## 4 Results and Discussion  
The economic performance indicators for Cases #1 to #3 were calculated for different RPW-HEX storage sizes, DHW storages sizes, and DHW storage charging strategies (operating modes). \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(C_{\text{interest,fix}}\) (EUR) & & \(\tilde{c}_{\text{interest,var}}\) (EUR/kWh) \\ \hline Manufacturing costs RPW-HEX & 500 & Aluminum & 137.0 \\ Three-way valve and additional & 20 & PCM & 61.7 \\ piping & &
\begin{tabular}{c} Insulation \\ (mineral wool) \\ \end{tabular} & 2.6 \\
**Total** & **520** & **201.3** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Constant and variable investment costs. The minimum payback time for Case #1, a passive house located in Helsinki, was found to be 12.4 years for an RPW-HEX storage size of 5 kWh operating in eco-mode with large DHW storage devices (Figure 2a). Interestingly enough, for all other parameter variations, the minimum payback time was also found for around the same RPW-HEX storage size of 5 kWh. For the parameter variation with the shortest payback time (RPW-HEX storage size of 5 kWh), the annual energy savings (Figure 2b) are 622 kWh/year and the minimum cost savings are 137 EUR/year (calculated with the electric energy price in the first year of operation). Generally, it can be observed that the annual energy saving per year increases with RPW-HEX storage size until 5-6 kWh. After that, the increase in energy savings becomes significantly smaller (and the payback time starts to increase, see Figure 2a). Therefore, it makes no sense to increase the RPW-HEX storage size beyond this point. For a system operating in standard-mode with medium DHW storage devices, the payback time is still 14.1 years and annual savings are 557 kWh/year or at least 122 EUR/year, respectively. For small DHW storage devices (140 L) operating in standard- or comfort-mode, the payback time is always more than 20 years. The reason for this strong dependence on the DHW storage device size, which is a characteristic for the system, arises due to the considerably lower return temperature of water from a large DHW storage device. In operating mode (c)--energy efficient DHW generation--the HP condenser delivers a significant amount of energy to the DHW storage devices as long as the condensing temperature does not exceed the condensing temperature during heating operation (see also different contributions to QDHWc in Figure 6). This contribution from the condenser is highly appreciated from an energetic point of view. If the water return temperature increases and the condensing temperature becomes higher in operating mode (c) than it is during heating, the controller turns the HP off and solely the energy discharged from the RPW-HEX is used for DHW generation. This control rule was defined because it is better to discharge the RPW-HEX (which was previously charged with a \"heating COP\") than to run the HP with a COP higher than the \"heating COP\". Due to this dependence on the water return temperature from the DHW storage devices, it is also more important for small DHW storages to be operated in eco-mode which guarantees these low return temperatures. Furthermore, if the RPW-HEX is fully charged but no DHW is needed, the RPW-HEX can still be discharged by charging the DHW storage beyond the upper limit. Therefore, more energy can be transferred to the DHW whilst the RPW-HEX storage capacity stays the same during operation with large DHW storage devices. Figure 2: Payback time (**a**) and savings per year (**b**) for Case #1 (passive house located in Helsinki). Markers “\(\blacktriangledown\)”, “\(\bullet\)” and “\(\blacktriangle\)” denote small (140 L), medium (210 L) and large (280 L) decentralized DHW storage devices. For Case #2, a low energy building located in Strasbourg, the minimum payback times for most of the parameter variations were found for an RPW-HEX storage size of 4 kWh (Figure 3a). However, the absolute minimum was found at 3 kWh, large DHW storage devices and eco-mode.