A demand response game and its robust price of anarchy

Increased variability in power generation due to large scale integration of renewable energy sources such as wind and solar power is a significant technical challenge in power systems operations and control. In addition, there is a compelling value in reducing the peak demand since it occurs only for a small fraction of time, while the power system is designed to reliably satisfy the peak demand. One promising approach to reduce variability of renewable generation and peak demand is to harness the inherent flexibility of electric power loads of consumers. Efficient control techniques are required to manage flexibility in consumer demands. Advancements in sensing, communications and computational technologies infused into the power system resulting in the cyber-physical-social electric grid, are creating opportunities for novel control solutions. In this paper, we first formulate a centralized demand side management approach. Next, we consider a decentralized approach for controlling the loads where the flexible load consumers play a non-cooperative game among each other. We show that Nash equilibria exist for this game. Our main technical result is that the demand response game in decentralized approach has the property of being a valid monotone utility game. This in turn leads to robust lower bounds on the price of anarchy (POA) for our game.