Convex Hull Model for a Single-Unit Commitment Problem With Pumped Hydro Storage Unit

Abstract

The single-unit commitment (1UC) maximizes the revenue within a time series of given electricity prices while respecting generator-specific constraints, leading to a mixedinteger program (MIP). To reduce the computational complexity of the 1UC with a pump storage unit (PSU-1UC), we construct the convex hull of PSU-1UC in this paper. Focusing on the possible combination of alternating generation and pumping time intervals, we first establish a dynamic programming (DP) model that can be solved in polynomial time. Then, we reformulate the DP model into a linear programming (LP) model in a higherdimensional space, which provides the convex hull of the PSU-1UC. It helps to speed up the large-scale unit commitment problems solved by decomposition algorithms from the perspective of formulation transformation. Numerical experiments demonstrate the effectiveness and efficiency of the proposed model.