Field solution in polluted insulators with non-symmetric boundary conditions

A finite difference (FD) method to calculate the electric field in polluted insulators with asymmetric boundary conditions is proposed. The method is based on neglecting the displacement currents that circulate through the porcelain and through the air, in comparison with the conduction currents that circulate over the semiconductive pollution layer covering the insulator. This assumption reduces the 3D problem to a 2D one over the insulator surface. The FD method is applied by superposing a grid composed of parallels and meridians over the insulator surface, setting up an FD equation for each mode, and solving the resultant set of simultaneous equations.