Fractal analysis of creeping discharge propagating over solid insulators immersed in gases at different pressures

This paper is aimed at the fractal analysis of the real creeping discharge patterns (i.e, observed experimentally) propagating over different solid insulators of different thicknesses immersed in sulphur hexafluoride (SF₆) at different pressures, under positive lightning impulse voltage in a point plane electrode arrangement. The considered solid insulators are circular samples of different thickness made of PTFE, glass and epoxy resin. It is shown that the creeping discharges propagate radially. By using the box counting method, we show that the discharge patterns present a fractal dimension D that depends on the thickness of the solid samples (e) and the type of insulator (dielectric constant) as well as the gas pressure. D decreases when e increases; and it increases with the dielectric constant ε_r of insulator It is the highest for glass (ε_r =5.5) and the lowest for PTFE (ε_r =2.1); D is in between for epoxy resin (ε_r =3.4). This dependency of D on the solid insulators (through ε_r) and their thickness reveals the existence of a relation between the fractal dimension and the physical parameters. On the other hand, for a given insulator, the stopping length and the branches density of discharges decrease when the gas pressure is increased. This is also observed on D which decreases when increasing the gas pressure.