Mathematical model for numerical simulation of current density in microvaristor filled insulation materials

This contribution deals with mathematical models for numerical simulation of the volume current density in microvaristor filled insulation materials. Due to the nonlinear material properties it is difficult to estimate the current and, even more important, the power losses depending on the applied voltage and electrical field, respectively. This is, however, essential to know for macroscopic simulation of the overall performance of such materials in insulation systems. This kind of insulating material should usually be operated in the pre-breakdown region of its nonlinear voltage-current characteristic. At voltages above the continuous operating voltage the material changes its resistance and becomes more conductive. In the first part of this contribution the pre-breakdown region of microvaristor filled materials is analyzed. Investigations on the field dependent conductivity and permittivity are performed. In the second part a mathematical model to describe the conductivity of microvaristor filled materials in all three regions of their nonlinear voltage-current characteristic is presented. Furthermore, a method is shown how to estimate the parameters from the mathematical model.