Development of a grey-box heat load prediction model by subspace identification method for heating building

The digital transformation of traditional heating systems in smart cities necessitates accurate heat load prediction for smart dispatch. Compared to black-box models, the grey-box modeling approach offers distinct advantages, such as eliminating the need for structural adjustments or optimization while providing stronger mechanistic interpretability. This study maps the mechanistic model of the building thermal process to a subspace identification method's structure, simplifying heat load prediction into a parameter identification problem of the system state matrix. Two data input strategies—rolling training and cumulative training—are employed to identify the parameters and construct an online prediction model for heat load and indoor temperature. Using a building in Harbin, located in China's severe cold region, as a case study, the method achieves mean absolute percentage error (MAPE) of 1.5–2.6 % for indoor temperature prediction. The optimal rolling period is identified as 36-hour for short-term and 27–28-day for medium-term prediction. Notably, the proposed approach reduces the number of required parameters by over 40 % compared to higher-order RC models and only needs readily available operational data, without requiring invasive measurements. The cumulative training strategy outperforms rolling training strategy for medium-term predictions, achieving the lowest root mean square error (RMSE) of only 34.9 kW, which is 12.5–24.1 kW lower than that of the rolling training strategy. Compared to intelligent algorithms, such as artificial neural networks, the proposed model demonstrates superior applicability in district heating systems, with significant advantages in both prediction accuracy and the simplicity of the parameter identification process.