Chordal Graphs and Partial Positive Passivity Assessment

This paper presents a novel approach to passivity assessment of multiport frequency-dependent rational models. The strategy exploits the interlacing properties relating the eigenvalues of a full transfer matrix and those of its submatrices plus some additional concepts from graph theory. Contrary to many existing approaches in which passivity assessment applies only to the full system, this novel scheme aims at identifying passive subsystems embedded into a non-passive system so that a partial positive system could be specified. This enables the identification of parameters contributing to passivity violations and how these are distributed across the system ports. We also propose an index to quantify how passivity violations permeate into the system and take as cases studies actual transformer data to demostrate its applicability.