Formal Synthesis and Validation of Inhomogeneous Thermostatically Controlled Loads

  • Sadegh Esmaeil Zadeh Soudjani
  • Sebastian Gerwinn
  • Christian Ellen
  • Martin Fränzle
  • Alessandro Abate
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8657)


This work discusses the construction of a finite-space stochastic dynamical model as the aggregation of the continuous temperature dynamics of an inhomogeneous population of thermostatically controlled loads (TCLs). The temperature dynamics of a TCL is characterized by a differential equation in which the TCL status (ON, OFF) is controlled by a thresholding mechanism, and which displays inhomogeneity as its thermal resistance changes in time according to a Poisson process. In the aggregation procedure, each TCL model in the population is formally abstracted as a Markov chain, and the cross product of these Markov chains is lumped into its coarsest (exact) probabilistic bisimulation. Quite importantly, the abstraction procedure allows for the quantification of the induced error. Assuming that the TCLs explicitly depend on a control input, the contribution investigates the problem of population-level power reference tracking and load balancing. Furthermore, for the corresponding closed-loop control scheme we show how the worst case performance can be lower bounded statistically, thereby guaranteeing robustness versus power-tracking when the underlying assumption on the inhomogeneity term is relaxed.


Thermostatically controlled load Markov chain Poisson process Formal abstraction Probabilistic bisimulation Stochastic optimal control Noisy optimization 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Sadegh Esmaeil Zadeh Soudjani
    • 1
  • Sebastian Gerwinn
    • 2
  • Christian Ellen
    • 2
  • Martin Fränzle
    • 2
  • Alessandro Abate
    • 3
    • 1
  1. 1.Delft Center for Systems and ControlTU DelftThe Netherlands
  2. 2.OFFISUniversität OldenburgGermany
  3. 3.Department of Computer ScienceUniversity of OxfordUnited Kingdom

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