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

Area of Science:

• Smart Grid Technology
• Game Theory
• Control Systems

Background:

• Smart grids require efficient energy consumption control strategies.
• Users' energy costs are influenced by aggregate consumption, which is typically unknown to individuals.
• Decentralized control mechanisms are needed for large-scale smart grid networks.

Purpose of the Study:

• To model and analyze energy consumption control in smart grids using an aggregate game framework.
• To develop and analyze Nash seeking strategies for decentralized energy consumption management.
• To investigate the convergence properties of these strategies under various conditions, including the presence of stubborn players.

Main Methods:

• An aggregate game model is employed for energy consumption control.
• An average consensus protocol is utilized to estimate aggregate energy consumption.
• Nash seeking strategies are developed based on neighboring communication and estimations.
• Singular perturbation analysis and Lyapunov stability analysis are used to prove convergence properties.

Main Results:

• The proposed Nash seeking strategies demonstrate convergence properties.
• Local convergence is achieved for games with multiple Nash equilibria.
• Nonlocal and exponential convergence are shown for unique Nash equilibria, including inner Nash equilibria.
• Rational players' actions are driven towards their best response strategies even with stubborn players.

Conclusions:

• The developed game-theoretic approach effectively manages energy consumption in smart grids.
• The Nash seeking strategies ensure stable and efficient energy usage through decentralized estimation and communication.
• The methods are validated through numerical examples, confirming their practical applicability for systems like HVAC networks.