Accelerating the Benders decomposition for network-constrained unit commitment problems

Abstract

This paper presents an optimization method by generating multiple strong Benders cuts for accelerating the convergence of Benders Decomposition (BD) when solving the network-constrained generation unit commitment (NCUC) problem. In NCUC, dc transmission network evaluation subproblems are highly degenerate, which would lead to many dual optimal solutions. Furthermore, the classical BD cuts are often low-density which involve only a limited number of decision variables in the master problem. Therefore, the dual optimal solutions and the corresponding Benders cuts are of crucial importance for improving the efficiency of the BD algorithm. The proposed method would generate multiple strong Benders cuts, which are pareto optimal, among candidates from multiple dual optimal solutions. Such cuts would be high-density in comparison with low-density cuts produced by the classical BD. The proposed multiple strong Benders cuts are efficient in terms of reducing the total iteration number and the overall computing time. The high-density cuts may restrict the feasible region of the master unit commitment (UC) problem in each iteration as they incorporate more decision variables in each Benders cut. The multiple strong Benders cuts would accordingly reduce the iteration number and overall computing time. Numerical tests demonstrate the efficiency of the proposed multiple strong Benders cuts method in comparison with the classical BD algorithm and the linear sensitivity factors (LSF) method. The proposed method can be extended to other applications of BD for solving the large-scale optimization problems in power systems operation, maintenance, and planning.