An analysis of the probability distributions of charge in electrical trees generated by needle tests

The problem of the stochastic description of the time to tree growth in insulation systems is addressed in this paper. Resorting to tests performed by the classic needle-plane configuration, it is shown that, depending on the amplitude of applied voltage and the growth time, data fit well either a two-parameter or a five-parameter Weibull function, but the former can be considered as the most representative of the investigated phenomenon. The values of the parameters of the Weibull function are connected with the shape of the tree, as well as its time evolution and applied electrical field, thus providing a useful tool for insulation characterization.