## 5 Conclusions  
This communication analyzes two modes of operation of a CO\({}_{2}\)-based two-stage refrigeration cycle with equivalent design that can be operated as cascade refrigeration system or as a CO\({}_{2}\) refrigeration plant with dedicated mechanical subcooling system. Both schemes are being considered now to spread the use of CO\({}_{2}\) in medium and warm regions of the planet for medium temperature applications.  
Using relations of the overall efficiency of compressors, adjusted from experimental data of a semi-hermetic CO\({}_{2}\) and a semi-hermetic R1234 yf compressors, a simplified model of both cycles was developed. With the thermodynamic models, the optimum operating conditions of each refrigeration cycle, covering evaporating temperatures from \(-20\) to 5 \({}^{\circ}\)C and environment temperatures from 15 to 40 \({}^{\circ}\)C, were determined. Then, by merging the COP values of each refrigeration solution, the external conditions at which each refrigeration solution is the best performing were established. Furthermore, the analysis was translated for the different climatic regions of Spain to compare the systems.  
Regarding the CO\({}_{2}\) refrigeration cycle with mechanical subcooling, it was concluded that the environment temperature that will limit the operation in subcritical or transcritical is 25.3 \({}^{\circ}\)C, thus the design of the gas-cooler would be always as condenser, since the region at which this system will operate in transcritical is very narrow. Furthermore, the optimum subcooling degree results higher at lowest evaporating levels and high environment levels. Nonetheless, the maximum ratio of power consumption of the mechanical subcooling compressor will not exceed from 21% of the power consumption of the CO\({}_{2}\) compressor.  
It was concluded that the cascade configuration using CO\({}_{2}\) as low temperature refrigerant will have highest performance than the MS cycle when the temperature lift between the cold and heat sources is higher than 28.5 K. However, in this case the power consumption of the high-temperature cycle will be even higher than the power consumption of the CO\({}_{2}\) rack.  
The analysis was extended to the different climatic regions of Spain using a based temperature-BIN methodology. It was calculated that the MS cycle would offer highest energy efficiencies in overall-year operation than the cascade solution for evaporating levels below \(-15\)\({}^{\circ}\)C, including the air-conditioning application. However, at the evaporating level of \(-20\)\({}^{\circ}\)C the cascade solution will over perform the MS cycle. Also, the individual systems were compared to an ideal refrigeration cycle that could be operated as CO\({}_{2}\) with mechanical subcooling or as cascade at any climatic condition, which is called the best system. The average annual COP of each individual system was compared with the best system. It was observed that the MS cycle will have annual reductions of efficiency up to 5% at evaporating levels higher or equal than \(-15\)\({}^{\circ}\)C, and also reductions below 5% at the evaporating level of \(-20\)\({}^{\circ}\)C except for 4 climatic regions of Spain.  
As general conclusion of this work, it can be affirmed that if this cycle configuration is sized as cascade or as a single-stage cycle with mechanical subcooling, the configuration that will offer the best performing levels at the analyzed conditions would be the CO\({}_{2}\) refrigeration cycle with mechanical subcooling.  
The authors gratefully acknowledge the Spanish Ministry of Economy and Competitiveness (project ENE2014-53760-R.7) for financing this research work.  
[PERSON] suggested the idea and conceived the calculation models. [PERSON] and [PERSON] carried out the simulations and analyzed the data; [PERSON] and [PERSON] checked the calculations. [PERSON] and [PERSON] wrote the paper and [PERSON] contributed to the correction of the paper.  
The authors declare no conflict of interest.