Models for a Fast Computation of Internal Overvoltages in Medium-Frequency Transformers

The fast switching of wide-bandgap (WBG) devices and the resulting harmonics in the switching waveforms can cause significant overvoltages in medium frequency transformers (MFTs). To enhance the reliability and lifetime of MFTs, fast and accurate models for these high frequency effects in the windings are necessary. The effects can be described using large multiconductor networks. However, computing the frequency-dependent parameters of such networks – namely the impedance and capacitance matrices – typically involves time-consuming finite element analysis (FEA), hindering the investigation of multiple designs in a reasonable timeframe. Therefore, this paper presents an analytical approach to compute impedance and capacitance matrices for the equivalent networks, focusing on an efficient algorithm to compute the capacitance matrix as well as an appropriate length scaling of the calculated per-unit-length matrices. Simulation and measurement results show that the proposed models can compute internal overvoltages more than 500 times faster than FEA, while predicting the maximum overvoltage with an error of less than $7 \%$. The individual validation of all presented submodels not only confirms the applicability to overvoltage modeling, but also demonstrates a potential use of the models in other areas of high-frequency modeling.