ESTIMATION AND PLOT OF ELECTRICAL FIELD USING FINITE DIFFERENCE METHOD

Communication

Abstract

Calculation of electric fields with the aid of an computer is now an inevitable tool in various electricity-concerned technology, in particular, for analyzing discharge phenomenon and designing high voltage equipments .The calculation of electric fields generally require higher accuracy, because the highest electric field stress on insulator is usually the most important and decisive value in insulation design or discharge study. This is one of reason why the boundary-dividing methods are preferred to the region-dividing ones, such as finite difference method (FDM) or finite element method (FEM).
The finite difference method is a powerful numerical method for solving partial differential equations. An FDM method divides the solution domain into finite discrete points and replaces the partial differential equations with a set of difference equations. Thus the solutions obtained by FDM are not exact but approximate. However, if the discretization is made very fine, the error in the solution can be minimized to an acceptable level.
In this research grid of finite difference method divided (N by N), N represents number of nodes. In our calculation we take many cases, each case contains specific number of nodes such (7, 15, 25). Then we estimate electric field for different charges values and their locations. We depend on equation (AX = b) .Where A matrix represents node values (depend on boundary condition and operating nodes), X matrix represent electric potential, b matrix represents charges values. X estimation using gauss sideral method and successive over relaxation method .Then we calculate residual which calculated by equation (residual = b - AX). Then we estimated and plot Vx , and Vy. We approve accuracy of our calculation by less quantity of residual, which mean X reach to exact solution.
Also we approve the residual value increased with number of nodes increase because we need to more calculations also the distance between charges increase.