Real-time multi-variable optimization of the interstage subcooling vapor-injection based transcritical CO₂ HPWH: An integrated model predictive control approach

The interstage subcooling vapor-injection technique has been introduced to transcritical CO₂ heat pumps to alleviate performance degradation under conditions of low ambient temperature and high water-outlet temperature. This type of solution holds considerable appeal and finds utility across a wide range of applications. However, the efficacy and efficiency of such systems are contingent upon their management, which frequently requires the implementation of suitable control systems. The primary objective is to enhance the overall system operational performance, resulting in tangible advantages in terms of economic viability, energy conservation, and environmental sustainability. To achieve these objectives, one can utilize both explicit and implicit optimization methods ranging from Model Predictive Control (MPC) to Extremum Seeking Control (ESC), each with its strengths and weaknesses. This paper compares the performance of an ad hoc integrated MPC strategy and a multi-variable ESC one. Based on the results of the system operation employing the latter strategy, a significant linear correlation was discovered between the optimal medium pressure and the optimal discharge and suction pressure. Consequently, an intrinsic self-optimization strategy for the medium pressure was developed. Subsequently, a dynamic system identification was performed on the new system, incorporating this proposed strategy. To optimize the system Coefficient of Performance (COP) while maintaining the water outlet temperature, ensuring the thermal load constraint, the MPC strategy was employed. The main focus of the MPC was to determine the optimal Electronic Expansion Valve (EEV) opening degree and water pump settings. The integrated MPC strategy was evaluated and compared to the multi-variable ESC strategy under various conditions, including fixed design conditions, changing ambient conditions, and step-change water outlet temperature. The results clearly demonstrated the effectiveness and superiority of the integrated MPC.