An Evaluation of the Methods of Finite Elements and Finite Differences in the Solution of Nonlinear Electromagnetic Fields in Electrical Machines

Abstract

In this paper, an evaluation of the methods of finite elements and finite differences, as applied to nonlinear magnetic field problems in electrical machines, is presented. The evaluation covers the aspects of effectiveness, numerical accuracy, modeling implementation considerations as well as computer storage and execution time requirements of the two methods. The evaluation includes static as well as sinusoidally time varying fields. The method of finite elements is found to be superior in improved accuracy, computer time and storage requirements, as well as programming implementation aspects. A crucial finding of this investigation is that results derived from the finite element analysis tend to converge asymptotically to corresponding experimental test data, as the discretization mesh fineness is increased. This is not the case for finite differences, where the results strongly indicate that there are lower bounds beyond which inherent numerical error cannot be decreased by an increase in the degree of fineness of the corresponding discretization mesh. Details of the analysis, on which these findings stand, are presented here.