Model Predictive Control for Dynamic Hydraulic Balancing in Building Radiator Heating Systems: Modeling, Design, and Experimental Validation
Hydronic radiator systems are among the most widely used heating systems in buildings. In the literature, radiator heat outputs are often assumed to be independent of one another and arbitrarily adjustable in time when designing controllers. However, in practice, radiators are supplied by one or multiple common heat sources and are hydraulically coupled through the water circulation system. Maintaining occupant comfort in multi-zone buildings therefore requires not only an appropriate supply temperature but also proper hydraulic balancing to distribute the available water flow according to the heating demand of each zone. To this end, we develop a grey-box thermal model that captures the hydraulic interactions among radiators and the effects of radiator valves, circulation pumps, and heat sources. In a real building, we show that accounting for hydraulic interactions reduces the root mean square error (RMSE) between the measured and modeled zone temperatures by approximately 11% compared with a model that neglects these interactions. Additionally, we integrate the developed model into a model predictive control (MPC) framework for dynamic hydraulic balancing that jointly optimizes valve openings and the supply temperature to maintain thermal comfort in each zone while reducing energy consumption. Through both real-world experiments and numerical case studies, we demonstrate that, compared with existing MPC formulations that neglect hydraulic interactions or do not control radiator valves, the proposed MPC reduces comfort-range violations by at least 27% while requiring a similar or even lower cumulative supply temperature.