Constructing Valid Inequalities by Analytical Feasibility Conditions on Unit Commitment with Transmission Constraints

Abstract

Unit commitment (UC) is one of the core problems in short-term power generation scheduling and electricity market clearing. The problem is generally formulated as a mixed integer programming model that is computationally complex for large sized systems. Introducing valid inequalities (VIs) is an effective method to improve the computational efficiency. Recently the analytical necessary conditions for determining feasible commitment states are reported in literature, which provides an opportunity to form VIs for UC. In this paper, we equivalently convert the nonlinear necessary conditions into a group of linear inequalities by analyzing the problem structure, and add them to the original UC formulation as VIs. In the branch-and-cut framework, these VIs can quickly identify a large percentage of infeasible nodes and thus reduce the scale of the search tree. They can also assist in forming effective cuts to speed up the branch-and-cut process. A procedure of selecting the most effective VIs is developed to further improve the computational performance. Numerical results based on three testing systems show that the VIs added can significantly improve the computational efficiency in most cases.