  We consider an energy storage problem involving a wind farm with a forecasted
power output, a stochastic load, an energy storage device, and a connection to
the larger power grid with stochastic prices. Electricity prices and wind power
forecast errors are modeled using a novel hidden semi-Markov model that
accurately replicates not just the distribution of the errors, but also
crossing times, capturing the amount of time each process stays above or below
some benchmark such as the forecast. This is an important property of
stochastic processes involved in storage problems. We show that we achieve more
robust solutions using this model than when more common stochastic models are
considered. The new model introduces some additional complexity to the problem
as its information states are partially hidden, forming a partially observable
Markov decision process. We derive a near-optimal time-dependent policy using
backward approximate dynamic programming, which overcomes the computational
hurdles of classical (exact) backward dynamic programming, with higher quality
solutions than the more familiar forward approximate dynamic programming
methods.
