Table 3 Theoretical details of wind resource assessment

Wind speed distribution model (MLE-Weibull)

• Weibull probability density function (PDF) is commonly used to model the distribution of wind speeds

• The Weibull distribution is flexible and can closely approximate the distribution of wind speeds observed in many locations

• It is characterized by shape (k) and scale (c) parameters, offers flexibility in capturing wind speed variability

• MLE optimally estimates these parameters, providing efficient, consistent, and statistically sound results (Baloch et al., 2017)

\({\text{f}}({\text{v}}) = \frac{{\text{k}}}{{\text{c}}}{\left(\frac{{\text{v}}}{{\text{c}}}\right)}^{{\text{k}}-1}{\text{exp}}[-{\left(\frac{{\text{v}}}{{\text{c}}}\right)}^{{\text{k}}}], ({\text{k}}>0,\mathrm{ c}>0)\)

where

• v is the wind speed (m/s),

• c is the scale parameter (m/s),

and

• k is the shape parameter (dimensionless)

Average wind speed (m/s)

• Average wind speed is a measure of the average speed of the wind over a specified period of time at a particular location

\(\overline{{\text{v}} }=\mathrm{ c\Gamma }\left(\frac{1}{{\text{k}}}+1\right),\)

where

• \(\overline{{\text{v}} }\) is the average wind speed,

• c is the scale parameter (m/s),

and

• k is the shape parameter (dimensionless)

Wind power density (W/m²)

• Wind power density is a measure of the amount of power available in the wind at a particular location and is a crucial parameter in assessing the potential for harnessing wind energy

• It is referred as the power per unit area carried by the wind (Baloch et al., 2017; Hulio, 2021; Jiang et al., 2017)

\(\overline{\mathrm{w } }= \frac{1}{2}{\mathrm{\rho c}}^{3}\Gamma \left(\frac{3}{{\text{k}}}+1\right),\)

where

• \(\uprho\) is air density (kg/m³),

• c is the scale parameter (m/s),

and

• k is the shape parameter (dimensionless)

Annual average energy output (kWh)

• The annual average energy output refers to the amount of electrical energy generated by a wind turbine over the course of a year

It is a key performance metric that provides an indication of the system's overall efficiency and productivity (Baloch et al., 2017; Hulio, 2021; Jiang et al., 2017)

\({{\text{E}}}_{{\text{A}}}=\mathrm{ T }\times {\int }_{0}^{\infty }{{\text{P}}}_{{\text{A}}}\left({\text{v}}\right){\text{f}}({\text{v}}){\text{dv}}\)

\({{\text{P}}}_{{\text{A}}}\left({\text{v}}\right)= \left\{\begin{array}{c}{{\text{P}}}_{{\text{r}}}, {{\text{v}}}_{{\text{r}}}\le v\le {{\text{v}}}_{{\text{out}}}\\ P\frac{{\text{v}}- {{\text{v}}}_{{\text{in}}}}{{{\text{v}}}_{{\text{r}}}- {{\text{v}}}_{{\text{in}}}}, {{\text{v}}}_{{\text{in}}}\le v\le {{\text{v}}}_{{\text{r}}} \\ \\ 0, otherwise,\end{array}\right.\)

where

• \({{\text{v}}}_{{\text{in}}}\) is the cut-in wind speed,

• \({{\text{v}}}_{{\text{r}}}\) is the rated wind speed, the cut-out wind speed,

• \({\text{T}}\) is the time period of the wind turbine

operates,

• \({{\text{P}}}_{{\text{r}}}\) is the rated power, and

• f(v) is the optimal Weibull PDF

Capacity factor (%)

• The capacity factor (CF) serves as a crucial metric for assessing the performance of a wind turbine, valuable for both end-users and manufacturers

• It represents the ration of the real average power produced during a specific timeframe (assuming continuous turbine operation) and the rated peak power, which is the maximum theoretical power (Baloch et al., 2017; Hulio, 2021; Jiang et al., 2017)

\({\text{CF}}=\frac{{{\text{E}}}_{{\text{A}}}}{{{\text{E}}}_{{\text{R}}}}\)

\({{\text{E}}}_{{\text{R}}}=\mathrm{T }\times {{\text{P}}}_{{\text{R}}},\)

where

• CF is the capacity factor (Jiang et al., 2017)

Logarithmic wind profile law

• Average wind speed deviation with height is a concept that describes how wind speed changes as you move vertically above the Earth's surface

This phenomenon is often explained by wind shear, which is the variation in wind speed and direction with altitude (Hulio, 2021)

\({{\text{v}}}_{2}={{\text{v}}}_{1}\frac{{\text{ln}}(\frac{{{\text{h}}}_{2}}{{{\text{z}}}_{0}})}{{\text{ln}}(\frac{{{\text{h}}}_{1}}{{{\text{z}}}_{0}})},\)

where

• \({{\text{v}}}_{1}\) is the wind speed at height \({{\text{h}}}_{1}\),

• \({{\text{v}}}_{2}\) is the wind speed at height \({{\text{h}}}_{2}\), and

• \({{\text{z}}}_{0}\) is the roughness length of the terrain