SDP resolution techniques for the optimal power flow with unit commitment

The application of semidefinite programming (SDP) to the resolution of the Optimal Power Flow problem (OPF) has recently been the focus of significant research effort. In conjunction with sparsity-exploiting techniques, it can yield globally optimal solutions for well-conditioned large-scale networks. In this paper, we show that these techniques can theoretically be extended to a larger class of problems, incorporating binary variables to enable unit (de-)commitment, and we solve small-scale problems using package GloptiPoly as a proof of concept. We then study the influence of Unit Commitment variables on problem sparsity and show that the sparse structure is largely preserved, suggesting that sparsity-exploiting techniques may efficiently address Optimal Power Flow with Unit Commitment (OPF-UC) problems on mid-to-large-scale networks. Finally, we use the SparsePOP package to solve OPF-UC problems on networks with up to 39 buses to global optimality.