This work discusses a two-step procedure, based on formal abstractions, togenerate a finite-space stochastic dynamical model as an aggregation of thecontinuous temperature dynamics of a homogeneous population of ThermostaticallyControlled Loads (TCL). The temperature of a single TCL is described by astochastic difference equation and the TCL status (ON, OFF) by a deterministicswitching mechanism. The procedure is formal as it allows the exactquantification of the error introduced by the abstraction -- as such it buildsand improves on a known, earlier approximation technique in the literature.Further, the contribution discusses the extension to the case of aheterogeneous population of TCL by means of two approaches resulting in thenotion of approximate abstractions. It moreover investigates the problem ofglobal (population-level) regulation and load balancing for the case of TCLthat are dependent on a control input. The procedure is tested on a case studyand benchmarked against the mentioned alternative approach in the literature.
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