Aggregate model for heterogeneous thermostatically controlled loads with demand response

Due to the potentially large number of Distributed Energy Resources (DERs) - demand response, distributed generation, distributed storage - that are expected to be deployed, it is impractical to use detailed models of these resources when integrated with the transmission system. Being able to accurately estimate the transients caused by demand response is especially important to analyze the stability of the system under different demand response strategies, where dynamics on time scales of seconds to minutes are important. On the other hand, a less complex model is more amenable to study stability of a large power system, and to design feedback control strategies for the population of devices to provide ancillary services. The main contribution of this paper is to develop an aggregated model for a heterogeneous population of Thermostatic Controlled Loads (TCLs) to accurately capture their collective behavior under demand response. The aggregated 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. The developed aggregated model is validated against simulations of thousands of detailed building models using GridLAB-D (an open source distribution simulation software) under both steady state and severe dynamic conditions.