Aggregation and Control of Populations of Thermostatically Controlled Loads by Formal Abstractions

TL;DR

This paper presents a formal method for aggregating and controlling populations of thermostatically controlled loads using finite-state stochastic models, enabling precise error quantification and extension to heterogeneous populations.

Contribution

It introduces a formal abstraction technique that accurately models TCL populations, including heterogeneity, and addresses population regulation and load balancing with control inputs.

Findings

Exact error quantification for abstractions

Extension to heterogeneous TCL populations

Effective population regulation and load balancing

Abstract

This work discusses a two-step procedure, based on formal abstractions, to generate a finite-space stochastic dynamical model as an aggregation of the continuous temperature dynamics of a homogeneous population of Thermostatically Controlled Loads (TCL). The temperature of a single TCL is described by a stochastic difference equation and the TCL status (ON, OFF) by a deterministic switching mechanism. The procedure is formal as it allows the exact quantification of the error introduced by the abstraction -- as such it builds and improves on a known, earlier approximation technique in the literature. Further, the contribution discusses the extension to the case of a heterogeneous population of TCL by means of two approaches resulting in the notion of approximate abstractions. It moreover investigates the problem of global (population-level) regulation and load balancing for the case of TCL that are dependent on a control input. The procedure is tested on a case study and benchmarked against the mentioned alternative approach in the literature.