Mathematical analysis of partial discharges in an electrical insulation structure with AC ramp input voltage

In this work, a dynamic mathematical model is derived relating the ramp power frequency voltage applied to a rod-plane gap with a polymer nano composite dielectric barrier and the resultant values of maximum partial discharges. These partial discharges lead to an electric field which is intrinsically complex due to the charges being sprayed, recombined, trapped and redistributed thus leading to a constantly varying combined electric field that influences the consequent partial discharge behavior. Further, the interactions between the applied voltage and the emanating partial discharges are also governed by the dielectric characteristics of the base polymer as well as the type and content of the nanofiller. Since, a deterministic relation cannot be established between the applied voltage and maximum partial discharge magnitude, a dynamic mathematical model is derived between the two. In a practical insulation system, this technique will enable us to precisely predict the magnitude of partial discharges at a given applied voltage given the time history records of applied voltage and corresponding maximum partial discharge magnitudes. The methods adopted and the results obtained are presented.