## 2 Case Studies and Operation Modes of the System  
### Operation Modes of the HP with Integrated RPW-HEX  
The proposed system distinguishes between six operating modes (a-f), whilst a conventional system distinguishes mainly between three operating modes, namely heating, cooling and DHW generation, which have similar efficiencies to operating modes (d), (e), and (f) in the proposed system:  
1. heating operation and charging the RPW-HEX (\(0<\) SoC\(\uparrow\)\(\leq\) 1)
2. cooling operation and charging the RPW-HEX (\(0<\) SoC\(\uparrow\)\(\leq\) 1)
3. energy efficient DHW generation by discharging the RPW-HEX and pre-heating via the condenser (\(0\leq\) SoC\(\downarrow\)\(\leq\) 1)
4. conventional (inefficient) direct DHW generation (SoC = 0)
5. heating operation when the RPW-HEX is fully charged (SoC = 1)
6. cooling operation when the RPW-HEX is fully charged (SoC = 1)  
where SoC refers to the state of charge of the RPW-HEX [17]. Figure 1a-d show the operation modes (a)-(d) in a simplified system sketch with three apartments connected to the HP system as an example. The conventional operation modes (e) and (f) are omitted in the sketch for the sake of brevity. The HP is connected to the apartments with two hydraulic lines and the switching between charging the decentralized DHW storage, and heating/cooling takes place in the apartments. During heating mode (a), most of the sensible energy in the superheated hot gas charges the RPW-HEX (R). The amount of transferred heat depends on the hot gas temperature, the refrigerant mass flow, the phase transition temperature of the (solid/liquid) PCM, and the overall heat transfer coefficients of the RPW-HEX. Hot gas temperature and refrigerant mass flow result from the operating point, whereas the switching temperature range of the PCM and the heat transfer capabilities of the RPW-HEX are design-inherent (design parameters). For the proposed concept, R32 as a refrigerant was used and a PCM with a phase transition around 64 \({}^{\circ}\)C was selected in all three cases. Please note that it would also be possible to use PCMs with a lower phase transition temperature (e.g., 55 \({}^{\circ}\)C), because of the approach with decentralized DHW storage devices, which do not have a problem with legionella. R32 has a rather high hot gas temperature when compared to other refrigerants. To limit the compressor discharge temperature at low temperatures, liquid refrigerant from the condenser exit is injected into the compressor (which can handle a small amount of liquid refrigerant) entrance by means of a liquid injection valve (B). In doing so, the hot gas temperature can be limited to \(\approx\)115 \({}^{\circ}\)C. Furthermore, an additional HEX (F) is introduced to ensure that the refrigerant is in the liquid phase at the expansion valve (X) entry. Via the condenser (C), the heat is delivered to the apartments by the fan coils (H). Due to the missing contribution of the sensible energy from the hot gas for heating, the condensing pressure is slightly higher in operating mode (a) than in the conventional heating mode (e) for the same water inlet temperature to the heating system. Therefore, the heating COP is slightly smaller in the proposed system compared to a system without RPW-HEX. The inverse behavior is expected for cooling, where the dissipation of energy in the RPW-HEX increases the performance of the evaporator acting as a condenser in operating mode (b). Both contributions lead to a difference in electric energy consumption of typically \(\pm\)1-3% (see also relative numbers of calculated energy savings for heating and cooling per year in Table 3 for three different cases). In cooling mode (b), the four-way valve (W) switches to reverse mode and the evaporator (E) acts as a heat sink, whereas the condenser (C) cools the building via the heating and cooling network (H). Because the four-way valve (W) is located after the RPW-HEX, the PCM is also charged by the hot gas during the cooling operation.