Time of the week AutoRegressive eXogenous (TOW-ARX) model to predict thermal consumption in a large commercial mall

This paper proposes a procedure to build a Time of the Week AutoRegressive eXogenous (TOW-ARX) model, indexed with respect to time and day of the week, to characterize heat consumption in tertiary buildings. Models for building heat load characterization and prediction are crucial to enhance energy efficiency. The proposed model can be used for different purposes, e.g., control of indoor climate, or characterization of the thermal response of the building. A case study is described where the TOW-ARX model is used to characterize the energy consumption of a large retail building in Madrid. In order to discard the risk of model overfitting, cross validation is applied using the k-fold technique. The performance of the TOW-ARX model is compared with a set of different models: a reduced version of the model where similar segments are clustered using the k-means method (R-TOW-ARX), a general ARX model, a linear regression steady-state TOW model (TOW-LR), a version of the latter reduced through clustering (R-TOW-LR), and a general multiple linear regression model (LR). The results reveal that ARX-based models notably outperforms the rest. The TOW-ARX model shows the best metrics, but also outnumbers the number of coefficients of the other models by far. The selection of the most suitable model is not straightforward and should depend on the purpose of such model: the TOW-ARX model would arguably be the best for control purposes due to its low mean absolute error, but the ARX model would be preferable for an efficient characterization of the thermal response of a building due to its reduced number of parameters.