Sequential Relaxation of Unit Commitment with AC Transmission Constraints

This paper proposes a sequential convex relaxation method for obtaining feasible and near-globally optimal solutions for unit commitment (UC) with AC transmission constraints. First, we develop a second-order cone programming (SOCP) relaxation for AC unit commitment. To ensure that the resulting solutions are feasible for the original non-convex problem, we incorporate penalty terms into the objective of the proposed SOCP relaxation. We generalize our penalization method to a sequential algorithm which starts from an initial point (not necessarily feasible) and leads to feasible and near-optimal solutions for AC unit commitment. Once a feasible point is attained, the algorithm preserves feasibility and improves the objective value until a near optimal point is obtained. The experimental results on IEEE 57, IEEE 118, and IEEE 300 bus benchmark cases from MATPOWER [1] demonstrate the performance of the proposed method in solving challenging instances of AC unit commitment.