## 2 Materials and Methods
### Data and Procedures  
The data to analyse the local wind profile and building energy consumption were collected throughout the whole year of 2019. Wind data were collected over a 10 min sampling period at a height of 30 m. Regarding the energy consumed, to build the load profile, the data were collected with a sampling period of 60 min.  
Through the annual recording of the wind direction and speed, the graph in Figure 1, known as the wind rose, was obtained. One can observe the relative frequency of the wind speed range for the different wind directions that it can take. It can be highlighted that, in this case, the predominant wind directions are between 300 and 360 degrees, with the most predominant being 330 degrees, that is, from north-west to south-east.  
Table 1 summarizes the statistical measurements of the wind speed (\(u\)), such as mean (\(\overline{u}\)), median (Med), maximum, minimum, and sample standard deviation (s) for the record height (30 m) and extrapolated heights, 72 and 77 m. The speed extrapolation is performed by the application of the logarithmic law presented in (1) for each record collected. Comparing the average speed at 72 and 77 m with the reference speed at 30 m, an increase of 25-27% is observed, which corresponds to 1.05 m/s.  
\[\overline{u}(z)=\frac{u_{a}}{k}ln\frac{z}{z_{0}} \tag{1}\]  
Figure 1: Wind rose for the case study adopted.  
where \(\overline{u}(z)\) is the average value of the wind speed at height \(z\), \(u_{a}\) is the so-called friction speed, \(k\) represents the Von Karman constant whose value is equal to 0.4, and finally, \(z_{0}\) defines the characteristic length of the roughness of the soil.  
The wind speed directly influences the output power of wind turbines, which also depends on their technical specifications. This work considers two types of wind turbines, the Aeolos-V 10 kW and the Aeolos-H 20 kW [21]. To estimate the average annual load profile with the extrapolated calculations from the collected wind data, the power curves [21] from the wind turbines are needed. Figure 2 shows the power curve graph built from the information given by the wind turbine manufacturer. Extrapolated values have been rounded round off by default. Subsequently, a direct association was made between the extrapolated wind speed values and the turbine power curves. The power curve records the turbine power with an accuracy of 1 m/s.  
The power available in the wind depends on the kinetic energy associated with an air column moving at speed \(u\) (m/s) and can be calculated using Equation (2).  
\[P_{wind}=\frac{1}{2}(\rho Au)u^{2}=\frac{1}{2}\rho Au^{3} \tag{2}\]  
where \(P_{wind}\) is the power available in the wind (in W), \(A\) is the rotor blade sweep area (m\({}^{2}\)), \(u\) is the wind speed (m/s), and \(\rho\) is the air density, usually considered constant during the year, the standard value being equal to 1.225 kg/m\({}^{3}\). Equation (2) shows that the available power greatly dependents on wind speed. Wind power cannot be fully converted into mechanical power in the turbine because, by Betz's law, it is at most 59.3% [22] of the kinetic energy that it converted into mechanical energy to be used in the turbine.  
Knowing the wind profile and the turbine power curve, it is possible to determine the energy produced during a period for a single wind direction using Equation (3).  
\[PW=T\int_{u_{0}}^{u_{\infty}}P_{e}(u)f_{w}(u)du \tag{3}\]  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Height (m)** & \(\overline{u}\) & **Maximum** & **Minimum** & **Med** & \(s\) \\ \hline
30 & 4.08 & 19.90 & 0.00 & 3.59 & 2.61 \\
72 & 5.13 & 25.02 & 0.00 & 4.52 & 3.28 \\
77 & 5.21 & 25.42 & 0.00 & 4.59 & 3.34 \\ \hline \end{tabular}
\end{table}
Table 1: Statistical measures of wind speed at different heights.  
Figure 2: Turbine power curves.  
where \(E\) is the annual energy produced (kWh), \(T\) is the number of hours during the considered period, \(f_{w}\) is the Weibull probability density function, and \(P_{e}(u)\) is WT power (kW) for \(u\) wind speed [23].