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We consider an energy storage problem involving a wind farm with a forecastedpower output, a stochastic load, an energy storage device, and a connection tothe larger power grid with stochastic prices. Electricity prices and wind powerforecast errors are modeled using a novel hidden semi-Markov model thataccurately replicates not just the distribution of the errors, but alsocrossing times, capturing the amount of time each process stays above or belowsome benchmark such as the forecast. This is an important property ofstochastic processes involved in storage problems. We show that we achieve morerobust solutions using this model than when more common stochastic models areconsidered. The new model introduces some additional complexity to the problemas its information states are partially hidden, forming a partially observableMarkov decision process. We derive a near-optimal time-dependent policy usingbackward approximate dynamic programming, which overcomes the computationalhurdles of classical (exact) backward dynamic programming, with higher qualitysolutions than the more familiar forward approximate dynamic programmingmethods.

Backward Approximate Dynamic Programming with Hidden Semi-Markov Stochastic Models in Energy Storage Optimization