Application of the Trefftz method in an original variational formulation to the analysis of the current transformer field

Abstract

The previous papers by the author propose a new classification scheme of the boundary methods based on variational formulations. They contain initial numerical experiments conducted in order to compare nonsingular methods from the group generated by the original and inverse variational formulations. This paper is a continuation of that research and its aim is to apply one of the nonsingular Trefftz methods for modelling a magnetic field in a current transformer. It presents theoretical considerations and derivation of a mathematical model of the current transformer. A straightforward boundary approach analysed previously is now developed into a hybrid Trefftz method. Based on that, 2D numerical models are formulated and implemented in the Matlab environment. Some numerical tests are conducted in order to validate the performance of the method. Finally, some solutions concerning current transformer problems are presented. These results are compared to the ones obtained by Matlab's PDE Toolbox.