A Faster Passivity Enforcement Method via Chordal Sparsity

Abstract

Passivity enforcement methods entail the solution of optimization problems characterized by significant computational complexity. Optimal solutions require the use of positive-real lemma constraints which do not rely on linearization but scale rapidly in size owing to auxiliary slack variables. This paper presents how a chordal sparsity pattern can be used to solve this passivity enforcement problem more efficiently. The proposed algorithm uses graph theory and convex optimization to achieve a suboptimal solution that reduces the computation time required for the solution of the positive-real lemma passivity constraints by constraining the auxiliary Lyapunov variable to have a banded pattern. We provide numerical results using actual power system equipment to show that the proposed method gives faster suboptimal solutions.