INVESTIGATION OF ELECTRIC FIELD INTENSITY AND DEGREE OF UNIFORMITY BETWEEN ELECTRODES UNDER HIGH VOLTAGE BY CHARGE SIMULATIO METHOD

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1 INVESTIGATION OF ELECTRIC FIELD INTENSITY AND DEGREE OF UNIFORMITY BETWEEN ELECTRODES UNDER HIGH VOLTAGE BY CHARGE SIMULATIO METHOD Md. Ahsan Habib, Muhammad Abdul Goffar Khan, Md. Khaled Hossain, Shafaet Ashif Hossain Department of Electrical & Electronic Engineering Rajshahi University of Engineering & Technology Rajshahi-6204, Bangladesh Abstract This paper describes degree of uniformity and electric field intensity in the gap between two electrodes subjected to high voltage which is necessary to study the behavior of insulation for design of high voltage equipments. Here, 3-D arrangements of fictitious charges and contour points in Cartesian coordinates are considered to find out the desired outputs for Sphere-Sphere and Sphere-Plane electrodes by using well known Charge Simulation Method (CSM), using MATLAB. Both the symmetrical and asymmetrical applied voltages are considered for the investigation. From this investigation it is revealed that more uniform electric field having degree of uniformity of η= and has been obtained for symmetrical applied voltage of Sphare-Sphare and Sphare-Plane respectively, compared to η= and for asymmetrically It is also found that the probability of insulation breakdown is greater near the High Voltage electrode compared to other portion of the dielectric. The developed computer program can be used in designing HV equipments. Keywords: Schwaiger factor; Charge Simulation Method (CSM); Electric field intensity; MATLAB; High voltage. I. INTRODUCTION Electric fields have been employed in various applications over several decades. Electrodes of different sizes have a lot of importance in high voltage application, as sizes plays a vital role in electric field intensity and degree of uniformity. In this paper, Charge Simulation Method (CSM) is used in calculation of electric field intensity and degree of uniformity. CSM is accepted as the most superior and suitable method for 2-D and 3-D field configurations with electrode systems of any desired shape [1,2]. It is also found suitable for insulation systems comprising different types of dielectrics. The CSM has proved to be a highly accurate method as it even permits to take into consideration the effect of the surroundings on the main field in high voltage insulation system [2]. For this research work Cartesian co-ordinate system of Sphere-Sphere and Sphere-Plane electrodes are considered for the observation of the insulation behavior in high voltage [3]. Though idea for using vacuum for insulation purpose is very old, in prior works two dimensional arrangements is considered. In this investigation, 3-D arrangement is used for more accuracy instead of 2-D arrangement [4]. This paper shows the characteristics of Sphere-Sphere and Sphere-Plane electrode under both symmetrically and asymmetrically applied voltage on the electrodes. MATLAB is used for programming purposes of the research work which is an effective way for the three dimensional arrangement in non experimental works. This work has been conducted for a better and more effective application of Electrical engineering in high voltage applications [5]. II. METHOLODIGY Due to flexibility and better solution possibility CSM is chosen for the research work. In this work different electrode is consider in CSM for actual investigation purposes. 2.1 Charge Simulation Method (CSM) The basic principle of CSM method is that, the considered field is formed by superposition of many individual fields. The distributed charge on the surface of an electrode is replaced by discrete fictitious individual charges arranged suitably inside the electrode or outside the space in which the field is to be computed /14/$ IEEE 185

2 The potential contribution made by individual fictitious charges are obtained by the solution of Laplace`s and Poisson`s equations [1]. The value of these charge are evaluated by forcing the specified voltages at n numbers of selected points called contour points on the surface of the conductor. At any of these contour points on the electrode, the potential resulting from the superposition of the charge is equal to the electrode potential φ[6]. Thus φ = P Q (1) Where ij P is known as potential coefficients` which can be expressed as, P = 1 4πεR Where ij R the distance between the ith contour point to jth charge is points which can be expressed as, R = (x a ) + (y b ) + (z c ) Where, x, y i, z i are co-ordinates of i th contour points and a, b, c j are the coordinates of j th charge. The potential φ resulting from the superposition of the potentials due to individual charges will be equal to the conductor potential φ [2]. The equation (1) can be written as P Q = φ (2) Where Q is the value of j th charge point. The number of contour points is selected equal to the number of fictitious charges, i.e nb = nc = n. This equation for n number of contour points [6] is [P], [Q] = [φ] (3) To check the calculated sets of charges, potential is calculated at n numbers of check points by using equation (1), which are chosen on the surface of the electrode. The accuracy of CSM largely depends upon the positioning of the charges and the corresponding contour points. If simulation does not meet the accuracy criterion, calculations are repeated by changing displacement ratio β. It is the ratio of the distance between two successive contour points and their distance from the fictitious charges, i.e. β =. For efficient computation, β should lay between 0.7 and 1.5. Higher density of fictitious charges can also give more accurate results [1,7]. To characterize the field, electric field intensity E has been calculated at several points between two electrodes by the following equation:- E = (4) Where E is the value of E at p point in the dielectric, Rip is the distance between point p and the position of i th charge, Q and n is the total number of point charges adopted to simulate both the electrodes [1,5]. The degree of uniformity η is defined as- η= U/d.E max (3) Where E max is the maximum value of E, U is the potential difference and d is the gap distance between the two electrodes [2,5]. 2.2 Program flow chart For the investigation of High voltage electric field intensity and degree of uniformity in CSM, a program is simulated. For this simulation MATLAB is used as the technical tools. The total system is considered as 3-D arrangement and the program flow chart is presented here [5]. At first, I consider the co-ordinates of contour points and check points on the surface of the electrode and charge points inside the electrode. Then calculated charge on charge points and potential at check points to find the error. If the error is greater than 1% then read co-ordinates again. But in our investigation we have found that error is approximate 0.02% which is much better than 2-D arrangement. Therefore, it is found 3-D arrangement is more accurate than 2-D arrangement from this programming investigation /14/$ IEEE 186

3 Figure 2: Sphere-Sphere pair in 3-D Structure. The radius of Sphere electrode and Plane electrode were considered 5cm and 10cm. The gap distance was same for each combination and it was 10cm between two electrodes [8]. The asymmetrically applied voltage 100 KV and 0, and symmetrically applied voltage 50KV and -50KV were considered. In Figure 3 s (a) and (b), Sphere-Sphere electrode is shown whose field behavior is represented in Figure 4 and 5. And in Figure 3 s (c) and (d) combination of Sphere- Plane electrode is shown whose field behavior is represented in Figure 8 and 9. Figure 1: Flow chart of CSM programming. 2.3 Study on different electrodes The geometric model of the sphere-sphere gap with the image sphere is shown in figure. Image sphere is used to simulate the infinite ground plane. The sphere electrode radius, r is considered as 5 per unit. And with respect to this, the gap separation is, h per unit. It is the dimension of h in relation with r that decides the electric field non-uniformity of the geometry [8]. Figure 3: Different electrodes combination which were used for simulation /14/$ IEEE 187

4 III. RESULTS AND DISCUSSION The distribution of electric field depends upon the shape and the gap distance of the electrodes. Field behavior of Sphere-Sphere and Sphere-Plane electrode are discussed below Effect of Electric field of spheresphere electrode under symmetrical and asymmetrical applied voltage Figure 4: Equipotential lines for symmetrically the middle of the gap. As the equipotential line between the gap is not equally distributed, the dielectric stressed is not equal everywhere. The dielectric stressed comparatively more near the electrode where density of equipotential line is greater. In case of asymmetrically applied voltage in Figure 5 the equipotential lines are more unequally distributed, so the dielectric stressed more unequally than symmetrically Except 10%, all equipotential lines have a tendency to follow the curvature of HV electrode and 50% line is slightly shifted from the middle of the gap. So the field between Sphere-Sphere electrodes is non uniform Effect of changing the size of (upper) electrode for Sphere-Sphere pair The effect of variation of shapes of electrodes on electric field for symmetrically and asymmetrically applied voltages shown in Figure 6 and 7. In the Figure we observed that, the 10% line is shifted toward the upper electrode with decreasing it s radius in both symmetrical and asymmetrical cases. So the density of equipotential lines increases gradually near the smaller sphere with decreasing its size. Finally we can come in a decision that, the field intensity as well as the possibility of insulation breakdown is much near the lower size electrode than larger. Figure 5: Equipotential lines for asymmetrically In case of symmetrically applied voltage in Figure 4 equipotential lines are symmetrically distributed above and below the 0% line which passes through Figure 6: 10% Equipotential line for Sphere-Sphere electrode with variation of radius of upper sphere under symmetrical voltage /14/$ IEEE 188

5 17th Int'l Conf. on Computer and Information Technology, December 2014, Daffodil International University, Dhaka, Bangladesh Figure 7: 10% Equipotential line for Sphere-Sphere electrode with variation of radius of upper sphere under asymmetrical voltage. Figure 9: Equipotential lines for asymmetrically When symmetrical voltage is applied the equipotential lines are asymmetrically placed above and below the 0% line in Figure 8. The 0% line is shifted toward the sphere electrode from the centre of the gap. Most equipotential lines have a tendency to follow the curvature of the sphere electrode. Dielectric stressed comparably much nearer the spherical electrode than plane electrode due to density of equipotential lines. When asymmetrical voltage is applied, the equipotential lines, crowded near the spherical electrode in Figure 9.So the field as well as dielectric stressed varied widely between the gap and it is larger near the spherical electrode. Thus the field created under the Sphere-Plane electrode is weakly non-uniform. 3.2 Effect of Electric field of Sphere-Plane electrode under symmetrical and asymmetrical applied voltage 3.3 Effect of applied voltage on Electric field intensity along electrode axis Figure 8: Equipotential lines for symmetrically /14/$ IEEE 189

6 Figure 10: Variation of E along electrode axis. The variation of electric field intensity along the shortage distance between Sphere-Sphere and Sphere-Plane electrodes in both case of symmetrical and asymmetrical applied voltage is shown in Figure 10. In symmetrical cases the minimum electric intensity was obtained at the middle point of the electrode but in case of asymmetrically applied voltage was nearer to the grounded electrode. The maximum intensity was obtained at high voltage electrodes in all cases. It is comparatively greater for Sphere-Plane pair than Sphere- Sphere pair. From the figure it observed that the electric field intensity E for asymmetrically applied voltage greater than symmetrically applied voltage in all respective points. So its means that the electric field is more non uniform in asymmetrically applied voltage than symmetrically 3.4 Effect of applied voltage on degree of uniformity along electrode axis Figure 11: Degree of uniformity with variation of gap distance between two electrodes. In the above Figure the variation of degree of uniformity with variation of gap distance in both cases of symmetrically and asymmetrically applied voltage is shown in Figure 11. The degree of uniformity obtained maximum at lower gap distance and it decade exponentially with increasing gap distance. So the uniformity of electric field is inversely proportional to the gap distance. The degree of uniformity curve of symmetrically applied voltage is situated above the asymmetrically applied voltage curve. So it can be summarized that the field will be more uniform in symmetrically than asymmetrically applied voltage and Sphere- Sphere electrode pair than Sphere-Plane electrode system. It is important that the probability of insulation breakdown is greater near the High Voltage electrode compared to other portion of the dielectric. So the HV transmission line should be given better protection to avoid the danger. IV. CONCLUTION This paper has been presented on the investigation of electric field intensity and degree of uniformity through MATLAB programming. Charge Simulation Method has been used to characterize Sphere-Sphere, Sphere-Plane electrodes with gap distance under symmetrically and asymmetrically 3- D arrangement makes this simulation study more /14/$ IEEE 190

7 accurate and reliable. Here vacuum is considered as the dielectric in research condition, but this program is applicable for all other dielectrics by changing the value of dielectric constant. Therefore, these types of simulation will be very much helpful for selecting proper size and shape of electrodes which can reduce time and cost in designing various HV applications. REFERENCES [1] M.A.G Khan and R. Arora, Application of charge simulation method (CSM) for the estimation of field between HV and grounded electrodes, Proc. Of 3rd workshop and conference on EHV technology, Bangalore, India, [2] Singer,H., Steinbigler, H., Weiss,P., A charge simulation method for the calculation of high voltage fields, Trans, IEEE, PAS 93 (1974), pp [3] Muhammad Abdul Goffar Khan, Md.Rabiul Islam, and Rizoan Toufiq, Characterizattion of Symmetrical Electrode system to Estimate the Degree of Uniformity under Symmetrically and Asymmetrically Applied High voltage, 7th international Conference on Electrical and Computer Engineering, December 2012, Dhaka, Bangladesh. [4] Ryo Nishimura, Katsumi Nishimori, Arrangement of fictitious charges and contour points in charge simulation method for electrodes with 3-D asymmetrical structure by immune algorithm, Journal of Electrostatics 63 (2005) [5] M. A. G. Khan, Investigation of insulating properties of vacuum under high voltage, Ph.D thesis, Electrical Engineering Department, IIT Kanpur, India, [6]Malik, N.H., A Review of Charge Simulation Method and it s Applications, IEEE Transactions on Electrical Insulation, EI-24 No (1989). [7] P. K. Mukherjee and C. K. Roy, Computation of fields in and around insulators by fictitious point charges, IEEE Trans. Electr. Insul. Vol EI-13, No1, February [8] Gururaj S Punekar, N K Kishore Senior Member IEEE, H S Y Shastry, Effect of non Uniformity Factors and Assignment Factors on Errors in charge Simulation Method with Point Charge Model, World Academy of Science, Engineering and Technology 46, /14/$ IEEE 191