Optimal large-scale storage placement in single generator single load networks

Large-scale storage will play an increasingly important role in future power grids. As a result, how to optimally place storage in such networks, is an important investment problem. Furthermore, since the allocation of storage resources is static, i.e., it is not feasible to move storage around in a dynamic fashion, it is important to derive optimal such allocations that are robust to the values of the load profiles and other network parameters, such as the line flow constraints. For a single generator single load network, and for a cost of generation that is quadratic in the generation power, we show that, for any given amount of storage resources, placing storage at the demand node is always optimal. This result is true regardless of the demand profile and flow constraints, and therefore is robust. As a byproduct of this result, for a fixed demand profile, we characterize the dependence of the optimal production cost on the flow constraints and on the available storage resources.