We consider a smart grid with an independent system operator (ISO), and distributed aggregators who have energy storage and purchase energy from the ISO to serve its customers. All the entities in the system are foresighted: each aggregator seeks to minimize its own long-term 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 long-term 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 entities is complicated for two reasons. First, the information is decentralized: the ISO does not know the aggregators states (i.e. their energy consumption requests from customers and the amount of energy in their storage), and each aggregator does not know the other aggregators states or the ISOs state (i.e. the energy generation costs and the status of the transmission lines). Second, the coupling among the aggregators is unknown to them. Specifically, each aggregators energy purchase affects the price, and hence the payments of the other aggregators. However, none of them knows how its decision influences the price because the price is determined by the ISO based on its state. 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 local information. The proposed framework can achieve the social optimum despite being decentralized and involving complex coupling among the various entities.
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