Probabilistic Characterization of Thermostatically Controlled Loads to Model the Impact of Demand Response Programs

Abstract

Flexible models for aggregated residential loads are needed to analyze the impact of demand response policies and programs on the minimum comfort setting required by end-users. This impact has to be directly deduced from the probability profiles of thermal and electrical performance variables. The purpose of this paper is to compare different aggregation techniques in order to estimate, as accurately and flexibly as possible, the probability distribution function of thermal and electrical variables of thermostatically controlled loads. Two different approaches are considered: on the one hand, intensive numerical simulations-Monte Carlo process-combined with either Euler-Maruyama discrete approximation method or smoothing techniques; and, on the other hand, a numerical resolution of the Fokker-Planck partial differential equations. In all cases, a stochastic differential equation system-based on perturbed physical models-is used to model the individual load behavior. This individual system was previously developed and validated by the authors.