*2.3. WT Model*

The Weibull PDF has been regularly used to model wind speed and can be expressed as

$$PDF\_w(\upsilon) = \left(\frac{d}{\overline{\mathcal{C}}}\right) \left(\frac{\upsilon}{\overline{\mathcal{C}}}\right)^{d-1} \exp\left[-\left(\frac{\upsilon}{\overline{\mathcal{C}}}\right)^d\right] \tag{6}$$

The hourly output of a WT unit is highly dependent on wind speed. The mathematical expression for converting the hourly wind speed to power is as follows:

$$P\_w(t) = \begin{cases} 0 & \text{if } v\_t < v\_{ci} \\ P\_r \times \frac{(v\_l - v\_{ci})}{(v\_r - v\_{ci})} & \text{if } \ v\_{ci} \le v\_l < v\_r \\\ P\_r & \text{if } \ v\_r \le v\_l < v\_{co} \\\ 0 & \text{if } v\_{co} \le v\_t \end{cases} \tag{7}$$
