Thermostatically controlled loads (TCLs) account for more than one-third of the U.S. electricity consumption. Various techniques have been used to model TCL populations. A high-fidelity analytical model of heterogeneous TCL (HrTCL) populations is of special interest for both utility managers and customers (that facilitates the aggregate synthesis of power control in power networks). We present a deterministic hybrid partial differential equation (PDE) model which accounts for HrTCL populations and facilitates analysis of common scenarios like cold load pick up, cycling, and daily and/or seasonal temperature changes to estimate the aggregate performance of the system. The proposed technique is flexible in terms of parameter selection and ease of changing the set-point temperature and deadband width all over the TCL units. We investigate the stability of the proposed model along with presenting guidelines to maintain the numerical stability of the discretized model during computer simulations. Moreover, the proposed model is a close fit to design feedback algorithms for power control purposes. Hence, we present output- and state-feedback control algorithms, designed using the comparison principle and Lyapunov analysis, respectively. We conduct various simulations to verify the effectiveness of the proposed modeling and control techniques.
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October 2015
Research-Article
Modeling, Control, and Stability Analysis of Heterogeneous Thermostatically Controlled Load Populations Using Partial Differential Equations
Azad Ghaffari,
Azad Ghaffari
Department of Mechanical &
Aerospace Engineering,
University of California, San Diego,
La Jolla, CA 92039-0411
e-mail: aghaffari@eng.ucsd.edu
Aerospace Engineering,
University of California, San Diego,
La Jolla, CA 92039-0411
e-mail: aghaffari@eng.ucsd.edu
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Scott Moura,
Scott Moura
Department of Civil and
Environmental Engineering,
University of California, Berkeley,
Berkeley, CA 94720
e-mail: smoura@berkeley.edu
Environmental Engineering,
University of California, Berkeley,
Berkeley, CA 94720
e-mail: smoura@berkeley.edu
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Miroslav Krstić
Miroslav Krstić
Department of Mechanical &
Aerospace Engineering,
University of California, San Diego,
La Jolla, CA 92039-0411
e-mail: krstic@ucsd.edu
Aerospace Engineering,
University of California, San Diego,
La Jolla, CA 92039-0411
e-mail: krstic@ucsd.edu
Search for other works by this author on:
Azad Ghaffari
Department of Mechanical &
Aerospace Engineering,
University of California, San Diego,
La Jolla, CA 92039-0411
e-mail: aghaffari@eng.ucsd.edu
Aerospace Engineering,
University of California, San Diego,
La Jolla, CA 92039-0411
e-mail: aghaffari@eng.ucsd.edu
Scott Moura
Department of Civil and
Environmental Engineering,
University of California, Berkeley,
Berkeley, CA 94720
e-mail: smoura@berkeley.edu
Environmental Engineering,
University of California, Berkeley,
Berkeley, CA 94720
e-mail: smoura@berkeley.edu
Miroslav Krstić
Department of Mechanical &
Aerospace Engineering,
University of California, San Diego,
La Jolla, CA 92039-0411
e-mail: krstic@ucsd.edu
Aerospace Engineering,
University of California, San Diego,
La Jolla, CA 92039-0411
e-mail: krstic@ucsd.edu
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received May 4, 2014; final manuscript received June 6, 2015; published online July 27, 2015. Assoc. Editor: Umesh Vaidya.
J. Dyn. Sys., Meas., Control. Oct 2015, 137(10): 101009 (9 pages)
Published Online: July 27, 2015
Article history
Received:
May 4, 2014
Revision Received:
June 6, 2015
Citation
Ghaffari, A., Moura, S., and Krstić, M. (July 27, 2015). "Modeling, Control, and Stability Analysis of Heterogeneous Thermostatically Controlled Load Populations Using Partial Differential Equations." ASME. J. Dyn. Sys., Meas., Control. October 2015; 137(10): 101009. https://doi.org/10.1115/1.4030817
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