Infeasibility Cutting Plane for Unit Commitment Problem

This paper introduces a new type of cutting plane for the unit commitment (UC) problem, namely “infeasibility cutting plane”. The infeasibility cutting plane refers to a type of logic constraint that eliminates the combination of integer variables causing infeasibility of the UC problem while not affecting any feasible integer solutions. This paper demonstrates that under certain conditions, such a cutting plane is effective for tightening the linear programming (LP) relaxation of UC, thus achieving a valid acceleration of UC without the loss of accuracy. A theoretical and easy-to-implement criterion is provided to identify valid infeasibility cutting planes. Then, an efficient framework for constructing the infeasibility cutting planes is presented to quickly obtain multiple combinations of integer variables causing infeasibility of UC through solving a batch of relaxed LP problems. The condition that the constructed infeasibility cutting plane does not provide overlapped information is provided. Based on the test on 30 public and utility cases, the proposed cutting plane method achieves an acceleration of 1.14 to 2.41 times with full optimality guarantee. Also, results show that the proposed cutting planes also work with existing cutting plane methodologies embedded in modern solvers.