Aggregate Power Control of Heterogeneous TCL Populations Governed by Fokker-Planck Equations

TL;DR

This paper develops a control framework for heterogeneous TCL populations modeled by Fokker-Planck equations, using feedback linearization to achieve stable aggregate power management validated through simulations.

Contribution

It introduces a novel control approach for TCL populations modeled by coupled Fokker-Planck equations, including stability analysis and validation.

Findings

Control scheme effectively stabilizes aggregate power.

Model accurately captures TCL population dynamics.

Simulation results confirm approach validity.

Abstract

This paper addresses the modeling and control of heterogeneous populations of thermostatically controlled loads (TCLs) operated by model predictive control (MPC) schemes at level of each TCL. It is shown that the dynamics of such TCLs populations can be described by a pair of Fokker-Planck equations coupled via the actions in the domain. The technique of input-output feedback linearization is used in the design of aggregate power control, which leads to a nonlinear system in closed loop. Well-posedness analysis is carried out to validate the developed control scheme. The closed-loop stability of the system is assessed by a rigorous analysis. A simulation study is contacted, and the obtained results confirm the validity and the effectiveness of the proposed approach.