A PDE--based Power Tracking Control of Heterogeneous TCL Populations

TL;DR

This paper develops a PDE-based control scheme for managing the aggregate power consumption of heterogeneous TCL populations, ensuring stability and effectiveness through feedback linearization and boundary analysis.

Contribution

It introduces a novel PDE control approach for TCL populations using boundary and domain actions, with stability analysis and simulation validation.

Findings

Effective power tracking demonstrated in simulations

Stable control achieved with PDE-based feedback linearization

Handles time-varying boundaries in TCL populations

Abstract

This chapter presents the development and the analysis of a scheme for aggregate power tracking control of heterogeneous populations of thermostatically controlled loads (TCLs) based on partial differential equations (PDEs) control theory and techniques. By employing a thermostat--based deadband control with forced switching in the operation of individual TCLs, the aggregated dynamics of TCL populations are governed by a pair of Fokker--Planck equations coupled via the actions located both on the boundaries and in the domain. The technique of input-output feedback linearization is used for the design of aggregate power tracking control, which results in a nonlinear system in a closed loop. As the considered setting is a problem with time-varying boundaries, well-posedness assessment and stability analysis are carried out to confirm the validity of the developed control scheme. A simulation study is contacted to evaluate the effectiveness and the performance of the proposed approach.