Improving Clique Decompositions of Semidefinite Relaxations for Optimal Power Flow Problems

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.