Empirical Conductivity Equation for the Simulation of Space Charges in Polymeric HVDC Cable Insulations

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Space charge accumulation in High Voltage Direct Current (HVDC) cables are a result of many factors, e.g. the injection of charges, a conductivity gradient or the local electric field. For an accurate description of the time dependent charge distribution such effects have to be considered. Further, small time steps are necessary to resolve fast charge dynamics in time and also to satisfy the Courant-Friedrichs-Lewy (CFL) stability condition of the numerical time stepping schemes in use. Because of the long lifetime of power cables, only the stationary charge distribution is needed to assess the reliability of the cable insulations. To simulate the stationary charge and electric field distribution, an empirical conductivity equation is developed, where the stationary hetero charges distribution are simulated. The new introduced constants are determined by several space charge measurements, which indicate hetero charge accumulation near the electrodes of about 25% of the insulation thickness. Thus, two sigmoid functions create a conductivity gradient near the electrodes, resulting in accumulated hetero charges. The simulation results conform well to published measurements, meaning that the introduced model constitutes a good approximation to simulate the stationary charge distribution.