Mean Field Control for Efficient Mixing of Energy Loads

TL;DR

This paper introduces a mean field control approach for coordinating energy device ensembles, enabling faster recovery to steady states and efficient demand response with minimal device discomfort.

Contribution

It demonstrates that nonlinear feedback in mean field control significantly accelerates ensemble relaxation and improves energy management in demand response scenarios.

Findings

Faster transition to steady state with nonlinear feedback

Observation of super-relaxation phenomenon

Minimal device discomfort during transition

Abstract

We pose an engineering challenge of controlling an Ensemble of Energy Devices via coordinated, implementation-light and randomized on/off switching as a problem in Non-Equilibrium Statistical Mechanics. 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 regime, i.e. transition to a statistical steady state, significantly faster than in the case of the fixed feedback. Moreover when the nonlinearity is sufficiently strong, one observes the phenomenon of "super-relaxation" -- where the total instantaneous energy consumption of the ensemble transitions 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.