A deterministic model for the growth of non-conducting electrical tree structures

Electrical treeing is of interest to the electrical generation, transmission and distribution industries as it is one of the causes of insulation failure in electrical machines, switchgear and transformer bushings. In this paper a deterministic electrical tree growth model is described. The model is based on electrostatics and local electron avalanches to model partial discharge activity within the growing tree structure. Damage to the resin surrounding the tree structure is dependent on the local electrostatic energy dissipation by partial discharges within the tree structure and weighted by the magnitudes of the local electric fields in the resin surrounding the tree structure. The model is successful in simulating the formation of branched structures without the need of a random variable, a requirement of previous stochastic models. Instability in the spatial development of partial discharges within the tree structure takes the role of the stochastic element as used in previous models to produce branched tree structures. The simulated electrical trees conform to the experimentally observed behaviour; tree length versus time and electrical tree growth rate as a function of applied voltage for non-conducting electrical trees. The phase synchronous partial discharge activity and the spatial distribution of emitted light from the tree structure are also in agreement with experimental data for non-conducting trees as grown in a flexible epoxy resin and in polyethylene. The fact that similar tree growth behaviour is found using pure amorphous (epoxy resin) and semicrystalline (polyethylene) materials demonstrate that neither annealed or quenched noise, representing material inhomogeneity, is required for the formation of irregular branched structures (electrical trees). Instead, as shown in this paper, branched growth can occur due to the instability of individual discharges within the tree structure.