A Damping Factor-Based White-Box Transformer Model for Network Studies

Transformer manufacturers make routine use of white-box detailed transformer models for ensuring that the transformer will pass the lightning impulse test. For use in general simulation studies, the model should additionally be multiphase and properly reproduce the transformer's input impedance characteristics and voltage ratios at 50/60 Hz. One challenge in such general modeling scope is to properly represent the frequency-dependent damping of the transformer's many resonances. In this work, we show how to properly include empirical damping factors in a multiphase admittance-based formulation of the state-equations. It is shown that the substitution of the real part of the state matrix eigenvalues causes some undesired changes to the model's behavior at lower frequencies, but this deficiency is mitigated by a correction to the output matrix. The resulting model can be directly included in EMTP-type simulation programs via a companion model, or via a terminal model with an add-on model for optional calculation of selected internal node voltages. Application of the modeling approach to a single-phase three-winding transformer demonstrates its merit in terms of accuracy and efficiency. Finally, the limitations of the model are discussed regarding accuracy and applications scope.