Approximating Input-Output Curve of Pumped Storage Hydro Plant: A Disjunctive Convex Hull Method

Pumped storage hydro (PSH) plant is a valuable resource with storage and fast ramp capabilities, which can manage the intermittency of renewable energy. An accurate model for the input-output curve of PSH plant can capture its varying efficiency feature and enable accurate evaluations of available generating/pumping capability. However, the trade-off between approximation accuracy and computation time poses a significant challenge for input-output curve modeling. In this paper, we develop a hypograph-relaxation-based input-output curve modeling framework, wherein sufficient conditions for exact hypograph relaxation are defined, proved, and analyzed for fixed-speed PSH considering the value of water in the upper reservoir. Under this framework, a novel disjunctive convex hull model is proposed to balance the aforementioned trade-off. Our model can take advantage of high accuracy in time-consuming piece-wise approximation models, and acceptable computation burden in less-accurate convex hull models. To divide a given input-output curve into various components that can be approximated by their respective convex hulls, we propose to use an approximate convex decomposition (ACD) based approach. The proposed model is tested for profit maximization problems using real-world Ludington PSH station data. Numerical results demonstrated the superior computational advantage of the proposed approach.