  The integration of intermittent and volatile renewable energy resources
requires increased flexibility in the operation of the electric grid. Storage,
broadly speaking, provides the flexibility of shifting energy over time;
network, on the other hand, provides the flexibility of shifting energy over
geographical locations. The optimal control of general storage networks in
uncertain environments is an important open problem. The key challenge is that,
even in small networks, the corresponding constrained stochastic control
problems with continuous spaces suffer from curses of dimensionality, and are
intractable in general settings. For large networks, no efficient algorithm is
known to give optimal or near-optimal performance. This paper provides an
efficient and provably near-optimal algorithm to solve this problem in a very
general setting. We study the optimal control of generalized storage networks,
i.e., electric networks connected to distributed generalized storages. Here
generalized storage is a unifying dynamic model for many components of the grid
that provide the functionality of shifting energy over time, ranging from
standard energy storage devices to deferrable or thermostatically controlled
loads. An online algorithm is devised for the corresponding constrained
stochastic control problem based on the theory of Lyapunov optimization. We
prove that the algorithm is near-optimal, and construct a semidefinite program
to min- imize the sub-optimality bound. The resulting bound is a constant that
depends only on the parameters of the storage network and cost functions, and
is independent of uncertainty realizations. Numerical examples are given to
demonstrate the effectiveness of the algorithm.
