Dimensional analysis of partial discharge initiated by a metallic particle adhering to the spacer surface in a gas-insulated system

Partial discharges (PDs) constitute important phenomena in a Gas-Insulated System (GIS) that warrant recognition (and, subsequently, mitigation) as they are obvious symptoms of system degradation. This paper proposes the application of dimensional analysis, based on Buckingham pi theorem, for characterizing PDs provoked by the presence of metallic particles adhering to the spacer surface in a GIS employing SF6 (Sulphur hexafluoride). The ultimate goal of the analysis is to formulate the relationships that express three PD indicator quantities, namely current, charge, and energy, in terms of six independent quantities that collectively influence these indicators. These six quantities (henceforth referred to as the influencing, determining or affecting variables) include the level of applied voltage, the SF6 pressure, the length and position of the particle on the spacer, the duration of voltage application, and the gap between electrodes. To compute the pertinent dimensionless products, we implement three computational methods based on matrix operations. These three methods produce exactly the same dimensionless products, which are subsequently used for constructing the models depicting the relationships between each of the three PD dependent quantities and the common six determining variables. The models derived provide partial quantitative information and facilitate qualitative reasoning about the considered phenomenon.