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

Abstract

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 multi-phase 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 multi-phase admittance-based formulation of the state-equations. It is shown that the substitution of the real part of the state matrix eigenvalues causes some loss of accuracy 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. IEEE

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