Optimal strategies for operating energy storage in an arbitrage or smoothing market

We characterize cost-minimizing operating strategies for an energy store over a given interval of time [0, T]. The cost functional here can represent, for example, a traditional economic cost or a penalty for time-variation of the output from a storage-assisted wind farm or more general imbalance between supply and demand. Our analysis allows for leakage, operating inefficiencies and general cost functionals. In the case where the 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 ∈ [0, T] requires cost information over only some usually much shorter subinterval of time [t, tk] ⊂ [t, T].