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Optimal strategies for operating energy storage in an arbitrage market

We characterize profit-maximizing operating strategies, over some time horizon [0,T], for an energy store which is trading in an arbitrage market. Our theory allows for leakage, operating inefficiencies, operating constraints and general cost functions. In the special case where the operating cost of a store depends only on its instantaneous power output (or input), we present an algorithm to determine the optimal strategies. A key feature is that this algorithm is localized in time, in the sense that the action of the store at a time t only requires information about electricity prices over some subinterval of time [t,t_k] contained within [t,T]. To introduce more complex storage models, we discuss methods for an example which includes minimum switching times between modes of operation.