Convergence improvement in two-dimensional finite element nonlinear magnetic problems—a fuzzy logic approach

Abstract

A fuzzy-logic based factor for improving the convergence in nonlinear magnetostatic problems is proposed. The Newton–Raphson method is modified by a relaxation factor which is obtained by a fuzzy logic system. It is shown that the proposed factor improves convergence in nonlinear operating points where the conventional Newton–Raphson algorithm fails. A comparison with other techniques is made to show that the method requires less computing time and less iterations to meet the convergence criteria. The fuzzy relaxation factor was applied to a nonlinear finite element model of an electric power transformer. The set of finite element equations was obtained by applying a nodal formulation, which is based in Ampere's law, and it solves Maxwell's equations. The resulting set of nonlinear equations were solved in terms of the magnetic vector potential. Two finite element meshes were employed and different excitations were also considered. The obtained results show that fuzzy-logic relaxation factor can be successfully applied in improving the Newton–Raphson method.