Modelling of electric tree progression due to space charge modified fields

Abstract

Tree initiation and growth require localized field enhancement that results in material erosion and formation of tree channels. Tree progression is linked to partial discharges within the tree tubules, characterized by recurrent periods of activity followed by quiescent states. Charge builds up across the non-conducting tree channels during the inactive regime, and discharge follows. In this work, the role of the space charge modified field during the non-discharging regime in deciding the site of subsequent discharges and thereby shaping tree structures is studied. A simple stochastic model was developed, in order to understand the respective effects of charges trapped on the walls of tree tubules, at channel tips, or in the volume of the dielectric. While some charge distributions are seen to arrest tree growth, others encourage axial growth towards the other electrode, and some aid in producing bushy trees clustered around the needle tip. The effect of carbon deposition within tree channels, making them effectively conducting, was also investigated. The insights gained from the simulations were successfully used to explain tree growth in the laboratory under high- and low-field conditions.