## 2 Material and Methods  
### The Investigated Buildings  
#### 2.1.1 Detailed Description of the Buildings and Climatic Conditions  
The present energy analysis examines two residential buildings that were designed and simulated in the DesignBuilder v7 software [23]. The building energy analysis was executed with a 5 min timestep, or 12 timestep per hour, which was selected after a sensitivity analysis. Both buildings are characterized by the same gross area of 1000 m\({}^{2}\) and a total volume of 3000 m\({}^{3}\). The first building, referred to as B1, is a five-story multifamily building, with a ground and roof slab area equal to 200 m\({}^{2}\). The second building, referred to as B2, is a two-story multifamily building, with a five-times-greater ground and a roof slab area of 1000 m\({}^{2}\). For both buildings, the floor height was considered equal to 3 m, whereas the window-to-wall ratio was selected at 20%. The total building external surface, including the external walls, roof and ground slab, was calculated at 1249 m\({}^{2}\) and 1537 m\({}^{2}\) for buildings B1 and B2, respectively, whereas the ratio of total building external surface to volume was calculated at 41.6% for B1 and 51.2% for B2. Table 1 gives the basic geometrical dimensions of the examined buildings. Additionally, Figures 1 and 2 depict an axonometric and plan view, as well as each of the four sides of the examined buildings, B1 and B2, that correspond to the four horizon points. The orientation of the examined buildings was considered the same for each of the four investigated locations. Figure 1: Depiction of examined building B1: (**a**) south-east axonometric view, (**b**) plan view, (**c**) east side, (**d**) west side, (**e**) south side and (**f**) north side. Regarding the operational data of the examined buildings that are summarized in Table 2, each building was occupied by 30 occupants, with a specific thermal load of 80 W per occupant and an average operating factor of 75%. Additionally, the specific load of appliances and lighting was considered equal to 2 and 4 W/m2, with an average operating factor of 75%. The transient schedule profiles of the occupants, appliances and lighting were inserted as a daily distribution load profile which was properly adapted to a typical residential operational schedule [24]. The infiltration rate was considered equal to 0.4 air changes per hour (ACH), whereas the ventilation rate was 0.8 ACH. The buildings were \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Building B1** & **Building B2** \\ \hline Gross floor area per floor [m2] & 200 & 500 \\ Roof and ground slab area [m2] & 200 & 500 \\ Total building external surface [m2] & 1249 & 1537 \\ Gross exterior wall area [m2] & 849 & 537 \\ Net wall area [m2] & 679 & 429 \\ Total windows area [m2] & 170 & 107 \\ Window-to-wall ratio & 0.2 & 0.2 \\ Number of floors & 5 & 2 \\ Floor height [m] & 3 & 3 \\ Gross building volume [m3] & 3000 & 3000 \\ Ratio of total external surface to volume [m2/m3] & 0.416 & 0.512 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Basic geometrical dimensions of the examined buildings. Figure 2: Depiction of examined building B2: (**a**) south–east axonometric view, (**b**) plan view, (**c**) east side, (**d**) west side, (**e**) south side and (**f**) north side. equipped with highly efficient reversible water-to-air heat pump units that satisfied the building's heating and cooling needs through fan coils, as well as the DHW demand. The temperature setpoint was set to 20 \({}^{\circ}\)C for the winter period and 26 \({}^{\circ}\)C for the summer period. Additionally, the DHW temperature setpoint was set to 45 \({}^{\circ}\)C, whereas the daily demand was considered equal to 50 L per person. The buildings were examined for the climatic data of Athens, Barcelona, Munich and Stockholm. Table 3 summarizes the basic climatic parameters of each studied location, namely the average annual air and water temperature, the total horizontal irradiation, and the heating and cooling degree days.