## 3 Fundamentals of Electricity Production from Wind  
For thousands of years, wind has been an important resource from which humans have harnessed the necessary energy to perform various activities such as sailing, grain milling, water pumping, and electricity generation [10]. The energy that can be harnessed from wind is proportional to its speed, which is not affected by terrain conditions at high altitudes. However, in the lower layers of Earth's atmosphere, wind varies as a function of surface friction or ground surface roughness (affected by vegetation cover and buildings, among other factors). In short, wind speed is proportional to the height above ground. As anemometer towers cannot always be erected at the height at which wind turbines operate, wind speed is extrapolated using functions such as Equation (1), known as the Hellman function or power-law profile and Equation (2), called logarithmic wind profile [11; 12]. \[\frac{v}{v_{1}}=\left(\frac{z}{z_{1}}\right)^{\alpha}, \tag{1}\]  
\[v=\frac{v_{*}}{k}\ln\frac{z}{z_{0}}, \tag{2}\]  
where:  
\(v\) = wind speed at height \(z\);  
\(v_{1}\) = wind speed at height \(z_{1}\); and  
\(v_{*}\) = friction velocity;  
\(k\) = the von Karmann constant;  
\(z_{0}\) = roughness length; and  
\(\alpha\) = friction or Hellman coefficient. As the amount of available wind energy varies as a function of wind speed, which changes constantly, statistical models and probability distributions, such as Gaussian, Rayleigh, and Weibull distributions, are used to quantify the performance of this variable at a specific location over time. The Gaussian or normal distribution is the probability density function that best describes wind variations. This model is represented according to Equation (3), whereas the probability of a specific wind speed at a given interval is provided by Equation (4). In the wind industry, Rayleigh and Weibull are the most commonly used probability distributions [13]. The equations of these models and their respective cumulative distribution functions (probability of a wind speed lower than or equal to a specific value) are presented in Equations (5)-(8) [14; 15]. \[p(v)=\frac{1}{\sigma_{v}\sqrt{2\pi}}exp\left[-\frac{\left(v-\overline{v} \right)^{2}}{2\sigma_{v}^{2}}\right], \tag{3}\]\[p\ (v_{a}\leq v\leq v_{b})=\int_{v_{a}}^{v_{b}}p(v)dv, \tag{4}\]  
\[p(v)_{1}=\frac{\pi}{2}\bigg{(}\frac{v}{v^{2}}\bigg{)}\textit{exp}\bigg{[}-\frac{ \pi}{4}\bigg{(}\frac{v}{\bar{v}}\bigg{)}^{2}\bigg{]}, \tag{5}\]  
\[F(v)_{1}=1-\textit{exp}\bigg{[}-\frac{\pi}{4}\bigg{(}\frac{v}{\bar{v}}\bigg{)} ^{2}\bigg{]}, \tag{6}\]  
\[p(v)_{2}=(\frac{k}{c})(\frac{v}{c})^{k-1}\textit{exp}\bigg{[}-(\frac{v}{c})^{ k}\bigg{]}, \tag{7}\]  
\[F(v)_{2}=1-\textit{exp}\bigg{[}-(\frac{v}{c})^{k}\bigg{]}, \tag{8}\]  
where:  
\(v\) = wind speed;  
\(\overline{v}\) = mean wind speed;  
\(p(v)\) = probability density function of wind speed;  
\(\sigma_{v}\) = standard deviation of wind speed;  
\(p(v)_{1}\) = Rayleigh distribution;  
\(F(v)_{1}\) = cumulative distribution function;  
\(p(v)_{2}\) = Weibull distribution;  
\(F(v)_{2}\) = cumulative distribution function;  
k = shape factor; and  
\(c\) = scale factor. The wind power per unit area or wind power density may be determined using Equation (9), whereas the hourly mean is calculated according to Equations (10) and (11). In practice, for increased reliability in predicting the production of wind power using wind turbines, the mean speed determined in our study was not used; instead, the value calculated by applying a correction factor was used. This correction factor is a percentage of the differences between the mean wind speed of our study and those provided by databases with wind speed records from several years [14; 15; 16]. In this research study, databases such as Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2) and Climate Forecast System Reanalysis (CFSR2) were used for comparison purposes.