We consider a smart-grid connecting several agents, modeled as stochastic dynamical systems, who may be electricity consumers producers. At each discrete time instant, which may represent a 15 minute interval, each agent may consume generate some quantity of electrical energy. The Independent System Operator (ISO) is given the task of assigning consumptions generations to the agents so as to maximize the sum of the utilities accrued to the agents, subject to the constraint that energy generation equals consumption at each time. This task of coordinating generation and demand has to be accomplished by the ISO without the agents revealing their system states, dynamics, or utility cost functions. We show how and when a simple iterative procedure converges to the optimal solution. The ISO iteratively obtains electricity bids by the agents, and declares the tentative market clearing prices. In response to these prices, the agents submit new bids. On the demand side, the solution yields an optimal demand response for dynamic and stochastic loads. On the generation side, it provides the optimal utilization of stochastically varying renewables such as solar wind, and generation with fossil fuel based generation with dynamic constraints such as ramping rates. Thereby we solve a decentralized stochastic control problem, without agents sharing any information about their system models, states or utility functions.
We show below that the ISO Problem is an example of a decentralized control system with non-classical observation patterns in which signaling can successfully result in globally optimum performance. The agents need not reveal their observations, state values, their individual system dynamics or their individual cost-functions. We construct concrete signaling schemes which encode-decode the information required in order to recover the same performance as that of centralized control. From the economics side, this work is an extension of general equilibrium theory @cite_2 . To the authors' knowledge there does not appear to be any similar result for coordinating multiple LQG systems or the efficiency of the simplified signaling.
@cite_2
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In this paper, the problem of feedback and active user selection in multiple-input single-output (MISO) wireless systems such that the system’s stability region is as big as possible is examined. The focus is on a system in a Rayleigh fading environment where zero forcing precoding is used to serve all active users in every slot. Acquisition of the channel states is done via uplink training in time division duplexing mode by the active users. Clearly, only a subset of users can perform uplink training and the selection of this subset is a challenging and interesting problem especially in MISO systems. The stability regions of a baseline centralized scheme and two novel decentralized policies are examined analytically. In the decentralized schemes, the transmitter broadcasts periodically the queue state information and the users contend for the channel in a carrier sense multiple access-based manner with parameters based on the outdated queue state information and real-time channel state information. We show that, using infrequent signaling between the base station and the users, the decentralized policies outperform the centralized policy. In addition, a threshold-based user selection and training scheme for discrete-time contention is proposed. The results of this paper imply that, as far as stability is concerned, the users must be involved in the active user selection and feedback training decision. This should be leveraged in future communication systems.