A techno‐economic assessment and optimization of Dumat Al‐Jandal wind farm in Kingdom of Saudi Arabia

One major criterion in the selection of wind farm location is the cost of energy (COE). COE is the cost of producing 1 kWh electric energy on an annual basis. Mathematical model of COE includes site‐specific constants (such as reference height, mean wind speed, shape factors, wind shear coefficient, average temperature, and turbine altitude) and wind turbine parameters (such as maximum power coefficient, total loss of energy, cut‐in/cut‐off wind speed, rated wind speed, rated power, and the fix charge rate). In this work, we evaluate the COE of an onshore wind farm located at Dumat Al‐Jandal (Saudi Arabia) according to the hub height and rotor size. The 99 Vestas turbines can be mounted at a hub height ranging from 105 to 166 m with available rotor diameters of 105, 112, 117, 126, 136, 150, 155, or 163 m. Particle swarm optimization with a normal distribution is used to optimize the COE. Results show that COE is varying around the average value of $0.029335/kWh by ±$0.00021/kWh. The minimum COE was achieved with a rotor diameter of 150 m at hub height of 105 m. COE increases with the increase of hub height. At 105 m‐hub height, COE is almost the same, with a variation of 0.03% (It ranges between $0.029125/kWh and $0.029133/kWh). COE is more sensitive to rotor size than hub height. This investigation revealed that the COE estimation is in a range of 39%–48% greater than that announced COE by the developing project consortium.

with a positive projection that it will be cheaper than fossil fuel powered electricity by 2050. 3,4Indeed, between 2010 and 2020, the global average of total installed cost for onshore wind decreased by 32%, from $1971/kW to $1349/kW.2020 counted 93 GW of new wind power installed globally (93% are onshore), increasing the total installed capacity to 743 GW, an increase of 14% compared to the prior year. 5Kingdom of Saudi Arabia (KSA) plans to generate 30% of its energy from renewables and other sources by 2030 (under its national program called Vision 2030), with nuclear power playing a key role.This program also highlighted wind energy as a potential field, as technological developments are making wind farms more economically viable.By 2030, KSA hopes to produce 20 GW of renewable energy from wind power.The first stage of the Saudi National Renewable Energy Program (NREP) plan is to build a 415 MW onshore wind farm at Dumat Al-Jandal (Al-Jouf region) with a 1,517,600 MWh electrical energy expected to be generated from the project which will make it the largest wind farm in the middle east region.The project will feature 99 wind turbines with a power output of 4.2 MW each.The turbines have been supplied by Danish turbine company Vestas, which is also the engineering, procurement and construction contractor for the project.The techno-economic evaluation of this project concluded that the cost of energy is estimated to be between $19.9 and $21.3 per MWh. 6n 2019, the global average cost of electricity for recent onshore wind farms stood at $53 per MWh.It ranges from $51 to $99 per MWh based on the country.Without financial governmental aid, the most competitive constructions now costs as low as $30/MWh. 2 Costs are projected to continue to drop, with no signs of a slowing down due to continued breakthroughs in wind turbine technology (which result in greater energy yields and consequently capacity factors.),][9] The techno-economic investigation for developing the wind power farms can be handled from various perspectives.1][12] In the "National Renewable Energy Laboratory Wind Turbine Design Cost and Scaling Model" report, COE denotes the cost of producing 1 kWh electric. 13Other economic considerations can be used to evaluate the economic profitability of a wind farm.This includes the present value of the incoming and outgoing cash flow from the investment, and thus shows the total benefit to be derived from the investment in a project, named the net present value, 14,15 the period in which the cost of the initial investment is recovered through annual cash flows, named the pay-back period, 16,17 and the return on investment, named the internal rate of return. 18,19he performance investigation on WT focuses on the WT design (such as control design optimization 20,21 and blade design optimization [22][23][24][25] ) and the site specifications.The site specification deals with the wind statics such as altitude, air density, scale factor, shape factor and Holloman exponent. 11The global average rotor diameter increased by 46% from 82 m in 2010 to 119.4 m in 2020, owing to advances in turbine technology and a desire to save costs.During this period, the average hub-height climbed by 27%, from 81.3 m in 2010 to 103.2 m in 2020.The global average capacity factor of onshore wind increased about one-third from just over 27% in 2010 to 36% in 2020, thanks to higher hub heights and larger swept areas.As a consequence, the global levelized cost of energy (i.e., the average net present cost of electricity generation for a generator over its lifetime) average of onshore wind declined 56% between 2010 and 2020, from $89/MWh to $39/MWh. 1,2his work is a techno-economic study of Dumat Al-Jandal wind farm.We investigate the effect of rotor size and hub height on the energy cost as the other designed parameters, such as rated power, rated wind speed and tip speed ratio, are already fixed by the constructor.
The remaining sections are arranged as follows: in Section 2, the Dumat Al-Jandal onshore wind farm is introduced.Section 3 describe the cost of energy model.Section 4 is dedicated to the optimization methodology based on the widely used particle swarm optimization technique.A results discussion is conducted in Section 5. Finally, Section 6 concludes the study.

| DUMAT AL-JANDAL WIND FARM
Dumat Al-Jandal wind farm (Al Jouf region, north-west KSA, 900 km from capital city Riyadh) is a 415 MW onshore wind farm development that will become the KSA's first wind power source and the largest wind farm in the Middle East region by 2030.This site is located at an altitude ranging from 570 to 710 m (Figure 1).According to the free web-based application "global wind atlas," the annual mean wind speed is equal to 4.8, 5.9, 6.95, and 7.79 m/s at 50, 100, 150, and 200 m, respectively.The project features 99 V150-4.2MW™ wind turbines supplied by Danish turbine company Vestas.Each wind turbine will generate 4.2 MW.The V150-4.2 MW™ is one of the industry's highest producing onshore low wind turbines.Technical specifications are summarized on Table 1 and the rated power evolution is depicted on Figure 2. 26

| COE MODEL
COE is dependent on site-specific constants and wind turbine settings, according to the techno-economic model created by the National Renewable Energy Laboratory of the US Department of Energy 13 and Song et al. investigations. 11Site-specific constants are the reference height H 0 (50 m), mean wind speed at reference height V m (4.8 m/s), shape factor at reference height k 0 (2), 27 wind shear coefficient α (0.1), 27 average temperature T (300.15K) and turbine altitude H alltitude (600 m).Wind turbine parameters include maximum power coefficient C p max (0.48), 28 total loss of energy η (0.17), 29 cut-in wind speed V cut-in (3 m/s), cut-off wind speed V cut-off (22.5 m/s), rated wind speed V r (9.9 m/s), rated power P r (4000 kW) and the fix charge rate FCR (0.1158). 11sing the site specific constants and wind turbine parameters, COE evaluation starts by calculating the scale factor at reference height c 0 [30][31][32][33] : ( ) were Γ is the Gamma function.
The scale factor c and shape factor k are functions of the hub height H: The hourly energy production P m (kWh) is function of H and the rotor radius R, and is defined by the following equation: where V (m/s) is the wind speed.The annual energy production AEP (kWh) is expressed as: The annual operating cost AOC ($), which take into account different costs such as replacement, land leasing, operations and maintenance, is expressed as: The annual production cost APC ($) depends on the initial capital cost ICC ($), the fixed charge rate FCR and AOC, as detailed by equation: The ICC is governed by the cost of wind turbine C Turbine ($) and the cost of infrastructure C Infrastructure ($): C Turbine and C Infrastructure can be expressed as follows: Finally, COE is defined by: The COE expression depends on 15 parameters.Six parameters depends on the site specifications {H 0 , k 0 , α, V m , H altitude , T}, nine on the WT design parameters {C p max , η, V cut-in , V cut-off , V r , P r , FCR, R, H}.For Dumat-Al-Jandal wind farm, 13 of these parameters are already known and only {R, H} can be optimized.Otherwise, COE can be minimized by selecting the suitable hub height and rotor size.The fitness function and structure restrictions are provided as follows to formulate the wind turbine efficiency problem:

| OPTIMIZATION APPROACH
The parameters to be optimized are the rotor radius and the hub height.The optimization objective is to minimize COE, which is a classic single objective optimization problem.][36] The fitness function and constraints are presented in Equation (12).
The particle swarm optimization (PSO) first establishes the workspace boundaries by determining the maximum and minimum variables values, population size n, maximum number of iterations i max , and other constants.For each particle, the starting position and velocity were generated at random.The inertia weight, particle position, and particle velocity were then calculated at each iteration.
The inertia weight is expressed using a normal model 37 : where ψ max and ψ min are the maximum and minimum inertia coefficient of the particle swarm, respectively.f, f max , f min , and f aver are the fitness value, the maximum, the minimum and the average fitness values of the particle swarm, respectively.η 1 , η 2 , and σ are constants in the range of 0-1.The acceleration coefficients, c 1 and c 2 , reflect the impact of the particle self-cognition on its trajectory, and return the degree of information exchange between all particles in the swarms.Indeed, c 1 (self-acceleration) and c 2 (global acceleration) describe the acceleration weights of particles moving toward their own extremums and global extremums, respectively.They are expressed by: where c 1 start , c 2 start , c 1 end , and c 2 end are the initial and end values of the acceleration coefficients, respectively.The velocity and position for each individual particle are calculated in each iteration as follows: where t represents the current number of iterations, i represents the particle number, and j represents the jth dimension of the particle.r 1 and r 2 are random real numbers in the range of 0-1.BP i j t , , that is, best personal position, is the best previous position of the particle and BG j t , that is, best global position, is the best position obtained from the whole population.More details on the PSO theory and programming are available on Marouani. 37he diagrammatic representation of the PSO algorithm and used parameters are represented in Figure 3.

| RESULTS AND DISCUSSION
The PSO algorithm is programmed using Matlab R2022a, and the program was run on an AMD Ryzen™ 9 5900HS processor at 3.0 GHz with 32 GB of Random Access Memory.Twenty-five calculations were made for each rotor diameter, which means that the search domain for the particles has 25 alternative initial positions and initial velocities.Stochastic discrepancy shows a variation less than 0.1%.Herein, the average solutions are reported.
Table 2 reports the COE values for each rotor diameter and for hub height ranging from 105 to 166 m (note that only some selected hub height values are represented for the sake of simplicity).Values in bold represent the minimum COE obtained for each Hub height.COE values are depicted in Figure 4.The minimum COE is $0.029125/kWh and it correspond to a rotor diameter of 150 m at hub height of 105 m.The maximum COE is $0.029546/kWh and it correspond to a rotor diameter of 150 m also but at hub height of 166 m.The min-max difference is $0.0004205/kWh which correspond to 1.44% of the minimum COE.
Figure 5 Shows the COE distribution for each rotor diameter.The disparity for each rotor size ranges from 0.72% to 1.13%, except for the case of 150 m which is more sensitive to hub height.
COE increases with the increase in hub height for all rotor sizes (Figure 6).At 105 m-hub height, COE is almost same.It ranges between $0.029125/kWh and $0.029133/kWh (0.03% variation).The higher the hub, the larger the disparity.At 166 m-hub height, COE ranges between $0.029343/kWh and $0.029545/kWh (0.69% variation).It shows that the COE is more sensitive to rotor size than hub height.
The literature illustrates different COE analysis, especially for the high-altitude cases.In comparison, Haykel et al. 29 show that COE ranges from $0.052431/ kWh at 2500 m to $0.057057/kWh at 4000 m.Song et al. 11 show that COE is between $0.05059/kWh and $0.05041/kWh at Huitengxtile wind farm (China, 2020 m altitude), and between $0.05153/kWh and $0.05172/kWh at Maanshan wind farm (China, 3200 m altitude).For the case of low altitude, Dalabeeh 38 presented a rich analysis for Jordan case.In his work, four sites were selected, and eight wind turbine models from six different manufacturers were investigated.COE for Amman (777 m altitude), Alaqaba (6 m altitude), Irbid (620 m altitude), and Deir Alla (314 m altitude) ranges from $0.04/kWh to $0.22/kWh (evaluated in 2014).Mattar and Guzman-Ibarra 17 shows that at 140 m altitude, COE range from $0.072/kWh to $0.114/kWh.This large disparity highlights the importance of site selection (altitude, wind speed characteristics, temperature, etc.) and wind turbine design parameters (rotor size, hub height, power rated, etc.).Dumat Al-Jandal COE estimation range from $0.029546/kWh to $0.029125/ kWh, which is a little bit higher than initially announced by the contractor for the project (between $0.0199/kWh and $0.0213/kWh).However, for all rotor diameters, COE increases as hub height rises.This work shows that COE estimation is 39%-48% greater than that announced by the project contractor.
To diversify electricity generation sources, KSA plans to generate 30% of its energy from renewable sources such as biogas, biomass from waste, solar, and wind.Dumat Al-Jandal is one of the pillars of the wind energy program.This work investigates the cost of energy model, using 15 parameters divided into two parts: the site specifications and the wind turbine design parameters.For our case study, only hub height and rotor size are subject to optimization.Hub height ranges from 105 to 166 m and rotor diameters are 105, 112, 117, 126, 136, 150, 155, or 163 m.Particle swarm optimization with normal distribution is used for this purpose.Results shows that cost of energy range from $0.029125/kWh to $0.029546/kWh, which allow us to express the COE as $0.029335/kWh ± $0.00021/kWh.The minimum COE correspond to a rotor diameter of 150 m at hub height of 105 m.COE is nearly the same at 105 m-hub height.
Flowchart of the PSO algorithm.COE values function of rotor diameters and hub heights.
F I G U R E 4 Surface evolution of COE function of R and H. COE, cost of energy.