Distributed Dual Model for High-Frequency Transformer Windings: Electromagnetic Transients and Solid State Transformers

This paper presents a novel model for transformer windings to accurately represent the duality between electrical and magnetic circuits. The model can be used for the calculation of high-frequency transients in power systems and the design of high-frequency transformers, for example, those to be used in solid-state (utility-grade) transformers and power electronic converters. Existing circuit models do not consider the flux linkage in the winding thickness in a physical (dual) way. Duality is achieved by discretizing the winding thickness into thin sub-sections and distributing the proposed model building block across the winding. Analytical calculations are carried out to compare the accuracy of the proposed circuit for the computation of the terminal impedance, flux duality, and current distribution in the physical geometry of the winding. Further discretization is performed to extend the circuit to represent high-frequency phenomena: eddy currents and capacitive effects. The model can be easily implemented in any circuit simulation program using available circuit elements. The circuit parameters are computed with very simple expressions. The model is validated with finite element simulations. Differences of around 1% are obtained for relatively low model orders for high frequencies.