01_FEA - 612 IEEE Transactionson Dielectrics and Electrical...

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612 IEEE Transactions on Dielectrics and Electrical Insulation Vol. 8 No. 4, August 2001 Finite Element Based Kerr Electro-optic Reconstruction of Space Charge A. UstundaCjl and M. Zahn M. I. T. Dept. of Elect. Eng. and Comp. Sciences Cambridge, MA ABSTRACT Recently we used the onion peeling method to reconstruct the axisymmetric electric field distri- bution of point/plane electrodes from Kerr electro-optic measurements. The method accurately reconstructed the electric field from numerically generated data. However in the presence experimental noise the performance was less satisfactory. The measurements were especially noisy and unstable near the needle tip which is also the interesting region since most charge injection initiates here. We develop a new algorithm for Kerr electro-optic reconstruction space charge in axisymmetric poidplane electrode geometries. The algorithm is built on the finite element method (FEM) for Poisson's equation and will be called finite element based Kerr electro-optic reconstruction (FEBKER) hereafter. FEBKER calculates the space charge density di- rectly to avoid the numerical problems associated with taking the divergence of the electric field, uses single parameter light intensity measurements to enable transient analysis, which otherwise is difficult since multiple parameter intensity measurements are slow due to the ro- tation polarizers, and is capable of reconstruction even when the number and/or position of measurements are limited by the electrodes andlor the experimental setup. The performance of the algorithm is tested synthetic Kerr electro-optic data obtained for an axisymmetric poidplane electrode geometry in transformer oil with specified space charge density distri- butions. The impact of experimental error is analyzed by incorporating random error to the synthetic data. Regularization techniques that decrease the impact of experimental error are applied. In principle is applicable to arbitrary three-dimensional geometries as well. 1 INTRODUCTION N HV environments electric field phenomena is governed by Poisson's I equation 024(.') = -m (1) E. where 4 is the electric potential, p is the space charge density, E the dielectric permittivity, and Cis the position vector. If the space charge distribution is known then (1) can be solved by various numerical meth- ods. The solution can then be used to find the electric field which is an important quantity in power apparatus design since break- down of the dielectric materials occurs when the electric field magni- tude exceeds certain values. Unfortunately the physical laws that govern space charge injection and transport are not fully known. Thus p(F) in (1) cannot be mod- eled adequately and designs often take space charge to be zero. Such designs cannot predict where the electric field magnitude may exceed safe maxima in the presence of space charge. Indeed some failures in iq.3 = -04(.') (2) power apparatus are attributed to unexpected accumulation of space and surface charge which result in spark discharges. Thus it is of great
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This note was uploaded on 06/08/2011 for the course ELECTRICAL 124 taught by Professor Ghjk during the Spring '11 term at Institute of Technology.

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01_FEA - 612 IEEE Transactionson Dielectrics and Electrical...

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