Avoiding Numerical Instabilities in the Universal Line Model by a Two-Segment Interpolation Scheme

The universal line model is among the most accurate frequency-dependent transmission-line model available in Electromagnetic Transients Program-type simulation tools. One major drawback of this line model is that it sometimes gives unstable simulation results. The instability is related to the occurrence of close poles in the rational model of the propagation function which leads to large residue-pole ratios. In time-domain simulation, these large ratios give a magnification of the error associated with the interpolation of the reflected current wave which acts as the stimulus of the propagation function. An approach is described for avoiding the instability problem by introducing a two-segment interpolation scheme for the extraction of the current wave. The approach gives zero interpolation error when used together with the integration scheme known as recursive convolution and so error magnification becomes inconsequential. The new approach is demonstrated for pertinent examples, including one case with residue-pole ratios exceeding one million.