Submodularity of energy storage placement in power networks

Abstract

This paper studies the problem of optimally placing energy storage devices in power networks. We explicitly model capital and installation costs of storage devices because these fixed costs account for the largest cost component in most grid-scale storage projects. Finding an optimal placement strategy is a challenging task due to (i) the discrete nature of such placement problems, and (ii) the spatial and temporal transfer of energy via transmission lines and distributed energy storage resources. To develop an efficient placement framework with performance guarantees, we investigate the structural properties of the optimal value function for the multi-period economic dispatch problem with storage dynamics, and an analytical characterization of optimal storage controls and locational marginal prices. In particular, we provide a tight condition under which the optimal placement value function is submodular and an efficient computational method to certify the condition. When this condition is valid, a modified greedy algorithm for maximizing a submodular function subject to a knapsack constraint provides a (1 – 1/e)-optimal solution.