Integral Equation for Analysis of Partial Discharge Pulses under Sinusoidal Voltage Stress

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. In the model, the stochastic behavior of PD fluctuation is assumed to arise from the fluctuation of PD delay time after the inception voltage and the fluctuation of residual voltage after PD occurred. For simplicity of calculation, the distribution of delay time is assumed to obey an exponential distribution, and the distribution of residual voltage is assumed to obey a normal distribution. Based on these assumptions, it is found that the proposed integral equation provides the basic characteristics such as the PD pulse distribution in applied voltage phase angle domain. The authors solved the equation with numerical method and showed several ϕ-n distribution patterns. The authors analyzed the relationship among ϕ-n distribution patterns and several discharge parameters such as the delay time constant, the partial discharge inception voltage, the mean residual voltages and the standard deviation of residual voltage, the applied voltage.