Collective Target Tracking Mean Field Control for Markovian Jump-Driven Models of Electric Water Heating Loads

Load control has traditionally been viewed as a useful tool for peak load reduction in power systems. With the increasing renewable energy penetration in the grid, load control is also considered as a tool to exploit the storage in dispersed devices naturally present in power systems such as electric water heaters to mitigate generation variability. Tapping into the storage dispersed across the power system is challenging because of the large number of devices that need to be coordinated to produce desirable system level behavior. In this paper a mean field game theoretic based control architecture is proposed as a load control mechanism to limit the required flows of information, and produce local constraints conscious decentralized individual controls which aggregate to a desired mean behavior. A Markovian jump-driven model of individual electric water heating loads is employed where the mean field effect is mediated through the quadratic cost function parameters under the form of an integral error. The corresponding system of mean field Nash equilibrium inducing equations is developed and numerical simulation results are presented.