Pumped storage hydro (PSH) plants have been proven to be a valuable resource in providing storage ability and fast ramp to address power system uncertainties such as renewable energy intermittency. An accurate model for the input-output curve of PSH plants can capture the varying efficiency and 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, proofed, and analyzed for fixed-speed PSH considering the value of water in the 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 problem using real world data of Ludington PSH station. Numerical results demonstrated the superior computational advantage of the proposed approach.