Power Tracking Control of Heterogeneous Populations of TCLs with Partially Measured States

TL;DR

This work addresses how to steer the aggregate power of heterogeneous TCL populations to follow a reference profile using a PDE-based population model. It adopts a late-lumping control design with input-output linearization that is independent of uncertain diffusion parameters, relying only on end-point state measurements and a sliding-model-like FTISS-tracking scheme. The main contributions are (i) redefining the power-tracking output to ensure controllability, (ii) a parameter-robust controller with FTISS guarantees for the tracking error, and (iii) rigorous stability and non-negativity analyses of the governing PDEs, plus simulation validation for populations spanning two orders of magnitude in size. The results demonstrate robust performance with significantly reduced communication in large-scale TCL ensembles, highlighting the practical potential for distributed demand-response and grid-support applications in smart grids.

Abstract

This paper presents a new aggregate power tracking control scheme for populations of thermostatically controlled loads (TCLs). The control design is performed in the framework of partial differential equations (PDEs) based on a late-lumping procedure without truncating the infinite-dimensional model describing the dynamics of the TCL population. An input-output linearization control scheme, which is independent of system parameters and uses only partial state measurement, is derived, and a sliding model-like control is applied to achieve finite-time input-to-state stability for tracking error dynamics. Such a control strategy can ensure robust performance in the presence of modeling uncertainties, while considerably reducing the communication burden in large scale distributed systems similar to that considered in the present work. A rigorous analysis of the closed-loop stability of the underlying PDE system was conducted, which guaranteed the validity of the developed control scheme. Simulation studies were performed while considering two TCL populations with a significant difference in their size, and the results show that the developed control scheme performs well in both cases, thereby confirming the effectiveness of the proposed solution.

Figures (6)

• Figure 1: Hybrid thermostat-based deadband control scheme.
• Figure 2: Illustration of probability density functions of a TCL population at a given time.
• Figure 3: Ambient temperature.
• Figure 4: Desired power profile.
• Figure 5: Control performance for a population of 1,000 TCLs

Theorems & Definitions (12)

• Definition 2.1
• Remark 2.1
• Definition 2.2
• Lemma 2.1
• Remark 3.1
• Remark 3.2
• Theorem 4.1
• Remark 4.1
• Remark 4.2
• Theorem 4.2