## 4 Discussion of Results
### Operation in Different Climate Conditions  
As mentioned by [PERSON] et al. [31], the superiority of one refrigeration system regards another in terms of energy efficiency must be discussed with reference to the climatic conditions of the installation site and the characteristics of cooling profile. In agreement with them, and in order to obtain conclusions about the performance of the MS cycle configuration regards the cascade design, in this subsection an evaluation of the systems at different climate conditions is reported. In this case, a climatic evaluation was made using the BIN temperature methodology [32] with the Energy Plus meteorological data ([[https://energyplus.net/weather](https://energyplus.net/weather)]([https://energyplus.net/weather](https://energyplus.net/weather))) for different locations in Spain. This methodology groups the number of annual hours in which a certain temperature was recorded, allowing an accurate representation of the annual climate. In fact, the energy performance of the systems was evaluated for the twelve climatic regions of Spain [33], Table 1, covering cold, mild and warm climates, using 20 temperature BINs from \(-3\) to 33 \({}^{\circ}\)C of dry bulb temperature. For the evaluation, two simplified cooling load profiles were considered. Representing air-conditioning (AC) applications, no cooling load was considered below 21 \({}^{\circ}\)C, a linear dependence on the cooling load from temperatures above 21 up to 29 \({}^{\circ}\)C and 100% from 29 \({}^{\circ}\)C on. For commercial applications a constant value of 50% of cooling load up to 23 \({}^{\circ}\)C, linear dependence from 23 to 31 \({}^{\circ}\)C and 100% from 31 \({}^{\circ}\)C on. Cooling load profiles are detailed in Table 1.  
Figure 14: Compressor’s displacements of a plant with 50 kW capacity at an environment at 30 \({}^{\circ}\)C.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline  & **City** & **León** & **Pamplona** & **Teruel** & **Albacete** & **La Coruna** & **Barcelona** & **Granada** & **Toledo** & **Casticolin** & **Scvilla** & **Malaga** & **Almeria** \\  & Spanish climatic region & E1 & D1 & D2 & D3 & C1 & C2 & C3 & C4 & E3 & B4 & A3 & A4 \\  & Average annual temperature (\({}^{\circ}\)C) & 10.7  
Using the meteorological data of dry-bulb temperature, an averaged COP value for both cycle configurations was evaluated using Equation (13). Where _COP_ (\(T_{env,i}\)) is the COP of each system evaluated at the average temperature of the 'i' temperature BIN, \(NH_{i}\) is the number of hours of operation inside the 'i' temperature BIN and \(FQ_{i}\) the cooling load fraction inside the 'i' temperature BIN. \[\overline{\text{COP}}=\frac{\sum_{\text{i}=1}^{\text{nbin}}[\text{COP}(\text{T }_{\text{env,i}})\times\text{NH}_{\text{i}}\times\text{FQ}_{\text{i}}]}{\sum_{ \text{i}=1}^{\text{nbin}}(\text{NH}_{\text{i}}\times\text{FQ}_{\text{i}})} \tag{13}\]  
Averaged COP values for both refrigeration systems, for the different climatic regions using the cooling load profiles detailed in Table 1, are summarized in Table 2. Regarding AC application (\(\text{T}_{\text{o}}\) = 5 \({}^{\circ}\)C), it can be seen that the MS cycle over performs the cascade configuration for all the climatic regions except for the D3, C3, C4 and B4, that are regions with high environment temperatures during summer, where both configuration perform similar. Regarding the general application, for evaporating temperatures from 0 to \(-\)20 \({}^{\circ}\)C, the MS cycle also presents highest performance for all the climatic regions up to an evaporating level of \(-\)10 \({}^{\circ}\)C. At \(-\)15 \({}^{\circ}\)C both solutions perform similar and for \(-\)20 \({}^{\circ}\)C the cascade solution is the best performing. The differences between both refrigeration systems for the different climate conditions and the different evaporating levels and cooling load profiles are represented in Figure 15 as percentage variation from the MS cycle COP values, according to Equation (14).