Research Papers

Demand Response Using Heterogeneous Thermostatically Controlled Loads: Characterization of Aggregate Power Dynamics

[+] Author and Article Information
Donald Docimo

Department of Mechanical and
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

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 139(10), 101009 (Jun 28, 2017) (9 pages) Paper No: DS-16-1221; doi: 10.1115/1.4036557 History: Received April 29, 2016; Revised April 06, 2017

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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Fig. 1

Oscillatory displacement of a population of mass-springs with heterogeneous natural frequencies

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Fig. 2

Expected displacement of uniformly distributed mass-springs, with ωn,min=0.9 rad/s and ωn,max=1.1 rad/s

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Fig. 3

Ratio of beat maximum amplitude to initial system amplitude for a uniform distribution of frequency

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Fig. 4

Temperature variation of a single TCL unit

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Fig. 5

Power demand profile of a single TCL unit

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Fig. 6

Expected power demand for a uniform distribution of frequency with ωmin=3.88 rad/h and ωmax=4.74 rad/h

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Fig. 7

Time-varying damping ratios describing the expected power demand damping over time

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Fig. 8

(a) Expected power demand from the Monte Carlo model and the reduced-order model (N = 1) and (b) difference in expected power demand between the Monte Carlo model and the reduced-order models over time

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Fig. 9

Histogram of difference in expected power demand between the Monte Carlo model and the reduced-order models



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