The study area of the present work concerns three small towns located at the heart of the Bodélé triangle in the Saharan zone of Chad, the geographical coordinates of which are given in Table 1 . Figure 1 shows the area of the triangle in which the three towns under study are located, with their geographical coordinates.

The meteorological data used in this study were obtained from the NASA website due to a lack of on-site (in situ) data for the studied locations. This includes monthly average wind speed data measured at 10 meters above the ground over a 22-year period, as well as hourly wind direction data for 2022.

The software used for this study includes Microsoft Excel and LibreOffice Calc for data processing and analysis. MATLAB was used to perform numerical simulations. ArcGIS was used for the spatial visualization of the study areas. Wind roses, which illustrate the distribution of wind directions, were generated using WRPLOT software. These tools allowed us to perform an in-depth analysis of the meteorological data and to better understand the atmospheric phenomena at play.

The Weibull distribution is a continuous probability distribution that has a particularly interesting application in the field of wind energy. It is used to model the distribution of wind speeds, a crucial parameter for assessing the wind potential of a site and designing wind turbines [10] [11] . This distribution is characterized by two key parameters:

$f\left(v\right)=\left(\frac{k}{c}\right){\left(\frac{v}{c}\right)}^{k-1}exp\left(-{\left(\frac{v}{c}\right)}^k\right)$ (1)

The scale parameter c: This represents the most frequent wind speed. The higher c, the higher the average wind speed.

The shape parameter k: This indicates the shape of the distribution. For values of k close to 2, the Weibull distribution tends towards a Rayleigh distribution, often used as a first approximation for wind speeds. A k value below 2 indicates a flatter distribution, while a k value above 2 suggests a sharper distribution.

The Weibull distribution is an indispensable tool for studying and exploiting wind energy. Thanks to the parameters c and k, it provides a precise and concise description of the variability of wind speeds, a key element in the assessment of wind potential and the design of wind energy systems.

The hybrid Weibull distribution function is used when the frequency of calm wind recorded at the site is greater than or equal to 15%. This proportion of calm wind becomes very important and cannot be neglected and must be considered when studying a wind project [12] - [14] . The mathematical expression of this distribution is given by:

$f\left(v\right)=\left(1-f{f}_0\right)\left(\frac{k}{c}\right){\left(\frac{v}{c}\right)}^{k-1}exp\left(-{\left(\frac{v}{c}\right)}^k\right)forv>0$ (1)

$f\left(v\right)$= $f{f}_0$ for v = 0

Where $f{f}_0$ represents the calm wind frequency.

The Rayleigh speed distribution function is a statistical distribution used to model the distribution of wind speeds. It is often used in addition to the Weibull distribution to characterize the behavior of the wind at a given site more precisely [7] [8] [15] . The Rayleigh speed distribution is generally used to represent wind speeds in the absence of specific directional phenomena, such as obstacles or significant topographical effects. It assumes that the wind speed follows a Rayleigh distribution, which describes the probability of the wind speed reaching a given value. This distribution is characterized by a single parameter, called the scale parameter, which determines the shape of the distribution curve. Using wind speed data collected on-site, engineers can adjust this parameter to obtain an accurate representation of the wind speed distribution according to the Rayleigh distribution [7] [15] . This is a special case of the Weibull distribution. When the form factor k = 2, we obtain the Rayleigh distribution function [16] - [18] by:

$f\left(v\right)=\left(\frac{2v}{c^2}\right)exp\left(-{\left(\frac{v}{c}\right)}^2\right)$ (3)

Vertical extrapolation of wind speed consists of estimating the wind speed at different heights above ground based on measurements of wind speeds taken at a single height [19] [20] . This extrapolation plays a very important role in the study of wind potential, as wind speed varies with altitude and can be significantly different at different heights. By extrapolating the wind speed at different heights, we can obtain a better estimate of the available wind resource and therefore better plan the installation of wind farms to maximize their efficiency and energy production [20] - [23] .

Given V₁, a wind speed extrapolated from an altitude Z₁ to another altitude Z₂ according to the relationship given by equation (4), the speed V₂ can be calculated as follows [24] :

$V_2=V_1{\left(\frac{Z_2}{Z_1}\right)}^{\alpha }$ (4)

Where V₁ and V₂ represent respectively the wind speed at a height of 10 m and the speed at altitude Z₂.

α is the roughness coefficient represented by relation (5) [24] :

$\alpha =0.37-0.088\ln \left(V_{10}\right)$ (5)

The Weibull scale factor and shape parameters determined at a height of 10 m are adjusted to any desired height, as indicated by [20] [21] [25] :

$C_z=C_{10}{\left(\frac{z}{10}\right)}^n$ (6)

$k_z=\frac{k_{10}}{1-0.00881\ln \left(z/10\right)}$ (7)

k_z is the form factor at height z and C_z is the scale factor at height z.

The exponent n of the power law is given by [26] [27] :

$n=\left[0.37-0.0088\ln \left(10\right)\right]$ (8)

There are several methods for determining Weibull parameters, depending on the site. In our case, we use the so-called Moroccan method. This method is generally used for areas with high wind speeds [17] [19] . The shape parameter k and the scale factor c are determined by the following relationships:

$k=1+{\left(0.483\left(\bar{v}-2\right)\right)}^{0.51}$ (9)

$c=\frac{\bar{v}}{\Gamma \left(1+\frac{1}{k}\right)}$ (10)

Considering the variability of wind speed and the characteristics of a wind turbine as a function of its starting speed v₁, rated speed v_n and stopping speed v_s, the usable power of a wind turbine is given by the following relationship [12] [28] :

$\langle P_u\rangle =\frac{1}{2}\rho A\langle v_u^3\rangle$ (11)

With:

ρ: the volume density ρ = 1.225 kg/m³; A: the area swept by the blades.

The speed v_u is deduced from the curve representing the Weibull distribution between the limits of the machine [12] [29] . The lower limit is represented by the starting speed [30] [31] . Only speeds above the starting speed v_i are considered in the calculation. In the second case, when the nominal speed v_n is reached, the increase in wind speed has no effect on the wheel speed. Finally, when the stopping speed v_s is reached, the system is automatically braked and higher speeds are not considered in the calculation of v_u.

The mathematical expression of the usable power density is given by the following equation [22] [31] [32] :

$\langle P_u\rangle =\{\begin{array}{l}\begin{array}{ccc}0& for& v<v_i\end{array}\\ \begin{array}{ccc}\frac{1}{2}\rho \langle v^3\rangle & for& v_i<v<v_n\end{array}\\ \begin{array}{ccc}\frac{1}{2}\rho v_n^2& for& v_n<v<v_s\end{array}\\ \begin{array}{ccc}0& for& v>v_s\end{array}\end{array}$ (12)

The mean usable cubic velocity is obtained by integrating the cubic velocity weighted by the probability function, taking the integration limits given by the turbine manufacturer as [16] [33] :

$\langle P_u\rangle ={\displaystyle {\int }_{v_i}^{v_n}f\left(v\right)v^{3}dv}+v_n^3{\displaystyle {\int }_{v_n}^{v_s}f\left(v\right)dv}$ (13)

Or by integration using the normalized gamma distribution:

$\langle \overline{v_v^3}\rangle =\left[{\text{Γ}}_n\left({\left(\frac{v_n}{c}\right)}^k,1+\frac{3}{k}\right)-{\text{Γ}}_n\left({\left(\frac{v_i}{c}\right)}^k,1+\frac{3}{k}\right)\right]\overline{v^3}+v_n^3\left[exp\left(-{\left(\frac{v_n}{c}\right)}^k\right)-exp\left(-{\left(\frac{v_s}{c}\right)}^k\right)\right]$ (14)

With:

${\text{Γ}}_n\left(x,a\right)=\text{Γ}\left(x,a\right)/\text{Γ}\left(x\right)$ (15)

Any wind energy conversion system is designed to operate at maximum efficiency within the limits of the rated wind speed and power. Therefore, once the Weibull scaling and shape parameters are estimated, the performance of a wind turbine at a given site can be easily calculated using the average power and capacity factor. In this paper, the electrical power of a model wind turbine is simulated using [4] [14] [27] [34] :

$P_e=\{\begin{array}{l}\begin{array}{cc}0& \left(v<v_D\right)\end{array}\\ \begin{array}{cc}{P}_{en}\frac{v^k-v_d^k}{v_n^k-v_d^k}& \left(v_d\le v\le v_n\right)\end{array}\\ \begin{array}{cc}{P}_{eR}& \left(v_N\le v\le v_c\right)\end{array}\\ \begin{array}{cc}0& \left(v_c<v\right)\end{array}\end{array}$ (16)

Where:

$P_{en}$: rated electrical power.

$v_d$: the speed of startup of the wind turbine.

$v_n$: rated speed.

$v_c$: cutting speed.

The power produced by a wind turbine depends on the specifications given by the turbine manufacturer.

Each turbine has three essential speed data as its technical parameters. These are [34] [35] :

The total wind power at wind turbine output is:

$P_u={\displaystyle {\int }_{v_d}^{v_n}{P}_{i}f\left(V\right)dV}+{\displaystyle {\int }_{v_a}^{v_n}{P}_{n}f\left(V\right)dV}$ (17)

By replacing the instantaneous power and the velocity distribution function f(V) with their expressions, we have:

$P_u=\frac{\rho A}{2}\underset{v_d}{\overset{v_n}{{\displaystyle \int }}}{C}_p\left(V\right)V_{av}^3\left(\frac{k}{c}\right){\left(\frac{V}{c}\right)}^{k-1}exp\left(-{\left(\frac{V}{c}\right)}^{k-1}\right)dV+\frac{\rho A}{2}\underset{v_n}{\overset{v_a}{{\displaystyle \int }}}\left(\frac{k}{c}\right){\left(\frac{V}{c}\right)}^{k-1}exp\left(-{\left(\frac{V}{C}\right)}^k\right)dV$ (18)

After integration, we will have:

$P_u=C_f{P}_n$ (19)

With:

$C_f=\left[\frac{e^{-{\left(\frac{V_d}{c}\right)}^k}-e^{-{\left(\frac{V_n}{c}\right)}^k}}{{\left(\frac{V_n}{c}\right)}^k-{\left(\frac{V_D}{c}\right)}^k}-{\left(\frac{V_a}{c}\right)}^k\right]$ (20)

Thus, the power output of a wind turbine can be written in the form [11] [29] :

With $C_f$ the capacity factor and plays a very important role in the study of a wind site. The capacity factor can be estimated from the Weibull parameters and the different operating speeds that are provided by the turbine manufacturer. The rated power P_n of a wind turbine is given by the manufacturer. Knowing the useful power produced by a wind turbine, we can calculate the energy produced by a wind turbine during a given period. The energy produced by a wind farm E (KWh) is the total annual wind energy available at a given site. This energy can be calculated as a function of the number of hours, such as [29] [36] :

$P_u=\left[\frac{e^{-{\left(\frac{V_d}{c}\right)}^k}-e^{-{\left(\frac{V_n}{c}\right)}^k}}{{\left(\frac{V_n}{c}\right)}^k-{\left(\frac{V_D}{c}\right)}^k}-{\left(\frac{V_a}{c}\right)}^k\right]P_n$ (21)

$E=P_{u}T.$ (22)

With T the number of hours in a period:

$E=P_{u}d24$ (23)

d being the number of days.

The average usable (produced) wind energy is [37] - [39] :

$\eta =2\frac{P_n}{\rho A{v}_n^3}$ (24)

Large-capacity wind turbines, also known as high-power wind turbines, are large-scale wind turbines designed to generate large amounts of electricity [33] [37] [39] [40] . They are different from small wind turbines in terms of size, power and production capacity [40] - [44] .

Size: The height of high-power wind turbines can reach 200 meters, with rotors more than 100 meters in diameter.

Power: The rated power of high-powered wind turbines generally ranges from 2 to 5 megawatts (MW), up to 10 MW for the latest models.

Power generation: A single large-capacity wind turbine can generate enough electricity to power approximately 4000 homes.

High-power wind turbines use the principle of electromagnetic induction to convert wind’s kinetic energy into electricity. The wind rotates the rotor blades, which in turn causes a generator inside the wind turbine’s nacelle to rotate. Table 2 shows high-power wind turbines with their data sheets. Figure 2 shows the performance curves of different wind turbines for applications at our three sites [42] .

Figure 3 , Figure 4 and Figure 5 show the different monthly speed diagrams for the three cities. Figure 6 , Figure 7 and Figure 8 show the different monthly distributions of Weibull for the following cities: Koro Toro, Nedeley and Salal. The observation of the different curves shows us that the values of the shape factors oscillate around 2, showing that the different velocity distributions are very close to the Rayleigh one. The fact that the form factor oscillates around 2 indicates a relatively sharp Weibull distribution. This means that wind speeds are mainly concentrated around an average value, with few very strong or very weak winds. This is favorable for wind energy production because it ensures a relatively constant flow of energy. The scale factor has a marked seasonal variation, with higher average velocities in winter (December) and lower in summer (September). This variation is typical of many regions and is explained by differences in atmospheric pressure and general circulation between seasons.

Table 3 shows the different values of wind speeds, Weibull parameters and the application to the Vestas V164-10.0 MW wind turbine. The analyzed data shows the monthly wind speeds for a specific location in Koro Toro. Key observations of the monthly speeds show that the average wind speed throughout the year is 4.75 meters per second. There appears to be some seasonal variation in wind speeds. December has the highest wind speed of 5.692 m/s, while September has the lowest at 3.423 m/s. The standard deviation of the wind speeds is 0.81 m/s, indicating that there is some variability in wind speeds throughout the year. Overall, the data suggest that the town of Koro Toro experiences moderate wind speeds with some seasonal variation. December has the strongest winds, while September has the weakest winds. Extrapolating the results to the hub height of the Vestas V164-10.0 MW turbine shows a significant increase in average wind speed. This increase is consistent with the laws of wind turbines, according to which wind speed generally increases with altitude. The scale factor at this height increases exponentially, confirming this trend.

The capacity factor of 0.614 is relatively high, indicating that the site has good wind power potential. This means that the wind turbine produces an average of 61.4% of its maximum possible energy over a year. Variations in the daily flow pumped are directly linked to variations in wind energy production, which in turn depends on wind speed. The highest flows are observed in winter, when wind speeds are highest, and the lowest flows in summer, when wind speeds are lowest.

The results of this study show that the study site has interesting wind energy potential, with relatively high average wind speeds and a good consistency in the distribution of speeds. However, wind energy production is subject to significant seasonal variations, linked to variations in wind speed. The Vestas V164-10.0 MW wind turbine appears to be well suited to the site conditions, given the high wind speeds at hub height. Wind energy production will be highest in winter and lowest in summer. It is important to take these seasonal variations into account when planning the operation of the wind turbine. An energy storage system could be considered to smooth out energy production and better meet water requirements, particularly during periods of low wind production.

The wind study evaluated the performance of two other wind turbine models: Siemens Gamesa SG 14-222 DD and Enercon E-126 EP4 in Tables 4-5 . Given that the wind speed at Koro Toro shows marked seasonal variability, with a maximum in March (5.658 m/s) and a minimum in October (3.42 m/s). The vertical profile of the wind is close to that observed at 10 meters, which simplifies the estimation of the speed at different heights. The scaling factor, which characterizes the increase in wind speed with altitude, reaches maximum values in March (18.41 m/s) and minimum in October (11.31 m/s). In terms of application, the Siemens Gamesa SG 14-222 DD wind turbine presents the capacity factor, which represents the ratio between the energy produced and the maximum energy that can be produced, varies between 0.52 and 0.682 depending on the month. The daily flow of water pumped by this turbine fluctuates between 1,398,900 and 6,110,000 m³/day. For the Enercon E-126 EP4 wind turbine, the capacity factor is slightly higher than for the Siemens Gamesa, with values between 0.5258 and 0.7447. The daily flow of water pumped by this turbine is lower than that of the Siemens Gamesa, varying between 755,800 and 3,377,800 m³/day. The results of this study show that the Koro Toro site has an interesting wind energy potential, with sufficient wind speeds to ensure significant electricity production. The two wind turbine models studied show satisfactory performance, with relatively high capacity factors. However, electricity production is strongly influenced by the seasonal variability of the wind.

The wind power study conducted in Salal allowed to characterize the wind power potential of the site and to evaluate the performance of three wind turbine models: Siemens Gamesa SG 14-222 DD, Vestas V164-10.0 and Enercon E-126 EP4 in Tables 6-8 . The wind at Salal has marked seasonal variability, with a peak speed in February (4.77 m/s to 10 m) and a trough in October (2.986 m/s). The vertical profile of the wind is relatively stable, with a form factor close to 2 - 10 m. The scale factor, which expresses the increase in wind speed with altitude, varies between 8709 m/s and 13,745 m/s, with a maximum in December at the height of the turbine. The application to different Aeolian Turbines gives us significant results. For the Siemens Gamesa SG 14-222 DD: The capacity factor, which represents the efficiency of the turbine, varies between 0.4463 and 0.6605, depending on the evolution of wind speed. The water flow at a total manometric height of 50 m of the turbine fluctuates between 928,700 m 3/day and 3,716,800 m³/day. For Vestas V164-10.0. The capacity factor is relatively stable, with values between 0.6327 and 0.8115. Daily throughput is lower than other models, ranging from 485,640 m³/day to 1,944,300 m³/day. For the Enercon E-126 EP4 wind turbine: The capacity factor is comparable to that of the Siemens Gamesa, with values between 0.4534 and 0.6960. The daily flow is the highest of the three models, varying between 501,150 m³/day and 12,014,400 m³/day.

The Salal site has an interesting wind potential, with sufficient wind speeds to power wind turbines. The three models studied showed satisfactory performance, although the yield varies according to weather conditions. The choice of a wind turbine will depend on the specific constraints of the project, in particular in terms of cost, available area and desired energy production.

Tables 9-11 present the study of the wind potential at Nedeley with different wind turbines of different capacities, as shown in Figure 2 . The results reveal favorable conditions for the exploitation of this renewable energy resource. The maximum wind speed observed in February reaches 5575 m/s, classified as “moderate wind” according to the Beaufort scale, while the minimum, recorded in September, is 3306 m/s, corresponding to a “soft breeze”. This seasonal variability is typical of wind regimes and must be considered in the design of the pumping system. The scale factor, which expresses the increase in wind speed with altitude, reaches a maximum of 15,061 m/s in February and a minimum of 8998 m/s. This seasonal variation is consistent with that of the wind speed at 10 meters. The capacity factor, which is the ratio of the actual energy produced by a wind turbine to the maximum energy it could produce under ideal conditions, varies between 0.4166 and 0.7042 depending on the month. These values indicate an interesting potential for wind energy production, although seasonal variations are expected.

The daily water flow, which is directly related to the available power for pumping, reaches a maximum of 3.0865 × 10⁶ m³/day for the wind turbine Vestas V164-10.0. The other wind turbines studied, Siemens Gamesa SG 14-222 DD and Enercon E-126 EP4, have maximum daily flows of 5.8551 × 10⁶ m³/day and 3.1779 × 10⁶ m³/day, respectively. These values are directly related to rotor size and wind speed. These results suggest that the Nedeley site has an interesting potential for pumping water using renewable energy. However, several factors must be considered for a more accurate assessment.

The interpretation of wind roses from the cities of Koro Toro, Nedeley and Salal is essential to assess the wind potential of these sites. Figure 9 , representing Koro Toro, shows a dominant wind from the east-northeast with a maximum frequency of 40%. The absence of calm winds in this region is a promising indicator for wind energy as it eliminates the hybrid distribution of Weibull, often seen in areas where quiet periods are common. The absence of calm wind suggests a consistency in the wind conditions, which is favorable for the installation of wind turbines. Figure 10 shows Nedeley, which has a similar pattern with a dominant wind from the same east-northeast sector and a maximum frequency above 40%. Although the frequency of calm winds is low at 0.13%, it remains significant relative to Koro Toro. This reinforces the idea that Nedeley also has good wind potential, although slightly less optimal than Koro Toro due to the presence of calm winds. Figure 11 shows data for Salal, where the dominant wind also remains from the east-northeast, with a maximum frequency of 40% and a calm wind frequency of 0.27%. These results indicate that Salal, as well as Koro Toro and Nedeley, has viable wind potential. In summary, these analyses demonstrate that the three sites are suitable for wind energy projects, thanks to reliable and constant wind conditions.

The analysis of the effectiveness of high-capacity wind turbines for water pumping in the towns of Koro Toro, Nedeley, and Salal, located in the heart of the Bodélé triangle, has yielded promising results. The mean wind speeds in these locations were found to be significant, indicating substantial wind potential.

These findings align with and corroborate the previous work of M. Nediguina (2022) [46] - [48] , who obtained similar water flow rates while studying wind potential in comparable areas. Similarly, they are consistent with the research of A.M. Tahir, who highlighted the importance of wind-powered water pumping in the Saharan zone of Chad [49] . The convergence of these studies confirms that wind energy is a viable solution for water pumping in arid regions.

In regions like the Sahara, where access to water is a daily struggle, implementing wind-powered pumping solutions is of critical importance. The local population, especially women and children, often travels long distances—sometimes several kilometers—under extreme temperatures to reach rare and often unsanitary water points. The suffering of these communities is immense.

The installation of wind turbines for water pumping in Koro Toro, Nedeley, and Salal would significantly reduce these distances, ensuring easier and more regular access to drinking water. This initiative directly aligns with the United Nations Sustainable Development Goals (SDGs), particularly SDG 6, which aims to ensure access to water and sanitation for all.

From an energy perspective, the region faces a near-total dependence on fossil fuels, which are often costly and polluting. The integration of wind energy for water pumping addresses an immediate and local need while also being part of the broader context of global energy challenges.

1) Local Energy Independence: By using locally available wind energy, the population is no longer dependent on imported fuel to operate diesel water pumps. This reduces costs, improves the community’s energy resilience, and fosters a more sustainable local economy.

2) Fighting Climate Change: On a global scale, the transition to renewable energy is crucial for reducing greenhouse gas emissions. A wind pumping project in the Bodélé, though local, contributes to this global effort by demonstrating the viability of clean solutions in challenging environments.

The technical feasibility of this project relies on selecting robust equipment designed to withstand sand and extreme temperatures, along with rigorous maintenance. Financially, despite a high initial cost, the project is profitable in the long run. It eliminates the dependence on diesel fuel, reduces operating costs, and aligns with global energy transition goals. The analysis of the wind roses, which confirms a dominant East-Northeast direction with an almost complete absence of calm winds, reinforces the project’s viability. These results, combined with the promising theoretical water flow rates, show that wind energy is a reliable and sustainable solution for these areas. It not only solves a water scarcity problem but also contributes to energy autonomy and environmental protection, thereby aligning local needs with global imperatives.