Intelligent Optimized Wind Turbine Cost Analysis for Different Wind Sites in Jordan

: Choosing the right wind site and estimating the extracted energy of the wind turbines are essential to successfully establishing a wind farm in a specific wind site. In this paper, a method for estimating the extracted energy of the wind farms using several mathematical models is proposed. The estimating method, which was based on five wind turbines, Q 1 , Q 2 , Q 3 , Q 4 , and Q 5 and three wind distribution models, gamma, Weibull, and Rayleigh, was used to suggest suitable specifications of a wind turbine for a specific wind site and maximize the extracted energy of the proposed wind farm. An optimization problem, developed for this purpose, was solved using the whale optimization algorithm (WOA). The suggested method was tested using several potential wind sites in Jordan. The proposed wind farms at these sites achieved the maximum extracted energy, maximum capacity factor ( CF ), and minimum levelized cost of energy ( LCoE ) based on the solution of the developed optimization problem. The developed model with Q 3 and the Rayleigh distribution function was validated with real measurement data from several wind farms in Jordan. Error analysis showed that the difference between the measured and estimated energy was less than 20%. The study validated the provided model, which can now be utilized routinely for the assessment of wind energy potential at a specific wind site.


Introduction
Throughout history, humanity has always strived to maximize the utilization of natural resources. A good illustration of how this has been accomplished is through renewable energy resources. Renewable energy has become an urgent and critical requirement to address the concerns caused by using fossil fuels.
Wind power is now the most cost-competitive technology all over the world. In particular, the global wind sector hit a new high in 2017 [1]. This increase in wind capacity was attributed to a number of factors by the Global Wind Energy Council (GWEC), including a) the introduction and deployment of a new generation of turbines with a larger shelf area and thus higher production; b) increasing investor confidence; c) technology and management improvement; and d) industry maturity.
Wind speed and direction cannot be predicted precisely because of wind's stochastic nature [2]. The natural behavior of wind at a prospective site must be observed and evaluated to identify wind characteristics. Once the wind characteristics have been recognized, the components of the wind energy conversion system (WECS) can be efficiently developed. As a result, a wind energy assessment procedure can be completed flawlessly [3].
In general, evaluating wind resources involves four processes. The first stage entails measuring and gathering wind data from meteorological stations or airports. Wind data are often recorded every ten minutes at a height of 10 meters, which is considered standard. The second stage comprises utilizing statistical distribution models to analyze the collected data in order to establish the frequency distribution of average wind velocity for the candidate site over a certain time period. Each distribution model has a set of parameters that must be assigned using a combination of numerical approaches and optimization algorithms. By comparing the available distribution models, the best distribution function can be determined. Several goodness of fit indices, such as root mean square error (RMSE), coefficient of determination (R 2 ), and others, are used to do this. The distribution model can be depicted using a probability distribution function (PDF). The distribution function and the PV curve are used to analyze the wind energy that could be extracted from a certain wind turbine existing in a potential wind site. At the 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.
Many parametric distribution models have been used to evaluate wind energy resources, including the Weibull [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], Rayleigh [10][11][12][14][15][16][17][18][19], gamma [5,10], log-normal [10,13], log-logistic [13], and other distributions. The Weibull distribution has been used by the majority of researchers. In [10], Jiang et al. compared the Weibull distribution to the Rayleigh, gamma, and log-normal distributions to assess the energy potential of low wind speeds in China. When optimization methods were applied to find its parameters, the Weibull distribution was the best option. Wang et al., in [11], determined the Weibull model to be the best acceptable distribution among the five chosen distribution models after examining it using the RMSE. Wu et al., in [13], employed the Weibull, log-logistic, and log-normal distributions to estimate wind energy at typical sites in Inner Mongolia and China. The log-logistic and log-normal distributions performed better than the Weibull distribution, which had the lowest results. The authors in [14] presented a detailed review of 46 publications published between 2010 and 2018. In this investigation, the Weibull distribution was found to be superior (44 out of the 46 studies used the Weibull distribution). In [20], Li et al. compared the characteristics of onshore and offshore wind, as well as their wind energy potentials, in two locations along China's southeast coast. The data showed that offshore wind energy was more available than onshore wind energy, and the authors confirmed the accuracy of applying the Weibull distribution for both onshore and offshore wind energy. In [21], Bilir et al. employed the Weibull distribution to analyze power density based on wind data collected over a year from a measurement station on the Atlm University campus area in Ankara, Turkey. However, the Weibull distribution does not always consider the optimal alternative [14,[22][23][24][25]. According to [14], a variety of mixture distributions, including the bimodal Weibull function (WW), truncated normal-Weibull function (NW), gamma-Weibull function (GW), and mixed truncated normal function (NN), outperformed the standard Weibull distribution.
In recent years, metaheuristic optimization approaches have been used to estimate the parameters of various distribution models. Some examples of such methods are particle swarm optimization (PSO) [27][28][29][30], cuckoo search optimization (CS) [14,29], genetic algorithm (GA) [26,28], differential evolution algorithm (DEA) [28], and grey wolf optimizer (GWO) [26]. The authors in [29] evaluated three optimization techniques, PSO, CS, and GWO, and compared them with four numerical methodologies. The performance of the algorithms was generally excellent, with GWO being the most precise technique. Saeed. et al. in [26] proposed artificial intelligence (AI)-based optimization techniques based on the Chebyshev measure for assessing wind potential at a site near Pakistan's coastline region. According to their findings, AI optimization outperformed numerical approaches by a factor of ten. In [27], a new metaheuristic optimization algorithm method called social spider optimization (SSO) was recommended for assessing wind potential in seven areas in Saudi Arabia. According to the results, the proposed technique outperformed the other heuristic methods. However, several drawbacks limited the use of the parametric distribution models. One such drawback was the need for using estimating methods to determine the values of the parameters accurately. Therefore, some academics have suggested nonparametric distribution models. The most well-known method employed is the kernel density model (KDM) [5]. Normal scale (NS), plug-in, biased cross-validation, and least-square cross-validation were the four bandwidth selections presented by the authors of [5]. For comparisons with the KDE model, popular parametric distribution models were also introduced. The performance and resilience of both parametric and KDE models were examined exhaustively on a regional scale using five-year day-average wind speed data from 698 wind stations across China. Wind power density (WPD) and wind turbine power output (WTPO), which are the priorities in WEA, were then calculated based on the estimated PDWS models. The four KDE models outperformed the parametric models in fitting the PDWS, according to the results of four individual metrics. In comparison with the other three KDE models, the KDE-NS model performed the best.
The economic aspect is among the most important for the wind energy project [31][32][33][34][35][36]. Several shortcomings in the cost analysis of wind power projects have been identified in the literature. Some studies have used simplified cost-analysis models [35]. Such models are simple and easy to evaluate; however, they are free of detailed economic parameters and have a low accuracy level. Therefore, several research studies have used detailed economic models that are intrinsically about the time value of money [36][37][38][39][40][41][42][43][44][45][46][47][48]. Nevertheless, these models assume that the capital cost is constant for different energy production. In addition, the cost of the turbine system is not detailed for each component. Moreover, in these studies, the turbine selection process was not defined well but based on a trial-and-error procedure [15,23,36]. Alsaad, in [35], presented a study to assess wind energy resources in four selected sites in Jordan. The cost model adopted in this study was based on a net profit calculation. This model involved subtracting the total turbine cost from the total value of the energy sold, taking into account the salvage value throughout the operational period of the project. The weakness of this model is that it did not take into account the time value of money. This problem was avoided in [23,36]. The present value cost (PVC) model was used to calculate the cost of a wind turbine system. The limitation of this model is that the turbine price is specified as a particular USD/kWh rate multiplied by the turbine's rated power, and it is not adequately detailed. Therefore, the total cost of the turbine cannot be accurately predicted. Perkin et al., in [49], suggested an optimal approach for choosing wind turbine models in Iceland. This approach was based on utilizing the blade element theory and a detailed cost-analysis model. An optimization problem was established based on minimizing the cost of unit energy. The optimization variables were rotor length, rated power, hub height, pitch angle range, and rotations per minute. The same procedure was followed by the authors in [50], in which an optimal model was proposed to optimize the wind turbine parameters and achieve the minimum cost of unit energy for three sites in Iran.
This paper aims to fill the gap by providing a comprehensive study on the assessment of wind energy potential in Jordan. The study addressed the topic of wind energy estimation for wind turbine systems. Furthermore, the economic aspects of the wind systems installed at the selected wind sites were studied. This study addressed the previously identified shortcomings of cost analyses. It also presented an optimal cost analysis intended to minimize the cost of unit energy using the whale optimization algorithm (WOA). In addition, the detailed turbine cost model developed by the U.S. National Renewable Energy Laboratory (NREL) is discussed and was used in this study [51].
The rest of the paper is organized as follows: Section 2 describes the evolution of wind energy in Jordan; the energy extracted from wind turbines is presented in Section 3; cost analysis of the designed systems is presented in sections 4 and 5; the optimization problem is defined in Section 6; extrapolation method of wind speed is illustrated in Section 7; results and discussion are presented in Section 8; real measurements and the validation process are discussed in Section 9; and conclusions are presented in Section 10.

Evolution of Wind Energy in Jordan
In 1988, the city of Al-Ibrahimia built Jordan's first wind farm. It consists of four 320 kW wind turbines. In 1996, in Hofa, Jordan, the second wind farm was established. It has a total capacity of 1.125 Mw and is made up of five wind turbines. Two new wind farms have recently been built. The first is in Tafila province, with 38 turbines rated at 3.075 MW apiece and a total capacity of 117 Mw. The second wind farm is in Ma'an, with seven turbines rated at two MW each and a total capacity of 14 MW.
The evolution of Jordan's wind energy capacity is depicted in Figure 1. Wind farms that were operational in 2017 produced 132 MW of energy. Wind farms with a capacity of 155 MW are now being built and will be connected to the grid soon [43]. Table 1 provides additional information on Jordanian wind farms that have been operated or were currently under development between 1988 and 2017.

Energy Extracted from Different Wind Turbine Models
The power of the wind passing through the wind turbine PT can be expressed as follows [52][53][54]: where ρa is the air density in (kg/m 3 ), A is the rotor swept area in(m 2 ) and v is the wind speed (m/s). The output power generated by the wind turbine can be given in terms of the turbine power coefficient (Cp), as follows [55]: where Cp is the blade aerodynamic efficiency factor, ηm and ηg are gearbox and generator efficiencies, respectively. These factors are given by the manufacturer depending on blade design, blade shape and type of wind turbine [47]. Each wind turbine has its own Power-Velocity (P-V) curve, which consists of two performance regions: performance region 1 (non-linear region) and performance region 2 (constant region). Figure 2 shows the P-V curve of a typical turbine model and its performance regions. The non-linear region is expressed using several mathematical expressions in terms of rated power (Pv) cut-in speed (vi), rated speed (vr), and cut-out speed (vo) [29].
where Q(v) represents the mathematical expression of the non-linear region of the P-V curve, which can be linear, quadratic, cubic, or exponential [9,56]. The linear expression shows several deficiencies and less accuracy according to [56]. Therefore, in this paper five different expressions, excluding the linear model, are used to represent the non-linear region of the turbine model [56]: where α is a constant value in terms of rated speed (vr), α=0.70335986vr -0.00049995. And: Therefore, the energy produced by the wind turbine in both performance regions can be calculated as follows [3]: where T is the number of hours in a specific period, Eir is the energy produced by the wind turbine in performance region one in MWh. Ero is the energy produced by the wind turbine in performance region two in MWh, Etotal is the total energy produced by the wind turbine in the two performance regions in MWh and μ is the total turbine losses, which comprise power converter losses, electrical grid losses, and soiling losses, in addition to some losses that are related to the turbine design and wind distribution [57]. The ability of the wind turbine to produce electricity can be examined by the definition of the capacity factor (CF). This factor is the major indicator to choosing a proper wind turbine in a specific wind site and it can be expressed as follows [52].
In this paper, using the power curve model presented by (4)-(8), the total energy extracted by the wind turbine (ETotal) is derived based on Weibull and Gamma distribution functions. This will be presented in the following subsections.

Energy Extracted by Q1(v) Based on Weibull Distribution
The distribution function of Weibull model is expressed as follows [57]: where and refer to shape and scale parameters, respectively. Substitute (4) and (17) in (15) and simplify, yields: where Γ(a, x) is the upper incomplete gamma function.

Energy Extracted by Q1(v) Based on Gamma Distribution
The distribution function of Gamma model is expressed as follows [57].

Energy Extracted by Q2(v) Based on Weibull and Gamma Distribution
Similarly, the total energy extracted by Q2(v)has been calculated for each distribution model. Substitute (5) and (17) in (15) and simplify, yields: where EQ2_w is the total energy extracted by the turbine model Q2 and Weibull distribution. Additionally, substitute (5) and (19) in (15) and simplify to find EQ2_G: where EQ2_G is the total energy extracted by the turbine model Q2 and Gamma distribution.

Energy Extracted by Q3(v) Based on Weibull and Gamma Distribution
The total energy extracted by the exponential power curve Q3(v)has been calculated for each distribution model. Substitute (6) and (17) in (15) and simplify, yields: where EQ2_w is the total energy extracted by the turbine model Q2 and Weibull distribution. Additionally, substitute (6) and (19) in (15) and simplify to find EQ3_G: where EQ3_G is the total energy extracted by the turbine model Q3 and Gamma distribution.

Energy Extracted by Q4(v) Based on Weibull and Gamma Distribution
The total energy produced by the cubic power curve Q4(v)has been calculated for each distribution model. Substitute (7) and (17) in (15) and simplify, yields: where EQ4_w is the total energy extracted by the turbine model Q4 and Weibull distribution. Additionally, substitute (7) and (19) in (15) and simplify to find EQ4_G: where EQ4_G is the total energy extracted by the turbine model Q4 and Gamma distribution.

Energy Extracted by Q5(v) Based on Weibull and Gamma Distribution
Finally, the total energy produced by Q5(v) has been calculated for each distribution model. Substitute (8) and (17) in (15) and simplify, yields: where EQ5_w is the total energy extracted by the turbine model Q5 and Weibull distribution. Additionally, substitute (8) and (19) in (15) and simplify to find EQ5_G: where EQ5_G is the total energy extracted by the turbine model Q5 and Gamma distribution.

Cost Analysis
The Net Present Value CostNPVC method, which can be mathematically presented as in [51], is used to perform the cost analysis in this study. where,

Pa=(CC-Pd) CRF
Additionally, Pa and Pd are the annual and down payments on system cost, respectively. Cc is the capital cost of the system. and Pd is the down payment on system cost. CRF is the capital recovery factor, based on the loan interest rate(b), rather than the discount rate (r). i is the inflation rate in (%), Nis the loan period, Lis the system lifetime, foM is the annual operating and maintenance cost (fraction of the capital cost) and Y(K, l)is a function used to obtain the present value of a series of payments which can be evaluated by (31): For simplifications and research purposes, it is assumed that Pd and b are equal to zero. By applying (31) and considering the previous assumptions, (29) can be rewritten as follows: Accordingly, the Levelized cost of energy (LCoE) can be expressed as follows [51]: where CRF can be expressed as follows [47]:

Capital Cost Model and Its Correction Factor
The capital cost model can be divided into four main parts: (a) turbine system cost, (b) network connection cost, (c) civil work cost, and (d) other costs, including engineering permits, consultancy, transactions, and monitoring systems [46,[58][59][60][61][62].
The original capital cost model which was developed by the National Renewable Energy Laboratory (NREL) has been evaluated based on the value of the US dollar in 2002 [51]. Therefore, in this study, the resultant capital cost of this model is corrected by a factor of 1.6. This correction factor was used to consider the difference in currency value between the 2002 cost model (NREL cost model) and the value of currency during the periods at which the wind projects were built. It has been calculated as follows: the actual turbine cost for each project, which is given by several sources [63][64][65][66][67][68][69][70][71][72][73][74][75], was divided by the turbine cost and evaluated based on the NREL model to find the individual correction factor for each project. Then, an average value of the correction factors for all projects was calculated, as illustrated in Table 2.

Optimization Problem
In this study, nine wind sites in Jordan were selected for wind farms installation purposes. These wind sites are Queen Alia Airport, Amman Civil Airport, King Hussein Airport, Irbid, Mafraq, Ma'an, Safawi, Irwaished, and Ghor Es Safi. They have been se-lected based on two main factors: the first one is the geographical distribution which allows us to carry out a comprehensive study that includes various regions in Jordan (from north, south, east, west, and center). The second factor is the average wind speed in these wind sites, which is considered to be strong and can potentially be compared with other wind sites. A map showing the locations of these wind sites in Jordan is presented in Figure 3. Based on the Global Wind Energy Atlas (GWEA), the recorded wind speed is the highest in these wind sites, as illustrated in Table 3. Therefore, in our study wind turbines with specific features are suggested for the proposed wind farms to obtain maximum extracted energy, maximum CF, and minimum LCoE. To solve the developed optimization problem, a whale optimization algorithm is used to obtain the desired objective functions for the selected wind sites.
According to (37), there are six optimization variables in the Levelized Cost of Energy ( ) equation which are ( , , , , , ). The number of variables can be reduced to only two optimization variables ( , ) by making some manipulations and assumptions which can be summarized in the following points: By rearranging (2), the rotor radius can be represented in terms of rated power and rated speed, as expressed in (35): The hub height can be expressed as a function of the rotor radius by the following empirical formula, according to European Wind Energy Association (EWEA) [76][77][78][79][80]: Most of the commercial wind turbines have cut-in speed in the range of 3-4 m/s(assumed vi=3.5 m/s), and a cut-out speed of 25m/s. By considering the previous points and assumptions, the LCoE can be simplified in terms of rated power and rated speed, as follows: The entire steps of the optimization problem are summarized in a flowchart illustrated in Figure 4.

Extrapolation of Wind Speed at Different Height
Wind speed is varying with height by a power-law expressed as follows [77,78]: where vref is the wind speed at reference height Href, is the wind speed at the hub height H. The factor α represents the wind shear exponent. Accordingly, the shape and scale factors can be calculated at the hub height H for different distribution models.

Results and Discussion
The utilized algorithms were implemented in MATLAB R2007 b, with the following specifications: Intel® core (TM) i3-2330 M CPU @ 2.20 GHz, Installed memory (RAM): 4.00 GB, System type: 64-bit Operating system. The optimization process considered a stopping criterion of 150 iterations and a population size of 50 for each algorithm. The statistical information for each site is presented in Table 4. The wind shear exponent (α) determined for each site according to different terrain types is also presented in Table 4, except for the King Hussein site, in which the shear exponent factor is evaluated using (77). These data are used as input for our optimization problem. Furthermore, the detailed parameters of the LCoE model are provided in Table 5. The rated power PR and rated speed vr have ranges of (0.5-4) MW and (8-16) m/s, respectively. Table 6 provides the optimal values of the objective function for each site, which are obtained by the utilized optimization algorithm. A closer inspection of this table shows that the ranges of the rotors' lengths and hubs' heights are between (37-45 m) and (77-88 m), respectively. The annual energy production, capacity factor, and the minimum cost of energy for all sites are summarized in Table 7. It is clear from the results obtained in this table that the exponential power model Q3(v) shows a clear superiority over the other power models in calculating the capacity factor and LCoE. Accordingly, King Hussein Airport achieves the best results among other sites by recording the minimum LCoE and maximum CF, 33.81 $/MWh and 0.54, respectively. The higher LCoE are recorded by Ghor Es Safi with a value of around (405.00 $/MWh) and a CF value of around 0.11. Table 8 provides a comparison between the results obtained in this study and those presented in [41]. Ammari at el. in [41] presented an assessment study of the wind energy potential of five wind sites in Jordan. The Weibull distribution model and five commercial wind turbines were utilized to calculate the Annual Energy Produced (AEP) and the corresponding CF in each site. The common wind sites between our study and the study in [41] are compared with each other in terms of AEP and CF. These wind sites are Queen Alia Airport, King Hussein Airport (Aqaba), and Safawi. To conduct a comparative analysis, the developed optimal approach in our model has been applied to the same turbine models used in the study of [41]. Table 8 shows the comparison between the results obtained by the two studies. A closer inspection of this table shows that the results of our study are superior to those obtained by [41] for most wind turbines. The presented results are significant and confirm that our proposed approach is recommended to be applied for wind energy estimation.
The model described in this study can be used at any wind site in the world. To implement the wind distribution with a high level of precision, it just requires high-resolution wind speed data. This can be calculated using data from the nearest meteorological station to the intended wind site, adjusted to the proposed wind farm's hub height.       Table 7. AEP, CF, and LCoE results.

Real Measurements and Validations Process
Since Q3 model has provided the minimum LCoE, as shown in Table 7, only this model will be validated with real measurements data. Therefore, a comparison study has been established between the measured energy output obtained from several wind farms in Jordan and the estimated value based on the exponential power model (Q3) for the corresponding wind farms. Table 9 shows the measured data of four wind farms operated in Jordan for the year 2019. The data, which are provided by the National Electric Power Company (NEPCO), includes the total energy production of the wind farm, its capacity factor, and the cost per unit of energy. The technical specifications of these wind farms are presented in Table 9.
The average wind speed data required for this analysis are provided by the National Energy Research Center (NERC). These data, which are recorded at different heights, are corrected to the hub height of the wind farms using (74). , which represents the wind shear exponent selected to be 0.15 for all wind farms as open terrain areas. The corrected wind speeds are also presented in Table 10.
Rayleigh distribution, which is a simplified model of Weibull distribution and depends only on the average wind speed of the wind sites, is utilized to perform this analysis to keep consistency with the available wind data. The complete derivation of wind energy extracted by the turbines based on the Rayleigh exponential power model (R-Q3) is derived in this section. The probability distribution function PDF of Rayleigh in terms of mean wind speed Vm can be written, as follows [43].
The estimated energy produced by wind turbines based on the exponential power model (6) is given by the following formula.
where, is the total turbine losses, which is assumed to be 15%. Substituting (6) and (39) in (40) yields the following: Evaluating the integrals in first and third terms in (6). Thus, the estimated energy produced using (Q3) and Rayleigh model can be expressed, as follows.
The estimated capacity factor of selected wind farms has been estimated by (16). Error analysis is performed between the measured and estimated energy produced, which can be expressed, as follows [43].
The estimated cost per unit energy LCoE is calculated using Life Cycle Cost (LCC) method. The capital cost for each turbine model is evaluated based on modified NREL's cost model. The input parameters of the analysis are presented in Table 11.  Table 12 presents the results for the comparison study between the measured output data and the estimated data based on (R-Q3) model for the selected wind farms. The error analysis shows that Al-Rajaf wind farm achieves the lowest percentage error with around 6.16%, followed by Al-Fajeej and Tafila Wind farms which recorded 13.03% and 18.18%, respectively. The worst result was achieved by Al-Hussein University wind farm with an error value of around 20%. Regarding the estimated CF results, Tafila wind farm recorded the highest value of around 42%. All results obtained in this comparison study are provided in Table 12.

Conclusions
This paper proposed a method for estimating the extracted energy of wind farms using several mathematical models. The developed models include five turbine models and three wind distribution models. They were used to suggest suitable wind turbines with specific features for wind farms to be installed in nine potential wind sites in Jordan, which are: Queen Alia Airport, Amman Civil Airport, King Hussein Airport, Irbid, Mafraq, Ma'an, Safawi, Irwaished and Ghor Es Safi. The suggested wind farms achieved maximum extracted energy, maximum capacity factor and minimum Levelized Cost of Energy. The whale optimization algorithm was used to solve the developed optimization problem. The results showed that King Hussein Airport achieves the best results among other sites by recording the minimum LCoE and maximum CF with values of 33.81 USD/MWh and 0.54, respectively.
The developed model with Q3 and Rayleigh distribution function was validated with real measurements data from several wind farms in Jordan. Error analysis showed that the difference between the measured and estimated energy is less than 20%. The study has validated the provided a model which can now be utilized routinely for the assessment of wind energy potential in a specific wind site. Moreover, the model is very useful to estimate the wind potential before the wind farm is built, so that a decision can be made on the type of wind turbine that can be used.
The limitations of this methodology can be divided into two main parts. The first one is the accuracy of the wind speed representation using the distribution function, which is mainly dependent on the resolution of the wind speed data. The second one is the accuracy of estimation of the correction factor of the National Renewable Energy Laboratory (NREL) modified cost model, which is mainly dependent on the actual cost of the wind project.