Robust Passivity Enforcement Scheme for Time-Domain Simulation of Multi-Conductor Transmission Lines and Cables

This paper proposes an algorithm to enforce passivity on the time-domain simulation model for a multi-conductor cable or transmission line. The model is first reformulated in a form which reduces the severity of passivity violations. The frequency sweep method is then used to identify any remaining passivity violating regions of the model´s frequency response. These small passivity violations are then removed using a linear constrained least squares algorithm to perturb the diagonal elements of propagation matrix. The passivity enforcement algorithm is applied to the Universal Line Model (ULM), a widely used robust phase domain formulation implemented in many commercial electromagnetic transients simulation programs. Two examples of multi-conductor underground cable systems, one for ac and the other for HVDC transmission are presented to demonstrate the proposed approach.