## 4 Discussion of Results
### Operation in Different Climate Conditions
Values of Equation (14) represent the average annual COP advantage of the MS cycle regard the cascade cycle. It can be observed that the MS cycle is recommended from an energy point of view for any evaporating level higher or equal to \(-\)10 \({}^{\circ}\)C, both systems similar perform at \(-\)15 \({}^{\circ}\)C and the cascade should be recommended for the temperature level of \(-\)20 \({}^{\circ}\)C.  
\[\Delta\text{COP}\;(\%)=\frac{\text{COP}_{\text{MS}}-\text{COP}_{\text{casc}} }{\text{COP}_{\text{casc}}}\times 100 \tag{14}\]  
Figure 15: COP percentage variation of MS cycle vs. the cascade system at different climatic condition. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Climatic Region** & **E1** & **D1** & **D2** & **D3** & **C1** & **C2** & **C3** & **C4** & **B3** & **B4** & **A3** & **A4** \\ \hline \multicolumn{10}{c}{Cascade cycle annual averaged COP} \\ \(\mathrm{T_{o}=5^{\circ}C}\) (AC) & 3.74 & 3.72 & 3.57 & 3.41 & 4.30 & 3.79 & 3.33 & 3.33 & 3.66 & 3.34 & 3.63 & 3.63 \\ \(\mathrm{T_{o}=0^{\circ}C}\) & 4.51 & 4.45 & 4.42 & 4.23 & 4.53 & 4.26 & 4.13 & 4.04 & 4.11 & 3.87 & 4.00 & 3.94 \\ \(\mathrm{T_{o}=-5^{\circ}C}\) & 3.75 & 3.70 & 3.68 & 3.54 & 3.77 & 3.56 & 3.46 & 3.39 & 3.45 & 3.26 & 3.37 & 3.32 \\ \(\mathrm{T_{o}=-10^{\circ}C}\) & 3.18 & 3.14 & 3.12 & 3.01 & 3.19 & 3.03 & 2.95 & 2.90 & 2.95 & 2.80 & 2.88 & 2.84 \\ \(\mathrm{T_{o}=-15^{\circ}C}\) & 2.73 & 2.70 & 2.69 & 2.60 & 2.74 & 2.61 & 2.55 & 2.51 & 2.54 & 2.42 & 2.49 & 2.46 \\ \(\mathrm{T_{o}=-20^{\circ}C}\) & 2.37 & 2.35 & 2.33 & 2.26 & 2.38 & 2.27 & 2.22 & 2.18 & 2.22 & 2.12 & 2.17 & 2.15 \\ \hline \multicolumn{10}{c}{MS cycle annual averaged COP} \\ \(\mathrm{T_{o}=5^{\circ}C}\) (AC) & 3.92 & 3.88 & 3.65 & 3.43 & 4.82 & 4.00 & 3.32 & 3.33 & 3.80 & 3.34 & 3.76 & 3.76 \\ \(\mathrm{T_{o}=0^{\circ}C}\) & 6.55 & 5.52 & 5.48 & 5.14 & 5.67 & 5.16 & 4.97 & 4.81 & 4.89 & 4.49 & 4.68 As previously mentioned, both refrigeration cycle designs could be implemented in a system if some of the components are oversized, mainly the high temperature compressor, subcooler and gas-cooler/condenser, although it is not commonly done. Nonetheless, if only one cycle of operation is selected, it is important to quantify what would be its overall performance regards a plant with possibility to operate as cascade or as MS cycle, that would be the plant that will offer the best average annual COP values. To quantify the differences of the individual systems, their average annual COP values according to Equation (13) were compared to the ones obtained by an ideal refrigeration system with COP values equal to the maximum COP values of the MS or the cascade system. Percentage annual COP deviations regards the ideal system are specified in Table 3 for the different Spanish climate regions, and represented for two representative cases in Figure 16, which correspond to the operation at \(-5\)\({}^{\circ}\)C and \(-20\)\({}^{\circ}\)C of evaporating temperature. As it can be observed, any individual system has reductions of annual COP values regards the optimum or best system, since in some hours of the year the other solution would be more performing. That occurs for all the climatic regions and evaporating levels except for the climatic region C1 with evaporating levels from 5 to \(-5\)\({}^{\circ}\)C. In general, for all the climatic regions, the system that better performs is the MS cycle configuration, with annual deviations from the best system up to 5% at evaporating levels higher or equal than \(-15\)\({}^{\circ}\)C. On the other side, if the considered evaporating level is \(-20\)\({}^{\circ}\)C, the solution with less deviation from the ideal system is the cascade, however, it is important to note that the MS cycle will have deviations lower than 5% regards the ideal system for all the climatic regions except for the C4, B4, A3 and A4.