An Electric and Stress Field-Driven Electrical Tree Growth Model

Abstract

Electrical trees have different shapes and growth rates under different voltage conditions. This article proposes an electric and stress field-driven electrical tree simulation model. The stress field describes the gas expansion of the partial discharge (PD) process. This model introduces the driving energy to determine the tree shape according to multiphysical fields instead of controlling the tree shape manually by artificial parameters. The electrical tree simulations and experiments were carried out to analyze the electric and stress field distributions under 11- and 15-kV voltages. The tree under 11 kV is branch-shaped (fractal dimension = 1.33), with the electric and stress fields concentrated at the tree tips. Meanwhile, a significant densification effect of the electric field replaces the concentration effect and causes a bush-shaped tree (fractal dimension = 1.72) under 15 kV. The tree-driving energy during tree growth under 15 kV constantly decreases faster than 11 kV. Consequently, the tree length under 15 kV is 69% shorter than 11 kV due to the decrement of the driving effect of the stress field. The proposed model explains the geometric shapes and growth rates of electrical trees under different voltages.