distribusi medan dan potensial listrik karena adanya suatu tetesan air pada permukaan isolator pasangan luar secara numerik berbasis metoda elemen hingga. Parameter yang digunakan dalam analisis ini adalah bentuk, ukuran dan sudut kontak tetesan air tersebut.
Hasil komputasi menunjukkan bahwa medan listrik pada sekitar tetesan air bulat lonjong vertical akan meningkat secara signifikan sebesar 15.39 V/m bilamana sumbu vertical bertambah, dan pada bentuk lingkaran sebesar 1.95 V/m terhadap pertambahan jari-jari lingkaran. Sementara medan listrik akibat tetesan air bulat lonjong horisontal meningkat sebesar 1.37 V/m dengan bertambahnya sumbu horisontal persatuan skala dan 0.397 V/m setiap derajad kenaikan sudut kontak. Arah medan listrik cenderung melewati tetesan air tersebut. Pada sisi lain, distribusí ekuipotensial listrik pada umumnya cenderung menghindari tetesan air, sebagai akibat dari penumpukan garis-garis ekuipotensial pada perbatasan, air-udara atau air-isolator.
Kata kunci: medan listrik, permukaan isolator, potensial listrik, sudut kontak, tetesan air
1. Introduction
Overhead transmission and distribution lines are widely used in present power systems to transmit power from generation stations to distribution points. Their proper function depends to a large extent on the insulation with the supporting structures [1]. The performance of insulators is influenced by their environments considerably. One of among environmental parameters is existence of water drop on their surfaces.
In fact, water drops on insulator surface of may cause corona because they can enhance the electric field nearby. Water drop coronas play an important negative role in the long term performance of insulators [2,3,4].
Hydrophobic condition is a most useful properly for outdoor insulation, it prevents the formation of water films between the ends of insulator [5,6]. Control of the electric field within and around high voltage equipment, such as insulators, is very important aspect of the design of them. One possible consequence of high electric field is premature aging of insulation [7, 8]. A knowledge of the field distribution around insulators is very important to determine the electric stresses occurring on the insulator surface [9].
The hydrophobic condition is usually evaluated by using the measurements of the contact angle between water drops and the surface. Past experience has shown that hydrophobic condition can effectively be evaluated by means of the receding angle, but the applicability of such measurements in the field is practically reduced [1]. It is difficult to understand how much the electric field and potential values on water drop vicinities experimentally. To approach this real condition, it is necessary to make simulations to express them on water drop vicinities. The well known method of computation for electric field and potential values on every point is finite element method (FEM).
Finite element method was presented in 1960, and firstly applied in electrical engineering in 1965. Now, FEM has been widely used in electrical engineering as a main numerical
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computation method for the quantity analysis and optimum design of electromagnetic fields engineering problems [10].
In these computations, it is used the software based on finite element method. It is a powerful interactive environment for modeling and solving scientific and engineering problems based on partial differential equations (PDEs). Indeed, it can be built many useful models by defining the participating physical quantities rather than defining the equations that describe them. The software runs the method in conjunction with adaptive meshing and error control as well as with a variety of numerical solvers [11].
High voltage apparatus are involved in applications of electrostatics mode. The
“statics” implies that the time rate of change is slow, and the wavelengths are very large compared to the size of the domain of interest. In electrostatics, the scalar potential V is related to the electric field E by
E
= − ∇
V (1) and, using one of Maxwell’s equations,
.
D
(2) and the relationship
D
=
0
r
E
(3) where polarization is assumed as zero. It is arrived at the equation
− ∇ .
(
o
.
r
∇
V
)
= − ∇ .
(
∇
V
)
=
(4) where this is called Poisson ’s equation, ε is the coefficient of dielectricity and ρ is the space charge density [11, 12, 13].
Using the electrostatics application mode, it can be solved electrostatic problems modeled by the equation above. The boundary conditions for electrostatic problems can be of Dirichlet or Neumann type. For Dirichlet conditions, the electrostatic potential V is specified on the boundaries, and for Neumann ones, the surface charge n.D is specified on the boundaries [11,12].
This manuscript gives the results of the computations numerically on electric field and potential distributions with the basis of FEM, on the outdoor insulator due to the various water drop conditions. The parameter of various water drop conditions are the radii of hemisphere, vertical and horizontal elliptical water drops, and its contact angles.
2. Simulation Method
Firstly, it was drawn the geometry of insulator. In the insulator drawing, it was necessary to avoid an act of sharpening, although on a bend. It was also drawn a conductor, in this particular case, it was in a circle form, and a ground. Furthermore, it was drawn the water drop, which the form, size and position were varied. The basic shapes of water drop were parts of circle, vertical and horizontal elliptical forms. The final step in this drawing, it was drawn the domain of solution thoroughly, as indicated on Figure 1.
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Figure 1. The drawn geometrical domain of solution
Afterwards, it was done ‘composite object’, a combination of some objects or component correctly on above figure. In this case, such combination was ‘CO1+R1+E2-(E1+CO2)’, where the conductor and ground were as substracter. The composite result of that combination is shown on Figure 2.
Figure 2. The composite result of geometrical domain
After that, it was determined the boundary conditions,
Dirichlet
and
Neumann
. In this case, the conductor was as Dirichlet boundary condition, its value was 11500 Volt, and the ground was zero. Whereas top-bottom-left-right rectangular borders were acted as zero values of
Neumann
boundary conditions.
Furthermore, it was done entering the medium parameters of partial differential equation, air, insulating material and water, as their permitivity values. The relative permitivities were 1.00059, 6 and 81 for air, porcelain insulating material and water drop respectively. Then, such quantities were multiplied by 8.854.10
-12 as vacuum permitivity
ε o
[10,11,12,14]. Whereas the charge densities were assumed as zeroes. The geometrical domain of solution on PDE mode is shown on Figure 3.
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Figure 3. The geometrical domain of solution on the PDE mode
Further step was meshing, that was discretization of domain in elements. This step was the running of simulation, so that it was as the success key in the process of solution domain. The meshing result is shown on Figure 4, where, in this case, it was obtained
21272 nodes and 42260 triangles of element.
Figure 4. The geometrical domain of solution after meshing
3. Simulation Results and Discussion
3.1. Hemisphere Water Drop as Radius Function
Figure 5 shows the distribution of electric equifield on two dimension of medium voltage insulator. On first shed of left side from the top, there is a hemisphere water drop with the radius of 5 in drawing scale unit.
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Figure 5. The electric field distribution and equifield contour lines on the outdoor insulator with 5 scaled radius water drop
The light colour represents the electric field in low values, and vice versa for the dark one. The value of electric field rise as the darkness of colour increase, as the colour scale shown on the right side of the figure. Around the conductor, i.e. the top part of insulator, the colour is very dark. Thus, the electric field values are very high. Around such conductor, these electric fields are about 4500 V/m.
In this case, the maximum value of electric field computation was 4570 V/m, i.e. accurred on the bottom part of conductor surface, and the minimum one was 1.05 V/m, i.e. occurred on the bottom of grounding part. It is clear, based on the colour, generally the closer to the conductor, the higher the electric field.
Nevertheless, on an insulator surface, there are many indentations. Every indentation will enhance local electric field, rather than those other parts. These phenomena are also occurred if there is a water drop. On the water drop vicinity of such figure, it is occurred a local electric field enhancement. On such condition, it is occurred the maximum electric field as 80.3 V/m on the water drop vicinity, on the side near the conductor. The local electric field on the water drop vicinity rise as the radius of water drop increases. Besides colour representation, it is presented the electric field distribution on equifield contour lines. On that figure, there are as many as 300 contour lines. It is shown that the densest contour lines are occurred around the conductor. This means that the electric field gradients on that part are the highest than those other parts. The second parts those encounter conciseness of electric field contour are the indentation of insulator surface and water drop, as shown on such figure.
On Figure 6, it is shown the maximum electric field on water drop vicinity as function its radius. From both end points, it is obtained the slope of curve as 1.95 V/m as per radius increase. This enhancement of electric field is dominated by propinguity to the conductor rather than caused by the sharpness of indentation on the water drop. Indeed, such propinguity is caused by the radius of water drop.
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80
75
70
65
90
85
60
0 1 2 3 4 5 6 7 8 9 10 11
WATER DROP RADIUS (SCALE UNIT)
Figure 6. The electric field maximum on the hemisphere water drop vicinity as function of its radius
Figure 7 shows the distribution of electric field direction. The electric field directional lines originate on the conductor surface, and it will end on the grounding part.
On this figure, there are 100 electric directional lines. The existence of water drop will modify the electric field directional contours. Such water drop tends to attract the directional contours, i.e. the contours tend to approach, even to pass, it. The bigger the water drop, the stronger it attract the electric field directional contours.
Figure 7 The electric field directional distribution on the outdoor insulator with 5 scaled radius of water drop
Whereas Figure 8 shows distribution electric potential on the outdoor insulator with 5 scaled radius of water drop. The electric potential will be the highest on the conductor surface, 11500 Volt, and it will be lowest on the ground, as zero. On this figure, there are 100 equipotential contour lines. On the borders between at least two different materials, such as air-insulating material or air-water, the equipotential contour lines will be modified. It is shown, that on the water drop vicinity the equipotential contour lines tend to avoid the water drop, because such water dielectric constant is higher than other materials. Consequently, it is occurred an accumulation of equipotential contour lines on the water drop vicinity. Furthermore, the gradient of electric potential will be higher, of course, the electric field will be higher too than those other places around it. The bigger the water drop, the more the accumulation of equipotential contour lines.
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Figure 8. The electric potential distribution on the outdoor insulator with 5 scaled radius of water drop
3.2. Elliptical Water Drop as Horizontal Radius Function
Figure 9 shows the distribution of electric equifield on two dimension of medium voltage insulator. On first shed of left side from the top, there is a part of horizontal elliptical form of water drop with the radius of 8 x 2 in drawing scale unit. The 8 is horizontal radius and the 2 is vertical radius of elliptical form.
Figure 9. The electric field distribution and equifield contour lines on the outdoor insulator with 8 x 2 scaled radius of horizontal elliptical water drop
As the previous, the light colour represents the electric field in low values, and vice versa for the dark colour. The value of electric field rise as the darkness of colour increase.
Around the conductor, on the top part of insulator, the colour is very dark. Thus, the electric field values are very high. Around such conductor, these electric fields are about
4500 V/m.
Otherwise, the least value of electric field approaches to zero. In this particular case, the minimum value of electric field computation result is 0.63 V/m, occurred on the bottom of the grounding part of insulator. The maximum value of electric field computation was 4570 V/m, occurred on the bottom part of conductor surface. It is clear, based on the colour, generally the closer to the conductor, the higher the electric field.
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Nevertheless, on an insulator surface, there are many indentations. Every indentation will enhance local electric field, rather than those other parts. These phenomena are also occurred if there is a water drop. On the water drop vicinity, it is occurred a local electric field enhancement. On such condition, its local maximum electric field is 64.3 V/m on the water drop vicinity. The local electric field on the water drop vicinity rise as the horizontal radius of water drop increases. Besides colour representation, it is presented the electric field distribution on equifield contour lines. On above figure, there are as many as 300 contour lines. It is shown that the densest contour lines are occurred around the conductor. This means that the electric field gradients on that place are the highest than those other places. The second places those encounter conciseness of electric field contour are the indentation of insulator surface and water drop.
On Figure 10, it is shown the maximum electric field on water drop vicinity as function its horizontal radius. From both end points, it is obtained the slope of curve as
1.37 V/m as per horizontal radius increase. This is less than the former. This local enhancement of electric field is dominated by the sharpness of indentation on the water drop rather than the propinquity to the conductor. Indeed, such sharpness is caused by the increment of water drop horizontal axis.
70
60
50
40
30
20
10
0
0 1 2 3 4 5 6 7 8 9 10 11
LENGTH OF RADIUS HORIZONTAL AXIS (SCALE UNIT)
Figure 10. The maximum local electric field on the water drop vicinity as function of horizontal radius of elliptical water drop
Figure 11 shows the distribution of electric field direction, as corresponding to
Figure 9. The electric field directional lines originate on the conductor surface, and it will end on the grounding part. On this figure, there are 100 electric directional lines. As previous one, the existence of water drop will modify the electric field directional contours. The water drop tends to attract the directional contours, the contours tend to pass it. The bigger the horizontal axis of water drop, the stronger it attract the electric field directional contours. However, its attraction is weaker than that previous section.
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Figure 11. The electric field directional distribution on the outdoor insulator with 8 x 2 scaled radius horizontal-elliptical form of water drop
Whereas Figure 12 shows distribution electric potential on the outdoor insulator with 8 x 2 scaled radius horizontal-elliptical form of water drop. The electric potential will be the highest on the conductor surface, 11500 Volt, and it will be lowest on the ground, as zero.
On the borders of different materials, the equipotential contour lines will be modified. On this figure, there are 100 equipotential contour lines. The equipotential contour lines tend to avoid the water drop, because its dielectric constant is higher than other materials.
Consequently, it is occurred an accumulation on the water drop vicinity. Furthermore, the gradient of electric potential will be higher. Thus, the electric field will be higher than those other parts around it. The bigger the water drop, the more the accumulation of equipotential contour lines. However, they are less dense than the former.
Figure 12. The electric potential distribution on the outdoor insulator with 8 x 2 scaled radius horizontal-elliptical form of water drop
3.3. Elliptical Water drop as Vertical Radius Function
Figure 13 shows the distribution of electric equifield on two dimension of medium voltage insulator. On first shed of left side from the top, there is a part of vertical elliptical
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form of water drop with the radius of 2 x 8 in drawing scale unit. The 2 is horizontal radius and the 8 is vertical radius of elliptical form.
Figure 13. The electric field distribution and equifield contour lines on the outdoor insulator with 2 x 8 scaled radius vertical-elliptical form of water drop
As previous one. The value of electric field rise as the darkness of colour increase.
Around the conductor, these electric fields are about 4500 V/m. In this case, the maximum electric field computation result was 4610 V/m, occurred on the bottom part of conductor surface. Otherwise, the least value of electric field was 1.05 V/m, occurred on the bottom of the grounding part.
Nevertheless, the local electric field enhancement would be occurred on water drop vicinity. On above figure, it is occurred the maximum local electric field as 166.39 V/m on the top of its vicinity. The maximum local electric field on the water drop vicinity rises as the vertical radius increases. It is also presented the distribution of equifield contour lines.
On that figure, there are as many as 300 contour lines. It is shown that the densest contour lines are occurred around the conductor, as its gradients on that part are the highest than those other places. The second places those encounter conciseness of local electric field contour are on the indentations of insulator surface and water drop.
On Figure 14, it is shown the maximum electric field on water drop vicinity as function of its vertical radius. From both end points, it was obtained the slope of curve as 15.39
V/m as per vertical radius increase. This is higher than the formers. This enhancement of local electric field is dominated by both the sharpness of water drop indentation and the propinguity to the conductor.
250
200
150
100
50
0
0 1 2 3 4 5 6 7 8 9 10 11
LENGTH OF VERTICAL AXIS RADIUS (SCALE UNIT)
Figure 14. The maximum local electric field on the elliptical water drop vicinity as function of its vertical radius
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Figure 15 shows the distribution of electric field direction, as corresponding to
Figure 13. As previous one, the existence of water drop will modify the electric field directional contours. It does not change the directional contours significantly as the vertical axis radius.
Figure 15 The electric field directional distribution on the outdoor insulator with 2 x 8 scaled radius vertical-elliptical water drop
Figure 16 shows distribution electric potential on the outdoor insulator with 2 x 8 scaled radius vertical-elliptical form of water drop. The electric potential will be the highest on the conductor surface, 11500 Volt, and it will be lowest on the ground, zero. On the borders of different materials, the equipotential contour lines will be modified. On the water drop vicinity, the equipotential contour lines tend to avoid it, because the water dielectric constant is higher than other materials. Consequently, it is yielded an accumulation on the top vicinity. Furthermore, on this part, the gradient of electric potential or the electric field will be higher than those other parts around it. The accumulation of equipotential contour lines rose as the position of vertical elliptical water dro increased. The accumulation of such contour lines will be more and denser rather than the previous ones.
Figure 16. The electric potential distribution on the outdoor insulator with 2 x 8 scaled radius vertical-elliptical form of water drop
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3.4. Water Drops as Contact Angle Function
Figure 17 shows the distribution of electric equifield on two dimension of medium voltage insulator. On first shed of left side from the top, there is a part of spherical water drop with the radius of 6 drawing scale unit. The height of water drop center from the insulator shed surface is 2 drawing scale unit or its contact angle is 111 degrees.
Figure 17. The electric field distribution and equifield contour on the outdoor insulator with 2 scaled height radius or 111 degrees of water drop spherical part
As previous, the light colour represents the electric field in low values, and vice versa for the dark one. The value of electric field rise as the colour darkness increase.
Around the conductor, the electric fields are about 4500 V/m. The maximum electric field in this case is 4560 V/m, occurred on the bottom of conductor, and the minimum one is
0.65 V/m, on the bottom of grounding part.
On the water drop vicinity, it is yielded a local electric field enhancement, as maximum as 88.1 V/m. Its value rises as the position of water drop center goes up. In other word, the local electric field on the water drop vicinity rises as its contact angle increases. In this study, the contact angle variation is just cause the water drop to go upward and downward its position. The center of water drop is varied against to insulator shed surface. Thus, the volume of water drop on the insulator surface is also varied, according to the position or the contact angle of water drop.
On Figure 18, it is shown the maximum local electric field on water drop vicinity as function of its center position and its contact angle to the insulator shed surface. From both end points, it is yielded the slope as 0.39 V/m as per contact angle increase in degree, or
4.13 V/m as per position of water drop center rise. This enhancement of local electric field is dominated by both its position and contact angle.
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Figure 18. The maximum local electric field on the water drop vicinity as function of height (rectangular) or contact angle (triangle) of spherical water drop
However, not as previous one, the contact angle variation of water drop will not modify significantly the electric field directional contours. Figure 19 shows the electric potential distribution on the outdoor insulator with 6 scaled radius spherical of water drop, and its center position is 2 scaled unit above the insulator shed surface. The voltage and contours are same as previous one. It is yielded an accumulation on the top vicinity of water drop. Consequently, on this local part, the potential gradient or electric field will be higher than those other parts around it.
Figure 19. The electric potential distribution on the outdoor insulator with 2 of scaled height, 111 degrees of contact angle
4. Conclusions
Based on above computations and their analyses, it can be concluded, that the local electric field enhancements on water drop vicinities will rise as their radii increase. In sequence, form the highest to the lowest, the local electric field enhancements are yielded on the vertical radius of elliptical, the radius of hemisphere, the horizontal elliptical water drops, and the contact angle of water drop. The electric field directional distributions tend to pass by water drops, vice versa for the equipotential contours.
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Suggestion
The variation of water drop contact angle should be maintained in a constant area for twodimension distributions, as representation a constant volume as three-dimensional distributions.
Acknowledgment
Authors herewith respectfully offer thanks to Prof. Barmawi and Mr. H. Sutanto on permission and guide for using the software.
References
[1] Fernando, M.A.R.M., Gubanski, 1999,
Performance for Non-ceramic Insulators in
Tropical Environments , PhD Dissertation, Department of Electric Power
Engineering, Chalmers University of Technology, Goteborg-Sweden, pp.1-2.
[2] Guan, Z., Wang, L. Yang, B. and Liang, X., 2005, Electric Field Analysis of Water
Drop Corona,
IEEE Transactions on Power Delivery, Vol. 20, No. 2.
[3] Peng, Y., Ren, P.Z., Li, C., Peng, L. and Xuan, Z.P., 2005, Finite Element Calculation on Electric Field of Composite Insulator Used in 330 kV Compacted Transmission
,
Proceedings of the XIVth International Symposium on High Voltage Engineering,
Tsinghua University, Beijing, China, pp.A53.1-4.
[4] Phillips, A.J., Childs, D.J., and Schneider, H.M., 1999,
Aging of Non-Ceramic
Insulators due to Corona from Water Drops,
IEEE Transactions on Power Delivery,
Vol. 14, No. 3, pp.1081-1089.
[5] Raynders, J.P., Jandrell, I.R. and Raynders, S.M., 1999, Review of Aging and Recovery of Silicone Rubber Insulation for Outdoor Use
, IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 6, No. 5, pp.620-631.
[6] Seifert, J.M. and Hubl, W., 2001,
Hydrophobicity Effect of Silicone Housed Composite
Insulators and Its Transfer to Pollution Layers – Design and environmentant
Parameters Influencing the hydrophobic Surface Behaviour
, Iroklion Symposium,
Greece.
[7] Que, W. and Sebo, S.A., 2000,
Electric Field and Potential Distributions along Dry and Clean Non-Ceramic Insulators , www.Integrated.com/papers/research, accessed
June 2006.
[8] Zhao, T. and Comber, M.G., 2000, Calculation of Electric Field and Potential
Distribution along Nonceramic Insulators considering the Effect of Conductors and
Transmission Towers, IEEE Transactions on Power Delivery, Vol. 15, No. 1, pp.313-318.
[9] Chakravorti, S. and Steinbighler, H., 2000, Boundary Element Studies on Insulator
Slope and Electric Field around HV Insulators with or without Pollution
, IEEE
Transactions on Dielectrics and Electrical insulation, Vol.7 No. 2, pp.169-176.
[10] Dong, Y. F., Shan, X. W. and Yu, F. Z., 2005, Simulation of Electric Field
Distribution of Composite Insulator
, Proceedings of the XIVth International
Symposium on High Voltage Engineering, Tsinghua University, Beijing, China, ppA34.1-3.
[11] Comsol AB., 2001, ’Femlab, for Use with Windows, Matlab V5.3.1, V6.0’, Version
2.1,
Comsol, Stockholm, Sweden.
14

[12] Computer Solution Europe AB, 1996, Partial Differential Equation Toolbox, for Use with Matlab, User’s Guide
, The Mathworks, Inc., MA.
[13] Vahidi, B., Nasab, R.S. and Moghani, J.S., 2005, Analysis of Electric Field and
Voltage Distributions on ZnO Surge Arrester for Polluted Condition , Proceedings of the XIVth International Symposium on High Voltage Engineering, Tsinghua
University, Beijing, China, pp.A51.1-3.
[14] Sadiku, M.N.O., 1994,
Elements of Electromagnetics
, 2 nd Edition, Sounders College
Publishing, pp.783.
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