Extremum Seeking Control (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 an 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. A Modelica based dynamic simulation model is developed to perform the simulation study. Simulations are conducted for several scenarios: a fixed operation condition

change of ambient condition and real time varying ambient temperature conditions. Simulation results show that ESC is able to search both fixed and slowly varying optimum. The steady-state error of optimal discharge pressure is less than 1.0%. Compared to the optimum obtained by model based methods

the optimal discharge pressure deviations are less than 5%. The feasibility and accuracy of ESC control strategy are verified.