Admittance-Based Modeling of Transmission Lines by a Folded Line Equivalent

This paper describes a new transmission-line model for frequency-dependent modeling of untransposed overhead lines and underground cables. The nodal admittance matrix is decomposed into two blocks that, respectively, represent the open- and short-circuit conditions of a half-length line obtained by ldquofoldingrdquo about the middle. By subjecting these matrices to rational fitting with inverse magnitude weighting, one obtains a model where the eigenvalues of the associated nodal admittance matrix are effectively fitted with high relative accuracy. This is shown to overcome the error magnification problem that occurs with direct fitting of the nodal admittance matrix. In addition, the modeling process (fitting and passivity enforcement) becomes faster. We show that this folded line equivalent (FLE) is particularly suitable as a companion form for phase-domain traveling-wave-type models, to be used when the time step is selected shorter than the line travel time. In this situation, the required model order is low and so the FLE gives highly efficient time-domain simulations.