Assessment of Wind Energy Resources in Jordan Using Different Optimization Techniques

Abstract

Wind energy has become one of the world’s most renewable energy sources in recent years. It is regarded as a clean energy source because it produces no greenhouse gas emissions. The assessment of wind energy resources is an important step in the development of any wind energy conversion system (WECS). As a result, this article examines the wind energy potential of nine Jordanian wind locations: Queen Alia Airport, Civil Amman Airport, King Hussein Airport, Irbid, Mafraq, Ma’an, Ghor Al Safi, Safawi, and Irwaished. The available wind speed data were implemented using three statistical distribution models, Weibull, Rayleigh, and Gamma distributions, and one traditional estimation method, the Maximum Likelihood Method (MLM). Three optimization techniques were used to assign parameters to each distribution model: Particle Swarm Optimization (PSO), Grey Wolf Optimizer (GWO), and Whale Optimization Algorithm (WOA). To determine the optimal distribution model, the performance of these distribution models was tested. According to the findings, King Hussein Airport features the highest wind power density, followed by Queen Alia Airport, while Irbid features the lowest, followed by Ghor Al Safi.

1. Introduction

Throughout history, humanity has attempted to utilize and harness natural resources and use them in the best way. Renewable energy resources are a good example of how this might be done. To address the risks of using fossil fuels, renewable energy is currently an urgent and vital need. In 2019, the global renewable energy capacity was 2588 GW, and renewable energy accounted for around 27.3% of total power generation, compared to 72.7% for non-renewable resources [1]. As a result, governments all over the world must take all the necessary steps to make policies in this sector more accessible.

In the sphere of renewable energy, wind power is one of the most developed fields. In 2019, 60 GW of wind power capacity was added to electric networks around the world, making 2019 the second-largest annual growth year in wind power generation capacity, behind 2015, which produced the highest capacity of around 64 GW. As a result, in the same year, the percentage of wind power-sharing in electricity generation was 5.9%, with a total capacity of 651 GW [1].

Jordan features a climate that encourages the exploitation of renewable energy resources. It features several sites that are attractive for investment in the wind energy sector. In fact, Jordan still depends on traditional energy sources to generate its electric energy (85.1%). In 2019, renewable energy contributed about 14.9% of the energy mix, with wind energy sharing accounting for 4.4% of the energy produced overall [2].

The direction and speed of wind cannot be predicted exactly due to its unpredictable nature. Wind characteristics should be determined by observing and evaluating the natural behavior of wind at the prospective site. The components of the Wind Energy Conversion System (WECS) can be efficiently designed once the wind characteristics have been identified. As a result, a wind energy assessment process can be accomplished [3].

In general, there are four steps in the evaluation of wind resources. The first step involves gathering wind data, which is measured and gathered by meteorological stations or airports. Wind data are usually measured over ten minutes at a height of 10 m, which is considered the standard height. The second stage entails analyzing the acquired data using statistical distribution models to determine the frequency distribution of average wind velocity for the candidate site over a certain time period. Each distribution model features a number of parameters that must be assigned using several estimating methods divided into two main groups: numerical methods and optimization algorithms. The optimal distribution function must be chosen by comparing the available distribution models. This is accomplished through the use of several goodness-of-fit indicators, such as Root Mean Square Error (RMSE), Coefficient of Determination (R²), and others. A Probability Distribution Function (PDF) can be used to depict the distribution model. The extracted wind energy from a given wind turbine installed in a prospective wind site is evaluated using the distribution function and the power curve (P-V characteristic) model of the selected wind turbine. Upon completion of this stage, a judgment can be made as to whether a wind turbine can be installed/or not in a certain wind site.

To evaluate wind energy resources, many parametric distribution models are used [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26]. Weibull [4,5,6,9,10,11,12,13,14,15], Rayleigh [8,18,19,20,21], Gamma [21,26], Lognormal [24,26], Log–logistic [13], and others are among these models. The Weibull distribution is the model that most researchers utilize. In [7], Bilir et al. used Weibull distribution as an assessment tool to evaluate the power density based on wind data collected over a year, from a measuring station situated on the Atlm University campus area in Ankara, Turkey. The Weibull model, which was examined using the Root Mean Square (RMS) error, was found to be the most acceptable distribution among the five chosen distribution models by Wang et al. [11]. In [14], Li, et al. conducted a comparative assessment of onshore and offshore wind characteristics, as well as their wind energy potential, in two locations along China’s southeast coast. The authors confirmed the accuracy of using the Weibull distribution for both onshore and offshore wind energy, and the findings demonstrated that offshore wind energy is more available than onshore wind energy for a given region. In [18], Jiang et al. compared the Weibull distribution to the Rayleigh, Gamma, and Lognormal distributions to determine the energy potential of low wind speeds in China.

Weibull was the best choice, especially when optimization algorithms were used to determine its parameters. A comprehensive assessment of 46 papers between 2010 and 2018 was published in [27]. The Weibull distribution was shown to be the most commonly used in this study (44 out of 46 studies used Weibull distribution). On the other hand, the Weibull distribution is not always considered the best option [22,24]. The Weibull, Logistic, and Lognormal distributions were used by Wu et al. in [24] to measure wind energy at typical sites in Inner Mongolia, China. The performances of the Logistic and Lognormal were better than the Weibull, which was the worst. According to [28], numerous variants of mixture distributions surpass the traditional Weibull distribution, including the bimodal Weibull function (WW), the truncated Normal–Weibull function (NW), the Gamma–Weibull function (GW), and the mixed truncated normal function (NN).

Parametric distribution models might use a single parameter, two parameters, three parameters, or more. These parameters should be properly valued by several types of estimation method, such as the Maximum Likelihood Method (MLM) [4,7], the Moment Method (MM) [10,12,13,14,15], Least Square Estimation (LSE) [18,19], the Empirical Method (EM) [10,11,12,15], the Power Density Method (PDM) [14,26], and Energy Pattern Factor (EPF) [9,15]. Some modified methods are also utilized, such as Modified Maximum Likelihood (MMLM) [25], and the Modified Energy Pattern Method (MEPM) [12].

In recent years, metaheuristic optimization methods have been employed to estimate the parameters of various distribution models. Particle Swarm Optimization (PSO) [23,24], Cuckoo Search optimization (CS) [18,19], Genetic Algorithm (GA) [19,23], Differential Evolution Algorithm (DEA) [23,24], and Grey Wolf Optimizer (GWO) [11,15] are some examples of these methods.

Three optimization algorithms, PSO, CS, and GWO, were compared against four numerical approaches in [11]. In general, the performance of the presented algorithms was optimal, with the GWO being the most accurate technique. For estimating wind potential at a site near Pakistan’s coastline region, Saeed et al. [15] suggested Artificial Intelligent (AI) optimization algorithms based on the Chebyshev measure. The results demonstrated that AI optimization outperforms numerical approaches by a factor of ten. For wind potential assessment at seven locations in Saudi Arabia, a new metaheuristic optimization algorithm method dubbed Social Spider Optimization (SSO) was recommended in [19]. According to the results, the proposed technique outperformed the other heuristic methods. However, several drawbacks limit the use of the parametric distribution models. One is the need for using estimating methods to determine the values of the parameters accurately. Therefore, some academics suggested non-parametric distribution models. The best-known and frequently employed method is the kernel density method [16,17,29,30]. In recent years, interest has developed in urban wind energy, which represents an extraordinary jump in wind energy systems. Generally, energy exploitation in this type of system is performed by assembling small-scale wind turbines on different rooftop locations [31,32,33].

In Jordan, interest in wind energy began in 1979 through the Royal Scientific Society (RSS) [34]. Since then, several studies have been conducted to evaluate wind energy resources [35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52]. Generally, the observed in these studies is that they are limited to the use of Weibull or Rayleigh distribution models.

In this study, several wind sites in Jordan were selected as research objects to compare different types of distribution models for the purpose of wind energy assessment. The main objectives of this research study compared to other studies in the same area of research can be summarized as follows:

• Deriving the mathematical representation of the wind assessment based on Gamma distribution, which is not frequently used in other studies.
• Utilizing the optimization techniques to estimate the parameters values of the used distribution models.
• Estimating the wind energy in the candidate wind sites using the Weibull, Rayleigh, and Gamma models.

This paper is organized as follows. Section 2 describes the measured wind data. The mathematical model including the wind energy estimation based on the wind power density concept is developed in Section 3. The results are discussed in Section 4, prior to the conclusion in Section 5.

2. Measured Wind Data

For proper wind resource assessment, wind data must be collected from the closest meteorological stations to the candidate wind site. These data are usually gathered at a height of 10m and can be extrapolated to a higher elevation (usually the hub height of the wind turbine). For large-scale wind projects, this provides an accurate evaluation of the wind. Wind speed and direction are important data that can be categorized on a 10 min, hourly, daily, monthly, and yearly basis. The most frequent is a 10 min basis, which can provide a precise resolution for estimating wind potential [3].

For this study, wind data were collected for one year to represent the variations in the wind profile. Despite the increase in wind speed in the last ten years due to rising global temperatures, the wind speed for one year, which is the time interval used in our case, is considered a representative sample to represent the general distribution of winds in a particular region for longer periods. Because the external shape of the general distribution of the wind is not affected by the increase or decrease in the wind speed, but rather it is shifted to the right or left.

This study involves nine sites in Jordan: Queen Alia Airport, Civil Amman Airport, King Hussein Airport, Irbid, Mafraq, Ma’an, Irwaished, Safawi, and Ghor Al Safi.

Table 1. Distribution of wind sites in Jordan.

Site	Coordination		Elevation	Period
	Latitude	Longitude
Queen Alia Airport	31.43° N	35.59° E	722 m	January 2019 to December 2019
Civil Amman Airport	31.59° N	35.59° E	767 m	September 2018 to August 2019
King Hussein Airport	29.33° N	35.00° E	51 m	January 2018 to December 2018
Irbid	32.33° N	35.51° E	618 m	Mar 2018 to February 2019
Mafraq	32.22° N	36.15° E	686 m	September 2018 to August 2019
Ma’an	30.10° N	35.47° E	1069 m	Mar 2018 to February 2019
Safawi	32.09° N	37.12° E	647 m	January 2018 to December 2018
Irwaished	32.30° N	38.12° E	686 m	September 2017 to August 2018
Ghor Al Safi	31.02° N	35.28° E	−350 m	January 2018 to December 2018

illustrates the geographical locations and elevations of the meteorological stations at these sites. Moreover, the time periods of the wind data for each wind site are included in Table 1.

In order to organize the wind speed data, it was divided into several classes. Each class features an interval of 1 m/s. Figure 1 shows the measured wind speed distribution for all the wind sites. The wind speed data are analyzed using statistical tools to determine the mean value, the standard deviation, and the distribution pattern (see

Table 2. Mean wind speed, standard deviation, and distribution pattern of selected wind sites.

Site	Mean Value (m/s)	Standard Deviation (m/s)	Skewness	Kurtosis
Queen Alia Airport	5.8162	2.6629	1.2046	1.9258
Civil Amman Airport	5.0921	2.4621	1.2341	1.9504
King Hussein Airport	5.7137	2.0677	0.4670	0.4033
Irbid	2.4912	0.9650	1.5839	5.1378
Mafraq	4.7725	2.1551	2.0246	11.5537
Ma’an	5.4774	2.5552	1.7068	3.4912
Safawi	6.1416	2.5715	1.0783	0.8556
Irwaished	5.5053	2.7075	1.6378	3.4869
Ghor Al Safi	4.5337	2.7195	12.6675	261.3626

). It can be noted from this Table that the mean wind speed in this wind is around 5 m/s. A closer inspection of this Table shows that the mean wind speed for all the sites varies between 2.49 m/s and 6.15 m/s. The lowest standard deviation for the wind speed data in all the sites was in Irbid, with a value around 1 m/s, while the greatest was in Ghor Al Safi, with a value around 2.7 m/s.

The skewness value of the wind data in all the sites was positive, with a maximum value around 12.7 in Ghor El Safi. This value indicates an obvious asymmetry in its distribution curve, with a long thin tail to the right, as shown in Figure 1. Both Irbid and Safawi recorded the lowest values of kurtosis, around 0.4033 and 0.8556, respectively.

Interestingly, the maximum kurtosis value was recorded in Ghor El Safi. This makes the distribution curve for this site much steeper than the normal distribution (see Figure 1).

In general, the results presented in Table 1 and Table 2 and Figure 1 present clear differences between the properties and specifications of the candidate wind sites. This is due to the diversity in the topography of these regions.

The wind directions were determined based on the available wind data. The wind rose was drawn for each site, as shown in Figure 2. A closer inspection of this figure shows that the most prevailing direction was north–west, with an occurrence rate of 26.29% at all sites. Wind blowing from the east featured the lowest occurrence rate among all the directions, with only 3.87%. The occurrence rate of the wind blowing from the north at King Hussein Airport was the highest, with a percentage value of 68.55%. In general, knowing the prevailing wind direction in a specific wind site offers an indication as to the correct direction of the installed wind turbine, which should be ranged from northwest to southwest in most sites.

3. Mathematical Model

In this section, the mathematical model is formulated, including the wind distribution models and the estimation methods that were utilized to assign the models’ parameters. Three performance indicators are used to determine the optimal distribution model. Furthermore, wind energy calculations are evaluated based on the distribution models.

3.1. Wind Distribution Models

In this study, three different distribution models are used to represent the wind behavior of the selected locations. Weibull and Rayleigh are well known and commonly used by many wind researchers. The third function used in this study is the Gamma function, which is rarely used in the field of wind.

3.1.1. Weibull Distribution

The probability distribution function (PDF) of the Weibull model is expressed as follows [7,53]:

$$f_W\left(v\right)=\frac{k}{c}{\left(\frac{v}{c}\right)}^{k-1}{e}^{-{\left(\raisebox{1ex}{$v$}\!\left/ \!\raisebox{-1ex}{$c$}\right.\right)}^k}$$

(1)

where k and c are Weibull shape and scale factors, respectively.

3.1.2. Rayleigh Distribution

The Rayleigh distribution is a simplified case of Weibull distribution by substituting k = 2 into (1). Therefore, the probability distribution function is expressed as follows [13]:

$$f_R\left(v\right)=\frac{v}{c^2}{e}^{-\left(\raisebox{1ex}{$v^2$}\!\left/ \!\raisebox{-1ex}{$2c^2$}\right.\right)}$$

(2)

3.1.3. Gamma Distribution

Gamma distribution can be applied for wind energy assessment. The probability distribution function of Gamma is expressed as follows [11]:

$$f_G\left(v\right)={\left(\frac{v}{c}\right)}^k\frac{e^{-(\raisebox{1ex}{$v$}\!\left/ \!\raisebox{-1ex}{$c$}\right.)}}{\mathsf{\Gamma }\left(k\right) v}$$

(3)

where Г Gamma is the gamma function.

3.2. Estimation Method

Each distribution model includes shape and scale parameters that should be estimated correctly by two main methods: numerical estimation methods and optimization algorithm methods. Each is discussed individually below.

3.2.1. Numerical Estimation Method

MLM is represented as the most common traditional method that is utilized to estimate the parameters of the selected distribution models. The mathematical formulas of the parameters for these distribution models based on MLM are illustrated in the following:

Weibull’s Parameters Based on MLM

The shape and scale factors for the Weibull model are expressed as follows [54].

$$k={\left(\frac{{{\displaystyle \sum }}_{i=1}^n{v}_i^k\ln \left(v_i\right)}{{{\displaystyle \sum }}_{i=1}^n{v}_i^k}-\frac{{{\displaystyle \sum }}_{i=1}^n\ln \left(v_i\right)}{n}\right)}^{-1}$$

(4)

$$c={\left(\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$n$}\right.{{\displaystyle \sum }}_{i=1}^n{v}_i^k\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$k$}\right.}$$

(5)

Rayleigh’s Scale Parameter Based on MLM

The scale factors for the Rayleigh model are expressed as follows [54]

$$c=\sqrt{\frac{1}{2n}{{\displaystyle \sum }}_{i=1}^n{v}_i{}^2}$$

(6)

Gamma’s Parameters Based on MLM

The shape and scale factors for the Gamma model are expressed as follows [54]:

$${\mathsf{\Psi }}_0\left(\mathrm{k}\right)=\frac{1}{n}{{\displaystyle \sum }}_{i=1}^n\ln v_i-\ln \left(\frac{1}{nk}{{\displaystyle \sum }}_{i=1}^n{v}_i\right)$$

(7)

$$\mathrm{c}=\frac{1}{nk}{{\displaystyle \sum }}_{i=1}^n{v}_i$$

(8)

where ${\mathsf{\Psi }}_0$ is the Digamma function.

3.2.2. Optimization Algorithms Methods

Metaheuristic algorithms can be applied as estimation techniques. Three algorithms are used to estimate the parameters: Particle Swarm Optimization (PSO), Grey Wolf Optimizer (GWO), and Whale Optimization Algorithm (WOA) [55,56,57]. The objective function used in this study is based on minimizing the error between the measured wind speed and the estimated values using these optimization algorithms as follows [20]:

$$Error\left(v_i\right)=\frac{1}{2}{{\displaystyle \sum }}_{i=1}^n{\left[f_m\left(v_i\right)-f_c\left(v_i,{\varnothing }_i\right)\right]}^2$$

(9)

where f_m(v_i) represents the measured frequency distribution of ith wind data, f_c(v_i, φ_i) is the estimated values obtained by the distribution functions, which include the parameters φ_i, and n is the number of wind speed data. As mentioned, the main goal is to minimize the objective function value, Error (v_i), by using the aforementioned algorithms. Each algorithm is discussed individually in the following subsections.

Particle Swarm Optimization (PSO)

Eberhart and Kennedy proposed a stochastic algorithm inspired by the social behavior of bird swarms [55]. In a searching space with N-dimension, a set of particles merge to find the optimal solution. Each particle is identified by a position vector X_i = (x_i1, x_i2, x_i3, ……, x_iN) and velocity vector V_i = (v_i1, v_i2, v_i3, ……, v_iN). In each iteration, each particle features a local best position, defined as P_i = (p_i1, p_i2, p_i3, ……, p_iN). The best particle among the swarm possesses the best global position, which is defined as P_gi = (p_gi1, p_gi2, p_gi3, ……, p_giN). Each particle updates its position and velocity iteratively by the following equations [11]:

$$V_i^{\left(k+1\right)}=\omega V_i^{\left(k\right)}+\left[c_1{r}_1\left(P_i^{\left(k\right)}-X_i^{\left(k\right)}\right)\right]+\left[c_2{r}_2\left(P_g{}_i^{\left(k\right)}-X_i^{\left(k\right)}\right)\right]$$

(10)

$$X_i^{\left(k+1\right)}=X_i^{\left(k\right)}+V_i^{\left(k+1\right)}$$

(11)

where ω is the inertia weight factor, c₁ and c₂ are the acceleration coefficients that set to 2. The values r₁ and r₂ are both random numbers defined as r₁ and r₂ ∈ [0, 1]. The inertia weight value is updated at each iteration as follows:

$$\omega ={\omega }_{max}-\left({\omega }_{max}-{\omega }_{min}\right)\times \frac{k}{ite{r}_{max}}$$

(12)

where ω_max and ω_min are the maximum and minimum value of the inertia weight that set to 0.9 and 0.4, respectively. The value k is the current iteration and iter_max is the maximum number of iterations. The PSO is summarized in the following steps [11]:

• Step One. Define the following parameters (N, Population size, iter_max, c₁, c₂, ω_max, ω_min), then initialize the position of all particles X_i = (x_i1, x_i2, x_i3, ……, x_iN).
• Step Two. Calculate the fitness value for each particle and record the local and global best solutions.
• Step Three. Update the velocity V_i and position X_i of the ith particle by using Equations (10) and (11).
• Step Four. Calculate the fitness value for the new position X_i.
• Step Five. Check if the new position is better than the obtained best local solution. If yes, set the new X_i to be P_i; otherwise, keep the current P_i unchanged.
• Step Six. Repeat Step Five to check for the global best solution.
• Step Seven. Check whether all the particles are considered. If not, go to the next particle; otherwise, save the best global position.
• Step Eight. Check whether the limitation conditions are satisfied. If not, go to Step Three; otherwise, output the global best solution $P_g$ and associated fitness value.

The flow chart in Figure 3 summarizes the process of the PSO.

Grey Wolf Optimizer (GWO)

Mirjilalili et al. proposed an algorithm inspired by the social behavior of gray wolves during hunting [56]. Gray wolves mostly live in flocks, with 5 to 12 wolves per flock. Like any wild herd, they live in a hierarchal stratification system. Accordingly, wolf flocks are divided into four classes: Alpha, Beta, Delta, and Omega.

The GWO algorithm can be represented in the following stages [11,56]:

• Step One. Social strategy

The mathematical model of GWO considers (α) as the optimal solution, followed by (β) and (δ) as a second and third solutions, respectively. The value (ω) is assumed to be an alternative solution. In this algorithm, α, β, and δ mainly guide the process and ω (wolves) obeys them.

• Step Two. Encircling the prey

Encircling behavior can be represented as follows:

$$\overrightarrow{D}=\left|\overrightarrow{C}·\overrightarrow{X_p}\left(t\right)-\overrightarrow{X}\left(t\right)\right|$$

(13)

$$\overrightarrow{X}\left(t+1\right)=\overrightarrow{X_p}\left(t\right)-\overrightarrow{A}·\overrightarrow{D}$$

(14)

where t indicates the current iteration, and $\overrightarrow{X_p}$ and $\overrightarrow{X}$ represent the position vectors of the prey and grey wolf, respectively. $\overrightarrow{A}$ and $\overrightarrow{C}$ are coefficient vectors, expressed as follows:

$$\overrightarrow{A}=2\overrightarrow{a}·\overrightarrow{r_1}-\overrightarrow{a}$$

(15)

$$\overrightarrow{C}=2\overrightarrow{r_2}$$

(16)

where $\overrightarrow{a}$ is a component that decreases linearly from 2 to 0 throughout the iterations, and $\overrightarrow{r_1}$ and $\overrightarrow{r_2}$ are both random vectors defined as $r_1 \mathrm{and} r_2 \in \left[0,1\right]$. Equations (13) and (14) indicate that the grey wolf can update its position randomly around the prey.

• Step Three. Hunting

Hunting behavior can be simulated by assuming that α, β, and δ wolves identify the prey’s location perfectly. Therefore, the first three optimal solutions are saved while the rest of the search agents are compelled to update their positions accordingly. The following equations describe the hunting behavior mathematically.

$$\overrightarrow{D_{\alpha }}=\left|\overrightarrow{C_1}·\overrightarrow{X_{\alpha }}-\overrightarrow{X}\right|$$

(17)

$$\overrightarrow{D_{\beta }}=\left|\overrightarrow{C_2}·\overrightarrow{X_{\beta }}-\overrightarrow{X}\right|$$

(18)

$$\overrightarrow{D_{\delta }}=\left|\overrightarrow{C_3}·\overrightarrow{X_{\delta }}-\overrightarrow{X}\right|$$

(19)

$$\overrightarrow{X_1}=\overrightarrow{X_{\alpha }}-\overrightarrow{A_1}·\overrightarrow{D_{\alpha }}$$

(20)

$$\overrightarrow{X_2}=\overrightarrow{X_{\beta }}-\overrightarrow{A_2}·\overrightarrow{D_{\beta }}$$

(21)

$$\overrightarrow{X_3}=\overrightarrow{X_{\delta }}-\overrightarrow{A_3}·\overrightarrow{D_{\delta }}$$

(22)

$$\overrightarrow{X}\left(t+1\right)=\frac{\overrightarrow{X_1}+\overrightarrow{X_2}+\overrightarrow{X_3}}{3}$$

(23)

where $\overrightarrow{X}$ represents the best position obtained so far and $\overrightarrow{X}\left(t+1\right)$ refers to the mean of the first three best solutions in the next iteration.

• Step Four. Attacking the prey

The attacking course starts when the prey stops moving. This can be mathematically modeled by decreasing $\overrightarrow{a}$ component from 2 to 0. Consequently, the range of $\overrightarrow{A}$ is also decreases by $\overrightarrow{a}$. In other words, the value of $A$ ranges in interval of $\left[-a,a\right]$ when $\overrightarrow{a}$ decreasing iteratively. The attack occurs when $A\in \left[-1,1\right]$ to force the wolves to attack the prey.

• Step Five. Searching for prey

In this stage, wolves separate to search for better prey and gather when attacking the prey. This can be modeled by making the $A$ value greater than 1 or less than −1 i.e., $\left|A\right|>1$. This helps to push the search agents to seek better prey.

The GWO is summarized in the following steps:

1. 

Define the following parameters (N, Population size, iter_max), then initialize the coefficients a, A, and C.

2. 

Evaluate the fitness for each search agent and set α, β, and δ to be the first, second, and third best search agent.

3. 

Update the position of the current search agent by Equations (17)–(23).

4. 

Check whether all wolves (search agents) are considered. If not, go to the next search agent; otherwise, update the coefficients a, A, and C by Equations (15) and (16).

5. 

Evaluate the fitness for all the search agents.

6. 

Save the first, second, and third best solutions (X_α, X_β, and X_δ).

7. 

Check whether the limitation conditions are satisfied. If not, go to step three. Otherwise, output the best solution X_α and associated fitness value.

8. 

The flow chart in Figure 4 summarizes the process of the GWO.

Whale Optimization Algorithm (WOA)

The Whale Optimization Algorithm was proposed by Mirjilalili et al. in 2016 [57]. This algorithm was inspired by a distinctive social behavior of the humpback whale during foraging, named the bubble-net feeding method. This method is based on generating distinctive bubbles along a circular or 9 shaped path. The foraging behavior of the humpback whale can be mathematically represented in the following stages [57].

• Step One. Encircling the prey

The humpback whale has the ability to locate and encircle prey properly. It is assumed that the prey’s position is the optimal solution. Accordingly, the other whales (search agents) must update their positions according to the optimal whale’s position. The encircling behavior can be expressed as follows:

$$\overrightarrow{D}=\left|\overrightarrow{C}·\overrightarrow{X^{*}}\left(t\right)-\overrightarrow{X}\left(t\right)\right|$$

(24)

$$\overrightarrow{X}\left(t+1\right)=\overrightarrow{X^{*}}\left(t\right)-\overrightarrow{A}·\overrightarrow{D}$$

(25)

where t refers to the current iteration, $\overrightarrow{X^{*}}$ is the best position vector of the optimal solution, and $\overrightarrow{X}$ is the position vector of a search agent. $\overrightarrow{A}$ and $\overrightarrow{C}$ are both coefficient vectors that can be given by the following equations:

$$\overrightarrow{A}=2\overrightarrow{a}·\overrightarrow{r}-\overrightarrow{a}$$

(26)

$$\overrightarrow{C}=2\overrightarrow{r}$$

(27)

where $\overrightarrow{a}$ is a component that decreases linearly from 2 to 0 throughout the iterations and $\overrightarrow{r}$ is a random vector, defined as $r\in \left[0,1\right]$.

• Step Two. Bubble-net attacking method

The bubble-net behavior can be divided into two approaches as follows:

• A. Shrinking encircling mechanism

This mechanism is based on decreasing the value of $\overrightarrow{a}$. Hence, the fluctuation range of $\overrightarrow{A}$ coefficient is also decreased by $\overrightarrow{a}$, i.e., $\overrightarrow{A} \in \left[-a,a\right]$. Setting the range of $\overrightarrow{A}=\left[-1,1\right]$ or $\left|A\right|<1$ leads to locating the new position of a search agent anywhere in between the original position and the optimal current position.

• B. Spiral updating position

In this approach, the whale attacks the prey in a helix-shaped path. This can be expressed as follows:

$$\overrightarrow{D^{\prime }}=\left|\overrightarrow{X^{*}}\left(t\right)-\overrightarrow{X}\left(t\right)\right|$$

(28)

$$\overrightarrow{X}\left(t+1\right)=\overrightarrow{D^{\prime }}·e^{bl}·\cos \left(2\pi l\right)+\overrightarrow{X^{*}}\left(t\right)$$

(29)

where $\overrightarrow{D^{\prime }}$ represents the distance of the ith whale to prey (optimal solution obtained), and $l$ is a random number defined as $l\in \left[-1,1\right]$, $b$ is constant value related to the shape of the logarithmic spiral.

Notably, the humpback whale uses the two approaches at the same time when attacking and encircling its prey. Therefore, the algorithm assumes an equal probability of choosing between the two mechanisms. Consequently, the updated position of the whales can be modeled as follows.

$$\overrightarrow{X}\left(t+1\right)=\{\begin{array}{c}Eq.\left(25\right), p<0.5\\ Eq.\left(29\right), p\ge 0.5\end{array}$$

(30)

where $p$ represents the probability and is a random number defined as $p\in \left[0,1\right]$.

• Step Three. Searching for prey

Humpback whales search for prey at random, depending on each other’s positions. $\overrightarrow{A}$ coefficient can used to impel the whales (search agents) to separate in order to seek better prey. This can be modeled by making the $A$ value greater than 1 or less than −1, i.e., $\left|A\right|>1$. In this stage, the updated position is achieved by choosing a random search agent instead of the optimal agent obtained. This can be expressed as follows:

$$\overrightarrow{D}=\left|\overrightarrow{C}·\overrightarrow{X_{rand}}\left(t\right)-\overrightarrow{X}\left(t\right)\right|$$

(31)

$$\overrightarrow{X}\left(t+1\right)=\overrightarrow{X_{rand}}\left(t\right)-\overrightarrow{A}·\overrightarrow{D}$$

(32)

where $\overrightarrow{X_{rand}}$ is the random position vector.

The WOA is summarized in the following steps:

1. 

Define the following parameters $\left(N,Populationsize, ite{r}_{max}\right)$, then initialize the population $X_i\left(i=1,2,\dots \dots ,N\right)$ and the coefficients $a$, $A$, $C$, $l,$ and $p$.

2. 

Evaluate the fitness for each search agent and set $X^{*}$ to be the best search agent.

3. 

Update the following coefficients: $a$, $A$, $C$, $l,$ and $p$.

4. 

Check the $p$ value. (I) If $p<0.5$, then check the $\left|A\right|$ value. (i) If $\left|A\right|<1$, update the position by (25). (ii) Otherwise, if $\left|A\right|\ge 1$, select a random search agent $X_{rand}$, then update the position by (32). (II) Otherwise, if $p\ge 0.5$, then update the position by (29).

5. 

Check whether all the whales (search agents) are considered. If not, go to the next search agent; otherwise, check whether any search agent exceeds the search space and adjust it.

6. 

Evaluate the fitness for all the search agents.

7. 

Save the best solution $X^{*}$.

8. 

Check whether the limitation conditions are satisfied. If not, go to the step three; otherwise, output the best solution $X^{*}$ and associated fitness value.

The flow chart in Figure 5 summarizes the process of the WOA.

3.3. Performance Indicators

Three statistical performance tests are utilized to determine the optimal distribution model. These tests are: Root Mean Square Error (RMSE), Coefficient of Determination (R²), and Mean Absolute Error (MAE). Each is discussed in the following subsections.

3.3.1. Root Mean Square Error (RMSE)

The Root Mean Square Error calculates the difference between the predicted values of the distribution model and the observed values. The RMSE is defined as follows [7]:

$$RMSE=\sqrt{\frac{1}{n}{{\displaystyle \sum }}_{i=1}^n{\left(y_i-x_i\right)}^2}$$

(33)

where $y_i \mathrm{and} x_i$ are the ith observed and calculated values, respectively, and $n$ is the total number of observations. The lowest RMSE value means that the used estimation method achieves the best result.

3.3.2. Coefficient of Determination (R²)

This test measures the consistency degree between the observations and the theoretical values by the distribution models. The $R^2$ is expressed as follows [11]:

$$R^2=1-\frac{{{\displaystyle \sum }}_{i=1}^n{\left(y_i-x_i\right)}^2}{{{\displaystyle \sum }}_{i=1}^n{\left(y_i-\overline{y}\right)}^2}$$

(34)

where $\overline{y}$ represents the average value of the observations. The larger the $R^2$, the better the accuracy of estimation that is obtained.

3.3.3. Mean Absolute Error (MAE)

This test calculates the absolute error between the observed and predicted values. Like RMSE, the lower the MAE value, the better the results obtained. MAE is expressed as follows [19]:

$$MAE=\frac{1}{n}{{\displaystyle \sum }}_{i=1}^n\left|y_i-x_i\right|$$

(35)

3.4. Wind Energy Estimation

In this subsection, the assessment of the energy potential of wind regimes is evaluated using three distribution models: Weibull, Rayleigh, and Gamma. This assessment is based on evaluating the two main parameters of any wind regime: the wind power density ($E_D$) and the total wind energy ($E_T$) over one year:

$$E_D={{\displaystyle \int }}_0^{\infty }{P}_{v}f\left(v\right) dv$$

(36)

where $f\left(v\right)$ is the distribution function and $P_v$ represents the available wind power per unit area of the wind regime in $\mathrm{W}/{\mathrm{m}}^2$. It can be expressed as follows [58,59]:

$$P_v=0.5{\rho }_a{v}^3$$

(37)

where the ${\rho }_a$ is the air density in $\mathrm{kg}/{\mathrm{m}}^3$. The total energy can be calculated of a specific wind regime over a certain period (T) in $\mathrm{kWh}/{\mathrm{m}}^2$ as follows:

$$E_T=T{E}_D$$

(38)

The wind power densities of the Weibull and Rayleigh functions, ($E_{DW}$) and ($E_{DR}$) are given by (39) and (40), respectively [20,60]:

$$E_{DW}=\frac{{\rho }_a{c}^3}{2 }\mathsf{\Gamma }\left(1+\frac{3}{k}\right)$$

(39)

$$E_{DR}=\frac{3\times {\rho }_a{c}^3}{2 }\sqrt{\frac{\mathsf{\pi }}{2}}$$

(40)

The wind power density of the gamma function ($E_{DG}$) is derived by substituting (3) and (37) in (36):

$$E_{DG}=\frac{{\rho }_a}{2 \mathsf{\Gamma }\left(k\right)}{{\displaystyle \int }}_0^{\infty }{v}^2{\left(\frac{v}{c}\right)}^k{e}^{-\left(\frac{v}{c}\right)} dv$$

(41)

let $=v/c$; therefore, $dv=c dx$. Substituting into (41), yields:

$$E_{DG}=\frac{{\rho }_a{c}^3}{2 \mathsf{\Gamma }\left(k\right)}{{\displaystyle \int }}_0^{\infty }{x}^{k+2 }{e}^{-x} dx$$

(42)

Knowing that the standard Gamma integral is expressed as follows:

$$\mathsf{\Gamma }\left(n\right)={{\displaystyle \int }}_0^{\infty }{x}^{n-1 }{e}^{-x} dx$$

(43)

Comparing (42) with (43), the wind power density using the Gamma distribution function can be expressed as follows:

$$E_{DG}=\frac{{\rho }_a{c}^3}{2 }\frac{\mathsf{\Gamma }\left(k+3\right)}{\mathsf{\Gamma }\left(k\right)}$$

(44)

4. Results and Discussion

In this study, the parameter values for all the proposed models Weibull, Rayleigh, and Gamma, were estimated for the selected wind sites using one numerical estimation method (MLM) and three optimization algorithms (PSO, GWO, and WOA). As previously mentioned, three different performance indicators were used to test the accuracy of the estimated parameters.

Table 3. Distribution model parameters and performance indicator results based on numerical estimation method (MLM).

Site	Parameter and Indicator	Numerical Method (MLM)
		W-MLM	R-MLM	G-MLM
Queen Alia Airport	$k$	2.075	2.000	4.172
	$c$	5.272	3.697	1.114
	RMSE	0.02846	0.02904	0.02488
	R2	0.83287	0.82599	0.87232
	MAE	0.01502	0.01546	0.01417
Amman Civil Airport	$k$	4.277	2.000	2.191
	$c$	4.492	3.201	1.098
	RMSE	0.01848	0.01809	0.01082
	R2	0.93727	0.93985	0.97849
	MAE	0.00900	0.00944	0.00725
King Hussein Airport	$k$	2.806	2.000	6.339
	$c$	5.640	3.800	0.791
	RMSE	0.01760	0.03012	0.02257
	R2	0.93402	0.80674	0.89149
	MAE	0.00993	0.01663	0.01201
Irbid	$k$	2.462	2.000	6.588
	$c$	2.379	1.618	0.320
	RMSE	0.04226	0.07409	0.02086
	R2	0.93653	0.80491	0.98453
	MAE	0.02789	0.04231	0.01490
Mafraq	$k$	2.090	2.000	4.757
	$c$	4.269	2.987	0.792
	RMSE	0.03073	0.03214	0.02310
	R2	0.83973	0.82462	0.90938
	MAE	0.01169	0.01246	0.01062
Ma’an	$k$	2.033	2.000	4.592
	$c$	4.868	3.428	0.934
	RMSE	0.04812	0.04869	0.03512
	R2	0.71168	0.70478	0.84639
	MAE	0.02848	0.02873	0.01889
Safawi	$k$	2.312	2.000	5.276
	$c$	5.783	3.974	0.967
	RMSE	0.03341	0.03832	0.02301
	R2	0.80052	0.73750	0.90537
	MAE	0.02152	0.02536	0.01515
Irwaished	$k$	1.908	2.000	3.797
	$c$	4.764	3.412	1.107
	RMSE	0.03268	0.03135	0.02286
	R2	0.82588	0.83977	0.91482
	MAE	0.01941	0.01859	0.01388
Ghor Al-Safi	$k$	1.676	2.000	4.757
	$c$	2.683	2.065	0.503
	RMSE	0.04152	0.03221	0.01457
	R2	0.76558	0.85895	0.97114
	MAE	0.01203	0.01091	0.00481

summarizes the results related to the MLM estimation method. Through a close assessment of these results, it can be observed that the Gamma model based on the Maximum Likelihood Method (G-MLM) achieved the best results using all the indicator tests for all the candidate wind sites, except for King Hussein Airport. Based on the RMSE results, G-MLM recorded the lowest values among the other models. The lowest RMSE value was recorded by Amman Civil Airport, with a value of 0.01082. The MAE test values support the results of the RMSE, which confirmed the superiority of G-MLM over the other models. A closer inspection of the accuracy analysis results shows that the results obtained using the R² test indicate a high degree of consistency between the observations and the predicated PDFs, with a value of 0.9 for all the wind sites.

The results associated with King Hussein Airport are different from the other wind sites, in which the accuracy of the Weibull model based on the Maximum Likelihood Method (W-MLM) was the best model and the indicator values from the RMSE, R², and MAE tests were 0.0176, 0.934, and 0.0093, respectively.

Table 4. Distribution model parameters and performance indicator results based on optimization algorithms.

Site	Parameter and Indicator	Optimization Method
		W-PSO	W-GWO	W-WOA	R-PSO	R-GWO	R-WOA	G-PSO	G-GWO	G-WOA
Queen Alia Airport	k	2.220	2.221	2.220	2.000	2.000	2.000	4.036	4.034	4.024
	c	5.114	5.134	5.115	3.657	3.657	3.657	1.166	1.174	1.170
	RMSE	0.02783	0.02783	0.02783	0.02902	0.02902	0.02902	0.02481	0.02483	0.02481
	R2	0.84020	0.84016	0.84020	0.82627	0.82627	0.82627	0.87296	0.87285	0.87296
	MAE	0.01536	0.01527	0.01535	0.01554	0.01554	0.01554	0.01382	0.01368	0.01381
Amman Civil Airport	k	2.079	2.097	2.079	2.000	2.000	2.000	3.477	3.511	3.368
	c	4.307	4.311	4.308	3.062	3.061	3.062	1.149	1.141	1.194
	RMSE	0.01695	0.01697	0.01695	0.01732	0.01732	0.01732	0.01065	0.01067	0.01077
	R2	0.94722	0.94710	0.94722	0.94488	0.94488	0.94488	0.97917	0.97909	0.97869
	MAE	0.01068	0.01085	0.01067	0.00974	0.00974	0.00974	0.00704	0.00713	0.00690
King Hussein Airport	k	2.779	2.780	2.779	2.000	2.000	2.000	5.689	5.718	5.881
	c	5.933	5.886	5.932	4.217	4.217	4.217	0.971	0.968	0.938
	RMSE	0.01572	0.01577	0.01572	0.02751	0.02751	0.02751	0.01734	0.01734	0.01739
	R2	0.94736	0.94706	0.94736	0.83882	0.83882	0.83882	0.93597	0.93595	0.93559
	MAE	0.00997	0.00985	0.00997	0.01863	0.01863	0.01863	0.01122	0.01126	0.01119
Irbid	k	2.970	2.993	2.970	2.000	2.000	2.000	7.323	7.457	7.869
	c	2.309	2.307	2.309	1.720	1.720	1.720	0.301	0.296	0.280
	RMSE	0.02641	0.02644	0.02641	0.07216	0.07216	0.07216	0.00793	0.00802	0.00923
	R2	0.97522	0.97516	0.97522	0.81498	0.81498	0.81498	0.99777	0.99772	0.99698
	MAE	0.01888	0.01916	0.01887	0.04563	0.04563	0.04563	0.00592	0.00621	0.00714
Mafraq	k	2.440	2.434	2.445	2.000	2.000	2.000	5.331	5.296	5.690
	c	4.132	4.128	4.122	3.027	3.026	3.027	0.709	0.715	0.656
	RMSE	0.02830	0.02830	0.02830	0.03211	0.03211	0.03211	0.02251	0.02251	0.02267
	R2	0.86403	0.86402	0.86405	0.82496	0.82496	0.82496	0.91401	0.91399	0.91272
	MAE	0.01344	0.01345	0.01354	0.01225	0.01225	0.01225	0.01085	0.01078	0.01137
Ma’an	k	3.293	3.302	3.289	2.000	2.000	2.000	8.572	8.621	8.785
	c	4.093	4.084	4.094	3.222	3.222	3.222	0.458	0.456	0.446
	RMSE	0.02955	0.02955	0.02955	0.04800	0.04800	0.04800	0.02230	0.02230	0.02233
	R2	0.89126	0.89123	0.89126	0.71306	0.71306	0.71306	0.93807	0.93804	0.93791
	MAE	0.01998	0.01991	0.01999	0.02722	0.02722	0.02722	0.01577	0.01573	0.01547
Safawi	k	2.787	2.790	2.787	2.000	2.000	2.000	6.556	6.500	6.794
	c	5.223	5.229	5.228	3.994	3.993	3.994	0.751	0.759	0.721
	RMSE	0.02910	0.02910	0.02910	0.03832	0.03832	0.03832	0.02091	0.02092	0.02097
	R2	0.84863	0.84863	0.84863	0.73757	0.73757	0.73757	0.92185	0.92182	0.92140
	MAE	0.02252	0.02253	0.02252	0.02531	0.02531	0.02531	0.01638	0.01633	0.01658
Irwaished	k	2.303	2.317	2.301	2.000	2.000	2.000	4.515	4.466	4.409
	c	4.419	4.416	4.422	3.202	3.201	3.202	0.905	0.921	0.931
	RMSE	0.02746	0.02747	0.02746	0.03033	0.03033	0.03033	0.02126	0.02128	0.02129
	R2	0.87706	0.87700	0.87705	0.84996	0.84996	0.84996	0.92630	0.92618	0.92607
	MAE	0.01779	0.01794	0.01776	0.01864	0.01864	0.01864	0.01456	0.01439	0.01443
Ghor Al Safi	k	2.911	2.901	2.910	2.000	2.000	2.000	6.865	6.736	6.434
	c	2.510	2.511	2.510	1.879	1.879	1.879	0.349	0.355	0.375
	RMSE	0.01311	0.01312	0.01311	0.03032	0.03032	0.03032	0.00788	0.00793	0.00815
	R2	0.97662	0.97661	0.97662	0.87495	0.87495	0.87495	0.99155	0.99144	0.99097
	MAE	0.00468	0.00467	0.00469	0.00926	0.00926	0.00926	0.00287	0.00304	0.00313

provides the results of all the scenarios associated with the optimization methods. Through a close look at these results, it can be observed that the Gamma model achieved the best results using all the indicator tests for all the selected wind sites, except for King Hussein Airport. Based on the RMSE, the PSO method recorded the lowest values among the other methods in all the sites. The lowest RMSE value was recorded by Ghor Al Safi, with a value of 0.00788. The R² test values support the results of the RMSE, which confirmed the superiority of the PSO method over the other methods. A closer inspection of the R² results shows a high degree of consistency between the observations and the predicted PDFs, with values greater than 0.9 for most sites. Contrary to the RMSE and R² results, the MAE results show that the GWO method achieved the best results in five sites, Queen Alia Airport, King Hussein Airport, Mafraq, Safawi, and Irwaished (see Table 4). The probability distribution function (PDF) and the observation histograms are presented for all the sites based on the optimization methods (see Figure 6). It can be observed from this figure that Gamma model (lines shaded in red color) achieved the best fit in most sites.

Table 5. Comparison between the best optimization method (PSO) and numerical method (MLM) according to parameters, indicators, power density and total available energy.

Site	Best Method	$\mathit{k}$	$\mathit{c}$	RMSE	R2	MAE	${\mathit{E}}_{\mathit{D}}$ (W/m2)	${\mathit{E}}_{\mathit{T}}$ (kWh/m2)
Queen Alia Airport	G-PSO	4.036	1.166	0.02481	0.87296	0.01382	118.98	1042.28
	G-MLM	4.172	1.114	0.02488	0.87232	0.01417	112.81	988.21
Amman Civil Airport	G-PSO	3.477	1.149	0.01065	0.97917	0.00704	79.26	694.28
	G-MLM	2.191	1.098	0.01082	0.97849	0.00725	75.64	662.62
King Hussein Airport	W-PSO	2.779	5.933	0.01572	0.94736	0.00997	132.53	1161.01
	W-MLM	2.806	5.640	0.01760	0.93402	0.00993	113.30	992.54
Irbid	G-PSO	7.323	0.301	0.00793	0.99777	0.00592	9.53	83.48
	G-MLM	6.588	0.320	0.02086	0.98453	0.01490	8.64	75.70
Mafraq	G-PSO	5.331	0.709	0.02251	0.91401	0.01085	54.04	473.39
	G-MLM	4.757	0.792	0.02310	0.90938	0.01062	56.38	493.92
Ma’an	G-PSO	8.572	0.458	0.02230	0.93807	0.01577	51.17	448.28
	G-MLM	4.592	0.934	0.03512	0.84639	0.01388	84.47	739.93
Safawi	G-PSO	6.556	0.751	0.02091	0.92185	0.01638	110.04	963.93
	G-MLM	5.276	0.967	0.02301	0.90537	0.01515	133.60	1170.33
Irwaished	G-PSO	4.515	0.905	0.02126	0.92630	0.01456	73.75	646.06
	G-MLM	3.797	1.107	0.02286	0.91482	0.01388	87.66	767.87
Ghor Al-Safi	G-PSO	6.865	0.349	0.00788	0.99155	0.00287	12.49	109.44
	G-MLM	4.757	0.503	0.01457	0.97114	0.00481	14.43	126.36

presents a comparison between the best optimization method (PSO) and the numerical method (MLM). It is clear that PSO showed a clear superiority over the MLM in estimating parameters in all wind sites. The highest R² value recorded by the Gamma model based on G-PSO was 0.99777, while the highest value recorded by the G-MLM did not exceed 0.98500 (see Irbid wind site in Table 5). According to the RMSE and R² results, the PSO method achieved the best performance in all the sites. However, the results differed remarkably according to MAE indicator: MLM was the most accurate method in five sites, while PSO was the best in the remaining sites. In addition, Table 5 provides the wind power density and total available energy of the wind regimes for all the sites. The results according to the PSO method correspond to those provided by the MLM, but with noticeable changes in power density values. The highest value of wind power density was achieved by the King Hussein Airport, Queen Alia Airport and Safawi sites. On the other hand, Irbid achieved the lowest value of wind power density, followed by Ghor Al Safi. Figure 7 represents the PDF curves based on PSO and MLM, in addition to observation histograms. It can be observed that PSO achieved the best fit with the observed values, which is the red line. This confirms that PSO was the optimal estimation method for all the sites.

5. Conclusions

This paper presented a new assessment process of wind energy resources for nine wind sites in Jordan: Queen Alia Airport, Civil Amman Airport, King Hussein Airport, Irbid, Mafraq, Ma’an, Ghor El Safi, Safawi, and Irwaished. The wind energy assessment was performed using Weibull, Rayleigh, and Gamma distribution functions. This assessment was based on the estimation of two vital parameters of the wind regime: wind power density and total wind energy. This assessment can be applied in any wind site in the world, so a decision can be made whether a wind farm can be established in a specific wind site. Three statistical distribution models were utilized to implement the available wind speed data: Weibull, Rayleigh, and Gamma distribution functions. The Maximum Likelihood Method, Particle Swarm Optimization, Grey Wolf Optimizer, and Whale Optimization Algorithm were used to estimate the parameters associated with each distribution model. Three performance indicators were investigated to choose the optimal distribution model: Root Mean Square Error, Coefficient of Determination, and Mean Absolute Error. The highest wind power density was achieved by the King Hussein Airport wind site followed by Queen Alia Airport, while Irbid achieved the lowest values of wind power density, followed by Ghor El Safi.