General Analytical Model and Optimization for Leakage Inductances of Medium-Frequency Transformers

The leakage inductance of medium-frequency transformers (MFTs) significantly affects the operation and efficiency of isolated converters, that are one of the most important components in solid state transformers, and should be accurately controlled or be minimized. This paper proposes a general analytical model of leakage inductance based on the superposition theorem and Rogowski coefficients, taking non-ideal geometric factors, such as the different heights of the primary and secondary winding in practical implementations, into account, with only less than 4% error compared to most 3D finite element simulations and 7% to all experiments. Based on the proposed model, an optimization scheme to minimize the leakage inductance for typical winding structures through adjustment of the winding arrangement is proposed and mathematically proved, which can reduce the leakage inductance by up to over 40% compared with the traditional concentrated arrangement, also validated in experiments. In addition, the optimization method does not need to redesign other magnetic parameters, basically free to use at no cost.