## 2 Methodology  
### Thermal Comfort Model: Adaptive Setpoint Temperatures and Tolerances  
The European adaptive thermal comfort model currently in force is EN 16798-1:2019 [47]. This standard led to the update of EN 15251:2007 [46]. EN 16798-1:2019 establishes three different categories in which the internal operative temperature should oscillate according to the type of building and to occupants' expectations (e.g., category I should be used in spaces for people with special requirements, such as old people or ills, category II should be used in new buildings, and category III in existing buildings).  
Such categories indicate the values in which the internal operative temperature should oscillate through upper and lower limits. Equations (1) and (2) indicate the limit values of category II (i.e.,new buildings) [47], which is the aim of this research. Such limits are established through linear correlations whose independent variable is an external average temperature known as the running mean outdoor temperature (\(T_{m}\)). \(T_{m}\) is obtained by the weighted sum of daily mean external temperatures from the previous days (see Equation (3)) [47]. It is important to note that \(T_{m}\) will be useful not only to obtain the limits of the internal operative temperature, but to determine whether the adaptive comfort model from EN 16798-1:2019 could be applied. In this sense, EN 16798-1:2019 establishes that the adaptive comfort model could be applied if \(T_{m}\) is between 10 and 30 \({}^{\circ}\)C.  
\[\text{\emph{Upper limit} }(\text{\emph{Category II}})=0.33\text{-}T_{m}+21.8\ \left[{}^{\circ}\text{C}\right]\ \left(10\leq T_{m}\leq 30\right) \tag{1}\] \[\text{\emph{Lower limit} }(\text{\emph{Category II}})=0.33\text{-}T_{m}+14.8\ \left[{}^{\circ}\text{C}\right]\ \left(10\leq T_{m}\leq 30\right)\] (2) \[T_{m}= \left(T_{ext,day-1}+0.8T_{ext,day-2}+0.6T_{ext,day-3}+0.5T_{ext,day -4}+0.4T_{ext,day-5}+0.3T_{ext,day-6}\right.\] (3) \[\left.+0.2T_{ext,day-7}\right)/3.8\ \left[{}^{\circ}\text{C}\right]\]  
As discussed above, many research studies have analyzed the use of the upper and lower limits of the adaptive model as the setpoint temperatures of HVAC systems. The use of the limit values of the adaptive model could lead to significantly save the energy consumption. However, its use implies a higher level of users' adaptability, so it is necessary to analyze the effect of better users' thermal expectations with respect to the limit values of the adaptive thermal comfort model.  
For this purpose, the limit values related to category II were used. Heating and cooling limits were reduced in intervals of 0.25 \({}^{\circ}\)C, narrowing the comfort zone to a total of 0.5 \({}^{\circ}\)C in each interval. Figure 1 graphically represents the limits of the thermal comfort models used in this study. The numeric value indicates the designation of the adaptive thermal comfort model which coincides with the reduction in degrees with respect to the limit values of category II. Concerning the values assigned to setpoint temperatures when the adaptive thermal comfort model is not applied, the criterion used in other similar research studies was used [42; 48]: to horizontally extend the comfort limits. Furthermore, a static model was used as a reference model. The static model was designed by using the static setpoint temperatures set in the standard of adaptive comfort for HVAC systems: between 20 and 25 \({}^{\circ}\)C for heating periods, and between 23 and 26 \({}^{\circ}\)C for cooling periods. Table 1 summarizes the correlations and limit values used in each model.  
Figure 1: Limit values of the adaptive thermal comfort model for new buildings from EN 16798-1:2019 and the analyzed tolerances. Dashed lines show the tolerances considered.