Estimation of the Resonance Frequencies Using an Electrostatic Energy Based Capacitance Model of a Two-Winding Medium/High-Frequency Transformer

Abstract

Being an integral part of many high-power converters, it is imperative to estimate the natural resonance frequencies of a medium/high-frequency (MF/HF) transformer. Experiment/measurement based methods reported in literature determine the resonance frequencies based on the input impedance measurements. However, their applications are limited if these resonance frequencies are to be estimated prior to the transformer prototyping. To ameliorate the drawback, this article provides a comprehensive modeling procedure for the winding capacitances of a two-winding transformer and its resonance frequency estimation. By integrating the prior capacitance modeling techniques, this article establishes an electrostatic energy based transformation model, which directly translates the static winding capacitances into equivalent model based capacitances. These derived capacitances are further utilized to represent a reduced <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\pi }$</tex-math></inline-formula> -model of a two-winding transformer, compute its frequency responses and estimate the resonance frequencies. The proposed model based approach is simple and easily executable, and helps avoiding any infeasible transformer design during the preprototyping stage. Experimental results derived from MF transformer prototypes, constructed of solid round, foil, and litz wires, are used to corroborate the theoretical analysis and feasibility of the proposed model based approach.