# Integration of the Adaptive Approach in HVAC System Operation: A Case Study
## 2 Materials and Methods  
### Case Study  
The study was carried out in a building located in Seville (37 \({}^{\circ}\)N, 5 \({}^{\circ}\)W), in the southern region of Spain. The climate is classified as Csa (hot summer Mediterranean climate) according to the Koppen-Geiger classification [31], and as B4 according to the Spanish Building Technical Code [32]. The main characteristics of the climate in Seville are hot and dry summers, and mild, humid and temporary rainy winters. It is also characterized by one of the highest average annual temperatures in Europe, frequently exceeding 40 \({}^{\circ}\)C. During the sample period, spanning from July 2023 to June 2024, these temperatures, as shown in (Table 1), exceeded this threshold. This field study was carried out in an office room of a tertiary, non-residential building. Following the proposal of [PERSON] and [PERSON] [33], among the conditions for the adaptive approach, _\"It is essential that building occupants are free to adapt themselves, primarily through clothing adjustment, to the variable indoor climate regime prevailing inside such buildings\"_ (p. 267), so the present study allows users to make adaptive adjustments, although it focuses on the analysis of the inclusion of an adaptive algorithm into the building management system. The adaptive comfort algorithm applied in this area of the building was presented by [PERSON] et al. [34], in which a single adaptive model was proposed for both the NV and HVAC operation modes. The algorithm was based on an analysis of more than five thousand surveys, leading to the following equation (Equation (1)). \[T_{c}=0.2427\times T_{rm}+19.284 \tag{1}\]  
where T\({}_{c}\) is the indoor comfort temperature and T\({}_{\rm{rm{m}}}\) is the outdoor running mean temperature. Figure 1 shows the adaptive range corresponding to the behavior of this algorithm over a full year. Regarding Figure 1, in [34] a comparative analysis of the adaptive control algorithm considered for the development of the present case study was carried out with respect to other models, showing that the neutral temperatures obtained were lower than those proposed using the ASHRAE-55:2023 and UNE-EN 16798-1:2020 models for NV buildings. Moreover, according to [9] (pp. 6-7), where a summary of different adaptive regression models and their coefficients was carried out, most of the linear adaptive linear regression models are within the limits recommended in ASHRAE 55. As for the implementation of the adaptive control algorithm, in [35] a methodology is presented for implementing an adaptive control algorithm in a Building Management System (BMS). In the present study, the BMS was adapted to allow users to switch between natural ventilation and heating, ventilation, and air conditioning modes. During the study \begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline  & **July** & **August** & **September** & **October** & **November** & **December** & **January** & **February** & **March** & **April** & **May** & **June** \\  & **2023** & **2023** & **2023** & **2023** & **2023** & **2024** & **2024** & **2024** & **2024** & **2024** & **2024** & **2024** \\ \hline \(T_{\text{ent min}}\) (\({}^{\circ}\)C ) & 18.9 & 18.9 & 13.4 & 11.1 & 3.9 & 1.6 & 2.2 & 4.4 & 5.0 & 7.2 & 7.5 & 14.4 \\ \(T_{\text{ent max}}\) (\({}^{\circ}\)C ) & 41.1 & 42.8 & 36.1 & 36.7 & 26.6 & 20.0 & 22.8 & 22.8 & 27.2 & 31.1 & 37.8 & 37.8 \\ \(T_{\text{ent arg}}\) (\({}^{\circ}\)C ) & 31.7 & 32.6 & 25.7 & 23.3 & 16.8 & 12.0 & 13.3 & 14.7 & 16.0 & 20.2 & 23.9 & 26.1 \\ \(RH_{\text{arg}}\) (\%) & 35 & 30 & 53 & 59 & 70 & 79 & 81 & 73 & 68 & 53 & 39 & 47 \\ \hline \hline \end{tabular}  
**Note:**\(T_{\text{ent min}}\) (\({}^{\circ}\)C ), \(T_{\text{ent max}}\) (\({}^{\circ}\)C ) and \(T_{\text{ent arg}}\) (\({}^{\circ}\)C ) represent the minimum, maximum, and average outdoor temperatures, respectively. \(RH_{\text{arg}}\) denotes the average relative humidity.  
\end{table} 
Table 1: Monthly variation in outdoor temperature (T out) and average relative humidity (RH).