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

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. Semi-definite 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.

Automated summary

In this paper, a formulation of the unit commitment problem with AC power flow constraints is presented. The problem is solved by a Benders' decomposition approach, which formulates the unit commitment master problem as a mixed-integer problem with linearized power generation constraints for improved convergence. Numerical case studies demonstrate the effectiveness of the proposed method in improving convergence quality.