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Game Design and Analysis for Price-Based Demand Response: An Aggregate Game Approach

机译：基于价格的需求响应的博弈设计与分析：总体博弈方法

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摘要

In this paper, an aggregate game is adopted for the modeling and analysis of energy consumption control in smart grid. Since the electricity users’ cost functions depend on the aggregate energy consumption, which is unknown to the end users, an average consensus protocol is employed to estimate it. By neighboring communication among the users about their estimations on the aggregate energy consumption, Nash seeking strategies are developed. Convergence properties are explored for the proposed Nash seeking strategies. For energy consumption game that may have multiple isolated Nash equilibria, a local convergence result is derived. The convergence is established by utilizing singular perturbation analysis and Lyapunov stability analysis. Energy consumption control for a network of heating, ventilation, and air conditioning systems is investigated. Based on the uniqueness of the Nash equilibrium, it is shown that the players’ actions converge to a neighborhood of the unique Nash equilibrium nonlocally. More specially, if the unique Nash equilibrium is an inner Nash equilibrium, an exponential convergence result is obtained. Energy consumption game with stubborn players is studied. In this case, the actions of the rational players can be driven to a neighborhood of their best response strategies by using the proposed method. Numerical examples are presented to verify the effectiveness of the proposed methods.
机译：本文采用集合博弈对智能电网的能耗控制进行建模和分析。由于用电用户的成本函数取决于最终用户不知道的总能耗，因此采用了平均共识协议对其进行估算。通过用户之间关于他们对总能耗的估计的邻近沟通，开发了纳什寻求策略。探索了所提出的纳什寻求策略的收敛性。对于可能具有多个孤立的纳什均衡的能耗博弈，得出了局部收敛结果。利用奇异摄动分析和李雅普诺夫稳定性分析建立了收敛性。研究了供暖，通风和空调系统网络的能耗控制。根据纳什均衡的唯一性，可以证明玩家的行为非局部地收敛到唯一的纳什均衡的邻域。更特别地，如果唯一的纳什均衡是内部纳什均衡，则获得指数收敛结果。研究了顽固玩家的能源消耗游戏。在这种情况下，通过使用所提出的方法，理性参与者的行为可以被驱使到其最佳响应策略的附近。数值算例验证了所提方法的有效性。

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