## 2 Methodology
### Weibull and Rayleigh Distribution Functions
#### 2.2.1 Weibull Distribution  
The mean wind speed and standard deviation values of observed time-series wind data were calculated using Equations (1) and (2):  
\[v_{m}=\frac{1}{N}\left[\sum_{i=1}^{N}v_{i}\right] \tag{1}\]  
\[\sigma=\frac{1}{N-1}\left[\sum_{i=1}^{N}(v_{i}-v_{m})^{2}\right]^{1/2} \tag{2}\]  
where \(v\) is wind speed, \(v_{m}\) is the mean wind speed (m/s), \(\sigma\) is the standard deviation (m/s), and \(N\) is the number of hours within the time period. To evaluate the mean wind speed values accurately, it is essential to know the number of hours during a given time interval per month or year. Estimation of the wind power potential of any region is realized using previously measured data. In general, this process is performed through wind speed distribution functions. First of all, hourly wind speed values in a time-series format  
Figure 1: Location, elevation, annual average wind speed, and wind power density distribution of Canakkale [49]. are observed and then converted into the frequency distribution format for probability modelling because of the convenience [5]. Weibull distribution can be defined as the PDF, \(f_{w}(v)\), and the cumulative distribution function, \(F_{w}(v)\), as follows:  
\[f_{w}(v)=\frac{k}{c}\Big{(}\frac{v}{c}\Big{)}^{k-1}\exp\left[-\Big{(}\frac{v}{c }\Big{)}^{k}\right] \tag{3}\]  
\[F_{w}(v)=1-\exp\left[-\Big{(}\frac{v}{c}\Big{)}^{k}\right] \tag{4}\]  
where \(f_{w}(v)\) is the probability of a wind speed of \(v\) (\(m/s\)) occurring, \(v\) (\(m/s\)) is the measured wind speed, \(k\) (dimensionless) is the shape parameter, and \(c\) (\(m/s\)) is the scale parameter of the Weibull distribution. It is essential to know and interpret wind speed distributions for wind speed estimation. The data organized in the time-series format are rearranged in the frequency distribution format to make it more suitable for statistical analysis [5]. The following equation [5] describes the relationship between the Weibull scale parameter (\(c\)), the Weibull shape parameter (\(k\)), and the mean wind speed, \(v_{m}\):  
\[v_{m}=c\Gamma\left(1+\frac{1}{k}\right) \tag{5}\]  
\(\Gamma\) is the gamma function, which can be determined by the standard equation below:  
\[\Gamma(x)=\int\limits_{0}^{\infty}t^{x-1}\exp(-t)dt \tag{6}\]  
By transforming Equation (4) into a logarithmic form, Equation (7) can be defined as  
\[\ln[-\ln(1-F_{w}(v))]=k\ln v-k\ln c \tag{7}\]  
Here, if \(x=\ln v\), \(y=\ln[-\ln(1-F_{w}(v))]\), \(A=k\), and \(B=-k\ln(c)\) are assumed [50], a linear equation is obtained from the function. Then, \(y=Ax+B\) is acquired from Equation (7). Furthermore, the equation of \(c=\exp(-B/A)\) is computed from the equation of \(B=-k\ln(c)\). Then, A and B are calculated using the Least-Squares Method:  
\[A=\frac{\sum\limits_{i=1}^{N}\left(x_{i}-\overline{x}\right)\left(y_{i}- \overline{y}\right)}{\sum\limits_{i=1}^{N}\left(x_{i}-\overline{x}\right)^{2}} \text{, }B=\overline{y}-A\overline{x} \tag{8}\]  
Here, \(\overline{x}\) (average of \(x\) values) and \(\overline{y}\) (average of \(y\) values) are obtained from Equation (9):  
\[\overline{x}=\frac{1}{n}\underset{i=1}{\overset{N}{\sum}}f_{i}x_{i}\text{, } \overline{y}=\frac{1}{n}\underset{i=1}{\overset{N}{\sum}}f_{i}y_{i} \tag{9}\]  
A straight line should result when plotting \(\ln v\) against \(\ln[-\ln(1-F_{w}(v))]\). The line's slope is \(k\) and its \(y\)-axis intersection point is \(-k\ln(c)\). The captured graph as an example for 2019 is given in \[\sigma=\frac{1}{N-1}\left[\sum_{i=1}^{N}(v_{i}-v_{m})^{2}\right]^{1/2} \tag{2}\]0 Using wind speed data from CanadaRale Province, the Weibull parameters \(k\) and \(c\) in Equation (4) can be determined as 1.33 and 3.06, respectively.