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Demand Response is playing an increasingly important role in smart grid control strategies. Modeling the dynamical behavior of a large population of appliances under demand response is especially important to evaluate the effectiveness of various demand response programs. In this paper an aggregate model is proposed for a class of second-order Thermostatically Controlled Loads (TCLs). The model efficiently includes statistical information of the population, systematically deals with heterogeneity, and accounts for a second-order effect necessary to accurately capture the transient dynamics in the collective response. A good performance of the model however requires a high state dimension which dramatically complicates its formal analysis and controller design. To address this issue, a model reduction approach is developed for the proposed aggre-gate model, which can significantly reduce its complexity with small performance loss. The original and the reduced-order aggregate models are validated against simulations of thousands of detailed building models using GridLAB-D (an open-source distribution simulation software). The results indicate that the reduced-order model can accurately reproduce the steady-state and transient dynamics generated by GridLAB-D simulations with a much reduced complexity.
Zhang et al. (Sat,) studied this question.