New Local Search Methods for Improving the Lagrangian-Relaxation-Based Unit Commitment Solution

The unit commitment problem (UCP) for an electric power system is used to determine the schedules of power units that minimize the total production cost over a planning horizon while satisfying the load demand, spinning reserve, and operating constraints of individual units. When the number of units is large and the planning horizon is long, the UCP is a large-scale problem, for which an exact optimal solution is difficult to obtain within a reasonable computation time. The Lagrangian relaxation (LR) method is known to be useful for large-scale UCPs. The LR method first solves the dual problem of the UCP, and then constructs a feasible solution from the dual solution by using some heuristics. In this paper, we propose new local search (LS) methods for improving the feasible solution obtained by the LR method. We define the neighborhood of the local search as the feasible set in which the on-off states of all but one or two units are fixed. The neighborhood search can then be executed by solving the one unit or two UCPs, which are efficiently solved by dynamic programming if no ramp-rate limit constraint exists. Numerical results show that the proposed LS methods can find feasible schedules for which the costs are lower than those obtained by the existing methods. The applicability of the proposed methods to long-term UCPs is also demonstrated.