2003 zyxwvutsrqp Annual Report Conference on Electrical Insulation and Dielectric Phenomena zyxw Simulation of the electric field in the many homogeneous mediums by charges simulation method F. Rogti zyxwvuts , A.Mekhaldi*, and A.Boubakeur* Engineering electric department, university of Laghouat, Algeria *Engineering electric department. National School polytechnique, Algeria Abstract. We develop a code of calculation of the electrostatic fields based on the method of the fictive charges (charges simulation method) in mediums containing simultaneously several dielectrics. Complex structures can be easily solved by a simple code. The great advantage of zyxwv this method is the direct obtaining of the field, without numerical differentiation of the potential. The geometry is obtained by use of autocad, then exported in a given file. Intoduction The method of the fictive charges is certainly the most used and the most indicated to treat problems of electric fields. It was applied successfully in many high voltage systems [ 1.2 1. This method is very simple and can be applied to any system that includes one or more homogeneous mediums. The principal advantage of this method is its easier application to systems of complex geometries of three-dimensional fields without axial symmetry and the problems of space charges. This method zyxwvutsr has two stages. In the fmt one, the distribution of real surface charges is replaced by discreet fictive charges placed inside the electrodes. The magnitude of these charges can be calculated by the resolution of a hear system. The second phase of the method consists in fmding the single solution of the equation of Laplace (or Poisson) within the space [ 1 I. Method of resolution We take one or more electrodes whose potential is known, we place N fictive charges qj (punctual , linear or annular fictive charges according to the nature of the studied problem). The position of the charges is selected in an arbitrary way, hut after a certain experiment one can obtain to produce since the fust test a configuration that is not far away from the optimum at which one tries to arrive. We determine the value of these charges by the resolution of the system (1) with respect to qj: [9 j 1 = [Pij I-' [v, 1 (1) the values Vci of the potential are known values at the points Pc(i, J) located on the contour of the electrodes. Thus, it is necessary to check if the calculation of the whole of calculated charges satisfies the border conditions. We choose then N other Pvi checkng points located at the borders of the electrodes, and we calculate the potentials Uvi given by the charges qj [uv,I=kjlbjl (2) We charges the space arrangement with N fictive charges, we calculate again the values of the charges qj and we repeat the checking until aU the differences are smaller in order to achieve a reasonable precision of the simulation [ 2 1. Rounded conductor Figure zyxw 1: Ribbonmductor Analysis of borders results We uses the measurement of the errors to estimate the precision of the method of the fictive charges: Where V*j and V are the exact values calculated of the electric potential V of the border, We obtain: ERM=1.8.1W5 0-7803-7910-1/03/$17.0002003 IEEE 522