## 6 Numerical Results
### Thermoeconomic Analysis  
Once the balances of the first and second laws were calculated, the next step deals with the application of thermoeconomics. Consequently, by means of the productive structure, the vector of unit exergy costs of fuel and product (k\({}_{\text{F}}\)* and k\({}_{\text{p}}\)*) were calculated. Table 4 shows the obtained average annual values for each component. These vectors allow mapping the cost formation process following two main facts: \begin{table}
\begin{tabular}{c c c} \hline \multicolumn{2}{c}{**Unit Energy Cost [kWh/kWh]**} \\ \hline  & \(\mathbf{k_{F}^{*}}\) & \(\mathbf{k_{p}^{*}}\) \\ \hline
**C1** & 1.00 & 2.79 \\
**C2** & 1.00 & 2.82 \\
**M1** & 4.38 & 4.38 \\
**D1** & 4.28 & 4.57 \\
**HX1** & 4.20 & 4.95 \\
**T1** & 4.86 & 5.36 \\
**B1** & 1.00 & 6.21 \\
**B2** & 1.00 & 6.50 \\
**HC** & 6.69 & 6.76 \\
**H** & 6.71 & 28.65 \\
**HX2** & 6.66 & 7.13 \\
**T2** & 7.02 & 12.06 \\
**DHW** & 12.06 & **14.90** \\ \hline \multicolumn{2}{c}{} & \multicolumn{1}{c}{} \\ \end{tabular}
\end{table} 
Table 4: Unit exergy costs of each component fuel and product. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**EXERGY [kWh]**} \\ \cline{2-4}  & **Fuel** & **Product** & **\(\varphi\) [\%]** \\ \hline
**C1** & 58,612 & 20,983 & 36 \\
**C2** & 60,378 & 21,443 & 36 \\
**M1** & 105,835 & 105,835 & 100 \\
**D1** & 100,773 & 94,301 & 94 \\
**HX1** & 131,07 & 11,109 & 85 \\
**T1** & 11,647 & 10,563 & 91 \\
**B1** & 871,182 & 141,006 & 16 \\
**B2** & 82,483 & 12,717 & 15 \\ HC & 1,351,061 & 1,336,877 & 99 \\
**H** & 108,690 & 25,447 & 23 \\
**HX2** & 43,947 & 41,051 & 93 \\
**T2** & 42,133 & 24,525 & 58 \\
**DHW** & 24,525 & 19,849 & 81 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Yearly exergy efficiency of components. * On one side, for each \(i\)-th component, the difference between the unit exergy cost of the product (\(\text{k}_{\text{Pi}}\)*) and the unit exergy cost of the fuel (\(\text{k}_{\text{Fi}}\)*) sets forth the cost of irreversibilities in the \(i\)-th component itself per unit of product, since \(\text{k}_{\text{Pi}}^{*}-\text{k}_{\text{Fi}}^{*}=\text{k}_{\text{Fi}}^{*} \frac{\text{I}_{\text{i}}}{\text{P}_{\text{i}}}\). * On the other side, the difference between the unit exergy cost of the outgoing product of the \(i\)-th component (\(\text{k}_{\text{Pi}}\)*) and the exergy cost of incoming fuel of the \(j\)-th component (\(\text{k}_{\text{Pi}}\)*) refers to the irreversibilities associated with the productive chain structure. That means that while the productive process is going downstream the irreversibilities accumulate so the cost increases. The fuel in the boilers and cogeneration engines (natural gas) are considered as inputs to the system so, in the absence of external assessment, its exergy cost is equal to 1. By contrast, the hydraulic pumps are fed by the electricity coming from the micro-cogeneration engines so their exergy cost is equal to the cost of the electricity cogenerated \(\text{k}_{\text{FPump}}\)* = \(\text{k}_{\text{PCog}}\)*. When considering Table 4, it is worth emphasizing that the unit cost of the product of the emitting device, the final component in the energy chain, has increased significantly in respect to the unit cost of fuel, going from \(\text{k}_{\text{FH}}\)* = 6.71 to \(\text{k}_{\text{PH}}\)* = 28.65. This large increment is because the indoor air is included in that final component, so its product is very low as it is equal to the exergy of heating and the operating temperature is close to the environmental temperature. It is worth noting that the unit exergy cost of the fuel in DHW production is higher than the one of heating \(\text{k}_{\text{PDHW}}\)* \(\text{k}_{\text{FH}}\)*. This is because DHW generation requires more components than heating and, therefore, it accumulates more irreversibilities and cost increases. Consequently, the mean value of the exergy unit cost of heating is equal to 28.65, the unit DHW cost is 14.9 and the electricity cogenerated has an average unit cost of 2.8.