A reduced-order model for predicting transient performance of air-source heat pumps

This paper presents a transient, reduced-order model for variable-speed air-source heat pumps that captures start-up and cycling dynamics using only air-side inputs in heating operation. The model integrates two sub-models: a heating-capacity and a compressor power model identified via symbolic regression using high-fidelity simulations and experimental data. Validation was conducted on a 4-ton variable-speed heat pump tested in twin psychrometric chambers under diverse steady-state and dynamic start-up conditions. The models reproduce steady state operation with a mean absolute percentage error (MAPE) of 2.5% and 1.6% in heating capacity and power consumption, respectively. Dynamic error metrics remain below 4% for both the coefficient of variation of root mean square error (CVRMSE) and normalized mean bias error (NMBE) using only air-side temperatures, indoor fan supply, and compressor speed along with estimates of heat exchanger and zone air thermal mass. Sensitivity analyses confirm robustness to ±20% uncertainty in thermal mass assumptions. Unlike traditional approaches that rely on fixed degradation constants, the model explicitly differentiates between cold- and hot-start transients, enabling more accurate representation of start-up behavior. A representative cold-climate (Chicago, Illinois, USA) case study indicates that neglecting transient dynamics can bias seasonal performance and peak demand estimates by up to 4.9%. By enabling fast and accurate heat pump performance predictions, the model bridges the gap between high-fidelity physics-based simulations and the practical needs of building performance modeling while achieving simulation speeds over 106 times faster than real time.