## PV-HPWH contemporaneity
### Economic Analysis and Comparison between Systems  
The previous results demonstrated in which ways the selected plants could ensure comfort conditions while exploiting the thermal and/or electrical storage capacity of the systems. For the sake of clarity, the following systems were analyzed:  
* System (1), HPWH + grid: heat pump water heater without any RES plant assistance;
* System (2.1a), HPWH + PV, heat pump water heater with a PV plant having 2400 Wh storage capacity and 720 Wp
* System (2.2b), HPWH + PV, heat pump water heater with a PV plant having 2400 Wh storage capacity and 1200 Wp
* System (2.5), HPWH + GC PV, heat pump water heater with a 300-Wp PV plant directly connected to the grid;
* System (3), HPWH + ST: heat pump water heater coupled with a solar thermal plant
* System (4), ST plant: commercial solar thermal plant relying on a solar thermal collector with an electrical resistance back-up and DHW tank  
Systems HPWH (2.1b) and HPWH (2.2a) were \"discarded\" because the sizing was not proper. From the energy saving point of view, taking as a reference an ordinary ESWH system (with 1137 kWh electrical consumption per year), all plants achieved energy savings in a range from 100% for the PV plants to 86% for the HPWH + ST (3) system, with an average of 66.5% for the HPWH and ST (4) system (Figure 18).  
Figure 17: **Top**: electrical consumption of the systems; **bottom**: monthly setpoint index (SPI).  
Differences could be noted when looking at economic indices. In Figure 19 and in Table 5, the calculated net present value and the payback time (PBT) for the proposed systems are reported. System initial costs were estimated via an analysis of the Italian market [43; 44]. The average electricity cost from a user's bill was considered in the calculation (0.23 \(\upxi\)/kWh), while the selling price for the produced electricity for the grid-connected PV plant was considered equal to 0.10 \(\upxi\)/kWh.  
A 20-year useful lifetime was assumed for all the plants.  
First of all, it can be noted that, if no public subsidy is considered, stand-alone PV plants show a negative cash-flow rate, with a consequently negative NPV (Figure 19). At the same time, these systems present the worst payback time, higher than 21 years. On the other hand, all other systems present positive NPV varying from 760 \(\upxi\) for the HPWH system to 1902 \(\upxi\) for the solar thermal plant with electric back-up. ST (4) and HPWH + grid (1) systems, despite similar energy saving values, strongly differ in NPV and in PBT, with the latter having the lowest value, i.e., half of the first. Finally, low differences could be noted in all figures between the GC (2.5) and ST (4) plants.  
Figure 19: Cash flow and net present value of selected solutions (without national incentive).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & **HPWH + Grid (1)** & **HPWH (2.1a)** & **HPWH (2.1.b)** & **GC (2.5)** & **HPWH (3)** & **ST (4)** \\ \hline PBT (years) & 15.2 & 24.1 & 21.6 & 13.1 & 14.7 & 7.6 \\ NPV (\(\upxi\)) & 769 & \(-\)974 & \(-\)384 & 1.405 & 1065 & 1902 \\ \hline \end{tabular}
\end{table}
Table 5: Payback time and net present value (without national incentive).  
Figure 18: Comparison of the DHW energy saving.  
The Italian incentive mechanism for such a system allows for some reduction in the purchase price for plant components to be distributed in 10 yearly payments. Incentive values vary from 50% to 65% for PV components and for ST and HPWH components, respectively. Under such circumstances, all systems have a positive net present value estimated at 20 years (Figure 20).  
The best NPV is associated with the HP coupled with a stand-alone PV system and a small battery (system HPWH (2.1b)) and the solar thermal-assisted HP (system HPWH + ST (3)). The shortest payback time was calculated for the solar thermal system (Table 6).