Equivalent 3D Electric Field Modeling of Wound Transformers with Complex Insulating Media

The modeling of capacitances between transformer windings is a key aspect in achieving common-mode (CM) noise predictions and suppressions. The 3D finite-element method (FEM) can accurately extract these capacitances, but for highfrequency wound transformers with complex insulations, it consumes much time in solving the electric field. Given the shortcomings of existing insulation equivalence methods, the factors affecting the electric field distribution between windings are analyzed, and the equivalent media are properly divided into several regions. A method is proposed to determine the equivalent permittivity based on the features of small-scale 2D winding cross sections. This equivalence method can effectively shorten the solving time of the electric field without impacting the accuracy of the inter-layer capacitances. It also facilitates predicting capacitances for the transformer in the design stage.