Physics-Based High-Frequency Transformer Modeling by Finite Elements

This paper proposes a computational high-frequency transformer model. The model parameters are obtained by using coupled-circuit-finite-element (FE) nonlinear analysis. The frequency response of the transformer was obtained by coupling the transformer FE model and external electric circuits. This technique would allow the physical representation of the nonlinear magnetization behavior of the transformer as well as the strong frequency dependence of the transformer parameters. The self capacitance of each conductor and the mutual capacitances between the turns were calculated by an electrostatic FE analysis. The capacitance order was then reduced to a lower order by shifting the capacitances connected to internal nodes (windings) to the external ones (coil nodes). The resulting reduced capacitances, along with the inductances and resistances, were then used in the circuit domain of the coupled circuit-FE analysis. The transformer frequency response was then obtained from FE analysis. This response was then fitted with rational function approximation. This rational function approximation is then used to construct a frequency-dependent branch (FDB) which is connected in parallel with the nominal frequency transformer model. The FDB branch represents the transformer high-frequency behavior over a wide frequency range. The implementation is performed on a 125-kVA transformer. The developed model terminal behavior was tested under different operating conditions. This includes different switching frequencies and connecting cable length.