## 4 Results and Discussion
In this case, the payback time is 15.9 years. The energy and cost savings are 369 kWh/year and at least 81.1 EUR/year, respectively. The general behavior of payback time and savings per year is similar to Case #1, but the average minimum payback time is found for an RPW-HEX storage size of around 4 kWh, which is 1 kWh lower than the optimal size in Case #1. This fact is also reflected in the profits after 20 years for Cases #1 and #2 (Figure 4). One finds maxima around RPW-HEX storage sizes of 5 to 7 kWh for Case #1 and maxima around 4 to 5 kWh for Case #2. The maximum profits are gained for Case #1 with large DHW storages,  
Figure 4: Profit after 20 years of operation for (**a**) Case #1 (passive house located in Helsinki) and (**b**) Case #2 (low energy building located in Strasbourg). Markers “\(\blacktriangledown\)”, “\(\blacktriangledown\)” and “\(\blacktriangle\)” denote small (140 L), medium (210 L) and large (280 L) decentralized DHW storage devices. Please note that for some cases, no profit can be made after 20 years of operation, so they are not shown in the figures. Figure 3: Payback time (**a**) and savings per year (**b**) for Case #2 (low-energy building located in Strasbourg). Markers “\(\blacktriangledown\)”, “\(\blacktriangledown\)” and “\(\blacktriangle\)” denote small (140 L), medium (210 L) and large (280 L) decentralized DHW storage devices. Please note that for the case with small decentralized storage devices operated in comfort mode, the payback time is higher than 35 years for all RPW-HEX storage sizes. Therefore, this case is not shown in (**a**). an RPW-HEX storage size of 5 kWh and operation in eco-mode. In this case, the profit is 1083 EUR after 20 years. For Case #2, the maximum profit was also gained for the large DHW storage devices operating in eco-mode, but with an RPW-HEX storage size of 4 kWh. The maximum profit in this case is 398 EUR after 20 years. For Case #3, the refurbished building located in Athens, no scenarios exist where the payback times become less than 20 years (Figure 5a). Furthermore, the differences between eco-, standard- and comfort-charging modes is not as pronounced as in Case #1 and Case #2. The reason for this is that the share of the energy provided by the condenser for DHW generation during operating mode (c) is smaller than in the other two cases (compare also Case #1 and #3 in Figure 6). Hence, the dependence on the water return temperature and therefore on the storage size is not as strong as for the other cases. Table 3 gives an overview of the energetic and economic performances of a 5 kWh RPW-HEX operating in standard-mode with medium DHW storage devices. Although the relative energy savings are the highest for Case #3 (up to 5% of total energy savings per year and up to 25% of energy savings for DHW per year in Table 3) compared to the other two cases,  
Figure 5: Payback time (**a**) and savings per year (**b**) for Case #3 (refurbished building located in Athens). Markers \({}^{-}\)\(\blacktriangledown\), \({}^{-}\)\(\bullet\)\({}^{-}\) and \({}^{-}\)\(\blacktriangle\)\({}^{-}\) denote small (140 L), medium (210 L) and large (280 L) decentralized DHW storage devices.