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There has been widespread interest in the use of grid-level storage to handlethe variability from increasing penetrations of wind and solar energy. Thisproblem setting requires optimizing energy storage and release decisions foranywhere from a half-dozen, to potentially hundreds of storage devices spreadaround the grid as new technologies evolve. We approach this problem using twocompeting algorithmic strategies. The first, developed within the stochasticprogramming literature, is stochastic dual dynamic programming (SDDP) whichuses Benders decomposition to create a multidimensional value functionapproximations, which have been widely used to manage hydro reservoirs. Thesecond approach, which has evolved using the language of approximate dynamicprogramming, uses separable, piecewise linear value function approximations, amethod which has been successfully applied to high-dimensional fleet managementproblems. This paper brings these two approaches together using a commonnotational system, and contrasts the algorithmic strategies (which are both aform of approximate dynamic programming) used by each approach. The methods arethen subjected to rigorous testing using the context of optimizing grid levelstorage.

SDDP vs. ADP: The Effect of Dimensionality in Multistage Stochastic Optimization for Grid Level Energy Storage