## 4 Conclusions  
In this paper, the use of heat and electricity storage, as well as solar thermal and photovoltaic panels to be coupled to a heat pump, was investigated. To do this, four technologies from the marketplace were chosen, simulated, and analyzed: a heat pump water heater connected to the grid, a heat pump water heater coupled with a photovoltaic plant, a heat pump water heater coupled with a solar thermal collector, and a typical solar thermal plant. First of all, the electricity consumption of an ordinary ESWH for a family on Lampedusa Island was calculated through simulation (yearly 1137 kWh, varying from 125 kWh in January to 67 kWh in August). This value was used as a reference to calculate the energy savings achievable with the other systems. It was found that the replacement of the reference system with an electric heat pump could provide an average energy saving equal to 65%. Indeed, in this case, the yearly energy consumption can be reduced from 1137 to 375 kWh, avoiding 761 kWh of electricity withdrawal from the local grid. Regarding the heat pump water heater coupled with a PV plant, four further stand-alone and one grid-connected photovoltaic plants were considered. Moreover, two solar thermal-based systems introduced: one coupled with an electrical back-up resistance (called ST (4)) and the other with the heat pump itself (called HPWH + ST (3)). Firstly, all proposed solar assisted plants were run without accounting for electrical storage (photovoltaic plants) or a back-up system (solar thermal plant) in order to check for their performance by means of a set of comfort indices. Based on the comfort conditions, the most suitable size for a stand-alone PV-plant was detected. Some comfort issues were detected for the systems with 720 Wp. while a peak power of 1200 Wp could dramatically mitigate such a problem. Then, two alternative electric storages were evaluated through a calculation of values for the \"battery indices\". The following PV-based plants were then selected: a system characterized by a power of 1200 Wp and a storage capacity of 2400 Wh (called HPWH (2.1a)) and system characterized by a power of 720 Wp and a storage capacity of 4800 Wh (called HPWH \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & **HPWH + Grid (1)** & **HPWH (2.2a)** & **HPWH (2.1b)** & **GC (2.5)** & **HPWH (3)** & **ST (4)** \\ \hline PBT (years) & 6.9 & 11.9 & 9.5 & 12.1 & 6.7 & 3.6 \\ NPV (€) & 2357.02 & 2280.30 & 3015.43 & 1620.35 & 3061.53 & 2719.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Payback time and net present value (national incentive). Figure 20: Cash flow and net present value of selected solutions (with national incentive). (2.2b)). Similarly, the ST plant was firstly evaluated by means of comfort indices. The results showed that, if back-up systems are not included in the systems, setpoint temperature could only not be maintained in the tank during winter months and some potential discomfort events could be detected. By using the system characterized by 1200 Wp, the contemporaneity between the energy needed for domestic hot water production and PV useful yield achieved values higher than 90%. Looking at the comparison between the electrical consumption of the electricity-driven pump water heater and those driven by the solar thermal (called ST (4)) and the pump water heater coupled with solar thermal systems (called HPWH + ST (3)), the solar thermal (called ST (4)) one achieved an extra 4% of energy taken from the grid. By comparing the pump water heater consumption with that of the pump water heater coupled with solar thermal systems (called HPWH + ST (3)), a 58% reduction was evaluated. In general, from an energy-saving point of view, all plants achieved energy savings concerning the traditional electric storage water heater in use, varying from 100% for the selected photovoltaic plants to 86% for the pump water heater coupled with solar thermal systems (called HPWH + ST (3)), with an average 66.5% for the solely pump water heater and solar thermal systems (ST (4)).