Optimization on annual energy efficiency of heat pumps based on maximum solving of definition functions with multi constraints

Air conditioners is expected to be the second largest source of growth in global electricity demand. To promote electrification, heat pump air conditioner is encouraged to replace natural gas furnace. Improving heat pump's energy efficiency can help reduce global energy consumption and greenhouse gas emissions. Annual performance factor is one of the key metrics to evaluate heat pump systems’ energy performance. Seeking annual performance factor maximum belongs to an optimization problem with multi constraints. However, due to the nested variables, continuous non-differentiable and piecewise form of annual performance factor definition functions, the optimized objective function is usually based on the simplification with large errors. Meanwhile, the multi constraint boundaries are either ignored or considered but through complicated and high-cost tests. In this research, the variable iteration logic of the annual performance factor definition functions is sorted firstly. Then the above exact mathematical definitions are programmed as the objective functions without any simplification. Enumeration method is used to establish the annual performance factor maximum solution algorithm. More importantly, taking a 3.5 kW cooling capacity mini-split heat pump prototype as an example, energy performance tests are conducted to fit the multi constraints, namely using less global parameters to cover more local parameters, which greatly simplifies the test procedures and cost. Then, using our proposed method, the maximum annual performance factor is predicted and validated by experiments. The prediction accuracy is 99.6%, with a 38.4% improvement compared to the best reported value from literature. Based on the recommended variable values, the prototype's annual performance factor achieves the maximum with a 7.71% improvement from the baseline. The proposed method can save time and experimental resources in the product development stage compared with the traditional trial and error method.