Improving Clique Decompositions of Semidefinite Relaxations for Optimal Power Flow Problems

TL;DR

This paper investigates how different clique decomposition algorithms affect the efficiency of solving large-scale semidefinite relaxations for optimal power flow problems, highlighting that fewer additional edges do not always lead to better decompositions.

Contribution

The study reveals that minimizing additional edges in chordal extensions is not always optimal for clique decompositions in SDP-based power flow solutions.

Findings

Clique decomposition algorithms significantly impact SDP solution efficiency.

Reducing additional edges does not necessarily improve decomposition quality.

Sensitivity of SDP solutions to clique decomposition methods is demonstrated.

Abstract

Semidefinite Programming (SDP) provides tight lower bounds for Optimal Power Flow problems. However, solving large-scale SDP problems requires exploiting sparsity. In this paper, we experiment several clique decomposition algorithms that lead to different reformulations and we show that the resolution is highly sensitive to the clique decomposition procedure. Our main contribution is to demonstrate that minimizing the number of additional edges in the chordal extension is not always appropriate to get a good clique decomposition.