An Integral Equation for Analyzing Partial Discharge Fluctuation with Over-voltage Dependence

Abstract

This paper proposes an integral equation to describe the stochastic fluctuation of partial discharge (PD) occurrence under sinusoidal voltage stress based on a simple PD model (equivalent circuit model).In the model, the stochastic behavior of PD fluctuation is assumed to arise from the fluctuation of PD delay time after the inception voltage is build up across a discharge gap. For simplicity of calculation, the distribution of delay time is assumed to obey an exponential distribution and the average delay time is simply depending on the over-voltage across the discharge gap in a form of an exponential function. Based on these assumptions, the authors solved the equation with numerical method and showed several φ-n distribution patterns with the average delay time of 0.05 to 5 msec under low applied voltage conditions in which only one PD pulse can occur in a half a. c. voltage cycle.