Mean Field Control for Efficient Mixing of Energy Loads

Abstract

We study an Ensemble of Energy Loads controlled via coordinated, implementation-light, randomized on/off switching. We show that Mean Field Control with nonlinear feedback on the cumulative consumption, assumed available to the aggregator via direct physical measurements of the energy flow, allows the ensemble to recover from its use in the Demand Response significantly faster than in the case of the fixed feedback. When the nonlinearity is sufficiently strong, the total instantaneous energy consumption of the ensemble shows super-relaxation---it stabilizes to the steady state much faster than the underlying probability distribution of the devices over their state space, while also leaving almost no devices outside of the comfort zone.