Propagation of electrical tree structures in solid polymeric insulation

Two alternative theoretical approaches to electrical tree propagation exist. Stochastic models attribute tree structures to random probabilistic factors, whereas in the discharge-avalanche model mechanism-driven field fluctuations are responsible. Here we review the predictions of these approaches in the light of the available experimental evidence. It is shown that both models give the fractal structures and the form of structure distribution observed experimentally. The width of the distribution functions predicted are, however, less than those found experimentally. The quantitative formulation available to the physical model also enables it to reproduce several other features of tree propagation such as voltage dependence, growth laws, and discharge behavior patterns. This is not possible in the stochastic approach without mechanistic assumptions which are difficult to relate to the stochastic process. The connection between the discharge-avalanche model and deterministic chaos is explored. Experimental evidence is presented supporting the contention that the electrical treeing phenomenon is the result of a deterministic breakdown mechanism operating in a chaotic regime at fields lower than those required for runaway breakdown. Space-charge deposition and re-arrangement is proposed as the physical origin of the chaotic field fluctuations. Tree shapes are shown to be related to the variation in the fluctuation range available as the tree grows in accord with the predictions of the discharge-avalanche model.