## 1 Introduction
[11] proposed a heat pump dryer system using a R744/low-GWP working fluid mixture and compared it with traditional boiler drying systems. The results showed that under the influence of the R744/low-GWP working fluid mixture, the performance coefficient of the heat pump dryer was significantly improved, and the discharge pressure was reduced. When the ratio of R744/R32 was 0.1/0.9 mass ratio, the COP of system reached the highest level of 4.29, which is 7.42% higher than that under pure R744. [PERSON] et al. [12] designed a transcritical heat pump with an expander and studied the effects of different factors on system performance using experimental methods. The results showed that under the same working conditions, compared with the R744 transcritical system without an expander, the COP of the R744 transcritical system with an expander increased by about 6-10%. [PERSON] et al. [13] proposed a novel R744 transcritical cycle system with a mechanical superheat-assisted cycle and compared it with two different R744 transcritical systems. The results showed that compared with the traditional R744 system and the R744 system (with expander), the COP of the new system was increased by 15.72% and 12.19%, respectively, and the optimal pressure was reduced by 2.3% and 1.3%, respectively. [PERSON] et al. [14] established a theoretical model to study the effects of gas coolers and internal heat exchangers on the optimal discharge pressure and performance of an R744 transcritical system. The results showed that under the influence of the subcooling of the internal heat exchanger, the COP of the system was increased by 26.3%, and the optimal discharge pressure was also reduced. [PERSON] et al. [15] evaluated an R744 transcritical system from two perspectives, namely the actual operational thermal efficiency of the internal heat exchanger and the actual growth rate of COP. The results showed that under the given operating conditions, the addition of an internal heat exchanger significantly reduced the exergy efficiency of the system, and the influence of the internal heat exchanger on the exergy efficiency decreased with the increase in discharge pressure and ambient temperature. [PERSON] et al. [16] proposed a theoretical model to analyze the impact of different factors on the performance of R744 heat pump systems. The results showed that increasing the outlet water temperature from 60 \({}^{\circ}\)C to 80 \({}^{\circ}\)C resulted in a nearly 14%decrease in optimal COP and a 12.2% increase in optimal discharge pressure. When the evaporation temperature was increased from \(-10\)\({}^{\circ}\)C to \(10\)\({}^{\circ}\)C, the optimal COP increased by about 63%, while the optimal discharge pressure remained almost unchanged. [PERSON] et al. [17] proposed a transcritical R744 heat pump system with a mechanical subcooling-assisted cycle and established a mathematical model to study its annual energy and economic performance. The results showed that under the given operating conditions, the COP of the system can be increased by 24.4%, and the discharge pressure can be reduced by 2.093 MPa. Compared with traditional R744 heat pump systems, the proposed new system has lower power costs. [PERSON] et al. [18] proposed a CO\({}_{2}\) heat pump with an integrated tripartite gas cooler and conducted a comprehensive performance analysis on it. The results showed that when the ambient temperature and inlet water temperature are both 10 \({}^{\circ}\)C, combining SH with DHW can reduce the discharge pressure of the system by 7.9% and increase the COP by 7.5%, and compared with the DHW system, for every 5 \({}^{\circ}\)C increase in ambient temperature, the total exergy destruction cost rate of the DHW + SH system decreases by an average of 7.7%. In the field of subcritical cycle heat pumps, [PERSON] et al.