Optimal Placement of Energy Storage in Distribution Networks

We study the problem of optimal placement and capacity of energy storage devices in a distribution network to minimize total energy loss. A continuous tree with linearized DistFlow model is developed to model the distribution network. We analyze structural properties of the optimal solution when all loads have the same shape. We prove that it is optimal to place storage devices near the leaves of the network away from the substation, and that the scaled storage capacity monotonically increases towards the leaves. Moreover, under optimal storage placement, the locational marginal value of storage is equalized wherever nonzero storage is deployed and increases from the substation towards any leaf node over places where there is zero storage deployment. We illustrate through simulations that these structural properties are robust in that they hold approximately when some of our modeling assumptions are relaxed.