Dynamic Stochastic Demand Response With Energy Storage

Abstract

We consider a power system with an independent system operator (ISO), and distributed aggregators who have energy storage and purchase energy from the ISO to serve their customers. All the entities in the system are <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">foresighted</i> : each aggregator seeks to minimize its own <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">long-term</i> payments for energy purchase and operational costs of energy storage by deciding how much energy to buy from the ISO, and the ISO seeks to minimize the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">long-term</i> total cost of the system (e.g., energy generation costs and the aggregators’ costs) by dispatching the energy production among the generators. The decision making of the foresighted entities is complicated for two reasons. First, the information is decentralized among the entities, namely each entity does not know the others’ states. Second, an aggregator’s current decision affects its future costs due to the coupling introduced by the energy storage. We propose a design framework in which the ISO provides each aggregator with a conjectured future price, and each aggregator distributively minimizes its own long-term cost based on its conjectured price as well as its locally-available information. We prove that the proposed framework can achieve the social optimum despite being decentralized and involving complex coupling. Simulation results show that the proposed foresighted demand side management achieves significant reduction in the total cost, compared to the optimal myopic demand side management (up to 60% reduction), and the foresighted demand side management based on the Lyapunov optimization framework (up to 30% reduction).