Nonlinear three dimensional field computation methods in laminated iron cores under saturated conditions

Abstract

Two methods of accounting for magnetic saturation in nonlinear three dimensional magnetic field problems using finite elements, are given. The magnetic field formulation used here is based on the curl curl approach which was detailed in earlier papers. The three dimensional finite element method is used once in conjunction with the Newton Raphson technique and once with a Gaussian method to obtain solutions of such fields in the presence of magnetic saturation in laminated cores. The laminated iron core of an example transformer is represented by three composite reluctivities to account for the anisotropy of the core. The saturated values of these composite reluctivities are obtained by curve fitting the magnetization characteristics of composite materials using cubic spline polynomials in conjunction with special treatment of the highly saturated core regions. For comparison purposes, solutions obtained using the Newton-Raphson and the Gaussian methods of inclusion of saturation, are obtained for the same problems in the presence of same degrees of saturation. Very good agreement between calculated and measured data for the chosen problem is achieved. Comparison between convergence and implementation characteristics of the two methods used here are given.