Aggregation and Control of Populations of Thermostatically Controlled Loads by Formal Abstractions

This paper discusses a two-step procedure, based on the use of formal abstractions, to generate a finite-space stochastic dynamical model as an aggregation of the continuous temperature dynamics of a homogeneous population of thermostatically controlled loads (TCLs). The temperature of a TCL is described by a stochastic difference equation and the TCL status (ON, OFF) by a deterministic switching mechanism. The procedure is deemed to be formal, as it allows the quantification of the error introduced by the abstraction. As such, it builds and improves on a known, earlier approximation technique used in the literature. Furthermore, the contribution discusses the extension to the instance of heterogeneous populations of TCLs by means of two approaches. It moreover investigates the problem of global (population-level) power reference tracking and load balancing for TCLs that are explicitly dependent on a control input. The procedure is tested on a case study and benchmarked against the mentioned existing approach in the literature.