Silicon carbide (SiC) semiconductors enable more and more medium voltage (MV) applications, but their fast switching transients lead to undesired effects as e.g. oscillations in transformer windings due to parasitic capacitances. In order to consider these effects/parasitics in the design process, this paper presents an analytical model of the electric energy/capacitance per unit length within the winding window of foil-wound transformers. The model is based on calculating the electrical energy within basic regions using Schwarz-Christoffel (SC) transformations. It also considers the potential distribution introduced by the voltage-drop between different turns and achieves an error below 3 % compared to FEM simulations. The model can be used for calculating comprehensive lumped element equivalent circuits and is based on computationally efficient analytical equations.
A bottleneck in optimization procedures of magnetic components is the calculation of the electric field strength (e.g. for an optimized insulation design) since this is based either on a slow numerical field simulation or on rough approximations. Hence, a fast and accurate method for the electric field calculation in the winding window is crucial for a fast optimization process. This paper presents a novel electric field calculation method that combines a variable potential function with a Schwarz-Christoffel (SC) mapping. This leads to accurate results, that match Finite Element Method (FEM) simulations as close as 5 %. The proposed method is more than 200 times faster than FEM and robust against parameter changes.
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