A Mean Field control approach for demand side management of large populations of Thermostatically Controlled Loads

This paper presents a 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 broadcasts macroscopic 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 model-free feedback law is used to update the incentives, given the current aggregate demand of the TCL population only. The convergence of such algorithm is ensured for any population size, even in the presence of heterogeneous convex constraints. We illustrate our MF control approach via numerical analysis.