Passivity Enforcement for Transmission Line Models Based on the Method of Characteristics

The universal line model (ULM) has been implemented in several EMT programs for simulation of electromagnetic transients. In some cases, instability problems have been encountered. This paper shows that the current approach for rational function approximation adopted in ULM can lead to large out-of-band passivity violations, thereby causing an unstable simulation. An approach is introduced which prevents the occurrence of large passivity violations. Low-frequency violations are avoided by adding an artificial shunt conductance to the diagonal elements of the shunt admittance matrix while high-frequency violations are avoided by introducing artificial attenuation using a low-pass filter. In addition, high-frequency asymptotic passivity is enforced for the characteristic admittance. Any remaining violations are removed by adding a second-order correction term to the model ports. The approach is shown to mitigate instabilities from a cable system transient simulation, without impairing the quality of the model.