A Geometric Approach to Aggregate Flexibility Modeling of Thermostatically Controlled Loads

TL;DR

This paper introduces a geometric modeling approach for the aggregate flexibility of thermostatically controlled loads, enabling efficient control and integration into power systems.

Contribution

It proposes a novel geometric framework using polytopes and Minkowski sums to accurately and tractably model TCL flexibility, with optimization algorithms for approximation.

Findings

Algorithms improve flexibility characterization over existing methods.

Virtual battery model facilitates efficient control.

Case studies demonstrate effective frequency regulation tracking.

Abstract

Coordinated aggregation of a large population of thermostatically controlled loads (TCLs) presents a great potential to provide various ancillary services to the grid. One of the key challenges of integrating TCLs into system level operation and control is developing a simple and portable model to accurately capture their aggregate flexibility. In this paper, we propose a geometric approach to model the aggregate flexibility of TCLs. We show that the set of admissible power profiles of an individual TCL is a polytope, and their aggregate flexibility is the Minkowski sum of the individual polytopes. In order to represent their aggregate flexibility in an intuitive way and achieve a tractable approximation, we develop optimization-based algorithms to approximate the polytopes by the homothets of a given convex set. As a special application, this set is chosen as a \emph{virtual battery model} and the corresponding optimal approximations are solved efficiently by equivalent linear programming problems. Numerical results show that our algorithms yield significant improvement in characterizing the aggregate flexibility over existing modeling methods. We also conduct case studies to demonstrate the efficacy of our approaches by coordinating TCLs to track a frequency regulation signal from the Pennsylvania-New Jersey-Maryland (PJM) Interconnection.