Dynamic programming solution to distributed storage operation and design

Energy storage provides an important way to average temporal variability of intermittent energy generation. Grid level distributed storage enables additional spatial averaging effect by sending stored energy through the network. However, the problem of optimal storage operation in the network, coupling storage and network constraints with randomness of renewable generation, is challenging. An efficient solution method to this problem based on dynamic programming is presented in this paper. This approach also leads to analytical expressions for the expected system cost and the optimal control parametrized by dual variables, which can be computed by solving a simple deterministic convex program. These analytical expressions simplify tasks such as network storage system design. The approach is illustrated with numerical examples.