High-field saturation behavior of field-grading materials

The nonlinear field-grading materials (FGM) exhibit an electric conductivity that increases with the applied electric field. They can be used to reduce excessive field stress in critical regions of high-voltage equipment. Computer modeling of the field-grading effect is usually performed employing simplified analytical expressions for the conductivity as function of the electric field strength E. In particular, the conductivity is allowed to increase with E without limits. From measurements on actual FGMs, however, it is known that above a certain field strength the conductivity ceases to increase further. In this paper we study how the saturation of the conductivity affects the overall stress reduction and the heating of the material.