Estimation of partial discharge energy in a mathematical model of thermal fluctuation processes of a power cable

The article shows that the presence of impurities or oxidation products resulting from heating in insulation leads to leakage currents. The formula for calculating the power emitted by the active component of the leakage current is obtained. The basic mathematical model of thermal processes of a power cable line was refined by taking into account the values of internal heat sources. A mathematical model was obtained that allows calculating the power of partial discharges, as well as determining the location of the inclusion in the main insulation, due to the power of the active component of the leakage current, when it occurs in the main cable insulation. The calculation of the change in heat flux passing through the layers of cable insulation by the piecewise-specified functions method, taking into account the thermal resistance of the inclusion, is carried out. The mathematical model, along with the layer-by-layer calculation of isotherms in the cable section, makes it possible to determine the presence of inclusions in the insulating material and their influence on the temperature distribution profile at characteristic points of the cable section. The method proposed in the developed model makes it possible to account for heat losses based on the thermal and geometric dimensions of the inclusion. This will allow to obtain the temperature in all layers of the cable line, starting from the radial distances, inclusion parameters caused by the insulation core current, as the main temperature-forming factor.