Predicting electrical breakdown in polymeric insulators: from deterministic mechanisms to failure statistics

Breakdown theories yield a specified time to breakdown for fields exceeding a critical value, whereas experiment shows that times-to-breakdown and breakdown fields are different on a sample-to-sample basis. This has forced the use of a statistical approach to failure, often without a clear physical understanding of the pertinent parameters. A general methodology that allows failure statistics to be derived from a given breakdown mechanism is presented. A number of case studies are used to illustrate the way in which mechanistic features can be related to the parameters of the failure statistic. In particular it is shown that the Gumbel statistic and not the Weibull function is the one appropriate to failure initiation by random defects. Both the formative stage and initiation stage of breakdown is considered, and it is shown that features can be identified in the failure statistic related to known thresholds in the active breakdown mechanism. Ageing is examined through the three main control features: activation energy, field enhancement factor, and threshold factor. It is shown that distributions in each of these parameters could give rise to the observed statistics above the estimated characteristic threshold field. However, distributions in the material variables that define the local threshold value allow some failures to still occur in the sample set even at fields below the characteristic threshold level, whereas distributions in activation energy do not. Finally, the possibility of predicting the lifetime of individual specimens is briefly addressed.