A simple model for DC-conduction and space-charge formation in insulation materials

A universal conduction model is proposed for high-voltage direct-current (HVDC) insulation materials. The model is able to reproduce many well-known experimental facts and is very useful for finite-element electro-thermal simulations required in the design process of HVDC cables and cable-accessories. The proposed model generalizes the common approach of a field dependent conductivity, σ(E), in the way that σ is now a solution of a partial differential equation containing a diffusion and a relaxation term. The strength of the model is its simplicity, as it requires specification of only a few additional parameters associated with characteristic length and time scales and with contact conditions. The price for the simplicity is the phenomenological character of the model, which cannot be derived generally from transport equations based on pure solid-state physics. For illustration, hetero space-charge in a plate-sample of cable insulation material at DC stress is discussed.