## 2 Materials and Methods
### Case Study
#### 2.2.3. Systems with a Gas-Fired Boiler, CHP Unit, and HP  
The implementation of a water-to-water HP has been identified as a potential enhancement to the aforementioned systems. The present study considers an HP that uses water from a nearby river as a heat source. The river's length is 19 km, and the abstraction of river water is located 18 km downstream. The river's relatively short length results in a consistent water temperature at the abstraction point, which remains almost constant throughout the year. In this case study, a constant water temperature of 8 \({}^{\circ}\)C was adopted. Temperature fluctuations within a few degrees Celsius would not significantly affect the efficiency of the HP during the year. The configuration of the HP is such that it is connected to the return line of the heating system immediately before the CHP unit, as illustrated in Figure 7. This configuration ensures a lower temperature of the inlet water to the HP compared to a configuration in which the HP is placed in the supply line after the CHP unit. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**CHP Load** & **Electrical Output** & **Heating Output** & **Fuel Use** \\ \% & **kW** & **kW** & **kW** \\ \hline
100 & 140 & 209 & 384 \\ \hline
75 & 105 & 171 & 310 \\ \hline
50 & 70 & 130 & 227 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The technical specifications of the CHP unit with a gas engine. Figure 6: The annual duration of the required heating capacity and energy that can be covered by the operation of the CHP unit. The selection of HP is based on the required water temperature in the distribution network and the temperature of the heat source. When choosing an HP, the requirements of the current European legislation on the use of fluorinated greenhouse gases were taken into account, which will prohibit the installation of devices that work with a refrigerant that has a GWP of 150 or higher from the beginning of 2030 [25]. For this reason, the choice of HP is limited to devices that are available on the market and use natural refrigerants. Depending on the required heating capacity and temperature regime, units which are considered use R717 refrigerant. A range of HP units was selected using professional software GEA RTSelect [26]. All the HP units are selected under operating conditions of water at the condenser 70/60 \({}^{\circ}\)C and a heat source temperature of 8 \({}^{\circ}\)C. The smallest of the considered HPs has a heating capacity of 400 kW and requires 141.5 kW of electrical power. The criterion for selection of this unit was to match the required electrical power to the CHP electrical power at full load. The annual duration curve for this case is presented in Figure 8. It is visible that CHP with HP can cover the heating energy requirement for 7000 h in the year. Larger units are selected in increments of 100 kW heating capacity up to 1000 kW. Performance data and efficiency metrics for the HPs under variable temperature conditions and partial load operations, which are acquired using professional software, were used to simulate the operation of HPs using Trnsys Type 581 [22]. \begin{table}
\begin{tabular}{c} 400 kW–1000 kW \\ (100 kW increment) \\ \end{tabular} & From grid & Solid to grid \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Overview of system variants considered in the study: configuration, operational priority, and energy utilisation. Figure 7: Schematic of a DH system with a gas-fired boiler, CHP and HP units. In the HP/CHP/B system, the HP has the priority for heat production. When the HP cannot achieve the required water temperature, the CHP unit is activated, followed by the boiler as needed. The HP draws electricity from the grid, while the electricity generated by the CHP unit is sold back to the grid. In the CHP/HP/B system, the CHP unit has heat production priority. When it cannot reach the necessary water temperature, the HP is switched on, followed by the boiler if required.