# Parametric Analysis of a Polygeneration System with CO\({}_{2}\) Working Fluid
## 3 Results and Discussion
### Preliminary Analysis
Figure 11 shows that the exergy efficiency is enhanced by the improvement of the heat exchanger effectiveness but the energy efficiency is reduced with the increase of the effectiveness value. Figures 12 and 13 give the system performance for different refrigeration temperature levels. Figure 12 shows that refrigeration production is not so affected by the refrigeration temperature, as well as the high heating production. On the other hand, it is obvious that a higher refrigeration temperature leads to a significant increase in electricity production and an important decrease in low heating production. Figure 13 indicates that a higher refrigeration temperature increases the system exergy efficiency, while the energy efficiency is maximized for refrigeration production at around \(-25\)\({}^{\circ}\)C. Generally, the energy efficiency is not so variable in the range between \(-35\)\({}^{\circ}\)C and \(-15\)\({}^{\circ}\)C, while for higher refrigeration temperatures it shows a significant decrease. At this point, it is important to note that CO\({}_{2}\) operation in temperatures as low as \(-35\)\({}^{\circ}\)C is not a difficult task because CO\({}_{2}\) is used in supermarket refrigeration applications where temperature levels of around \(-35\)\({}^{\circ}\)C are usually applied. Figures 14 and 15 show the system behavior with different heat rejection temperature levels. Practically, this parameter is the temperature level in the outlet of the gas cooler and it has to be 3 to 5 \({}^{\circ}\)C more than the ambient temperature. In this work, it was studied from 20 \({}^{\circ}\)C to 45 \({}^{\circ}\)C and in all cases, the medium pressure was more than the critical pressure. Figure 14 shows that the electricity and the low heating production increase sightly with the heat rejection increase. On the other hand, the high heating and the refrigeration show more intense behavior with the first increasing and the other reducing with the heat rejection temperature augmentation. The behavior of these curves is a bit strange after 35 \({}^{\circ}\)C because of the variation in the CO\({}_{2}\) properties in this region (close to the critical point). Figure 15 shows that higher heat rejection temperatures lead to higher exergy efficiency and to lower energy efficiency. Figures 16 and 17 present the system behavior for different values of the high heating temperature. Practically, all of the useful outputs are not affected and only the high heating temperature is decreased with the increase of its temperature level, as Figure 16 shows. Figure 17 indicates that the energy efficiency reduces with the increase in the high heating temperature while the exergy efficiency is maximized at 65.4 \({}^{\circ}\)C with a value of 26.5%, and in this case, the energy efficiency is 85.57%. Table 4 summarizes the examined parameters, the range of the examined parameters and the range of the obtained results for the energy and exergy efficiency. It is important to note that the parameters that created the greatest variation in the energy efficiency were the medium pressure (67.51% to 117.10%) and the high heating temperature variation (65.63% to 95.83%). High energy efficiency values, which can be higher than 100%, are obtained by the proper management of the refrigeration input in the system. More specifically, the examined system acts simultaneously as a power cycle and a heat pump to produce four different useful outputs. With regard to the exergy efficiency, the high-pressure variation leads to great exergy efficiency deviation (8.69% to 28.38%) and the refrigeration temperature variation results in great variation in the exergy efficiency (12.67% to 27.16%). Moreover, Table 5 includes the \"derivative\" of the efficiencies to the examined parameters. Practically, the global maximum minus the global minimum efficiency values are normalized to the nominal efficiency and are divided with the parameter range normalized to the nominal value.