Simulation of low-frequency fields on high-voltage insulators with light contaminations

This paper deals with the numerical solution of the linear complex Poisson equation. The practical background of posing this problem are arc-overs on moist or contaminated insulators in high-voltage power plants. The electrostatic field of the charge-free space prevails; essentially below a critical voltage U_k. However, the dielectric material loses its insulating characteristics above U_k . It becomes the carrier of a discharge which builds up a conducting connection along the insulator. It is a matter of slowly varying fields (50 Hz), for which the displacement current is a significant quantity. These slowly varying fields can be determined by solving a complex potential problem. Discretization leads to a complex system of linear equations with symmetric matrix. This system is solved by various modern conjugate gradient-type methods. Numerical simulations for test and real life problems are presented