Equivalent representation of machine winding in frequency domain model for fast transient studies

Winding models based on transmission line theory are commonly used to predict the transient voltage distribution along machine coils. During a fast transient, the highest overvoltages and dielectric stresses usually appear on the first coil. Therefore, most computer models available consider only one coil and approximate the remaining of the winding by means of a constant lumped element. In this paper, a nonuniform transmission line model is used to predict the voltage distribution along machine windings. Electrical parameters of the model are computed using finite element method (FEM). Three strategies to represent the rest of the winding after the first coil as a function of frequency are proposed: Kron reduction, equivalent Pi circuit, and chain matrix. The results show that these strategies do not involve any loss of accuracy when compared to the behavior of the complete winding, which is not the case of the approximation by a constant lumped parameter.