## 3 Materials and Methods  
The analysis focused on a single-family building located in a climate zone with a temperate climate in Eastern Europe. Characteristic of this zone are cold winters and warm summers, which directly affect the energy demand for heating and cooling. The building is designed for four occupants, equipped with a domestic hot water system (DWS) featuring a storage tank with a capacity of 150 L. Water in the tank is heated from 10 \({}^{\circ}\)C to 60 \({}^{\circ}\)C. The total hourly heat demand for DWS purposes, considering water heating in the tank over 8 nighttime hours, is 1.1 kW. Additionally, the central heating system (CHS) is designed to operate in external temperatures down to \(-\)20 \({}^{\circ}\)C, with an hourly heat demand of 8 kW. The total heat demand of the building is 10.2 kW. The mechanical ventilation system (MVS) in the analyzed building, equipped with a rotary heat exchanger with a capacity of 300 m\({}^{3}\)/h, is crucial for maintaining high indoor air quality and energy efficiency. The heat recovery efficiency in the analyzed system is 73%, which corresponds to an energy demand for heating ventilation air at the level of 1.1 kW. Energy requirements for cooling during the summer period were not analyzed. Figure 1 illustrates the schematic of the analyzed baseline system. It is assumed that the air source heat pump (AHP) will operate with an electric heater in a monoenergetic system to ensure continuous heat supply for the building. The electric heater activates when the coefficient of performance (COP) for heating drops below 2.8. This value was selected as the minimum due to the economic efficiency of the AHP operation, given current electricity prices. To perform the calculations, it was necessary to determine the parameters of the air source heat pump (AHP). For this purpose, data from the existing market model HPA-O 10 Premium by Stiebel Eltron was used. Table 1 shows the technical data of the heat pump. The Coefficient of Performance (_COP_) at the working point A2/W35 is 3.26, whereas at A7/W35 it is 4.14. Based on this information, interpolation of the _COP_ values depending on the external temperature was conducted using a linear equation:  
\[COP=A\cdot T_{Z}+B \tag{1}\]  
where:  
\(A\)--constant of the equation, \(A=0.176\),  
\(B\)--constant of the equation, \(B=2.908\),  
\(T_{z}\)--value of the external temperature, \({}^{\circ}\)C.  
The bivalent temperature, at which the additional electric heater in the heat pump is activated, is \(-0.6\)\({}^{\circ}\)C. Below this temperature, the _COP_ value drops below 2.8. In such a situation, the AHP begins to operate in a parallel system with the electric heater until a _COP_ of 2.0 is reached, below which operation is limited only to the electric heater. \begin{table}
\begin{tabular}{c c} \hline Energy efficiency class of the heat pump W35 & A+++ \\ \hline Heating power at A7/W35 (EN 14511 [30]) & 7.84 kW \\ \hline Heating power at A2/W35 (EN 14511 [30]) & 8.33 kW \\ \hline Heating power at A-7/W35 (EN 14511 [30]) & 9.54 kW \\ \hline Coefficient of Performance at A7/W35 (EN 14511 [30]) & 5.09 \\ \hline Coefficient of Performance at A2/W35 (EN 14511 [30]) & 4.14 \\ \hline Coefficient of Performance at A-7/W35 (EN 14511 [30]) & 3.26 \\ \hline SCOP 35 \({}^{\circ}\)C (EN 14825 [31]) & 4.70 \\ \hline Sound power level (EN 12102 [32]) & 55 dB (A) \\ \hline Limit of use of lower source min./max. & \(-20/40\)\({}^{\circ}\)C \\ \hline Limit of use on the heating side max. & 65 \({}^{\circ}\)C \\ \hline Refrigerant & R410A \\ \hline \end{tabular}
\end{table} 
Table 1: Technical data of the heat pump. Figure 1: Diagram of the cooperative system involving an air source heat pump (AHP) with an electric heater in a monoenergetic system. The components are labeled as follows: 1—building installations; 2—air source heat pump (AHP); 3—electrical grid; 4—electric heater (EH); 5—electric power for the heat pump (NAPH); 6—electric power for the electric heater (EHM).