Comparison of Two Electro-Quasistatic Field Formulations for the Computation of Electric Field and Space Charges in HVDC Cable Systems

Electro-quasistatic (EQS) field simulations are used to calculate electric field and space charge distributions in high voltage direct current (HVDC) cable systems. The constant voltage results in the accumulation of space charges and a time varying electric field. To simulate the electric field, different EQS formulations are introduced in literature. In a first formulation, the electric field and the space charge density are updated consecutively via the continuity equation and the electrostatic Poisson equation. In the second EQS formulation, the continuity formulation is reformulated using the electric scalar potential and only the electric field is updated per time step. To compare both EQS formulations, the electric fields are simulated in different HVDC cable systems. Simulation results of the electric field in a cable insulation result in relative errors of less than 1 % between both numerical computations and the analytic solution. Simulation results of a cable joint show instabilities for the field-space charge update EQS formulation, due to an averaging process of the charge density, whereas the scalar potential EQS formulation yield stable results when simulating nonlinear electric conductivities.