The Investigation of electric fields in high voltage systems using the boundary element method

ABSTRACT PhD Thesis THE INVESTIGATION OF ELECTRIC FIELDS IN HIGH VOLTAGE SYSTEMS USING THE BOUNDARY ELEMENT METHOD Selçuk YILDIRIM Fırat University Graduate School of Natural and Applied Sciences Department of Electrical and Electronics Engineering 1999, Page: 113 In this thesis, two-dimensional electric field distribution in high voltage systems using Boundary Element Method (BEM) has been obtained. The computed results have been compared with both the analitical results and the results obtained from commercialy available software package *ELECTRO'. For this purpose, first the application area of the BEM has been investigated in the literature. Furthermore, the fundamental advantages of the BEM over Finite Difference Method and Finite Element Method are determined. First, Laplace and Poisson equations which model the electric field have been obtained. Boundary integral equations were obtained by applying weighted residual method to Laplace and Poisson equations. In order to put the boundary integral equations into matrix form they were discretized by linear boundary elements. Then a computer program called SINEL has been developed to analyse two- dimensional open boundary electrostatic fields. This program takes the coordinates of the problem geometry, boundary conditions and the properties of the material as input data.The coefficients of the matrices were computed by using Gauss numerical integration method. Then Dirichlet and Neumann boundary conditions were applied to get the linear set of equation which contains the unknowns on the boundary. The set of equation has been solved using Gauss Elimination Method. The potential values of the internal points can be calculated using computed boundary values. The high voltage electrode systems, a high voltage cable and a high voltage insulator have been analyzed using the developed program. The output of the program has been compared with both analitical and commercial program results. Key Words : Boundary Element Method, Boundary Integral Equation, Electrostatic Field, Laplace and Poisson Equations.