A deterministic method for the unit commitment problem in power systems

The unit commitment (UC) problem in power systems is generally formulated as a large-scale nonlinear mixed-integer combinatorial optimization problem, which is difficult to solve. This paper presents a deterministic method named cut-and-branch for solving UC, which is based on cuts and branch-and-bound search as well as heuristic rounding technique. First, a suitable mixed-integer quadratic programming (MIQP) model of UC is presented by some linearization technique, then the MIQP is solved by the proposed cut-and-branch method. In the proposed method, two classes of cuts are introduced to give a stronger representation of the corresponding continuous relaxed problem: one is the approximate integer cut derived from a natural understanding of the problem which is simple but highly efficient, and the other is the generalized flow cover inequality. Furthermore, the continuous relaxed problem incorporating the proposed cuts can obtain some better initial feasible solutions and reduce the numbers of nodes during the branch-and-bound search. The simulation results for six systems with up to 100 units and 24 h show that the proposed method has nice convergence, which can find global optimal solution in theory.