Characterizing statistical bounds on aggregated demand-based primary frequency control

An analytical approach is proposed in this paper to characterize statistical bounds and uncertainties associated with the aggregated response of frequency-sensitive Thermostatically Controlled Loads (TCLs) participating in primary frequency control. A set of random variables is first introduced to exemplify the intrinsic uncertainty associated with the instantaneous power consumption of a single TCL in a population. Physically-based models, laboratory analysis or field measurement data can be employed to characterize the proposed random variables. Then, a bottom-up aggregation methodology and statistical theory are employed to characterize the aggregated response of a population of TCLs. Monte Carlo simulations are used to verify the correctness of the proposed analytics. The proposed methodology can be employed by system operators as well as demand response aggregators to predict the aggregated response of a population of TCLs participating in primary frequency control.