This article presents an analysis of the damping and beating effects within the aggregate power demand of heterogeneous thermostatically controlled loads (TCLs). Demand response using TCLs is an appealing method to enable higher levels of penetration of intermittent renewable resources into the electric grid. Previous literature covers the benefits of TCL population heterogeneity for control purposes, but the focus is solely on the damping observed in these systems. This work, in contrast, characterizes the combined damping and beating effects in the power demand for different types of TCL parameter heterogeneity. The forced aggregate dynamics of TCLs have been shown to be bilinear when set point temperature adjustment is used as a control input. This motivates the article's use of free response dynamics, which are linear, to characterize both the damping and beating phenomena. A stochastic parameter distribution is applied to the homogeneous power demand solution, furnishing an analytic expression for the aggregate power demand. The time-varying damping ratios of this reduced-order model characterize the damping in the system. By analyzing a variety of case studies, it is determined that only a distribution of the TCL characteristic frequency creates damping in the aggregate power dynamics. The beating effect decays over time due to damping, and a relationship between the beat's amplitude and period is presented.
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October 2017
Research-Article
Demand Response Using Heterogeneous Thermostatically Controlled Loads: Characterization of Aggregate Power Dynamics
Donald Docimo,
Donald Docimo
Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: djd315@psu.edu
Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: djd315@psu.edu
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Hosam K. Fathy
Hosam K. Fathy
Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: hkf2@psu.edu
Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: hkf2@psu.edu
Search for other works by this author on:
Donald Docimo
Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: djd315@psu.edu
Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: djd315@psu.edu
Hosam K. Fathy
Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: hkf2@psu.edu
Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: hkf2@psu.edu
1Corresponding author.
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received April 29, 2016; final manuscript received April 6, 2017; published online June 28, 2017. Assoc. Editor: Umesh Vaidya.
J. Dyn. Sys., Meas., Control. Oct 2017, 139(10): 101009 (9 pages)
Published Online: June 28, 2017
Article history
Received:
April 29, 2016
Revised:
April 6, 2017
Citation
Docimo, D., and Fathy, H. K. (June 28, 2017). "Demand Response Using Heterogeneous Thermostatically Controlled Loads: Characterization of Aggregate Power Dynamics." ASME. J. Dyn. Sys., Meas., Control. October 2017; 139(10): 101009. https://doi.org/10.1115/1.4036557
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