One-dimensional model for nonlinear stress control in cable terminations

A one-dimensional model for field control in cable terminations is analyzed mathematically both for linear and nonlinear field grading materials. Far an applied ac voltage, the concept of the penetration length allows for a useful characterization of the voltage profile, even for materials where both the conductivity and the permittivity are field dependent. For lightning impulse events an analytical solution for purely resistive field control is presented, allowing for an arbitrarily strong nonlinearity of the conductivity. The model results yield a useful input for more detailed finite element calculations. The results show that conclusions for nonlinear field control based on linear calculations in general are misleading.