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.
Viewed from the power system end, there have been many efforts since the deregulation of the electricity sector on a market-based framework to clear the system. @cite_7 have proposed a two-layered approach that internalizes individual constraints of market participants while allowing the ISO to manage the spatial complexity. The approximated MPC algorithm is shown to perform well in many realistic applications. In order to analyze the strategic interactions between the ISO and market participants, game theoretical approaches have been proposed, e.g., @cite_10 uses a Stackelberg game framework for studying economic dispatch with demand response. @cite_1 pose the problem as a noncooperative game, and prove the existence of a Nash equilibrium under some assumtpions.
@cite_1 @cite_10 @cite_7
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In this paper, we raise the question: What is the value that demand response management (DRM) can bring to generation companies and consumers in the smart grid? The question is fundamental for understanding the efficiency and impact of DRM on the future power grid. To answer this question, we first establish a Stackelberg game framework that captures the hierarchical communication architecture of the energy system, and the rational behaviors of the consumers and the market operator. We define the value of demand response based on the Stackelberg equilibrium (SE) solution to the hierarchical two-person game problem, and the standard optimal solution to economic dispatch problem. In order to compute the equilibrium solution, we show that a consistency principle can be used to characterize the SE of the game in which the follower responds to the dual variable of the leader's problem. We use logarithmic utility functions to illustrate the solution concept and show that in some cases, DRM provides conflicting values to the gencos and consumers. This paper proposes an innovative game theoretic framework for a next-generation retail electricity market (Energy Internet) with high penetration of distributed residential electricity suppliers (Energy Cells). The envisioned Energy Internet is developed for plug-and-play of a large number of distributed renewable energy generation and energy storage. The residential customers, referred as Energy Cells, are not only the electricity consumers but can also be the electricity suppliers by locally operating and managing their own distributed generators, distributed energy storage devices, and dispatchable loads. This paper formulates a set of mathematical models of the retail electricity market participants with a number of local and global constraints. A numerical case study is performed to validate the proposed next-generation retail electricity market framework using game-theoretic methodologies. The numerical simulation results demonstrate the effectiveness of the proposed market clearing scheme with high penetration of distributed residential electricity suppliers. Dynamic spectrum access can significantly improve the spectrum utilization. For wireless service providers, the emergence of dynamic spectrum access brings new opportunities and challenges. The flexible spectrum acquisition gives a particular provider the chance to easily adapt its system capacity to fit end users' demand. However, the competition among several providers for both spectrum and end users complicates the situation. In this paper, we propose a general three-layer spectrum market model for the future dynamic spectrum access system, in which the interaction among spectrum holder, wireless service providers and end users are considered. We study a duopoly situation, where two wireless service providers participate in bandwidth competition in spectrum purchasing and price competition to attract end users, with the aim of maximizing their own profit. We believe we are the first one to explicitly study the relation of these two competitions in dynamic spectrum market. We formulate the wireless service providers' competition as a non-cooperative two-stage game. We first analyze the static game when full information is available for providers. Under general assumptions about the price and demand functions, a unique pure Nash equilibrium is identified as the outcome of the game, which shows the stability of the market. We further evaluate the market efficiency of the equilibrium in a symmetric case, and show that the gap with the social optimal is bounded within a small constant ratio. When the market information is limited, we provide myopically optimal adjustment algorithms for the providers. With such strategies, short term price updating converges to the Nash equilibrium of the