An Analytical Method to Obtain a Wide Frequency Range Equivalent $\pi$-Model of a Two-Winding Medium/High-Frequency Transformer

Resonance frequency estimation of a medium/high-frequency (MF/HF) transformer during the design stage is important to avoid unreliable operations, such as overvoltages inside windings, ringing, and spikes in the transformer current due to high $dv/dt$ , etc. However, conventional transformer design approaches do not comment on the frequency response behavior of a MF/HF transformer. Equivalent transformer models derived based on measurement based/experimental methods are helpful. But this necessitates to have a physical transformer and is not suitable to glean any information prior to prototyping. To circumvent these limitations, this article introduces a lumped parameter based frequency-dependent $\pi$ -model of a two-winding MF/HF transformer. This work incorporates the frequency-dependent characteristics of the magnetic and loss elements, and the winding capacitances into the equivalent transformer modeling. On account of the analytical modeling approach, the proposed $\pi$ -model integrates the effects of relevant geometric parameters, such as the wire geometry, winding scheme and configurations. The derived reduced-order $\pi$ -model is useful for circuit simulation purposes, such as estimating the resonance frequencies and studying the effect of $dv/dt$ during the pre-prototyping stage. This also has the potential to be used as an off-line diagnostic tool for identifying assembly faults during the post-manufacturing stage, such as open circuit and short circuit faults in a winding, unwanted airgap between cores. The proposed frequency-dependent $\pi$ -model is validated using experimental results obtained from frequency response analyses of transformer prototypes built using different conductor types, winding schemes and configurations.