## 3 Methodology  
### Simulation Models  
Simulation studies were carried out for both the novel system and the reference system without RPW-HEX. The following performance indicators were computed to calculate the annual efficiencies: coefficient of performance related to the hot side of the HP for heating and cooling: COP\({}_{\text{h}}\), coefficient of performance related to the hot side of the HP for DHW: COP\({}_{\text{DHW}}\) and RPW-HEX utilization factor: \(\varepsilon_{\text{RPW}}\). The latter is the ratio of energy transferred to the RPW-HEX compared to the total energy on the hot side of the HP. The simulations were carried out in the Dymola/Modelica modelling environment using ThermoCycle library components [21]. Additionally, models for the RPW-HEX, the outdoor unit and the four-way valve were developed in-house [22; 23]. Thermodynamic properties were taken from the CoolProp library [24]. A detailed description of the system model can also be found in [13; 14]. The performance indicators were derived from the dynamic simulation when  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Constraint**} & **Case \#1** & **Case \#2** & **Case \#3** \\  & **Passive House in** & **Low Energy Building** & **Refurbished Building** \\  & **Helsinki** & **in Strasbourg** & **in Athens** \\ \hline Apartments and total floor area per building & 7.75, 581 m\({}^{2}\) & 5.25, 394 m\({}^{2}\) & 1.75, 131 m\({}^{2}\) \\ \hline Heating demand per year and m\({}^{2}\) (kWh year\({}^{-1}\) m\({}^{-2}\)) & 14.8 & 31.5 & 61.7 \\ \hline Maximum heating demand (kW) & 6.97 & 9.89 & 7.15 \\ \hline Maximum cooling demand (kW) & 10.8 & 9.68 & 10.67 \\ \hline Daily DHW demand without losses (kWh) & 45.3 & 30.7 & 10.2 \\ \hline Annual heating demand (kWh) & 8598 & 12,413 & 8096 \\ \hline Annual cooling demand (kWh) & 6903 & 5360 & 9401 \\ \hline Annual DHW demand without losses & 16,534 & 11,200 & 3733 \\ \hline HP design load heating \(P_{\text{design,heating}}\) (kW) & 7.22 (at -22 \({}^{\circ}\)C) & 9.66 (at -10 \({}^{\circ}\)C) & 13.0 (at 2 \({}^{\circ}\)C) \\ \hline HP design load cooling \(P_{\text{design,cooling}}\) (kW) & 10.843 (at 35 \({}^{\circ}\)C) & 10.843 (at 35 \({}^{\circ}\)C) & 10.843 (at 35 \({}^{\circ}\)C) \\ \hline \(\delta_{\text{water,heating,distribution,in}}\) (\({}^{\circ}\)C) & 22–35 & 24–45 & 24–45 \\ \hline \(\delta_{\text{water,cooling,distribution,in}}\) (\({}^{\circ}\)C) & 7–11.5 & 7–11.5 & 7–11.5 \\ \hline Main purpose & mostly heating & heating & mostly cooling \\ \hline \hline \end{tabular}
\end{table}
Table 1: Constraints of the case studies.  
the system is in steady-state or when the SoC reached 50% for heating and cooling, respectively. Defrosting operation was neglected, and electric power consumption for COP calculations solely reflects the consumption of the compressor and the fan of the outdoor unit. All HP geometry/component design parameters, efficiencies and heat transfer coefficients were taken from design sheets or calculated from well-established equations and were later experimentally validated with measurements of the prototype air source HP used in the H2020 project HYBUILD [16] without RPW-HEX. Measured COPs of the HP without RPW-HEX for heating were 3.0, 4.3, 5.3 and 7.1 for ambient temperatures of -7, 2, 7, and 12 \({}^{\circ}\)C, inlet water temperatures to the heating system of 43, 37, 33, and 28 \({}^{\circ}\)C, and part load ratios of 88%, 54%, 35% and 15%, respectively. More information about the HP performance can be found in [15].