## 4 Results and Discussion
\begin{table}
\begin{tabular}{c c c c} \hline  & **Case \#1** & **Case \#2** & **Case \#3** \\ \hline Energy demand for heat-ing per year & 2990 kWh\({}_{\text{pl}}\)/ & 3972 kWh\({}_{\text{pl}}\)/ & 2231 kWh\({}_{\text{pl}}\)/ \\ (RPW/REF) & 2993 kWh\({}_{\text{pl}}\) & 3918 kWh\({}_{\text{pl}}\) & 2180 kWh\({}_{\text{pl}}\) \\ \hline Energy demand for cool-ing per year & 2000 kWh\({}_{\text{pl}}\)/ & 1692 kWh\({}_{\text{pl}}\)/ & 3520 kWh\({}_{\text{pl}}\)/ \\ (RPW/REF) & 2099 kWh\({}_{\text{pl}}\) & 1753 kWh\({}_{\text{pl}}\) & 3616 kWh\({}_{\text{pl}}\) \\ \hline Energy demand for DHW per year & 6086 kWh\({}_{\text{pl}}\)/ & 3713 kWh\({}_{\text{pl}}\)/ & 900 kWh\({}_{\text{pl}}\)/ \\ (RPW/REF) & 6634 kWh\({}_{\text{pl}}\) & 4150 kWh\({}_{\text{pl}}\) & 1191 kWh\({}_{\text{pl}}\) \\ \hline Energy savings for heating per year & -51.2 kWh\({}_{\text{pl}}\) (-1.74\(\%\)) & -55.5 kWh\({}_{\text{pl}}\) (-1.42\(\%\)) & -50.5 kWh\({}_{\text{pl}}\) (-2.32\(\%\)) \\ \hline Energy savings for cooling per year & 59.0 kWh\({}_{\text{pl}}\) (2.86\(\%\)) & 61.6 kWh\({}_{\text{pl}}\) (3.51\(\%\)) & 95.8 kWh\({}_{\text{pl}}\) (2.65\(\%\)) \\ \hline Energy savings for DHW per year & 549 kWh\({}_{\text{pl}}\) (8.27\(\%\)) & 436 kWh\({}_{\text{pl}}\) (10.5\(\%\)) & 291 kWh\({}_{\text{pl}}\) (24.4\(\%\)) \\ \hline Total energy savings per year & 557 kWh\({}_{\text{pl}}\) (4.78\(\%\)) & 442 kWh\({}_{\text{pl}}\) (4.50\(\%\)) & 336 kWh\({}_{\text{pl}}\) (4.81\(\%\)) \\ \hline Investment costs & 1526 EUR & 1526 EUR & 1526 EUR \\ \hline Payback time & 14.1 years & 18.3 years & 25.6 years \\ \hline Minimum cost savings per year (based on & & \\ first year) & 122 EUR & 97.3 EUR & 74.0 EUR \\ \hline Profit after 20 years & 760 EUR & 171 EUR & - \\ \hline \end{tabular}
\end{table} 
Table 3: Performance of systems with 5 kWh RPW-HEX and medium DHW storage devices working in standard-operation mode. the absolute cost savings or electric energy savings are smaller compared to Case #1 and #2. This can be explained by having a closer look at the daily DHW consumption for Case #1 and #3 in Figure 6.  
In Case #1, 7.75 families (apartments) are supplied with domestic hot water (45.3 kWh\({}_{\text{th}}\)/day), whereas in Case #3, only 1.75 families (apartments) are supplied with domestic hot water (10.2 kWh\({}_{\text{th}}\)/day). Remember that the number of apartments was calculated considering that the HP (same design for all case studies and parameters) is able to provide the maximum heating or cooling demand of the building. Accordingly, the DHW consumption for each building results from the calculated number of apartments. In Case #3 (Figure 6b), the energy gained from heating operation (a) with charging the RPW-HEX is most of the time more than enough to cover the entire daily DHW demand during the winter season (which is depicted as a dotted line in Figure 6b). Therefore, the HP often switches to operating mode (e)--heating without charging the RPW-HEX--simply because the RPW-HEX is already fully charged and cannot be discharged to the likewise fully charged DHW storage devices. In contrast to this, the DHW demand in Case #1 can never be covered entirely by energy efficient DHW operating mode (c), and therefore, the RPW-HEX can always be discharged to the DHW storage devices. In other words, the number of charging/discharging cycles are higher in Case #1 than in Case #3, and therefore, the daily heat transfer from the RPW-HEX to the DHW storages is higher in absolute numbers in Case #1 (15.7 kWh/day) than in Case #3 (6.78 kWh/day), whilst the relative daily DHW covering ratio is higher in Case #3 (66.3%) than in Case #1 (34.7%). As the savings in operating costs are directly connected to the absolute savings in electric energy, the cost savings for Case #1 are higher compared to Case #3.