Real-time efficiency optimization of a cascade heat pump system via multivariable extremum seeking

In this paper, the Extremum Seeking Control (ESC) is proposed as a model-free real-time optimizing control strategy for efficient operation of a cascade air source heat pump (CASHP). ESC is a model-free real-time optimization framework, which can search for the unknown and slowly varying input setpoint for optimizing specific performance index. The ESC strategy is realized for the scenarios of power minimization and COP maximization, respectively. For the power minimization, the ESC optimizes the setpoints of intermediate temperature and the superheat setpoints for the high-temperature and low temperature cycles; while for the COP maximization, the manipulated inputs are the compressor speeds of the high-temperature and low-temperature cycles and the evaporator fan speed. To validate the effectiveness of the proposed ESC strategy, a Modelica based dynamic simulation model of a CASHP water heater is built with Dymola and TIL Library. The CASHP is designed to provide the discharge water temperature of 85 degrees C, with R404A and R245fa as the refrigerants for the low temperature cycle and high temperature cycle, respectively. Under both fixed and realistic ambient temperature profiles, the simulation results show satisfactory convergence performance for both steady-state and transient characteristics. Thus, the feasibility of the proposed CASHP control strategy is validated.