We consider a storage device, such as a pumped storage hydroelectric generator, that has a state-of-charge together with mutually exclusive charging and generating modes. We develop valid inequalities for a storage model that uses binary variables to represent the charging and generating modes. To investigate the model, we consider two contexts, standalone and large-scale. The standalone context involves the hydroelectric generator purchasing or selling electricity based on known or forecast prices. We consider properties of an optimization formulation with objective that evaluates the profit from sale of net generation and value of stored energy, present conditions for the optimum of the continuous relaxation of this optimization formulation to have binary values for the charging and generation commitment variables, and demonstrate the result numerically with a small example system. Analysis of the standalone context helps to explain why the combination of features in the storage model results in a difficult problem. The large-scale context embeds the model into a unit commitment and dispatch formulation for multiple generators. For several large-scale test cases, we numerically verify that the valid inequalities can improve the computation compared to the standard model in the literature.
Working paper, March 2021