A theory for the economic operation of a smart grid with stochastic renewables, demand response and storage

We are motivated by the problems faced by independent system operators in an era where renewables constitute a significant portion of generation and demand response is employed by a significant portion of loads. We address a key issue of designing architectures and algorithms which generate optimal demand response over a time window in a decentralized manner, for a smarter grid consisting of several stochastic renewables and dynamic loads. By optimal demand response, we refer to the demand response which maximizes the sum of the utilities of the agents, i.e., generators, loads, load serving entities, storage services, prosumers, etc., connected to the smart-grid. By decentralized we refer to the desirable case where neither the independent system operator (ISO) needs to know the dynamics/utilities/states of the agents, nor do the agents need to know the dynamics/utilities/states of each other. The communication between the ISO and agents is restricted to the ISO announcing prices, and the agents responding with their energy generation/consumption bids. We begin with the deterministic case for which there is a complete solution. It features a price iteration scheme that results in optimality of social welfare. We also provide an optimal solution for the case where there is a common randomness affecting and observed by all agents. This solution can be computationally complex, though we provide approximations. For the more general partially observed randomness case, we exhibit a relaxation that significantly reduces complexity. We also provide an approximation strategy that leads to a model predictive control (MPC) approach. Simulation results illustrate the increase in social welfare utility compared to some alternative architectures.