Rational Function Approximation of Transformer Branch Impedance Matrix for Frequency-Dependent White-Box Modeling

Transformer white-box models are used by the manufacturers to calculate internal winding voltages during the lightning impulse test. The model can also be applied in general network studies, but the model accuracy should then be improved, considering the many different voltage waveforms and frequencies that can exist in the system. Accuracy improvements are achievable by including the frequency-dependency of the branch impedance matrix via rational function approximation, but the large size of the matrix makes such modeling very difficult. Two suitable methods for passive rational modeling are presented, based on vector fitting and residue perturbation in either phase domain or modal domain. Application to a power transformer shows that the two methods are capable of fitting a 213 x 213 branch impedance matrix with a 6th order passive pole-residue model in a few seconds. The resulting model is included in a complete white-box state-space model of the transformer that is compatible with a previously implemented model interface for EMTP. An efficient procedure is presented for validating the simulation result by the Numerical Laplace Transform. Comparison with a measurement shows that the inclusion of the frequency dependency gives a better reproduction of the measured waveshape than a previously proposed damping-factor model.