Non-linear grey-box modelling for heat dynamics of buildings

Christian Ankerstjerne Thilker*, Peder Bacher, Hjörleifur G. Bergsteinsson, Rune Grønborg Junker, Davide Cali, Henrik Madsen

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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This paper introduces a non-linear grey-box (GB) model based on stochastic differential equations that describes the heat dynamics of a school building in Denmark, equipped with a water-based heating system. The building is connected to a local district heating network through a heat exchanger. The heat is delivered to the rooms mainly through radiators and partially through a ventilation system. A monitoring system based on IoT sensors provides data on indoor climate in the rooms and on the heat load of the building. Using this data, we estimate unknown states and parameters of a model of the building's heating system using the maximum likelihood method. Important novelties of this paper include models of the water flow in the circuit and the state of the valves in the radiator thermostats. The non-linear model accurately predicts the indoor air temperature, return water temperature and heat load. The ideas behind the model lay a foundation for GB models of buildings that use different kinds of water-based heating systems such as air-to-water/water-to-water heat pumps. Such GB models enable model predictive control to control e.g. the indoor air climate or provide flexibility services.

Original languageEnglish
Article number111457
JournalEnergy and Buildings
Number of pages10
Publication statusPublished - 1 Dec 2021

Bibliographical note

Funding Information:
The authors received funding from the following projects; Sustainable plus energy neighbourhoods (syn.ikia) (H2020 No. 869918), Centre for IT-Intelligent Energy Systems (CITIES) (DSF 1305-00027B), Top-Up (Innovation Fund Denmark 9045-00017B), SCA+ (Interreg Öresund-Kattegat-Skagerrak), Research Centre on Zero Emission Neighbourhoods in Smart Cities (FME-ZEN) (Research Council of Norway, No. 257660), and Flexibile Energy Denmark (FED) (IFD 8090-00069B).

Publisher Copyright:
© 2021 The Author(s)


  • District heating
  • Grey-box models
  • Non-linear models
  • Smart energy systems
  • Stochastic differential equations


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