Many processes are involved in the accumulation of space charges within the insulation materials of high voltage direct current (HVDC) cables, e.g., the local electric field, a conductivity gradient inside the insulation, and the injection of charges at both electrodes. An accurate description of the time dependent charge distribution needs to include these effects. Furthermore, using an explicit Euler method for the time integration of a suitably formulated transient model, low time steps are used to resolve fast charge dynamics and to satisfy the Courant-Friedrichs-Lewy (CFL) stability condition. The long lifetime of power cables makes the use of a final stationary charge distribution necessary to assess the reliability of the cable insulations. For an accurate description of the stationary space charge and electric field distribution, an empirical conductivity equation is developed. The bulk conductivity, found in literature, is extended with two sigmoid functions to represent a conductivity gradient near the electrodes. With this extended conductivity equation, accumulated bulk space charges and hetero charges are simulated. New introduced constants to specify the sigmoid functions are determined by space charge measurements, taken from the literature. The measurements indicate accumulated hetero charges in about one quarter of the insulation thickness in the vicinity of both electrodes. The simulation results conform well to published measurements and show an improvement to previously published models, i.e., the developed model shows a good approximation to simulate the stationary bulk and hetero charge distribution.Commonly used cable insulation materials are cross-linked polyethylene (XLPE) and low-density polyethylene (LDPE). These materials are in use due to their good electrical characteristics, ease of processing, and acceptable cost [1,2].Depending on the charge type, high electric fields occur inside the insulation or in the vicinity of the electrodes. At low electric fields, the charge movement is higher than the charge injection. The injected charges move across the insulation, resulting in accumulated hetero charges and an increased electric field at both electrodes. At high electric fields, the charge movement is less than the charge injection and homo charges accumulate, resulting in decreased electric fields at the electrodes and increased electric fields within the insulation bulk [3,4].Typically, the insulation material in power cables contains a semiconducting layer at the anode and another one at the cathode. Moving injected charges are blocked at these layers and form hetero charges. Furthermore, with an applied electric field, ionized impurities move towards the electrodes and form hetero charges as well. The electric field of the applied voltage is superimposed by the electric field of the hetero charges. As a consequence, the resulting electric field stress can exceed the breakdown strength of the insulation [5].Without an applied temperature gradient, most of the charges accumulate in ...
