## 3 Results and Discussion
### Current Performance of Building  
The different characteristics of office buildings in the four selected cities are detailed in Table 3, and in the case of natural conditions, Equations (1)-(3) give the optimal comfort temperature, and the upper and lower acceptability limit.  
* Optimal comfort temperature (\({}^{\circ}\)C) [30; 31]: \[T_{ac}=0.31f(T_{o})+17.8\;10^{\circ}C\leq f(T_{O})\leq 33.5^{\circ}C.\] (1)
* Upper 90% acceptability limit is \[T_{ac}=0.31f(T_{o})+20.3\;10^{\circ}C\leq f(T_{O})\leq 33.5^{\circ}C\,.\] (2)
* Lower 90% acceptability limit is \[T_{ac}=0.31f(T_{o})+15.3\;10^{\circ}C\leq f(T_{O})\leq 33.5^{\circ}C,\] (3) where _f(To)_ is the prevailing mean outdoor air temperature in ASHRAE 55 for 2013 and 2017.  
In Table 3, it can be observed that, in natural ventilation, the operative temperature is between 22 \({}^{\circ}\)C and 28 \({}^{\circ}\)C and the relative humidity is between 57% and 76% in the four cities. This comfort range is recommended by ASHRAE55, which fixed the operative temperature between 23 \({}^{\circ}\)C and 26 \({}^{\circ}\)C and relative humidity between 30% and 60% [32]. Despite this, more than 80% of workers find their workplace comfortable. These results are very interesting. They show that over the comfort range requested, by several international standards, the occupants found their environment comfortable. In general, among the four cities studied, indoor air is less comfortable and more polluting in Mahajunga and more comfortable in Toamasina. It was concluded that the climate is harsher in the city of Mahajunga, which is located in the zone of hot tropical climate.  
Some detailed results of indoor air are shown in Table 4. The thermal comfort was analyzed during the hours of occupation from 8 am to 5 pm.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Cities** & **Antsiranana** & **Mahajunga** & **Toamasina** & **Taolagnaro** \\ \hline Operative temperature (\({}^{\circ}\)C) & 25–27 & 25–28 & 23–26 & 22–27 \\ Relative humidity (\%) & 57–72 & 57–74 & 72–76 & 64–71 \\ Discomfort rate (\%) & 17.8 & 19.4 & 34.5 & 25.9 \\ Cooling energy (kwh/m\({}^{2}\)) & 77.5 & 81.9 & 50.6 & 48.7 \\ Energy consumption (kwh/m\({}^{2}\)) & 173 & 186.7 & 130.4 & 127.1 \\ Operational carbon (kg\({}_{\text{CO2}}\)/m\({}^{2}\)) & 61.9 & 73.5 & 50.5 & 54.5 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Some characteristics of indoor building performance.  
In this table, we can see that the passive strategy allows the improvement in indoor air (relative humidity and air temperature) between 10% and 25%, according to the cities and seasons. These results support the conclusions of several researchers who demonstrated that the application of passive strategy techniques can have a significant effect on the indoor climate [33; 34]. Between 2017 and 2050, it is predicted that the indoor temperature will increase up to 1 \({}^{\circ}\)C, while the relative humidity will tend to decrease up to 5%. This is in agreement with the IPCC [35], which predicts that by 2050, if nothing is done to prevent the evolution of the weather, the weather temperature will increase to between 1.5 \({}^{\circ}\)C and 3.5 \({}^{\circ}\)C, depending on the regions and projection scenarios. Furthermore, the impact of this climate change will be visible with the high demand for energy in buildings [36]. In this sense, in the next subsection, we study the effects of PCM materials on the cooling energy consumption.