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.