Module Integral Method for the Calculation of Frequency-Dependent Leakage Inductance of High-Frequency Transformers

The accurate calculation of frequency-dependent leakage inductance of high-frequency transformers is critical for the optimized design of power electronic transformers. The leakage inductance can be obtained through the magnetic energy, usually calculated by the phasor integral of the magnetic energy density in the literature. This article analyzes the difference between the module and the phasor integral based on frequency-domain energy and proposes to take the module integral of magnetic energy density as the periodic averaged magnetic energy. Furthermore, the closed-form formula of the leakage inductance is given accordingly. The modules under different frequencies correspond to the intrinsic constant magnetic densities. Thus, the proposed method has a better physical interpretation compared with the previous phasor integral method. The finite element method simulation and experimental results of five transformers are taken as benchmarks to compare the proposed method with the phasor integral method. The comparison shows that the proposed module integral method has satisfying effectiveness and accuracy in the whole frequency band for all the cases involving both noninterleaved and interleaved windings.