A gray-box heat pump system model compatible with building energy modeling engines and reduced quantities of training data

This study applies a previously developed gray-box model for air-conditioning systems [1] to heat pump systems, extending it to accurately predict performance under heating operation. The model maintains its foundational approach as a steady-state, component-based framework that requires minimal data for training (as few as five points) and uses standard inputs for building energy simulation, such as air-side temperatures (outdoor dry and wet bulb, indoor dry bulb), indoor supply airflow rate, and rated system information. A key contribution from this work is reformulation for heat exchanger overall heat transfer coefficient (UA) correlations, utilizing Symbolic Regression (SR) to accommodate heat pump operation. The model was tested under a full training data set, four low-training data scenarios, and two extrapolation scenarios, demonstrating robust predictive performance. The data used for comparison is from three, advanced, split-system heat pump systems with capacities of 12.30 kW (3.5 tons), 14 kW(4 tons), and 17.60 kW(5 tons). The model achieved MAPE (mean absolute percentage error) that is under 3 % for heating capacity and 4 % for the coefficient of performance (COP). These results highlight the model's capability for accurate performance predictions and its potential for energy management and optimization in heat pump system under varied conditions.