Abstract
This paper proposes non-linear autoregressive models with exogenous inputs to model the air temperature in each room of a Danish school building connected to the local district heating network. To obtain satisfactory models, the authors find it necessary to estimate the solar radiation effect as a function of the time of the day using a B-spline basis expansion. Furthermore, this paper proposes a method for estimating the valve position of the radiator thermostats in each room using modified Hermite polynomials to ensure monotonicity of the estimated curve. The non-linearities require a modification in the estimation procedure: Some parameters are estimated in an outer optimisation, while the usual regression parameters are estimated in an inner optimisation. The models are able to simulate the temperature 24 h ahead with a root-mean-square-error of the predictions between 0.25 °C and 0.6 °C. The models seem to capture the solar radiation gain in a way aligned with expectations. The estimated thermostatic valve functions also seem to capture the important variations of the individual room heat inputs.
Original language | English |
---|---|
Article number | 100165 |
Journal | Energy and AI |
Volume | 9 |
Number of pages | 10 |
ISSN | 2666-5468 |
DOIs | |
Publication status | Published - 2022 |
Keywords
- Time series
- Non-linear models
- District heating
- Smart energy system