Quick Algorithm for Unit Commitment Based on Relaxation and Neighborhood Search

Abstract

In order to solve unit commitment (UC) problem, this paper presents a quick algorithm based on iteratively solving tight continuous relaxations and compact neighborhood search. A tight mixed integer programming with linear objective function (TLO-MIP) formulation for the UC problem is proposed by projecting the output of unit power into [0], [1] and tightening the continuous relaxation twice with the convex hull reformulation (CHR) technique. We use lift-and-project (L&P) technique to compress the continuous relaxation for TLO-MIP iteratively, and obtain a tighter formulation. Solutions can be obtained by solving the relaxations of this tight formulation, and these solutions can be viewed as good approximations for the optimal solutions of the UC problems. A compact neighborhood of current suboptimal solution is used to improve the quality of solutions of UC problems further more. The simulations are carried out based on the test cases with 10 to 100 units and considering one-day scheduling periods. The results show that the TLO-MIP is good tight UC formulation, furthermore, the proposed quick algorithm based on relaxation and neighborhood search can solve large-scale UC problems with excellent performance and high-quality sub-optimal solutions.