A homotopy continuation method for nonlinear electric field analysis

Abstract

Electric field analysis is an important basis for the insulation design of high-voltage direct-current equipment. The resistivity is a strong function of temperature and electric field, which may lead to the divergence of a numerical solution, and the initial approximations are the key to convergence. Therefore, a novel approach for nonlinear electric field indirect coupling analysis is developed. This algorithm converts the original nonlinear electric field into homotopy equations under a specific parameter, and uses the numerical continuation method to gradually approximate the true solution. Taking a fictive ±200 kV direct-current cable extrusion molded joint as an example, two homotopy equations are constructed to successfully calculate the nonlinear electric field based on the numerical continuation method combined with Steffensen iterative formula. On the contrary, divergence occurs in the conventional indirect coupling calculation method, indicating the superiority of this approach. Subsequently, some factors affecting the convergence of the homotopy continuation method are discussed. Finally, the calculated results and the solution times using the presented approach are compared with the direct coupling method by COMSOL. The proposed algorithm can enlarge the region of convergence in nonlinear electric field analysis based on the indirect coupling method and effectively overcome the divergent issue due to the inappropriate choice of initial approximations.