Improving Clique Decompositions of Semidefinite Relaxations for Optimal Power Flow Problems
This work addresses computational efficiency in power grid optimization, but it is incremental as it focuses on refining existing decomposition methods without introducing a new paradigm.
The paper tackled the problem of solving large-scale Semidefinite Programming relaxations for Optimal Power Flow by experimenting with clique decomposition algorithms, showing that resolution is highly sensitive to the decomposition procedure and that minimizing additional edges in chordal extensions is not always effective for good decompositions.
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.