Probability of partial discharge inception in small voids

Composite insulation materials may have small gaseous voids caused by the manufacture process and/or by mechanical stress. The time delay of partial discharge (PD) inception after voltage application in such small voids depends on various parameters including the gaseous volume, and it is subjected to considerable scatter. Average values for this time delay are reported in literature. However, the strong scatter implies a certain probability for the first PD, which has not been explicitly calculated so far. Therefore the probability of the inception of the first PD is calculated in this paper as a function of time and of AC (50 Hz) and DC field strength with the geometry as parameter. At first only one single cylindrical void is considered. Further, the calculation is extended to a large number of statistically distributed voids. It is shown that for sufficiently high field values the kind of voltage and the considered pressure range have a minor influence on the PD inception compared to its scatter whereas the geometry of the voids is more important. The calculation allows a better estimation of the delay of PD inception in small voids when performing measurements for material investigations and other test routines.