## 2 Materials and Methods  
Energy and comfort analyses were performed using EnergyPlus v.9.3. The main advantage of EnergyPlus [58] is that it can guarantee multidomain integration and physical interaction accounting for thermal, visual, mass-flow, and building service interactions [3; 59]. A good starting point for energy-efficiency-oriented research in EnergyPlus [60] is offered by the U.S. Department of Energy (DOE), which developed 16 reference building models in different climatic zones. These models have been calibrated using several references such as the Commercial Buildings Energy Consumption Survey (CBECS), ASHRAE Standards 90.1, and many other academic sources [61]. Offices and apartments represent two of the most diffused building types in Europe, and they respectively account for 6% and 75% of total European building stock [62]. Therefore, two representative reference models, the small office and the midrise apartment, were chosen for this study. The geometrical data and main characteristics of the two reference buildings are summarized in the table and pictures below (Table 1, Figure 1). The HVAC equipment of the reference buildings is modeled in accordance with ASHRAE Standard 90.1 and consider, for both the small office and the midrise apartment, a boiler for heating generation, a packaged air conditioning unit for cooling generation, and a single-zone constant-volume system for air distribution. Particular attention was paid to the reliability of consumption and, considering that the analyses were run for different building types and different locations, to the independence of the results from the HVAC system sizing process. Therefore, the original HVAC systems were substituted with properly calibrated ideal-load air systems. These systems are similar to a traditional HVAC unit in EnergyPlus; the main difference is that it is not connected to a \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Building Types** & **Number of Floors** & **Gross Floor** & **Floor-to-Ceiling** & **Window-to-Mo** & **Number of Thermal** \\  & **Floors** & **Area** & **Height** & **Wall Ratio** & **Zones** \\  & **[–]** & **[m2]** & **[m]** & **[\%]** & **[–]** \\ \hline Midrise & 4 & 3134.59 & 3 & 20\% & 32 \\ apartment & 1 & 511.16 & 3 & 22\% & 6 \\ Small office & 1 & 511.16 & 3 & 22\% & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main characteristics of reference buildings from the DOE. Figure 1: Reference buildings chosen from the DOE: small office (**a**) and mid-rise apartment (**b**). central system, and each ideal-load air system provides heating or cooling to satisfy the zone setpoint [63]. Starting from the ideal heating and cooling loads, the energy consumption is calculated by dividing the loads by an ideal energy efficiency ratio (EER) equal to 3 in cooling mode and by a coefficient of performance (CoP) equal to 3 in heating mode, which can be considered average values for packaged direct expansion air conditioning systems. Existing HVAC systems are characterized by a series of controls, such as the management of outdoor air and a night-cycle availability manager. Therefore, to guarantee the proper behavior of the ideal-load system, an energy management system (EMS) program was written in order to account for these controllers and obtain results close to the ones of the original DOE reference building. To confirm the reliability of the calibrated ideal-load model, a statistical analysis was performed and values of mean bias error (MBE) and cumulative variation of root mean squared error (CVRMSE) were obtained from hourly values of heating and cooling energy consumption of the reference and modified models. The analysis was performed for each thermal zone, starting from three different reference models, one for each of the chosen locations (Miami--ASHRAE Zone 1A, Chicago--ASHRAE Zone 5A, Fairbanks--ASHRAE Zone 8), for both small office and midrise apartment.