Optimization of Wind Farm Layout for Maximum Energy Production by Stochastic Fractal Search

NGUYEN, K. D. et al. VOLUME: 23 |NUMBER: 1 |2025 |MARCH Research Article OPTIMIZATION OF WIND FARM LAYOUT FOR MAXIMUM ENERGY PRODUCTION BY STOCHASTIC FRACTAL SEARCH Khoa Dang NGUYEN1,2, Tinh Trung TRAN2, Dieu Ngoc VO1,3,∗ 1Department of Power Systems, Ho Chi Minh City University of Technology (HCMUT), 268 Ly Thuong Kiet Street, District 10, Ho Chi Minh City, Vietnam 2College of Engineering, Can Tho University, Can Tho City, Vietnam 3Vietnam National University Ho Chi Minh City, Linh Trung Ward, Thu Duc City, Ho Chi Minh City, Vietnam [email protected], [email protected], [email protected] ∗Corresponding author: Dieu Ngoc VO; [email protected] DOI: 10.15598/aeee.v23i1.240404 Article history: Received Apr 13, 2024; Revised May 26, 2024; Accepted Jul 26, 2024; Published Mar 31, 2025. This is an open access article under the BY-CC license. Abstract. The wind power plant designs are different from the design of other conventional power plants such as hydropower plants, thermal power plants, and nuclear power plants because the input fuel of these types of power plants is controllable. Wind power plants depend on the speed of wind energy. Therefore, the problem of optimizing the location of turbines in a wind farm to achieve maximum annual energy output (AEP) is of great interest. In this paper, the Stochastic Fractal Search (SFS) algorithm is proposed to optimize the arrangement of turbines in the wind farm to minimize the wake effect so that the wind farm achieves the maximum generating capacity and the highest power factor (CF). SFS represents a significant advancement in optimization techniques, offering robust, adaptable, and efficient solutions to complex problems like wind farm layout optimization. Its innovative use of fractional dynamics and stochastic processes distinguishes it from traditional methods, providing superior performance in many scenarios. The proposed method was tested on a standard case with three types of turbines with different capacities of 850kW, 1000kW, and 1500kW to confirm the suitability of the algorithm and select the most appropriate turbine type. The results of AEP and wake loss calculated by the SFS algorithm were superior compared to those obtained by the PSO algorithm for these three turbine types. The turbine with the highest CF will be selected for application in the wind farm. Therefore, the proposed SFS algorithm can be a potential method to deal with the problem of optimization of wind farm layout. Keywords Stochastic Fractal Search Algorithm, Wake effect, WAsP software, Wind farm layout optimization, windPRO software. 1. Introduction The primary fuel sources for power plants such as coal, oil, and gas are gradually depleted. To ensure a stable power source and minimize the impact on the environment, countries are interested in developing sustainable energy. Using renewable energy sources such as wind energy with great potential in many countries. In 2021, wind power capacity rose by 93.6 GW, and the total global wind power capacity improved 837 GW, an improvement of 12%over the previous year. NZE2050’s goal in the next 5 years, the world needs more than 86 GW of wind power annually and the total global wind power capacity is about 469 GW. By 2050, the world is expected to install 2TW of wind power and offshore wind will reach 19%by 2024 [1]. To design a wind farm, there are a number of issues worth consider- ©2025 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 1 NGUYEN, K. D. et al. VOLUME: 23 |NUMBER: 1 |2025 |MARCH ing and most of them have been extensively studied in distinctly individual ways such as turbine placement, research on wind characteristics, analyze the interaction between wind turbines (wake effect), design ancillary items (turbine transport routes, electrical cable systems, turbine foundations), reliability, economic issues, environmental impact assessment [2]. The wake effect is a complex and interesting problem in solving the problem of wind turbine layout to achieve maximum power [3]. he most popular models built by N.O. Jensen [4] and improved by Katic [5]. Jensen treated the influence area behind the turbines as a wind disturbance and ignores the eddy effect [6], which affected only the region near the turbines. Two types of wake effect models have been presented: Computational fluid dynamics (CFD) model [7, 8] and analytical model [9, 10, 11, 12]. Recently, several methods have been proposed to calculate the wake effect such as the binary matrix method based on the Jensen model [13], the wake effect model combined with the multi-turbine effect has been proposed for energy loss analysis [14]. Many works have presented different methods to solve problems related to the optimal position of wind turbines such as Changshui et al. [15] have proposed the “lazy greed” algorithm used to optimize the wind turbines. Zhang Changshui et al. [16] presented a "submodule" nature for turbine placement in wind farms based on the Jensen wake model, Serrano et al. [17] applied by iterative method to increase the distance between turbines in offshore wind farm in order to decline the wake effect. In addition, there are a number of studies on determining the optimal location to install power systems for wind farms such as installing substations and cable systems [18, 19]. The study of wind speed reduction through the turbine is also a complex process involving the determination of the turbine location, wind conditions, and wind turbine control methods [20]. The initial data for calculating the turbine power is the measured wind speed and it is statically represented by the Weibull distribution [21, 22, 23, 24]. Currently, there are commercial software for wind energy efficiency assessment and wind farm design, the most popular one being WAsP [25]. The main function of this software is the assessment of wind resources after analyzing the measured wind data set. WAsP analyzes wind resources by analyzing wind flows using a CFD model. In addition, the WAsP software provides various tools to design the wind farm, such as an assessment of wind power production considering the wake effect, analyzing wind speed, wind distortion, and wind turbulence. The windPRO software involves optimizing the wind farm’s turbine layout for maximum power [26]. On the other hand, this software also has tools for environmental impact assessment and layout of turbines to respond to noise. Recently, metaheuristic optimization algorithms have been increasingly applied to engineering problems such as Evolutionary Strategy, Genetic Algorithms, Dolphin Echolocation, Cuckoo Optimization Algorithm, Artificial Bee Colony, Ray Optimization, Gray Wolf Optimizer, Colliding Bodies Optimization, and Chaotic Swarming of Particles [27]. These algorithms have proven themselves to be very competitive compared to modern hyper-simulation algorithms as well as other conventional methods. In this paper, an optimal search algorithm is proposed, which is based on a random fractal search to solve the problem of optimizing wind farms to achieve maximum power energy. The mathematical model of the problem includes a fitness function with the goal of obtaining maximum energy and the constraints of the turbine. To check the feasibility and efficiency of the proposed algorithm, the results calculated by SFS will be compared with the results calculated by PSO and simulation results by windPRO software. 2. Problem and Formulation 2.1. Assumptions To develop a general model for the problem of optimization of wind farm layout, a set of assumptions is considered in this paper. 1. The turbines have the same characteristics. 2. The same number of turbines for the case studies 3. The turbines are arranged onshore in twodimensional (x,y). 4. Wind speed (v) follows Weibull distribution [20, 23, 24, 28]. The Weibull distribution is commonly used in wind energy analysis to model wind speed data because it can provide a good fit for the wind speed probability distribution. The Weibull distribution is characterized by two parameters: shape (k) and scale (c). These parameters determine the shape and scale of the distribution, respectively. The probability density function of the Weibull distribution is given by: f(v, k, c) = k cv ck−1e−(v c)k(1) where, vis the wind speed; kis the shape parameter; cis the scale parameter. 2.2. Wake effect model The wind speed changes after passing through the upstream wind turbines, which affects the downstream ©2025 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 2 NGUYEN, K. D. et al. VOLUME: 23 |NUMBER: 1 |2025 |MARCH Fig. 1: A wind turbine inside the cone of another turbine [29]. wind turbines due to reduced wind speed and increased turbulence and is called the wake effect. This effect will affect the operation and energy production of wind turbines in the turbulence zone. Therefore, modeling the wake effect plays an important role in determining the location of turbines in a wind farm. The wake effect becomes more significant when the wind farm has multiple turbines. A considered turbine may be affected by wake effects from many other wind turbines [3]. The wake effect model is a crucial component in wind farm layout optimization. It simulates the interaction between wind turbines in a wind farm, accounting for the reduction in wind speed and turbulence caused by the wake of upstream turbines. A fairly simple wake effect model with extensive linear assumptions and a decaying wind speed that depends only on the distance behind the turbine was developed by N.O. Jensen [3]. Jensen treats the post-turbine influence as a wind disturbance and ignores the eddy effect, which affects only the region near the turbine. The angle βij,(0 ≤β≤π), between the vector originating from the top of the hypothetical cone to the ith turbine and the jth turbine, is calculated as [29]: βi,j =cos−1    (xi−xj) cos θ+ (yi−yj) sin θ+R/κ qxi−xj+R κcos θ2+yi−yj+R κsin θ2   (2) The wind turbine jth is inside the wake of turbine ith, if turbin jth is inside the cone. The distance between turbine ith and jth projected on the wind direction θ, dij, is expressed as follows [29]: di,j =|(xi−xj) cos θ+ (yi−yj) sin θ|(3) The fall in wind speed at a certain location dis [29]: Vdef = 1 −Vdown Vup =1−√1−Ct 1 + κdi,j R2(4) where, Ctis the thrust coefficient of turbine; d is the distance between turbine i and turbine j as a projection along with wind direction; kis the entrainment constant (decay coefficient) [30], which is empirically calculated as: k=0.5 ln H z0(5) where, His the hub height, and z0represents the surface roughness of the terrain. kis 0.075 for land areas and 0.04 for offshore areas [31]; di,j is the distance behind the turbine considering wind direction θ. Due to the wake effect (when a turbine is affected by multiple turbines in front) the wind speed is reduced [29]: Vdefi =v u u t N X j=1,j=i,βi,j <α "1−√1−Ct (1 + κdi,j/R)2#(6) It is easy to observe that Vdefi is a function of wind direction (θ) and all turbine positions. It is shown that only the scaling parameter cof the Weibull distribution will be affected by the wake loss [6]. The wake effect is statistically described as follows [32]: c′(θ) = c(θ).(1 −Vdefi)(7) 2.3. Wind turbine characteristics The exact pattern of turbine characteristics is very important in guessing wind power energy. There have been many approaches to the introduction of wind turbines, including approximate polynomials [33]. In this article, the 9th degree polynomial model is applied to calculate the turbine characteristic model because this is the most suitable observed model. f(v) = p0+p1v+p2v2+p3v3+p4v4+p5v5+ +p6v6+p7v7+p8v8+p9v9(8) The standard case is applied to the problem with turbine capacities of 850kW, 1000kW and 1500kW as shown in Table 1. Figures 2, 3, and 4 show the comparison between the polynomial model and the actual wind turbine characteristics proposed in this paper. The characteristics of the model are observed to be very similar to those of the actual turbine. The wind turbine characteristics are restated as follows: f(ν) =    0, vi< vcut in, vi> vcut out f(x)in Eq.(8), vcut in ≤vi≤vcut out Prated, vrated ≤vi≤vcut out (9) ©2025 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 3 NGUYEN, K. D. et al. VOLUME: 23 |NUMBER: 1 |2025 |MARCH Tab. 1: Types of turbines proposed for wind farms. Type of Turbine. GAMESA G52/850 NORDEX N-54/1000 VESTAS V63/1500 General data Model: G52/850 N54/1000 V63/1500 Rated power 850 kW 1,000 1,500 Rotor diameter 52 m 54 63.6 Swept area 2,124 m²2,291 3,177 Specific area 2.5 m²/kW 2.3 2.12 Number of blades: 3 3 3 Rotor Minimum rotor speed 19,44 14 rd/min - Maximum rotor speed 30,8 rd/min 21,5 rd/min 22,9 rd/min Cut-in wind speed 4 m/s 3,5 m/s 4 m/s Rated wind speed 16 m/s 15,5 m/s 16 m/s Cut-off wind speed 25 m/s 25 m/s 25 m/s Generator Type ASYNC ASYNC ASYNC Number 1 1 1 Maximum speed 1900 rd/min 1513 rd/min 1650 rd/min Voltage 690 V 690 V 690 V Fig. 2: GAMESA G52/850 turbine characteristics. Fig. 3: NORDEX N-54/1000 turbine characteristics. 2.4. Wind power model 1) Wind Model Wind model becomes very important in estimating wind power production. In wind pattern, wind speed and wind direction are two parameters that need to be carefully considered because they affect the power output of the wind turbine. The wind speed is usually described by the Weibull distribution and the wind direction is expressed by the probability of each sector of the wind rose [34]. This study proposes to use a 12-sector wind rose because it is widely used for wind farm design. Fig. 4: VESTAS V63/1500 turbine characteristics. 2) Wind Power Output The energy production of the turbine is shown in (10) [35]: E(P, θ) = ∞ Z 0 f(v)p(v, c(θ), k(θ))dv (10) where p(v, c(θ), k(θ)) is the Weibull probability density function of wind speed. Calculation of the energy produced by a turbine for wind direction from 0oto 360ois presented as follows [29]: E(P) = 360 Z 0 p(θ)dθ ∞ Z 0 f(v)p(v, c(θ), k(θ))dv (11) The numerical integration method will be applied to calculate the wind power output of the wind farm. The wind power output in each wind direction θis combined as follows [29]: E(P) = h P i=1 fi(θ) ∞ R0 f(v)ki(θ) c′i(θ)v c′i(θ)(ki(θ)−1)e−v c′i(θ)ki(θ) dv (12) ©2025 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 4 NGUYEN, K. D. et al. VOLUME: 23 |NUMBER: 1 |2025 |MARCH 3) Objective Functions This article presents a method for optimizing the arrangement of turbines in a wind farm to maximize annual energy output: Obj = max hXE(P)i(13) 3. Methodology The SFS algorithm is a metaheuristic optimization algorithm inspired by the principles of fractal geometry and randomness. It’s designed for solving complex optimization problems and is particularly useful for global optimization. SFS combines random sampling with self-similarity, creating a rich search landscape for finding the global optimum, This is based on the simulation of a dielectric breakdown process, so it becomes a suitable search engine for solving optimization problems at a general level. The procedure of the algorithm is divided into two processes as diffusive and update [36]. In the first phase, to increase search chances, each point will diffuse around the current location in response to growth characteristics. In the second phase, the simulation algorithm will work for an individual to update its location based on the location of other individuals, the second phase uses some random method such as update processes. An outline of the Stochastic Fractal Search Algorithm works: Step 1. Initialization: Initialize the search space and create an initial solution point within the defined bounds. Step 2. Self-Similarity: The algorithm generates new solution points by perturbing the current solution using a random vector with a specific structure based on a fractal pattern. Step 3. Evaluation: Evaluate the objective function for each generated solution point. Step 4. Selection: Choose the best solution point among the current one and the newly generated ones based on the objective function values. The selected solution becomes the current one. Step 5. Termination: The algorithm repeats steps 2-4 for a specified number of iterations or until convergence criteria are met. Step 6. Global Optimum: The algorithm aims to converge to the global optimum by exploring the entire search space through its self-similarity and randomness. 3.1. Fractals Some common methods are used such as an iterative functional system, L system, finite division principle, and random cracking to generate fractal shapes. These meta-heuristic algorithms are based on fractal features as a search algorithm that achieves good results both in terms of accuracy and convergence time [36]. 1) Random fractals Random processes such as Gaussian walk, fractal structure, Levy flight, osmotic cluster, Brown tree and Brownian motion trajectories are used to reduce the number of iterations of the algorithm and generate the stochastic fractal. For simplicity, consider forming a sequence with the initial term located at a random position. Then random particles are formed around the original particle and cause diffusion. The random walk algorithm is applied to simulate the diffuser. The particles produced by diffusion stick to the particles that make it up and form a group of particles. During the formation, the probability of particles being pulled to the edge is greater than that of particles entering the middle. Because of this property, it leads to a branched cluster as shown in Figure 6 [36]. 2) Dielectric breakdown Research on dielectric breakdown characteristics found that complex models can be applied to simulate the branching tendency of dielectric puncture. Examples are flashover and lightning. Niemeyer et al. [32] introduced dielectric breakdown using a random model and showed that branch discharge patterns follow fractal characteristics. This model is relatively similar to the new Diffusion Limited Aggregation (DLA) model. 3.2. Fractal search 1) Methodology of SFS The core methodology of the SFS algorithm revolves around two main components: fractional calculus and stochastic search. 2) Fractional Calculus - Fractional Order: Utilizes non-integer orders of differentiation and integration, providing a flexible framework to capture system dynamics with memory effects. - Memory Effect: Helps in retaining historical search information, which guides the current search process more effectively. ©2025 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 5 NGUYEN, K. D. et al. VOLUME: 23 |NUMBER: 1 |2025 |MARCH - Fractal search applies the following three hypotheses: - Each point will have an electric potential energy. - Each point will diffuse and randomly generate a number of points. - In each generation only keep some of the best points. Assume P(1 ≤P≤20) is the number of particles examined. Initially, each Piparticle is randomly placed in the search area with the same energy Eias follows: Ei=E P(14) where, the maximum energy is E. To optimize the fission, each particle will be diffused in each generation and generate a limit by the Levy flight. In this model, use Levy flight for the DLA development model. The Lévy flight is described by (13) as follows: L(x) = 1 π ∞ Z 0e(−αq−β)cos(qx)dx (15) where, αis the distribution coefficient; βis the distribution index, 0< β ≤2. Figure 7 shows the diffusion process that creates new particles around the original particle with random positions. As a result of the diffusion process, a number of particles are produced q(1≤q≤the maximum diffusion number (MDN)). To generate each of these particles, both the Levy flight and Gaussian are applied as formulas (12) and (13): xq i=xi+αq i⊗Levy(λ)(16) xq i=xi+β×G(17) where G=Gaussian(Pi,|BP|− (γ×BP −γ′×Pi); β=log(ge) ge;geis the number of generations; BP(Best Point) is the best score; γand γ′∈[0,1]. To get a good score for both the Lévy flight method and the Gaussian distribution, the fractal search method randomly uses both methods. Because the Lévy distribution gives a fast convergence algorithm, and the Gaussian distribution gives better results. Since the approaches all depend on stochastic processes, fast absorption cannot be guaranteed. Therefore, αis an important parameter for fast convergence. Two formulas are considered for α, one for a broader search, and the other for a higher precision search: αi=U−L (ge×log (Ei))ε(18) where, Eiis the energy of the Pi;Uis upper bound and Lis lower bound of the search area; εis usually taken as 3/2. After the diffusion has determined the position of the particles, the energy distribution between the particles is created. Particles with better target values will have a higher energy distribution. Each diffuse particle has a target value Fiwhere i= 1,2, . . . , q. The energy is distributed to the points as follows: Ej i= Fi Fi+Pq k=1 Fk×Ei(19) where, Fiis the point before diffusion. Because of the complex diffusion, only some of the best particles will be selected for the next. The energy of the discarded particles will be distributed to the selected particles and new particles will be created. The total energy of the removed points is Φ;µis the ratio of the energy distribution between the selected points and the newly created points. The energy distributed to the remaining points is as follows: Et+1 =Et Ft/ ξ X k=1 Fk!×Φ!×µ(20) where Et+1 and Etis the energy of the tth point after and before the energy distribution, ξis the total of number points in the iteration. For each diffuse point, the number of newly formed and randomly positioned points in the search space is calculated as follows: υ=log(Ne) log (MDN) (21) where, Neis the number of eliminated points. The energy distribution for each produced point is equal: E′ c=Φ (1 −µ) υ, c = 1,2, ..., υ (22) 3.3. Stochastic Fractal Search algorithm SFS is a modern optimization algorithm designed to address complex, multi-dimensional optimization problems that traditional methods often struggle to solve effectively. These problems are prevalent in various fields, including engineering, finance, and artificial intelligence, where finding the global optimum in a highly nonlinear and multimodal landscape is crucial. SFS is inspired by the natural process of fractal growth, characterized by self-similarity and recursive pattern generation. The methodology involves two main phases: diffusion and update [36]. ©2025 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 6 NGUYEN, K. D. et al. VOLUME: 23 |NUMBER: 1 |2025 |MARCH Generate candidate solutions by creating random walks influenced by the fractal dimension. Because Fractal Search does not exchange information between particles. Therefore, SFS adds an update process to balance the accuracy and convergence time of the algorithm. Lévy flight and Gaussian walking method have been applied to generate new particles by diffusion process [27]. The Gaussian steps involved in the diffusion phase are calculated as follows: Gaussian_walk1=G(µBP , σ)+(ε×BP −ε′×Pi) (23) Gaussian_walk2=G(µP, σ)(24) where, εand ε′are randomly distributed; µBP and σ are Gaussian parameters; µPand σare the second two Gaussian parameters. The standard deviation is as follows: σ=|β×(Pi−BP)|(25) The single search method is applied to reduce the size of the Gaussian walk log(ge)/ge, so the convergence time is faster. At initialization, points are randomly initialized based on upper and lower bound constraints. Initialize the jth point, Pjas follows: Pj=L+ε(U−L)(26) where, εis a random distribution and is limited to the interval [0,1]. The points will probe around the current position to consider the search space in the diffusion process. Besides, two statistical processes are performed for a better spatial search. The first statistic is performed on each vector, and then the next statistic is applied on all points. The first statistical process, rank all points by (27), Nis the total number of points in group. Then each ith point is assigned a probability value as follows: Pai=rank(Pi) N(27) Equation (27) means that the better the score, the greater the probability of that score. It helps the bad points increase the chance to change position. The chances of finding a better solution will improve in the next generation. P′ i(j) = Pr(j)−ε×(Pt(j)−Pi(j)) (28) where, P′ iis the new point; Prand Ptare randomly chosen points from the group. (a) The flowchart of the SFS algorithm. (b) The diffusion process of the SFS algorithm. Fig. 5: The SFS algorithm flowchart and Diffusion process algorithm flowchart [36]. This property is intended to better explore and satisfy the diverse nature of the algorithm based on two statistical processes [36]. All the points obtained from the previous process will be re-ranked according to (27) before the second process is performed. Similar to the first process, if the P′ isatisfies the condition Pai< ε, the position is changed according to (29). Pi′′ =Pi′−ˆε(Pt′−BP)|ε′≤0.5 Pi′′ =Pi′−ˆε(Pt′−Pr′)|ε′>0.5(29) where, P′ rand P′ tare randomly chosen points from the first process. The P”iis new point if its objective function value is better than P′ i. Step 1: Initialize population size: N,MDN, maxiter, and G. Step 2: Find the best score (BP) by calculating the fitness function. Step 3: Check condition: - If G≤maxiter: Output results. - If G>maxiter: Call Diffusion Process. ©2025 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 7 NGUYEN, K. D. et al. VOLUME: 23 |NUMBER: 1 |2025 |MARCH Step 4: Diffusion Process - Set MDN. - Generate new particles, if MDN is reached. - The new point will replace the current point. - Identify the BP for this phase. Step 5: Updating Process The First Updating Process: Rank point using Eq. (24). - Generate a new point P′ i(if Pai< ε), using Eq. (28). - The new point (P′ i) will replace the current point (Pi). - Identify the BP for this process. The Second Updating Process: Rank particles using Eq. (27). - Generate a new point P′′ i(if Pai< ε), using Eq. (29). - The new point (P′′ i) will replace the current point (P′ i). - Identify the BP. Step 6: Check process stop condition: The BP is the optimal solution if the maxiter is reached. Otherwise, go to Step 3:. Update Phase: Improve candidate solutions by employing random walks that allow for both local and global search capabilities. Selection: Evaluate the fitness of each candidate solution and select the best ones to form the new population. Convergence Check: Repeat the diffusion and update phases until convergence criteria, such as a predefined number of iterations or an acceptable fitness level, are met. Exploration and Exploitation Balance: SFS effectively balances exploration (global search) and exploitation (local search) through its dual-phase methodology, enhancing its ability to find the global optimum. SFS can handle large-scale optimization problems due to its inherent scalability and adaptability to different problem sizes. The iterative nature and extensive exploration mechanisms, like Levy flights, can be computationally expensive, especially for very large problems. The performance of SFS can be sensitive to its parameter settings, such as the step size in Levy flights and the fractal dimension, requiring careful tuning. Implementing SFS can be more complex compared to traditional optimization algorithms, necessitating a deeper understanding of fractal mathematics and stochastic processes. (a) The first update process. (b) The second update process. Fig. 6: The update processes of the SFS algorithm [36]. 4. Numerical Results Wind farm data is very important to the problem of determining the optimal location of turbines in a wind farm to reduce wake-up effects and achieve maximum generating capacity. The wind farm proposed in this paper is an onshore wind farm, referenced from the WAsP workspace sample, filename Version8Windfarm.wh [25]. The wind farm is a complex terrain with elevations ranging from 146.7m to 350m. The average wind speed of the project is 7.25m/s and the average wind energy density is 388 W/m2. The goal of the problem is the optimization of wind farm layout for each proposed turbine type so that the energy power output and the power factor of the wind ©2025 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 8 NGUYEN, K. D. et al. VOLUME: 23 |NUMBER: 1 |2025 |MARCH farm is the best, thereby proposing the selection of the appropriate turbine. Tab. 2: Input parameters. Input parameters Roughness (Z0)0.083 Wind velocity in free flow (V0)7.25m/s Hub height (h) 50m Wind Farm dimension 3200m x 4200m Thrust coefficient (Ct)0.75 Wind density 388W/m2 This paper proposes to select 3 types of wind turbines arranged on the same wind farm to determine the optimal layout and select the appropriate type of turbine. Case studies are summarized in the following Table 3. Among these parameters, SFS is sensitive to MDN. The research results show that the diffusion number can affect the performance of the problem, and depends on the optimization problem. Some research results show that some functions of the problem are significantly improved when increasing MDN. However, increasing MDN will affect the convergence time and convergence speed of the problem, so it needs to be consider [36]. S.Walk is a diffuse walk and an optional parameter. (S.Walk = 0 for the first Gaussian walk and simple problems. S.Walk = 1 for the second Gaussian walk and hard problems). The control parameters of the mentioned algorithm used in case studies are given according to Table 3. The energy produced by the wind farm is greatly affected by wind speed and wind direction. Specify the wind speed level to shut down the turbine as below 3m/s or above 25m/s [37]. The direction of the turbine must be perpendicular to the wind direction to receive maximum wind energy [38]. The wind atlas in the project area is calculated based on long-term corrected wind measurements taking into account the effects of obstacles, roughness, and terrain elevation. Below is the wind data of the project area referenced from the WAsP software [25] as shown in Figure 7. Figure 7 shows the prevailing wind direction of the project area with an angle from 2700 to 3000. A simplified wind rose is used, which is divided into 2 sectors (sectors 10 and 11). The highest probability occurs at a wind speed of 7.25m/s, accounting for about 12%. The case studies using the same data source from the WAsP software library. The terrain is complex and the altitude varies from 146.7m to 350 m. Fig. 7: The wind rose and wind speed distribution. 4.1. Case study 1 Case study 1 considers the optimal arrangement for 11 wind turbines, turbine capacity is 0.85MW. The results of the optimal arrangement of turbines in the wind farm by the SFS algorithm will be compared with the results calculated by the PSO algorithm and the simulation results by the windPRO software. 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