A simplified thermal model with robust extrapolation performance for cooling towers

This study presents a simplified thermal model with high prediction accuracy and robust extrapolation performance for cooling tower control optimization. The model modifies the effectiveness-NTU model by incorporating empirical expressions derived from detailed analyses of heat and mass transfer processes in cooling towers and the thermodynamic properties of moist air. The model has an explicit formulation with four bounded parameters that can be identified using measurement data. The prediction performance of the proposed model was thoroughly evaluated and compared with five known gray-box models using operating data from a counter-flow cooling tower system. The dataset spans a broad operational range, offering an ideal basis for analyses. The results demonstrate that the proposed model is the only model that consistently meets the accuracy thresholds in all comparative analyses. It also exhibits robust extrapolation performance, maintaining high accuracy under unseen conditions, regardless of whether the training dataset is diverse or limited in range. These qualities highlight the potential of the proposed model for future use in real-time control optimization, particularly for newly installed systems with limited data availability due to time constraints, and for systems in mission-critical facilities, such as data centers, where operational limitations restrict the data range. • Thermal model for cooling towers is developed based on effectiveness-NTU approach. • The proposed model modifies the formulas for effectiveness and enthalpy difference. • The proposed model has an explicit formulation with four bounded parameters. • The proposed model is validated using real operating data. • High prediction accuracy and robust extrapolation performance are demonstrated.