An integral equation for analyzing phase-resolved partial discharge characteristics under sinusoidal voltage waveform conditions

The authors have been developing a simple partial discharge model to analyze phase-resolved partial discharge characteristics such as ! -n characteristics. The simple model is simply based on the Whitehead's three-capacitance equivalent circuit model for partial discharges. The authors proposed an integral equation based on the fluctuation of delay time of each partial discharge inception. They already succeeded to obtain the solution of the integral equation at low voltage case, in which only one partial discharge can occur at a half cycle of an applied ac voltage with a triangular waveform and also with a sinusoidal waveform. The results have been published elsewhere. This paper describes the solutions of the integral equation for higher voltage conditions in which multi partial discharges can occur at the half cycle of a sinusoidal ac waveform. These solutions give basically pulse number distribution as a function of applied voltage phase angle, that is the ! -n characteristics. Those characteristics show good agreement with those obtained by Monte-Carlo simulation and also those obtained by experiments.