A Guaranteed and Efficient Method to Enforce Passivity of Frequency-Dependent Network Equivalents

Rational models of frequency-dependent network equivalents (FDNEs) must be passive to ensure numerical stability in time domain simulations. Therefore, passivity enforcement is an essential step in FDNE rational modeling procedures; however, current approaches are either not guaranteed or not efficient. Here, a positive real lemma based semidefinite programming model is first implemented to guarantee the passivity of the result obtained. Second, this paper incorporates an approach to significantly improve efficiency while guaranteeing passivity by exploiting an important feature of rational models: that constituent complex-pole terms corresponding to dominant resonance peaks can be adjusted to be passive through minor changes, and a partition-based scheme is proposed. Numerical investigations demonstrate that the proposed method is efficient while introducing little additional modeling error.