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Dynamic high-fidelity magnetic equivalent circuits (HFMEC) are viable tool for accurate, physics-based modeling of magnetic components. However, such model formulation typically requires hundreds or thousands of state variables to accurately represent the eddy current dynamics. A reduced-order HFMEC modeling approach has been recently introduced for single-winding systems, e.g., inductors. This letter extends the HFMEC approach to multiple-winding power-electronic transformers. First, a general full-order HFMEC model of the multiple-winding system is developed that incorporates magnetic saturation and the eddy current dynamics. Then, multiple-input/multiple-output linear and nonlinear order-reduction techniques are used to extract the desired essential system dynamics while preserving the model accuracy and gaining computational efficiency. The proposed methodology is validated on a typical power electronic transformer with both pulse width modulation and sinusoidal excitations using numerical simulations and experimental measurements.