# A Sustainable Polygeneration System for a Residential Building
## 2 Materials and Methods
### Economic Analysis  
The simple payback (SPB) has been selected first in this section. It is calculated as the ratio of the total capital cost and the savings achieved by PS concerning RS. In particular, 25 years of a lifetime is considered. \[SPB=\frac{TI_{PS}}{AS_{PS}} \tag{5}\]  
\[AS_{PS}=OC_{RS}-OC_{PS} \tag{6}\]  
In Equations (5) and (6), SPB is the simple payback of the investment, TI\({}_{\text{PS}}\) is the total investment in the proposed system, AS\({}_{\text{PS}}\) is the annual saving in the proposed system, and OC\({}_{\text{RS}}\) and OC\({}_{\text{PS}}\) are the operating cost in the reference system and proposed system, respectively. The yearly economic saving of the proposed system takes into account the economic gains concerning the reference system. In RS, electricity is provided only by the national grid. On the other hand, in PS, the electric user load is matched by the PV, PVT, and TEG in an overall yearly balance, but sometimes the electricity is supplied by the grid. Moreover, different prices are found when electricity is purchased or sold to the grid. A fee for natural \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Item** & **Parameter** & **Value** & **Unit(s)** & **Reference** \\ \hline PV & Inv. \& OM cost & 1000, 1 & \(\text{\textc/kW}_{p}\), \%/y & [31] \\ PVT & Inv. \& OM cost & 200, 2 & \(\text{\textc/m}^{2}\), \%/y & [32] \\ Water tanks & Investment cost & 495 + 808-V(m\({}^{3}\)) & \(\text{\textc}\) & [33] \\ Inverter & Investment cost & 180 & \(\text{\textc/kW}\) & [34] \\  & & 419 + 0.03 & & \\ Pumps & Inv. \& OM cost & -Q-2.16\(\cdot\)10\({}^{-8}\).Q\({}^{2}\), & \(\text{\textc, \%/y}\) & [35] \\  & & 0.5 & & \\ BB & Inv. \& OM cost & 282, 1 & \(\text{\textc/kW}_{\text{th}}\), \%/y & [24; 36] \\ Heat pump & Inv. \& OM cost & 350, 0.5 & \(\text{\textc/kW}_{\text{cl}}\), \%/y & [31; 37] \\ SEAC & Inv. \& OM cost & 600, 0.2 & \(\text{\textc/kW}_{\text{cl}}\), \%/y & [32; 37] \\ MED & Inv. \& OM cost & 1500, 0.5 & \(\text{\textc/(m}^{3}\)/d), \%/y & [38] \\ RO & Inv. \& OM cost & 800, 1.5 & \(\text{\textc/(m}^{3}\)/d), \%/y & [39] \\ PE\({}_{\text{P}}\) & Price & 0.2 & \(\text{\textc/kW}\)h & \\ PE\({}_{\text{S}}\) & Price & 0.08 & \(\text{\textc/kW}\)h & \\ PNG & Price & 0.07 & \(\text{\textc/kW}\)h & \\ PE\({}_{\text{E}}\) & Price & 0.052 & \(\text{\textc/kW}\)h & \\ PW & Price & 2.0 & \(\text{\textc/m}^{3}\) & [40] \\ fCO\({}_{\text{D}}\)E & Emission factor & 0.19 & kgCO\({}_{2}\)/kWh & [41] \\ fCO\({}_{\text{D}}\)NG & Emission factor & 0.204 & kgCO\({}_{2}\)/kWh & [42] \\ r & Interest rate & 2 & \% & \\ COP\({}_{\text{R}}\) & Efficiency & 2.6 & – & [43] \\ \(\eta_{\text{E}}\) & Efficiency & 0.42 & – & [43] \\ \(\eta_{\text{Q}}\) & Efficiency & 0.92 & – & [43] \\ SEC\({}_{\text{R}}\) & Specific cons. & 4 & kWh/m\({}^{3}\) & [40] \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Main economic and environmental parameters of the study. gas, biomass pellets (assuming a fixed low heating value, LHV), and water from the grid is also necessary to establish the annual cost of the reference facility to compare with the proposal (see Table 6). The yearly operating costs (OC) also include a percentage of the investment required for each central technology as a maintenance cost.