A Stable Iteration Procedure of Newton's Method in Finite-Element Computation of Nonlinear Magnetic Field Problems With a Vector Hysteresis Model

A stable iteration algorithm for solving nonlinear magnetic field problems using the finite-element method (FEM), incorporating a vector Jiles-Atherton hysteresis model and Newton's method, is introduced. The Jacobian matrix is calculated according to the information of the differential reluctivity of the hysteresis loops. In order to balance the FEM computation stability and efficiency, two time criteria are adopted. The proposed FEM procedure is applied to analyze a three-phase transformer made of electrical steel sheets. The numerical computation is stable and fast. The numerically computation results are compared with the experimentally measured ones. The computation efficiency and accuracy proves the effectiveness of the proposed algorithm.