Structured storage policies for energy distribution networks

We consider the problem of dynamically controlling a two-bus energy distribution network with energy storage capabilities. An operator seeks to dynamically adjust the amount of energy to charge to, or discharge from, energy storage devices in response to randomly evolving demand, renewable supply, and prices. The objective is to minimize the expected total discounted costs incurred within the network over a finite planning horizon. We formulate a Markov decision process model that prescribes the optimal amount of energy to charge or discharge and transmit between the two buses during each stage of the planning horizon. Established are the multimodularity of the value function and the monotonicity of the optimal policy in the energy storage levels. We also show that the optimal operational cost is convex and monotone in the storage capacities. Furthermore, we establish bounds on the optimal cost by analyzing comparable single-storage systems with pooled and decentralized storage configurations, respectively. These results extend to more general multi-bus network topologies. Numerical examples illustrate the main results and highlight the significance of interacting demand-side entities.