Field distribution in cable terminations from a quasi-static approximation of the Maxwell equations

A new model for the evaluation of the electric field in a cable termination realized through a nonlinear stress control tube (SCT), is presented in this paper. It is based on the electro-quasistatic approximation of the Maxwell equations: the Laplace equation describes the field in the nonconducting regions whereas a diffusion-like equation gives the field dynamics in the stress control tube. A numerical model is devised by solving the Laplace equation by finite difference and diffusion equations by the Galerkin method. It is shown that even the well-known RC transmission line model can be derived from this general approach. The underlying approximations leading to the circuital model are discussed in detail. The proposed model, in contrast with the circuital one, allows us to take into account properly the nonlinear SCT characteristics and the actual boundary conditions: in this way both spatial and temporal effects of the nonlinearity are considered. The numerical results obtained by considering the general field approach and by using the transmission line model are compared.