Ensemble of Thermostatically Controlled Loads: Statistical Physics Approach

Abstract Thermostatically controlled loads, e.g., air conditioners and heaters, are by far the most widespread consumers of electricity. Normally the devices are calibrated to provide the so-called bang-bang control – changing from on to off, and vice versa, depending on temperature. We considered a...

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Autores principales:	Michael Chertkov, Vladimir Chernyak
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2017
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/1fa6fdfa6cf74618b51b42f2505a3b3b
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spelling	oai:doaj.org-article:1fa6fdfa6cf74618b51b42f2505a3b3b2021-12-02T11:52:42ZEnsemble of Thermostatically Controlled Loads: Statistical Physics Approach10.1038/s41598-017-07462-82045-2322https://doaj.org/article/1fa6fdfa6cf74618b51b42f2505a3b3b2017-08-01T00:00:00Zhttps://doi.org/10.1038/s41598-017-07462-8https://doaj.org/toc/2045-2322Abstract Thermostatically controlled loads, e.g., air conditioners and heaters, are by far the most widespread consumers of electricity. Normally the devices are calibrated to provide the so-called bang-bang control – changing from on to off, and vice versa, depending on temperature. We considered aggregation of a large group of similar devices into a statistical ensemble, where the devices operate following the same dynamics, subject to stochastic perturbations and randomized, Poisson on/off switching policy. Using theoretical and computational tools of statistical physics, we analyzed how the ensemble relaxes to a stationary distribution and established a relationship between the relaxation and the statistics of the probability flux associated with devices’ cycling in the mixed (discrete, switch on/off, and continuous temperature) phase space. This allowed us to derive the spectrum of the non-equilibrium (detailed balance broken) statistical system and uncover how switching policy affects oscillatory trends and the speed of the relaxation. Relaxation of the ensemble is of practical interest because it describes how the ensemble recovers from significant perturbations, e.g., forced temporary switching off aimed at utilizing the flexibility of the ensemble to provide “demand response” services to change consumption temporarily to balance a larger power grid. We discuss how the statistical analysis can guide further development of the emerging demand response technology.Michael ChertkovVladimir ChernyakNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 7, Iss 1, Pp 1-9 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Michael Chertkov Vladimir Chernyak Ensemble of Thermostatically Controlled Loads: Statistical Physics Approach
description	Abstract Thermostatically controlled loads, e.g., air conditioners and heaters, are by far the most widespread consumers of electricity. Normally the devices are calibrated to provide the so-called bang-bang control – changing from on to off, and vice versa, depending on temperature. We considered aggregation of a large group of similar devices into a statistical ensemble, where the devices operate following the same dynamics, subject to stochastic perturbations and randomized, Poisson on/off switching policy. Using theoretical and computational tools of statistical physics, we analyzed how the ensemble relaxes to a stationary distribution and established a relationship between the relaxation and the statistics of the probability flux associated with devices’ cycling in the mixed (discrete, switch on/off, and continuous temperature) phase space. This allowed us to derive the spectrum of the non-equilibrium (detailed balance broken) statistical system and uncover how switching policy affects oscillatory trends and the speed of the relaxation. Relaxation of the ensemble is of practical interest because it describes how the ensemble recovers from significant perturbations, e.g., forced temporary switching off aimed at utilizing the flexibility of the ensemble to provide “demand response” services to change consumption temporarily to balance a larger power grid. We discuss how the statistical analysis can guide further development of the emerging demand response technology.
format	article
author	Michael Chertkov Vladimir Chernyak
author_facet	Michael Chertkov Vladimir Chernyak
author_sort	Michael Chertkov
title	Ensemble of Thermostatically Controlled Loads: Statistical Physics Approach
title_short	Ensemble of Thermostatically Controlled Loads: Statistical Physics Approach
title_full	Ensemble of Thermostatically Controlled Loads: Statistical Physics Approach
title_fullStr	Ensemble of Thermostatically Controlled Loads: Statistical Physics Approach
title_full_unstemmed	Ensemble of Thermostatically Controlled Loads: Statistical Physics Approach
title_sort	ensemble of thermostatically controlled loads: statistical physics approach
publisher	Nature Portfolio
publishDate	2017
url	https://doaj.org/article/1fa6fdfa6cf74618b51b42f2505a3b3b
work_keys_str_mv	AT michaelchertkov ensembleofthermostaticallycontrolledloadsstatisticalphysicsapproach AT vladimirchernyak ensembleofthermostaticallycontrolledloadsstatisticalphysicsapproach
_version_	1718394970571800576

Ensemble of Thermostatically Controlled Loads: Statistical Physics Approach

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