Hybrid White-Box/Black-Box Modeling and Control of a CO2 Heat Pump System Using Modelica and Deep Learning: A Case Study on Return-Water Temperature Control

This study presents a hybrid modeling framework integrating a deep learning-based black-box model of a CO2 heat pump with a physics-based white-box system model developed in Modelica. The approach reduces the complexity of thermodynamic modeling while maintaining system-level accuracy. A deep neural network (DNN) trained on measured data predicts outlet temperatures and compressor power, coupled with the Modelica model through the Functional Mock-up Unit (FMU) interface. The framework was applied to a ground-source CO2 heat pump system in Oslo, Norway, to evaluate hysteresis-based control strategies with different return temperature ranges (20–50 °C, 20–55 °C, 20–70 °C) and flow rates (1.3–1.5 kg/s). Results showed similar total heating but 25% lower compressor energy use for the 20–50 °C, 1.5 kg/s case compared to 20–70 °C. Temperature-based control improved coefficient of performance (COP) of the heat pump, while narrower temperature ranges and lower flow rates enhanced tank stratification and heat utilization. The findings demonstrate the effectiveness of the hybrid model for dynamic simulation and control optimization of CO2 heat pump systems.