For instance, the study in [20] conducts a technical assessment in two sites in Galati county, Romania. The wind speed data are characterized using Weibull and Rayleigh distributions, where the MOM is used to estimate their parameters. Study results reveal that the Weibull distribution best fits the wind speed in the two sites, while the Rayleigh distribution generates significant fitting errors. Bidaoui et al. [21] employ Weibull and Rayleigh distributions to evaluate the potential of wind energy in five remote areas in Northern Morocco, namely Larach, Tangier, Tetuan, Al-Hocima, and Nador. The Weibull distribution shows the superiority in accurately fitting the observed wind speed data at all the considered sites with low Root Mean Square Error (RMSE) values ranging between 0.0022 to 0.0004 m/s. The authors in [22] utilize Weibull distribution to analyze the wind speed in the Al-Salman site, Iraq. The shape and scale parameters of the Weibull PDF are estimated using the MLM. Results show that c and k values varied from 1.8 to 3.2 and from 5.93 to 8.3 m/s over various periods, respectively. On the other hand, results indicate that the average wind speed at 50 m above ground level (AGL) is 5.93 m/s.

Weibull distribution has been utilized in the techno-economic feasibility analysis of wind energy generation to evaluate the wind temporal and spatial variability and justify wind energy projects. The technical analyses use Weibull distribution to determine the best wind turbine technology for a specific location, wind power density, yearly energy output, and capacity factor (CF). In addition, Weibull distribution helps the economic assessments in determining the energy cost and the payback period of wind projects. For instance, the authors in [23] utilize EM, MLM, MLMLM, EPM, and GM to estimate Weibull parameters. These parameters are employed to determine the energy cost, CF, yearly energy yield, and wind power density for Hawke’s Bay in China. Statistical analysis shows that at 30, 60, and 80 m AGL, the yearly wind speeds are 5.04, 5.84, and 6.05 m/s, respectively, while the average power densities are 184.0, 231.5, and 307.5 W/m². The lowest energy cost based on 2.3 MW wind turbine generators (WTG) is 0.056 US$/kWh. In [24], the authors also evaluate the potential of wind power generation in the central region of Thailand. Weibull distribution is used to carry out techno-economic assessments and accurate feed-in-tariff of a 15 MW wind farm. Results exhibit that the annual wind speed at the study location is 5.8 m/s at 120 m AGL, while annual energy production (AEP) and CF for the 15 MW power plant are speculated to be 41 GWh/year and 30%, respectively. Finally, the Levelized Cost of Energy (LCOE) is determined at 0.093 US$/kWh.

In addition, wind energy for electricity is assessed in the Republic of Djibouti by authors in [25]. Wind speed data were collected at five meteorological stations from 2015 to 2019. Weibull distribution is used to evaluate the economic and technical feasibility of five wind farms with a capacity of 450 MW. The mean wind speed is between 5.52 and 9.01 m/s for the selected five locations. The estimated annual electrical energy output from the proposed wind farms is 1739 GWh, with LCOE varying from 6.94 to 13.30 US cents/kWh. Adnan et al. [26] use GM, EM, EPF, and MLM to obtain the two parameters of Weibull distribution in the Umerkot and Sujawal districts of Pakistan. Results show low statistical errors with EM, EPF, and MLM. Accordingly, the optimal combination of the shape and scale parameters are used to analyze the energy production of various wind turbine technology with rated power ranging between 600 to 2500 kW. Regarding the wind turbines, Nordes N90/2500 produces the most wind energy in Umerkot and Sujawal, with associated energy costs of 0.074 and 0.056 $/kWh, respectively. From the above studies, however, the literature lacks a study that compares the performance of CN and IOA to assess the technical and economic feasibility of wind energy production. Younis et al. [27] examine the efficacy of various WTG when used in various Sultanate of Oman locations. The authors calculate internal and external factors and show how they influence small-scale energy WT using a fuzzy analytical hierarchy process technique. According to the research, the small WTG technology has the potential to be useful for irrigation, homes, schools, and colleges.

Saudi Arabia has roughly 16% of the total world’s oil reserves and is the largest oil producer and exporter of the total petroleum liquid [28]. On the other hand, Saudi Arabia has the potential for wind and sun energy. For wind energy, the process of wind data recording and collection in Saudi Arabia began in 1970 [29]. The first work concerning wind data was done by Ansari et al. [30]. Rehman et al. [29] evaluated the potential of wind energy by assessing the cost of wind power utilizing three WTG at 20 locations in Saudi Arabia. The results showed that the minimum cost of kWh utilizing 2500, 1300, and 600 kW WTG was 0.0234, 0.0295, and 0.0438 US$/kWh at Yanbo, while the maximum appeared in Nejran with values of 0.0706, 0.0829, and 0.121 US$/kWh. In addition, Rehmana et al. [31] studied the potential of wind for pumping water in isolated areas not connected to the main power grid of Saudi Arabia. Results point out that a wind turbine with a size of 2.5 kW is the most suitable for powering the water pump at all the selected sites. It is also found that the cost of water pumping at the three locations is as low as 1.28 US cents/m³.

Most wind energy assessments in Saudi studies use CN methods to estimate Weibull parameters and accordingly evaluate the techno-economic assessments of wind energy production. Nevertheless, the advent of the IOAs revealed their capacity to obtain optimal Weibull parameters and represent wind speed data more accurately, thus, more precise wind energy evaluation. Therefore, the main objective behind this research is to conduct technical and economic feasibility studies for five sites in northern Saudi Arabia. This study proposes six wind turbine technologies with different wind speed characteristics and rated powers. The primary contributions of this research work are as follows:

Develop a framework to calculate the characteristics of the Weibull distribution to describe the wind speed at five different locations in Saudi Arabia: Aljouf, Rafha, Tabuk, Turaif, and Yanbo.

The paper is organized as follows: Section 2 explains the framework of the study and wind speed data source. In Section 3, Weibull PDF is presented together with the estimation approaches: CN and IOA. Section 4 describes the statistical indicators used to evaluate the accuracy of the study models. Section 5 discusses the wind power extrapolation at hub height, while Section 6 exhibits the economics analysis of wind turbines. The discussions and results of the comparison are presented in Section 7. Finally, the study concludes in Section 8.

The main goal of this study is to present a framework for assessing the wind energy potential at five locations in northern Saudi Arabia, namely Aljouf, Rafha, Tabuk, Turaif, and Yanbo. The proposed framework evaluates the performance of five CN and IOA estimation methods in obtaining the two parameters of Weibull distribution. In addition, a comparative analysis is conducted using technical and economic feasibility studies to assess the wind energy resources at the considered sites. Therefore, the proposed framework is shown to be accurate, reliable, simple to implement, and can help evaluate wind energy in different geographic areas.

This feasibility study conducts a comparative analysis between five CN and five IOA methods to estimate Weibull distribution parameters. Fig. 1 presents the overall framework adopted. The main steps of the proposed framework are as follows:

Step 1: Data collection: the wind speed data are initially collected. Afterward, the data preprocessing techniques are applied to organize the data by looking for missing values, noisy data, and other abnormalities before running the estimation methods.

Step 2: Statistical characteristics: the main objective of this step is to provide insights into the wind regimes in each site and approve the performance of the proposed algorithms.

Step 3: Weibull parameters estimation: the CN and IOA methods are applied to estimate c and k of the Weibull distribution.

Step 4: Building the estimation models: by using the best parameters mentioned in Step 3, ten models are generated for each considered site.

Step 5: Results comparison: the models generated by CN and IOA methods are evaluated utilizing RMSE, Coefficient of Determination (R²), and Mean Absolute Error (MAE).

Step 6: Annual energy: based on the comparison in Step 5, the best Weibull PDF function findings are used to estimate the annual energy produced by wind turbines.

Step 7: Energy cost: the feasible energy cost per kilowatt hour (kWh) for the chosen wind turbine is then calculated using the annual energy estimate.

The subsections below provide a detailed explanation of each step.

The wind data used in this study is obtained from the National Climatic Data Center, USA, Department of Commerce [32]. In this study, the wind speed regimes of five Saudi areas located in the northern parts are investigated, namely Aljouf, Rafha, Tabuk, Turaif, and Yanbo. These locations are chosen for the wind analysis primarily because they are spread out geographically in the northern parts of Saudi Arabia, where the wind speed is predominant. To accomplish a very accurate assessment of wind power, avoid uncertainty in the wind, and justify the economic feasibility of wind deployment, long-term averaged-daily wind speed data are considered in this study covering 40 years (1977–2017). Table 1 exhibits the geographic information and anemometer height at each site. Fig. 2 displays the Saudi Arabia wind speed map, while Fig. 3 shows the monthly mean of wind speed data at the five study locations.

Some statistics are calculated at the measurement heights to comprehend and analyze the wind speed data. Table 2 lists the statistics values, including Mean, Variance, Standard Deviation, Skewness, Kurtosis, and Maximum wind speed value. The Mean value tells about the central tendency of the wind speed data. Variance and Standard Deviations (SD) provide information about how observed wind speed deviate from the central value. In addition, to understand the pattern of the observed frequency distribution, Skewness and Kurtosis are utilized. The symmetrical characteristic of the wind speed data is measured by Skewness, while the steep degree of data is described by the Kurtosis value [12].

The following subsections explain the CN methods used to estimate the shape k and the scale c parameters of the Weibull PDF [35–37].

The metaheuristic optimization algorithms are nature-inspired techniques. The examined algorithms include PSO, GA, DE, COA, and SSO. With these algorithms, this study attempts to minimize the difference between the measured frequency distribution of the wind speed and theoretical values generated by the considered PDFs. Hence, the objective function is as follows: (15)Fitness(vi)=12∑i=0.5n(fm(vi)−fPDF(vi,θi))2where fm(vi) is the measured frequency distribution of wind speed class, fPDF(vi,θi).

Fig. 4 depicts the process of optimizing the Weibull parameters from the scope of the PSO algorithm. The c and k are generated, and their values evolve until we obtain the lowest error values, represented by Eq. (15). The optimization algorithms are compared to estimate the Weibull parameters. The outcomes of the algorithms are considered after 50 runs, each with 1000 iterations. The median values of the 50 runs were used to select the final fitness values. Fig. 7 displays the convergence rates of the algorithms to obtain the optimal set of Weibull parameters in the selected sites.

Fig. 5 shows the Weibull frequency distribution using CN methods and IOA with the original wind speed data histogram. Comparing the performance of CN methods and IOAs and according to Tables 4 and 5, which summarize the goodness of fit tests results of theoretical Weibull distributions, the IOAs outperformed CN methods in obtaining the optimal two-Weibull parameters and in describing the frequencies of actual wind data. In Table 4, the results of CN methods indicate that LSM is the least precise method among other approaches, while the best CN estimation methods for all five sites are ranked as EM, MOM, MLM, and EPFM, respectively.

In Table 5 and Fig. 7, results revealed that COA is the less accurate and the slowest algorithm to obtain the Weibull parameters. Yet, it performs better in tuning c and k than all CN methods. PSO, GA, DE, and SSO algorithms have similar performance in estimating Weibull parameters, resulting in high fitting accuracy. In Aljouf, for example, the RMSE, R², and MAEare 0.00565, 0.98453, and 0.00429, respectively. Therefore, for CN methods, the scale and shape parameters of Weibull for all five areas, Aljouf, Rafha, Tabuk, Turaif, and Yanbo, are determined by EM to carry out the technical and economic assessments and to compare its results with those obtained by SSO. Table 6 lists the Weibull parameters and PLC attained from EM and SSO at all Saudi sites. Fig. 6 shows the coefficient of determination values of the Weibull distribution using different models. The R² values of Weibull using LSM, EM, PSO, and COA are 0.916643, 0.961082, 0.980825, and 0.980280. This indicates that the models generated by IOAs are more accurate than CN methods.

Table 7 exhibits the energy output in MWh and the CF. This Table shows that the range of CF is between 10.86%–58.21% and 8.77%–56.52% using EM methods and SSO, respectively. For all Saudi sites, the CF of all six wind turbines examined in this study has higher values in the case of using Weibull parameters obtained from EM compared to those attained by SSO. That means that the annual energy output of wind turbines is overestimated with CN approaches than the intelligent optimization methods. For instance, WT4 output energy in Yanbo is 10228.71 MWh when employing values calculated from EM, while it is found to be 9140.67 MWh with SSO.

In addition, Table 7 illustrates that the values of the cost of energy (COE) of all wind turbines at the five Saudi locations have low $/MWh with the best model obtained by EM compared with the best model in IOA. Since SSO results provide high fitting accuracy to the original wind speed data, the COE prices are better estimated utilizing the evaluation conducted by SSO. Therefore, in terms of the annual energy output of the four wind turbines, the range is between 4422.42 to 14875.74 MW in Aljouf, 3493.37 to 12660.65 MW in Rafha, 2284.23 to 9668.24 MW in Tabuk, 4453.38 MW to 15664 in Turaif, and 3351.75 to 13081.5 MW in Yanbo. The highest annual energy output at all Saudi sites was 15664 MW in Turaif with the WT5 machine model, while the lowest was 2284.23 MW in Tabuk using WT1. WT5 generates the maximum energy for all Saudi sites compared to all other wind turbine technologies, making this WTG the optimal one to be installed.

In addition, Table 7 presents the COE at each site using the six wind turbine models. This Table shows that the lowest cost of electricity was found to be $0.016906/kW in Turaif with WT5, and the highest price was obtained to be $0.11067/kW in Tabuk with the WT6 model. Furthermore, for the WT5, the COE was found not to exceed $0.02739/kW for all five considered sites.