Mathematical Modelling of Surface Discharge on the Contaminated Surface of Insulator Using Nernst’s Planck Equation

Abstract

The outdoor insulator is exposed to the surface degradation due to the continuous electrical and environmental stresses. The contaminant flow due to the pollution that mixed with water like dew or rainwater will provide a conductive path that allowed the leakage current flow. This leakage current flow will heat-up the insulator surface and causing the formation of carbonize path due to the surface discharge. Thus, leakage current measurement had been widely used in the monitoring of surface discharge phenomena and to understand the insulator surface condition. However, study on the physical process of discharge phenomenon that leads to the conductive path and breakdown on the insulator are not well concerned and understood. Therefore, this study is concerned with modelling of surface discharge on the contaminated surface of insulator including the charge transport and generation mechanism. This model is used electro-migration model and considered the electric field dependent molecular ionization as the generation mechanism of charge carriers. The charge carrier generation and transport mechanism are accounted with the Nernst Planck theory to model the behaviour of the charge carriers while Poisson’s equation is used to determine the distribution of electric field on the insulator surface. A mathematical model of surface discharge on the insulator based on the Nernst Planck Theory is then discussed.