Large scale real-time bidding in the smart grid: A mean field framework

We model the power market as a dynamic large population game where suppliers and consumers submit their bids in real-time. The agents are coupled in their dynamics and cost functions through the price process. The control action computation complexity and information exchange requirements for each agent increase as the number of agents in the system increases, and this naturally leads to computational intractability. We apply the mean field methodology to study the limit behaviour of a large population of agents, and present a decentralized algorithm where agents submit their bids solely following the price signal and using statistical information that is measured from the entire population. We show that under some restrictions on the population parameter distributions the proposed algorithm gives rise to a situation where (i) all agent systems are L² stable, and (ii) the set of controls yields an ε-Nash equilibrium.