This paper 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 is, to the best of the authors’ knowledge, the first to characterize the combined damping and beating response of power demand versus the level of TCL population 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 paper’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 aggregate power demand. The resulting analysis shows that increasing parameter heterogeneity increases damping and shortens the beat period.

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