Electrical aging of extruded dielectric cables. A physical model

A model is proposed to describe all experimental results on electrical aging of cables reported in Part 1. It is based on simple thermodynamics concepts in the Eyring theory, includes the concept of submicrocavity formation proposed by Zhurkov, and supposes that the first step in electrical aging is essentially a molecular process, as in Crine and Vijh´s model. Our model of electrical aging under ac fields supposes that molecular-chain deformation is essentially a fatigue process and, therefore, that high frequencies generate more defects and thus reduce cable life, as indeed demonstrated by others. An original feature of the model is the submicrocavity formation above a critical field F_c, whose value can be approximately predicted knowing the energy of cohesion of the polymer. This leads to a simple lifetime equation depending on just two physical parameters ΔG₀ (energy of activation of the chain deformation process) and λ_max (the maximum size of submicrocavities) with no adjustable unknowns. Above F_c, there is an exponential relation between time and field, whereas below F_c, the breakdown strength of the insulation varies very little with time; in other words, there is very limited (if any) aging. The slope of the exponential regime gives the value of λ_max directly whereas the intercept gives the value of ΔG₀. The predictions made by the model are discussed in correlation with existing experimental data. In addition to these basic assumptions, the model confirms that there is a relation between cable endurance and insulation morphology. Actually, the size of submicrocavities is ultimately limited by the amorphous-phase thickness. The max values deduced from the slopes of the exponential regime between F and log t for polyethylene (PE) (Part 1), XLPE and EPR insulation are in excellent agreement with the size of the amorphous phase of these samples, as measured by X-ray spectroscopy. It is also shown that the presence of water results in a lower ΔG₀ value, i.e. a shorter life. The precise relation between ΔG₀ and the nature and concentration of the impurity (including water) needs more work. The impact of these conclusions on the experimental limits of a reliable accelerated aging test and on the final breakdown process are discussed in a subsequent paper