09_numericaltree_g - 1724 A. El-Zein et al.: A Numerical...

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A. El-Zein et al.: A Numerical Model of Electrical Tree Growth in Solid Insulation 1070-9878/09/$25.00 © 2009 IEEE 1724 A Numerical Model of Electrical Tree Growth in Solid Insulation A. El-Zein, M. Talaat Faculty of Engineering Zagazig University Egypt and M. M. El Bahy Faculty of Engineering Sinai University Egypt ABSTRACT A new model for investigating the electrical tree growth in solid insulation using a hyperbolic needle-to-plane gap is presented. The needle is embedded in the insulation medium. Classification of tree shape depends on the electric field value is presented. Then, accurate computation of the electric field is a pre-requisite for calculating electrical tree growth. The electric field distribution is obtained from Laplace's equation by treating the tree structure as an extension of the stressed electrode i.e., conducting medium. The electric field is redistributed during each growth of the electrical tree. This is achieved by using the charge simulation method. The charge at the needle surface is simulated by a group of ring charges. To determine the appropriate arrangement of simulating ring charges inside the needle, a genetic algorithm is used. A number of series finite line charge is used for simulating the charge over each branch and sub-branch during the treeing progress. The presented model for simulating electrical tree growth is a three dimensional field problem. The used needle tip radius was 3 μ m while the gap spacing varied from 0.3 to 15 mm. The results have been assessed through comparison with available analytical and experimental data. Index Terms - Electrical tree growth, tree channel, degradation phenomena, hyperbolic needle to plane gap, charge simulation method. 1 INTRODUCTION ELECTRICAL treeing phenomena in solid dielectric are directly related to electrical degradation of the insulating materials [1]. Polymeric insulation suffers from electrical treeing of long-term degradation when exposed to electric fields of low intensity relative to its intrinsic strength. Breakdown in solid dielectrics has been traced to a series of partial pre-breakdown channels emanating from a region of extremely high electric stress due to imperfections present in the insulation structure, especially, due to the present of voids, impurities in the dielectric and protrusions from the inner or outside semi-conductive layer [2]. These pre-breakdown channels formed around the defect site in the dielectric structure resemble the branches of a tree. Electric charges thus penetrate into the insulation, giving rise to channels, which form the electrical tree and grow with time until breakdown [3] There are basically three different stages in the formation of trees in the dielectrics: inception, propagation and completion [3]. In the inception phase, damage accumulates at existing defects. In the propagation phase, a branching structure originates from the defect and spreads across the dielectric. In the completion phase, the tree has bridged the gap between the electrodes [3].
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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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09_numericaltree_g - 1724 A. El-Zein et al.: A Numerical...

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