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Volume 2017 (2017), Article ID 5031505, 26 pages
Research Article

A Stability Analysis of Thermostatically Controlled Loads for Power System Frequency Control

1Centre for Complexity Science, University of Warwick, Coventry, UK
2Mathematics Institute, University of Warwick, Coventry, UK

Correspondence should be addressed to Ellen Webborn; ten.dargkciwraw@nrobbew.nelle

Received 30 June 2017; Accepted 10 October 2017; Published 6 December 2017

Academic Editor: Paul Hines

Copyright © 2017 Ellen Webborn and Robert S. MacKay. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Thermostatically controlled loads (TCLs) are a flexible demand resource with the potential to play a significant role in supporting electricity grid operation. We model a large number of identical TCLs acting autonomously according to a deterministic control scheme to provide frequency response as a population of coupled oscillators. We perform stability analysis to explore the danger of the TCL temperature cycles synchronising: an emergent phenomenon often found in populations of coupled oscillators and predicted in this type of demand response scheme. We take identical TCLs as it can be assumed to be the worst case. We find that the uniform equilibrium is stable and the fully synchronised periodic cycle is unstable, suggesting that synchronisation might not be as serious a danger as feared. Then detailed simulations are performed to study the effects of a population of frequency-sensitive TCLs acting under real system conditions using historic system data. The potential reduction in frequency response services required from other providers is determined, for both homogeneous and heterogeneous populations. For homogeneous populations, we find significant synchronisation, but very minimal diversity removes the synchronisation effects. In summary, we combine dynamical systems stability analysis with large-scale simulations to offer new insights into TCL switching behaviour.