## 1 Introduction
They finally concluded that the combination of a two-stage compression cycle with intercooler and dedicated subcooling from the absorption chiller is a very effective way of enhancing the COP, up to 207%. At this point, it is also important to state that the use of an absorption (or adsorption) chiller in a cascade system with CO\({}_{2}\) cycles has been also examined in the literature with encouraging results. More specifically, [PERSON] and [PERSON] [30] found that the incorporation of an absorption chiller in the high-stage stage of a cascade configuration is able to reduce the operation cost about 36% to 49% on a yearly basis. Moreover, [PERSON] [31] found a 30% decrease in electricity consumption with the use of a sorption chiller coupled to a compression system. Furthermore, the combination of CO\({}_{2}\) cycles with absorption machines for power and refrigeration production has been also studied in the literature. [PERSON] et al. [32] studied the use of an absorption chiller coupled to a gas turbine, while [PERSON] et al. [33] studied a CO\({}_{2}\)-Rankine cycle with an absorption chiller for power and refrigeration production. The use of a thermoelectrical subcooler has been studied by various researchers. [PERSON] [34] found a 25% increase in the COP with the thermoelectrical device compared to the simple vapor compression cycle. [PERSON] et al. [35] found a 3.3% COP enhancement and 7.9% cooling capacity increase with the thermoelectrical subcooling device. [PERSON] et al. [36] found 19% COP improvement with a thermoelectric device that consumes electricity. In the end, [PERSON] et al. [37] examined different configurations with a thermoelectrical subcooling device and expander, and they concluded that the combination of these two techniques increases the COP around 38%. Lastly, the work of [PERSON] et al. [38] should be highlighted, whereby they studied the use of a desiccant dehumidification system with air in order to enhance the performance of a transcritical CO\({}_{2}\) cycle. They found 77% enhancement in the COP compared to the conventional system with this technique. The previous literature review makes clear that the investigation of CO\({}_{2}\)-modified refrigeration cycles is of high interest and presents important enhancements in the COP that can be achieved in order to reduce the work consumption. The enhancement of the COP in the transcritical CO\({}_{2}\) refrigeration cycle is a critical issue because this cycle is less effective than the respective subcritical cycle with conventional refrigerants, such as R134a [39]. Dedicated subcooling techniques are important choices for increasing the performance of the system in a great way. Especially in the cases that solar energy is applied for driving the subcooling cycle, the overall configuration becomes environmentally friendly. There is plenty of studies about these techniques, but the studies about dedicated subcooling with absorption chillers are restricted. Only the studies [28; 29] are found in this area, but they do not make any comparison with the other usual technique: the mechanical subcooling. At this point, it has to be said that there are existing studies with vapor compression cycles and absorption chillers in a cascade configuration, but these configurations are different from the use of an absorption chiller as the subcooling device. In this direction, this study aims to cover this scientific gap and to compare the reference CO\({}_{2}\) refrigeration cycle, with dedicated subcooling system, with the mechanical compression cycle and the absorption chiller (single stage with a LiBr-H\({}_{2}\)O working pair) separately. To our knowledge, there is no other study which compares these two dedicated subcooling techniques and so this work is novel.