A Mean field control approach for demand side management of large populations of thermostatically controlled loads


S. Grammatico, B. Gentile, F. Parise, J. Lygeros


IEEE European Control Conference, February 20th, 2015




This paper presents a constrained Mean Field (MF) control approach for demand side management of large populations of flexible electric loads, such as electrical cooling/heating appliances, called Thermostatically Controlled Loads (TCLs). We model the switching dynamics of each individual TCL as the solution of a local optimization problem, characterized by individual cost function, comfort constraints, cooling/heating rates and external temperature. We consider that a central utility company is willing to broadcast macro- scopic incentives to steer the overall TCL population towards a convenient equilibrium, to avoid power demand peaks due to possible synchronization of the TCL duty-cycles. To find such pricing schemes we propose an iterative algorithm where, at every step, a simple feedback law is used to update the macroscopic incentives, given the current aggregate demand of the TCL population. The convergence of such algorithm is ensured for any population size, even in the presence of heterogeneous convex constraints. We illustrate the benefits of our MF control approach via numerical analysis.