Electro-thermal model for calculating the space charge around Defects in a 2-D thin film sample

In HVDC insulation, the accumulation of space charge in solid polymers is partly the consequence of the dependency of insulation conductivity on both the electric field and temperature. In practice, defects in the insulation will lead to electric field enhancement and inhomogeneous current density will give rise to local temperature gradients due to the local Joule heating losses. These factors will influence space charge formation and the electric field surrounding the defects. In this study, a numerical electro-thermal model is developed to calculate the time-dependent charge transport and the space charge accumulation around a defect using an empirical equation of field and temperature dependent conductivity. The results show that when the conductivity was only made field dependent, a significant amount of space charge accumulated around the defect. This had the effect of decreasing the electric field enhancement surrounding the defect that would have occurred in the absence of space charge. When the temperature dependence of the conductivity was also considered in the simulations, it was found that under low applied field <;40kV/mm, dielectric heating was small and did not have a significant effect on the accumulated space charge. However, increasing the applied voltage above 40kV/mm led to a significant increase in the local Joule heating surrounding the defect and resulted in a reduction of the accumulated space charge.