Stochastic Modeling of Space Charge Distortion in HVDC Cables using a Persistent Random Walk Approach

Space charge accumulation is a primary factor in the premature aging and electrical breakdown of High Voltage Direct Current (HVDC) cables. Conventional continuum models often fail to capture the stochastic nature of charge hopping in disordered polymeric insulations like cross-linked polyethylene (XLPE). This paper proposes a novel transport model based on the Persistent Random Walk (PRW) theory, specifically adapted to describe hopping conduction between discrete trap states. We map the trap depth and temperature-dependent Poole-Frenkel release rates to the scattering rate of the PRW. Our simulations demonstrate a strong temperature dependence of the internal electric field. At low temperatures (300 K), carriers remain trapped near the injection electrode, creating a severe local field enhancement (homocharge effect) exceeding 80% of the applied stress. Conversely, as temperature increases, thermal energy facilitates detrapping, leading to charge relaxation and a return to a uniform field distribution. Furthermore, a comparison with Space-Charge-Limited Current (SCLC) theory at the transition temperature (450 K) validates the model, showing the charge packet tail follows a power-law decay with a slope close to the theoretical − 2 / 3 prediction. These results highlight a competing physical mechanism where high temperature mitigates the electrostatic risk associated with space charge, providing critical insights for the design of reliable HVDC insulation systems