A Dynamic Model for Nonlinear Resistive Field Grading Materials

Electric field control in insulation systems can be achieved with nonlinear resistive field grading material (FGM). A typical FGM has low conductivity at low fields and high conductivity at high fields, which can be realized with composite materials consisting of an insulating polymer matrix filled beyond the percolation limit with particles having special properties. The strong nonlinearity is controlled by the electrical switching behavior of intrinsic interfaces being, e.g., particle-particle contacts in SiC-based FGMs or ceramic grain-boundaries in microvaristor-based FGMs. Most FGM-models used in simulations for designing the insulation of HV devices restrict the dynamics of the FG process to space-charge formation governed by the charge continuity equation with a given field-dependent conductivity function. In this purely theoretical work, a model is introduced which includes the short delay-time due to internal interface polarization, which can be relevant at fast voltage pulses. The macroscopic model considers the heterogeneous character of the material with an additional, spatially distributed degree of freedom on a mesoscopic scale with impedances for the insulating matrix, the conductive particles, and the switching interfaces. The fundamental properties and behavior of the model, which can be included in Multiphysics finite element simulations, are discussed and illustrated with simple examples.