  There has been widespread interest in the use of grid-level storage to handle
the variability from increasing penetrations of wind and solar energy. This
problem setting requires optimizing energy storage and release decisions for
anywhere from a half-dozen, to potentially hundreds of storage devices spread
around the grid as new technologies evolve. We approach this problem using two
competing algorithmic strategies. The first, developed within the stochastic
programming literature, is stochastic dual dynamic programming (SDDP) which
uses Benders decomposition to create a multidimensional value function
approximations, which have been widely used to manage hydro reservoirs. The
second approach, which has evolved using the language of approximate dynamic
programming, uses separable, piecewise linear value function approximations, a
method which has been successfully applied to high-dimensional fleet management
problems. This paper brings these two approaches together using a common
notational system, and contrasts the algorithmic strategies (which are both a
form of approximate dynamic programming) used by each approach. The methods are
then subjected to rigorous testing using the context of optimizing grid level
storage.
