Benders’ decomposition of the unit commitment problem with semidefinite relaxation of AC power flow constraints

•Master problem includes linearization of power generation constraints of subproblems.•ϵ-feasibility initialization is not required.•Our approach consistently reduced the number of iterations required for convergence.•Rank of active power SDP matrices is guaranteed to be 1 at the end of each iteration.•Rank reduction procedure is iteratively performed upon voltage variables. In this paper we present a formulation of the unit commitment problem with AC power flow constraints. It is solved by a Benders’ decomposition in which the unit commitment master problem is formulated as a mixed-integer problem with linearization of the power generation constraints for improved convergence. Semidefinite programming relaxation of the rectangular AC optimal power flow is used in the subproblem, providing somewhat conservative cuts. Numerical case studies, including a 6-bus and the IEEE 118-bus network, are provided to test the effectiveness of our proposal. We show in our numerical experiments that the use of such strategy improves the quality of feasibility and optimality cuts generated by the solution of the convex relaxation of the subproblem, therefore reducing the number of iterations required for algorithm convergence.