Indoor Temperature Forecasting and Control in Hydronic Systems Using Grey-Box Models and Model Predictive Control: A Field Experiment

Accurate indoor temperature forecasting is critical for effective indoor climate control and energy-efficient building operation. In radiator-heated buildings, a key modelling challenge is the dynamic discrepancy between the indoor air temperature experienced in the room and the local temperature measured at thermostatic radiator valves (TRVs). This discrepancy is often simplified as a constant offset, although it can vary during operation due to radiator activity, weather conditions, and local room dynamics. This paper presents a field implementation of a non-linear grey-box room model integrated in a model predictive control (MPC) framework for hydronic space heating in a school building. The model explicitly distinguishes between the indoor air temperature and the TRV sensor temperature and was deployed for rolling temperature forecasting and control in three classrooms during an experimental period from 28 February to 11 March 2025. The MPC maintained the measured indoor temperature within the comfort bounds for 90.3 % to 95.5 % of the evaluated period across the classrooms. Rolling forecast errors for indoor temperature were moderate, with room-level RMSE values between 0.47 ∘ C and 0.56 ∘ C. In the independent recursive multi-step validation, the indoor temperature RMSE at the 24-hour horizon remained between 0.50 ∘ C and 0.73 ∘ C, while TRV sensor temperature forecasts showed slightly larger errors. Benchmark reruns further indicated that the non-linear MPC formulation was computationally feasible for a 30-minute control interval under typical operating conditions (median 17.5 s, 95th percentile 37.6 s wall-clock time). The results demonstrate the practical feasibility of using a dynamic non-linear grey-box model with TRV dynamics in an operational MPC setting and highlight implementation challenges that remain important barriers to large-scale deployment of MPC-based room-level MPC in buildings.