PD characteristics as a stochastic process and its integral equation under sinusoidal voltage

This paper proposes an integral equation to describe the stochastic fluctuation of partial discharge (PD) occurrence under sinusoidal waveform voltage conditions based on a simple PD model (an equivalent circuit model). The stochastic behavior of PD fluctuation is assumed to arise from the fluctuation of PD delay time after the discharge inception voltage is built up across a discharge gap. The distribution of delay time is assumed to obey an exponential distribution and the dependence of the delay time on the overvoltage is assumed to be expressed by an exponential function of the overvoltage. The integral equation has been solved numerically under the low voltage condition in which only one PD can occur in a half AC voltage cycle. It is found that the proposed integral equation can provide the basic characteristics such as PD pulse repetition rate vs. applied voltage phase angle