Aggregation of thermostatically controlled loads by formal abstractions

This work discusses a two-step procedure based on formal abstractions, which generates a finite stochastic dynamical model as an aggregation of the continuous temperature dynamics of a population of Thermostatically Controlled Loads (TCL). The temperature of each single TCL is described by a stochastic difference equation and the TCL status (ON, OFF) by a deterministic switching mechanism. The procedure is formal as it allows the exact quantification of the error introduced by the abstraction. The work discusses extensions to the case of controlled TCL. The procedure is tested on a case study and benchmarked against an alternative approach in the literature.