Extremum seeking control of COP optimization for air-source transcritical CO2 heat pump water heater system

Air-source transcritical CO2 heat pump systems have found attractive applications in automobile air conditioning, regional heating and commercial water heating systems. The coefficient of performance (COP) of such systems is affected by several operational variables, such as ambient temperatures, water outlet temperature, and discharge pressure. For practical operation, it is desirable to maintain the maximum achievable efficiency or COP of such systems in real time. However, performance of model based control/optimization strategies can be quite limited by the difficulty in acquiring accurate system models due to system nonlinearity, large variations in ambient conditions and thermal load, as well as equipment variation and degradation. In this study, a self-optimizing control scheme is proposed to maximize the COP in real time by using the extremum seeking control (ESC) strategy. ESC is a class of self-optimizing control strategy that can search for the unknown or slowly varying optimum input with respect to certain performance index, which is effectively a dynamic realization of the gradient search based on a dither-demodulation scheme. For the air-source transcritical CO2 heat-pump water heater, the discharge pressure setpoint is taken as the input to the ESC controller, while the system COP is taken as the performance index, i.e. the feedback signal for the extremum seeking process. To evaluate the proposed ESC strategy, a Modelica based dynamic simulation model is developed for the plant to perform the simulation study. Simulations are conducted for several scenarios: a fixed operation condition, change of the water outlet temperature setpoint, change of ambient condition, and changes of both the ambient temperature and water outlet temperature setpoint. For all simulation cases, the water inlet temperature is fixed at 12 °C, the ambient temperature is assumed to range from −15 °C to −35 °C, while the water outlet temperature ranges from 55 °C to 80 °C. Simulation results show that ESC is able to search and even track both fixed and slowly varying optimum COP without need for system model. Significant recovery of energy efficiency can thus be obtained for practical operation of such systems in a nearly model-free fashion.