## 2 Materials and Methods  
The existing methodology of the advanced exergy analysis splits exergy destruction within each system component into the following parts [2; 12; 14]:  
* endogenous/exogenous parts \[\dot{E}_{D,k}=\dot{E}_{D,k}^{EN}+\dot{E}_{D,k}^{EX}\] (1)
* unavoidable/avoidable parts \[\dot{E}_{D,k}=\dot{E}_{D,k}^{AV}+\dot{E}_{D,k}^{UN}\] (2)
* and combined parts \[\dot{E}_{D,k}=\dot{E}_{D,k}^{UN,EN}+\dot{E}_{D,k}^{UN,EX}+\dot{E}_{D,k}^{AV,EN }+\dot{E}_{D,k}^{AV,EX}\] (3)The thermodynamic cycle-based approach was used to split the exergy destruction into parts [12; 15; 16]. The product exergy rate (i.e., the cooling capacity) of the investigated refrigeration system in all the analyzed cycles remained the same. The endogenous exergy destruction (\(\dot{E}^{EN}_{D,k}\), being associated with the k-th component, is caused only by the actual irreversibilities occurring in the same component as all other components operate in an ideal way. For estimating the endogenous part of the exergy destruction within each component of the refrigeration system, the hybrid cycles with only one irreversible component were analyzed. The separate introduction of irreversibilities within each system component provides the possibility to calculate the endogenous exergy destruction for each component. The exogenous part of exergy destruction (\(\dot{E}^{EX}_{D,k}\)) within the k-th component is related to the irreversibilities occurring in the remaining components or caused by the structure of the overall system. \(\dot{E}^{EX}_{D,k}\) in the k-th component was estimated by subtracting the endogenous exergy destruction from the total one [2; 12; 14]. For determining the unavoidable and avoidable parts of exergy destruction, hybrid cycles with unavoidable thermodynamic inefficiencies occurring within each component needed to be implemented. The avoidable exergy destruction (\(\dot{E}^{AV}_{D,k}\)) was calculated as the difference between the total and unavoidable parts of exergy destruction [2; 12; 14]. For further splitting exergy destruction, the thermodynamic cycle-based approach was applied only for the estimation of the unavoidable endogenous exergy destruction (\(\dot{E}^{UN,EN}_{D,k}\)) [2; 12]. A similar approach applied for calculating the endogenous part of the exergy destruction could be used for this purpose. However, for this case, the unavoidable thermodynamic efficiency of each component was assumed [2; 12; 14]. The remaining parts of the exergy destruction were then calculated as [2]  
\[\dot{E}^{UN,EX}_{D,k}=\dot{E}^{UN}_{D,k}-\dot{E}^{UN,EN}_{D,k} \tag{4}\]  
\[\dot{E}^{AV,EN}_{D,k}=\dot{E}^{EN}_{D,k}-\dot{E}^{UN,EN}_{D,k} \tag{5}\]  
\[\dot{E}^{AV,EX}_{D,k}=\dot{E}^{AV}_{D,k}-\dot{E}^{AV,EN}_{D,k} \tag{6}\]  
According to [2; 3], the endogenous avoidable part of exergy destruction (\(\dot{E}^{AV,EN}_{D,k}\)) can be decreased by improving the efficiency of the considered component. The exogenous avoidable part of the exergy destruction (\(\dot{E}^{AV,EX}_{D,k}\)) can be reduced by a structural improvement of the overall system or by increasing the efficiencies of the remaining components. Taking into account that the investigators need to consider possibilities for the reduction of the avoidable parts of exergy destruction occurring in each system component, this work was based uniquely on these irreversibilities and proposes a new calculation method to compute them.