Breakdown statistics of the space-charge ageing model for polymeric insulation

In recent work based on the ageing model proposed by Dakin (1948), it was suggested that local space charge concentrations modified an existing chemical ageing process via electro-mechanical contributions to the free energy of the reactant. Two contributing factors were distinguished. The increase of ground state free energy both accelerated the chemical conversion and in reversible reactions increased the degree of conversion attainable. Under the assumption that a breakdown initiating state required a critical amount of conversion A* from the initial non-equilibrium state, an expression relating the insulation life, L, to A* and the field dependent free energy increase (A₁ E^4b) was obtained and fitted to experiment. Here we show how breakdown statistics can be obtained from the model, by assuming A* or A₁ to be distributed in the samples, with the extreme value controlling the sample life. The results are compared to the DC failure data of PET films