Fast calculation of steady‐state charge distribution in high voltage power cables

Abstract

AbstractModern high voltage direct current (HVDC) power cables consist of nonlinear electric field and temperature depending insulation materials, eg, polyethylene (PE) or mass‐impregnated paper (MI). Within the insulation material, slowly time varying electric fields are the result of accumulated space charges. Due to the long operation time of power cables, the stationary charge distribution and the resulting additional field stresses inside the insulation material need to be taken into account, to ensure a stable operation of the cable system. The long accumulation time of charges in comparison to fast charge dynamics usually requires extended computation times within transient electro‐quasistatic simulation models. An alternative approach to calculate the final steady‐state charge distribution arises from the simultaneous solution of both, the stationary current and the electrostatic potential problem, which are nonlinearly coupled by Ohm's law. Each of the two potential equations are discretized using the finite difference method. Utilizing a nonlinear fixed point iteration for the electric potential, the steady‐state solution of the charge distribution is computed until convergence is obtained. During this pseudo time stepping process, oscillations may occur that yield incorrect results of the charge distribution. These oscillations are eliminated utilizing underrelaxation strategies. Numerical tests on a cylindrical and a plane parallel problem, using both approaches for the calculation of the steady‐state charge distribution, show a faster computation with the nonlinear fixed point iteration, reducing the computation time by at least one order of magnitude.