A step towards digital operations - A novel grey-box approach for modelling the heat dynamics of ultra-low temperature freezing chambers

Tao Huang, Peder Bacher, Jan Kloppenborg Møller, Francesco D’Ettorre, Wiebke Brix Markussen

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Ultra-low temperature (ULT) freezers store perishable bio-contents and have high energy consumption, which highlight a demand for reliable methods for intelligent surveillance and smart energy management. This study introduces a novel grey-box modelling approach based on stochastic differential equations to describe the heat dynamics of the ULT freezing chambers. The proposed modelling approach only requires temperature data measured by the embedded sensors and uses data from the regular operation periods for model identification. The model encompasses three states: chamber temperature, envelope temperature, and local evaporator temperature. Special attention is given to the local evaporator temperature state, which is modelled as a time-variant system, to characterise the time delay and dynamic variations in cooling intensity. The model has three states, of which a time-variant model with nonlinear input for the local evaporator temperature state is specifically established to adapt to the variation of the cooling intensity at the position of the embedded chamber control probe. Two ULT freezers with different operational patterns are modelled. The unknown model parameters are estimated using the maximum likelihood method. The results demonstrate that the models can accurately predict the chamber temperature measured by the control probe (RMSE < 0.19C) and are promising to be applied for forecasting future states. In addition, the model for local evaporator temperature can effectively adapt to different operational patterns and provide insight into the local evaporation cooling supply status. The proposed approach greatly promotes the practical feasibility of grey-box modelling of the heat dynamics for ULT freezers and is a step forward in future digital operations can serve several potential digital applications. A major limitation of the modelling approach is the low identifiability, which can potentially be addressed by inferring model parameters based on relative parameter changes.
Original languageEnglish
Article number121630
JournalApplied Energy
Number of pages15
Publication statusPublished - 2023


  • Grey-box models
  • Heat dynamics
  • Smart energy system
  • Stochastic differential equations
  • Ultra-low temperature freezers


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