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