Mean field based control of power system dispersed energy storage devices for peak load relief

The demand response problem is investigated where it is required that the mean temperature of a massive number of electric devices associated with energy storage (e.g. electric water heaters, electric space heaters, etc.) follow a target temperature trajectory computed as part of a system wide optimization problem in smart grids. The classical control approach is to compute the required signal centrally for each device and to send that signal. However, the corresponding computational and communication requirements can be forbidding. Instead, in this paper the presence of large numbers of such devices justifies the use of a decentralized mean field control based approach to the problem. A novel agent cost structure including an integral term is utilized for this purpose. The corresponding system of mean field equations is developed, a fixed point analysis is given for a particular case, an ε-Nash theorem is presented, and numerical simulation results are provided.