# Parametric Analysis of a Polygeneration System with CO\({}_{2}\) Working Fluid
## 3 Results and Discussion  
### Preliminary Analysis  
The first part of the present work was the preliminary study of the examined system for the nominal operating conditions. Figure 2 shows the thermodynamic state at various points in a pressure-specific enthalpy (p-h) diagram, while Figure 3 shows the temperature-specific entropy (T-s). The vertical axis of Figure 3 is a logarithmic axis with a ten-based logarithm. These figures show that the examined cycle is a combination of a Brayton power cycle (supercritical region) and a transcritical mechanical compression cycle. So, the total configuration is characterized as a transcritical thermodynamic cycle. Table 2 includes all the state points of the examined cycle and more specifically, the given properties are pressure, specific enthalpy, temperature and specific entropy. \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Symbol** & **Value** \\ \hline Heat input & Q\({}_{\text{b}}\) & 100 kW \\ Boiler efficiency & \(\eta_{\text{b}}\) & 95\% \\ Lower heating value & H\({}_{\text{u}}\) & 15290 kJ kg\({}^{-1}\) \\ Pitch point in heat exchangers & PP & 5 \({}^{\circ}\)C \\ Exergy factor of the fuel & \(\psi_{\text{b}}\) & 1.119 \\ Low heating temperature & T\({}_{\text{heat,Low}}\) & 45 \({}^{\circ}\)C \\ Nominal high heating temperature & T\({}_{\text{heat,high}}\) & 80 \({}^{\circ}\)C \\ Nominal high pressure & P\({}_{\text{high}}\) & 200 bar \\ Nominal medium pressure & P\({}_{\text{med}}\) & 85 bar \\ Nominal refrigeration temperature & T\({}_{\text{ref}}\) & 5 \({}^{\circ}\)C \\ Nominal turbine inlet temperature & TIT & 700 \({}^{\circ}\)C \\ Nominal heat exchanger effectiveness & T\({}_{\text{hex}}\) & 90\% \\ Nominal heat rejection temperature & T\({}_{\text{hr}}\) & 35 \({}^{\circ}\)C \\ \hline \end{tabular}
\end{table} 
Table 1: Information about the examined configuration. Figure 2: Pressure-specific enthalpy (p-h) diagram for the examined polygeneration system in nominal operating conditions. Table 3 includes the main results for the operation in nominal operating conditions. These conditions were selected as typical conditions for producing adequate amounts of all the useful outputs. These conditions correspond to a system that is able to produce cooling and heating at two temperature levels for building applications (e.g., domestic hot water and heating purposes). In this scenario, the net power production was 24.50 kW, the cooling production was 30.73 kW, the heating production at 45 \({}^{\circ}\)C was 9.24 kW and the heating production at 80 \({}^{\circ}\)C was 13.60 kW. The system energy efficiency was 78.07% and the system exergy efficiency was 26.29%. Moreover, biomass consumption was calculated as 0.00654 kg s\({}^{-1}\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**State-Points** & **Pressure-P** & **Temperature-T** & **Specific Enthalpy-h** & **Specific Entropy-s** \\  & **(bar)** & **(\({}^{\circ}\)C)** & **(kj kg\({}^{-1}\))** & **(kj kg\({}^{-1}\) K\({}^{-1}\))** \\ \hline
1 & 39.7 & 5.0 & –79.3 & –0.923 \\
2 & 85.0 & 65.4 & –45.2 & –0.907 \\
3 & 85.0 & 50.0 & –80.9 & –1.015 \\
4 & 85.0 & 35.0 & –197.9 & –1.388 \\
5 & 200.0 & 61.8 & –177.7 & –1.379 \\
6 & 200.0 & 508.8 & 477.3 & –0.062 \\
7 & 200.0 & 800.0 & 844.2 & 0.337 \\
8 & 85.0 & 679.0 & 695.3 & 0.356 \\
9 & 85.0 & 123.5 & 40.2 & –0.673 \\
10 & 85.0 & 85.0 & –12.3 & –0.812 \\
11 & 85.0 & 35.0 & –197.9 & –1.388 \\
12 & 39.7 & 5.0 & –197.9 & –1.349 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Thermodynamic state-points in nominal operating conditions. Figure 3: Temperature-specific entropy (T-s) diagram for the studied polygeneration system in nominal operating conditions (logarithmic vertical axis). Figure 5: Energy and exergy efficiencies for different values of the turbine inlet temperature. Figure 6: Useful energy products for different values of the high pressure. Figure 8: Useful energy products for different values of the medium pressure. Figure 7: Energy and exergy efficiencies for different values of the high pressure.