Optimization of Non-Uniform Onshore Wind Farm Layout Using Modified Electric Charged Particles Optimization Algorithm Considering Different Terrain Characteristics

Abstract

Designing an onshore wind farm layout poses several challenges, including the effects of terrain and landscape characteristics. An accurate model should be developed to obtain the optimal wind farm layout. This study introduces a novel metaheuristic algorithm called Modified Electric Charged Particles Optimization (MECPO) to maximize wind farms’ annual energy production (AEP) by considering the different terrain and landscape characteristics of the sites. Some non-uniform scenarios are applied to the optimization process to find the best combination of decision variables in the wind farm design. The study was initiated by a uniform wind farm layout optimization employing identical wind turbine hub heights and diameters. Following this, these parameters underwent further optimization based on some non-uniform scenarios, with the optimal layout from the initial uniform wind farm serving as the reference design. Three real onshore sites located in South Sulawesi, Indonesia, were selected to validate the performance of the proposed algorithm. The wind characteristics for each site were derived from WAsP CFD, accounting for the terrain and landscape effects. The results show that the non-uniform wind farm performs better than its uniform counterpart only when using varying hub heights. Considering the impacts of the terrain and landscape characteristics, it is observed that sites with a higher elevation, slope index, and roughness length exhibit a lower wake effect than those with lower ones. Moreover, the proposed algorithm, MECPO, consistently outperforms other algorithms, achieving the highest AEP across all simulations, with a 100% success rate in all eight instances. These results underscore the algorithm’s robustness and effectiveness in optimizing wind farm layouts, offering a promising avenue for advancing sustainable wind energy practices.

1. Introduction

Over the past decade, the wind energy capacity has seen a remarkable surge, propelled mainly by the declining costs of wind energy production and the implementation of international policies to achieve global net-zero emissions. Forecasts by the Global Wind Energy Council (GWEC) indicate that the trajectory of wind energy development is poised to reach a historic milestone, with an anticipated installation of 1 terawatt (TW) by mid-2023 [1]. This rapid expansion marks a pivotal moment in advancing renewable energy, underscoring the profound impact of concerted global sustainability efforts.

The optimization of a wind farm’s layout stands as a crucial stage in the design and planning of new wind farms. An optimal layout amplifies the wind farm’s energy output and plays a pivotal role in reducing wind energy costs. The wake effect is of significant concern in the placement of wind turbines (WTs) within a wind farm, wherein downwind turbines experience a reduced energy yield due to their upwind counterparts’ extraction of wind speed. This wake effect holds substantial implications, potentially diminishing the total energy production of a wind farm [2]. Balancing the positioning and alignment of turbines to mitigate the wake effects is pivotal in optimizing the wind farm’s overall energy output and cost efficiency.

Extensive research efforts have been dedicated to the optimization of wind farm layouts. Among many methods used, metaheuristic algorithms represent a widely embraced and effective tool utilized by numerous researchers to address the Wind Farm Layout Optimization (WFLO) problem. These nature-inspired stochastic algorithms have showcased their capabilities to resolve diverse optimization challenges that conventional methods, like linear programming, struggle to handle. Mosseti et al. [3] pioneered this field, leveraging a Genetic Algorithm (GA) to optimize potential WT locations across a 100 square area. Their work has been pivotal in advancing the understanding of positioning turbines in a wind farm to achieve maximum energy. A model developed by N.O Jensen [4,5] is employed to simulate and analyze the wake effect, encompassing single and variable wind directions. This model offers an intricate and comprehensive framework for studying the impact of wake effects on turbine placements, further enhancing the capacity to fine-tune wind farm layouts for optimal performance. Grady et al. [6] improved the study proposed by Mosseti by implementing the total energy and production cost as a single objective function. The results show a better performance than the previous study regarding the locations of the WTs in the wind farm.

Among the most renowned metaheuristic algorithms employed in tackling WFLO are the GA [7,8,9,10,11] and Particle Swarm Optimization (PSO) [12,13,14,15]. Many other metaheuristic algorithms are also used to solve single-objective WFLO problems. Bilbo et al. [16] utilized simulated annealing (SA) to enhance the annual profit of a wind farm. Changsui et al. [17] employed a lazy greed algorithm to efficiently optimize the positioning of WTs at a wind farm, with the cost of energy serving as the main objective function. Chen et al. [18] adopted the greedy algorithm to identify the optimal positions of WTs at wind farms, with the LCOE as the objective function. At the same time, Dupont et al. [19] used an extended pattern search (EPS)-multiagent system (MAS) optimization approach to maximize the profit by optimizing both the position and size of a WT, encompassing variables such as the rotor diameter and hub height for the wind farm.

Ramli et al. [20] introduced a novel algorithm named the Binary Most Valuable Player Algorithm (BMVPA), where the energy cost is set as the primary objective function. Their study demonstrated the superiority of the proposed algorithm compared with a GA and PSO. Wang et al. [21] employed a differential evolution algorithm featuring a new encoding mechanism to address the WFLO problem to maximize the power output. Aggarwal et al. [22] applied a biogeography-based optimization (BBO) algorithm to assess the energy cost as a single objective function, showcasing the better performance of the BBO algorithm compared to the PSO and GA algorithms. Kiamers et al. [23] used the imperialist competitive algorithm (ICA) to maximize the output power of a wind farm using three different scenarios. In Ref. [24], the author used a teaching–learning-based optimization algorithm to concurrently minimize the cost and maximize the power output of a wind farm.

Numerous researchers have made substantial efforts to refine the accuracy of the WFLO model. For instance, Hou et al. [15] maximized offshore wind farms’ energy outputs by considering restricted zones influenced by seabed conditions and marine traffic limitations. The exclusion zones are excluded for the decision variables by implementing a penalty function. Meanwhile, in [25], Reddy et al. modeled intricate land-based constraints within the WFLO process. This approach navigates the complexities of varied terrains within wind farm regions, accounting for restricted areas by introducing a new framework called the Support Vector Domain Description (SVDD). This framework derives analytical expressions from diverse areas within the wind farm site while employing quadtree decomposition to streamline the complexity of grid data interpolation, ensuring a more precise and comprehensive WFLO process.

Furthermore, Sorkhabi et al. [26] navigated the complexities of land-use constraints within multi-objective WFLO by employing static and dynamic penalty functions. These innovative functions served as a tool in confronting a spectrum of constraints. A significant addition to this study was the introduction of a uniformity parameter, crucial for gauging the spatial distribution of non-feasible areas throughout the wind farm domain. This parameter was a pivotal metric in assessing the severity of land-use limitations while quantifying the percentage of viable land available for utilization. Hoxha et al. [27] investigated the effects of terrain characteristics on the wind farm efficiency in mountainous areas. The results show that continually increasing the WT distance does not always yield better wind farm efficiency.

In parallel, Gonzales et al. [28] emphasized load-bearing soil and forbidden areas as pivotal constraints within the WFLO framework. By implementing a grid-based methodology, each WT’s placement was mapped onto individual grid cells, enabling a comprehensive consideration of all constraints within the specified grid area. This detailed approach facilitated a holistic evaluation of the wind farm space, ensuring that every turbine’s placement met the imposed limitations and optimizing the overall layout to achieve the maximum efficiency.

However, despite the literature’s exhaustive consideration of various land constraints, terrain and landscape characteristics are inadequately addressed. A comprehensive model needs to be developed to incorporate the influences of terrain and landscape characteristics on the wind farm’s wake effect. This model would further refine our understanding of how these two factors impact the turbines’ overall performance and energy output, fostering a more thorough and nuanced approach to the WFLO process.

The design of onshore wind farms, particularly in complex terrains, presents challenges, as conventional wake models, initially designed for flat terrains, prove unsuitable. The intricate interactions between wake flow patterns and diverse terrains complicate the design process. Tools like WAsP utilize linear models (e.g., BZ model) and sophisticated Computational Fluid Dynamics (CFD) simulations for wind resource assessments. However, the computational expense of CFD simulations underscores the necessity for efficient wake models tailored to complex terrains.

Feng and Sheng [29,30,31] introduced an adapted Jensen wake model that assumes the wake aligns with the local terrain, offering a notable solution. Brogna et al. [32] refined Feng’s model, addressing limitations and capturing the wake physics more accurately. Tang et al. [33] used OpenFOAM^® to assess the wind flow in complex terrains before optimizing layouts. Song et al. [34,35] leveraged a bionic method and greedy algorithm to optimize wind farm layouts with a virtual particle wake flow model. In a different approach [36], a wake model combining CFD with Mixed-Integer Programming (MIP) for layout optimization effectively balanced the computation costs and precision in complex terrains.

Numerous decision variables beyond WT positions are set in the WFLO problem. Ali et al. [37] used a GA to maximize the output powers of two wind farms in Pakistan by considering the hub height and WT spacing as the decision variable. Authors in [38,39,40] utilized the WT hub height as a key decision variable in optimizing wind farm layouts. Their research outcomes demonstrate that adjusting the hub height can reduce the wake effect of a wind farm. Similarly, Feng et al. [41] and Abdulrahman et al. [42] have integrated WT selection and hub height as joint decision variables in the optimization process. Their findings underscore the efficacy of a non-uniform wind farm design in achieving a lower levelized cost of energy compared to a uniform layout. Moreover, their research highlights the preference for larger diameter and lower-rated speed WTs in the selection process, revealing these characteristics as paramount for optimizing a wind farm’s efficiency and cost effectiveness. This multifaceted approach to decision variables refines the layout and underscores the significance of turbine selection and height adjustments in achieving optimal performance and cost efficiencies within wind farms.

This study introduces a new metaheuristic algorithm called Modified Electric Charged Particles Optimization (MECPO) to optimize wind farms at some real onshore areas with different terrain and landscape characteristics deriving from meteorological and geographical data. In the proposed algorithm, some steps are added to enhance the algorithm’s exploration capability to find an optimal layout for the wind farm. The exploration capability is important in a coordinate-based WFLO problem, which has many constraints.

Moreover, a real terrain and landscape model was also implemented in the study to enhance the accuracy of the wind farm. The meteorological and geographical data from a real onshore area on South Sulawesi, Indonesia, are used to model the wind farm’s area. WAsP CFD is used to consider the effect of the terrain on the wind flow in the wind farm. In addition, several non-uniform wind farm scenarios are simulated by varying several wind farm parameters, including the hub height, rotor diameter, and WT type, to compare the wind farm’s performance with that of the uniform counterpart. The annual energy production (AEP) is set as the single objection function of the optimization process and the parameter used to compare each scenario.

This research makes several contributions as follows: (1) introduces a novel single-objective metaheuristic algorithm, the MECPO, demonstrating its superior performance compared to established algorithms in the field; (2) includes the model of terrain and landscape characteristics in the optimization process to increase the accuracy of the wind farm design; (3) implements the proposed algorithm and the model to optimize the wind farms at real onshore areas using meteorological and geographic data; and (4) analyze some scenarios of the non-uniform wind farm to find the best layout model for the wind farm.

The paper is organized as follows: Section 2 presents wind farm modeling. Section 3 provides a detailed description of the proposed algorithm. Section 4 shows the methodology. Section 5 presents the results and discussion, while Section 6 offers the conclusions.

2. Wind Farm Modeling

2.1. Wind Turbine Modeling

The market offers diverse types of WTs, providing consumers with a range of options to consider. Power output is a primary consideration among the crucial factors influencing the WT selection process. WTs are characterized by several key parameters, including their power curve profiles (cut-in speed, rated speed, and cut-out speed), power rate, and dimensions such as the diameter and hub height. These parameters play a pivotal role in determining the overall performance of a WT. The choice of a specific turbine type hinges on evaluating wind distribution patterns at the intended site, coupled with a thorough assessment of the associated costs. A comprehensive analysis is essential to determine the most suitable WT type for a given location.

The WT power rate determines the AEP of a wind farm. A WT is characterized by a specific power curve that determines the relationship between the power and wind speed. Figure 1 shows the power curve for a WT, and the respective power produced by a WT in each wind speed range is shown in Equation (1).

$$P\left(v\right)=\left\{\begin{array}{c}0 if V<V_{cut-in}\\ \lambda v+\eta if{ V}_{cut-in}<V<V_{rate}\\ P_{rate }if{ V}_{rate}<V<V_{cut-out}\end{array}\right.$$

(1)

The blades of a WT will start to spin when the wind speed is greater than V_cut-in. The power produced by the WT will increase as the wind speed increases between the V_cut-in and V_rate, and after the wind speed achieves the value V_rate, the power produced continues at P_rate until the V_cut-out.

The AEP can be calculated using Equation (2), which considers the wind distribution for all directions and speeds [43].

$$AEP=8760 {\int }_{A}p \left(\theta \right){\int }_V{p}_v\left(v;c_i; k_i|\theta \right) \eta \left(v\right)$$

(2)

where c and k denote the scale and shape parameters within the Weibull distribution, characterizing the wind resource’s intricate nature, while $\eta \left(v\right)$ is the power curve, and $p\left(\theta \right)$ and $p_v\left(v;c_i;k_i|\theta \right)$ are wind resource scenarios. These parameters encapsulate the nuanced characteristics of the wind, aiding in providing a comprehensive understanding and modeling of the characteristics of the wind resource.

2.2. Terrain and Landscape Modeling

The terrain and landscape characteristics of a site play a significant role in shaping its wind conditions. Specifically, the slope index determines the predominant features of the terrain. A site is deemed to have a flat terrain when the slope index exhibits minimal variation across all regions. Conversely, a complex terrain is characterized by a higher variability in the slope index. In areas with a flat terrain, it is reasonable to assume uniform wind conditions across an entire site. However, in a region with a complex terrain, a variation in the wind conditions emerges due to the alteration of the flow field, especially in areas with differing slope indexes. Therefore, the application of nonlinear models, such as CFD, becomes essential to accurately consider the impact of a complex terrain on the wind conditions at specific locations.

Moreover, the slope index influences the wind speed, with sites featuring a higher slope index generally experiencing elevated wind speeds. This phenomenon is attributed to wind acceleration due to the variation in the air density between higher-elevation and lower-elevation areas. Consequently, WTs situated in areas with higher slope indexes tend to generate more energy compared to those in regions with lower slope indexes.

The landscape characteristics influence the wake effect in WTs. Each landscape type has a different roughness length (Z₀), affecting the expansion coefficient of the wake effect (k), as shown in Equation (3). A greater roughness length has a notable impact on diminishing this expansion coefficient, leading to a reduction in the wake area trailing behind an upwind WT. The reduction in these affected areas translates to fewer WTs influenced by the wake effect. Consequently, the energy output from each WT in such conditions is higher.

Table 1. Roughness lengths for different landscapes [44].

Landscape	Roughness Class	Z0
Tall forest	4	1.5
City	4	1
Forest	3	0.8
Suburban	3	0.5
Shelterbelt	3	0.4
Many tresses and bushes	3	0.2
Farmland with a closed appearance	2	0.1
Farmland with an open appearance	2	0.05
Farmland with very few buildings/trees	1	0.03
Airport area with buildings and trees	1	0.02
Airport runway area	1	0.01
Mown grass	1	0.008
Bare soil (smooth)	1	0.005
Snow surface (smooth)	1	0.001
Sand surface (smooth)	1	0.0003
Water surface in the Atlas	1	0.0002
Water area (lake, fjord, open area)	1	0.0001

shows the roughness length for several types of landscape characteristics. By this factor, the reduced power because of the wake effect will differ for different landscape types.

$$k=\frac{0.5}{\ln \frac{z}{z_0}}$$

(3)

In this study, we used WAsP CFD to obtain the wind characteristics for each selected site. Each site is divided into a number of grids defined by a range of coordinates x (x₁, x₂,…., x_n) and y (y₁, y₂,…, y_n). The wind resource characteristics, including Weibull-A, Weibull-k, and the frequency for each direction sector (θ₁, θ₂,…, θ_n) are defined for each grid. The difference between the wind characteristics will affect the energy produced and the wake effect by a WT located in specific grids.

2.3. Wake Effect Model

The wake effect, characterized by a reduction in the wind velocity and power after a turbine extracts energy, poses a significant challenge in large wind farms, potentially diminishing the efficiency of each turbine by up to 15% [2]. Addressing this concern becomes a primary objective in wind farm design, with a key focus on minimizing the wake effect. Strategic turbine placement in specific locations is crucial to achieving this goal, aiming to mitigate the impact of power loss on adjacent turbines.

Modeling a wake effect in a complex terrain is challenging due to the complex interplay between the terrain and wake flow. Several studies have proposed models to calculate the wake effect for complex terrains, such as in [34,35], which presented a virtual particle wake model for a complex terrain WFLO. Moreover, Brogna et al. [32] and Feng et al. [30] used an adapted Jensen wake model by combining it with wind characteristics from a WAsP CFD simulation.

In this study, we adapted the wake models in [30,32] to model the wake effect in all the sites to account for the impact of the terrain. The terrain flows obtained from WAsP CFD simulations are coupled with the Jensen wake model, which assumes that the wake model centerline of a WT wake follows the terrain at the same height above the ground along the local inflow wind direction, with the wake zone expanding linearly. Figure 2 illustrates the wake expansion of two WTs at two locations, (x_i, y_i) and (x_j, y_j), with different elevations. The assumption is that the wind, flowing from wind WT_i to WT_j, has a distinct local wind speed due to the terrain effect. The wind speed in WT_i is V_i, and the wind speed in WT_j is V_j. The wind characteristics from both WT locations are modeled by the Weibull distributions (A_i, k_i, θ_i) and (A_j, k_j, θ_j).

The wake radius will expand linearly by the distance from the upwind turbine. In the distance dy_ij from the upwind turbine, the wake radius will be r_w = kdy_ij + r_i, where k is the wake expansion coefficient. The hub height z determines the coefficient k, and the surface roughness index Z_o defines Equation (3).

The wind speed V_j at this WT V_j will be reduced by Equation (4), where C_T is the thrust coefficient of the WT.

$$v_j^{\prime }=v_j\left[1-\sum _{i=1}^n\left(1-\sqrt{1-C_T}\right){\left(\frac{r_i}{r_i+k{dy}_{ij}}\right)}^2\frac{A_s}{A_j}\right]$$

(4)

For a wind farm, the wake areas between upstream and downstream WTs depend on their hub height, rotor diameters, and the changes in the wind direction. The wake areas A_s can be calculated by using Equation (5).

$$\begin{array}{cc}\hfill A_s={r_w}^2{\cos }^{-1}& \left(\frac{{{dx}_{ij}}^2+{r_w}^2+{∆h}^2-{r_j}^2}{2r_w\sqrt{{∆h}^2+{{dx}_{ij}}^2}}\right)\hfill \\ & +{r_j}^2{\cos }^{-1}\left(\frac{{{dx}_{ij}}^2+{r_j}^2+{∆h}^2-{r_w}^2}{2r_j\sqrt{{∆h}^2+{{dx}_{ij}}^2}}\right)\hfill \\ & -r_w\sqrt{{∆h}^2+{{dy}_{ij}}^2}.\sin \left({\cos }^{-1}\frac{{{dx}_{ij}}^2+{r_w}^2+{∆h}^2-{r_j}^2}{2r_w\sqrt{{∆h}^2+{{dx}_{ij}}^2}}\right)\hfill \end{array}$$

(5)

The position of upwind and downwind WTs will also change when the direction of the wind changes. Suppose two WTs are located at coordinates (x_i, y_i) and (x_j, y_j). The new coordinate of each WT based on the wind direction θ is shown in Equation (6). The latitudinal and longitudinal distance (dx_ij, dy_ij) can be expressed as Equation (7) [45]:

$$\left[\begin{array}{c}{x}_i^{\prime }\\ y_i^{\prime }\end{array}\right]=\left[\begin{array}{cc}\cos \theta & -sin\theta \\ \sin \theta & \cos \theta \end{array}\right]\left[\begin{array}{c}{x}_i\\ y_i\end{array}\right]$$

(6)

$$\begin{gathered} {dx}_{ij}=x_i^{\prime }-x_j^{\prime } \\ {dy}_{ij}=y_i^{\prime }-y_j^{\prime } \end{gathered}$$

(7)

The downwind WT will be influenced by upwind WT if and only if

$${dx}_{ij}<0 \& \left|{dx}_{ij}\right|-\frac{D_j}{2}<\frac{D_{wake,ij}}{2}$$

(8)

where

$$D_{wake,ij}=2(k {dy}_{ij}+r_j)$$

(9)

3. Optimization Algorithm

A metaheuristic algorithm is an optimization technique typically inspired by natural phenomena. It is particularly valuable for addressing diverse problems, especially those deemed challenging for conventional methods due to their inherent complexity. These algorithms draw inspiration from various natural phenomena such as biology, physics, and chemistry [46], and their procedural steps often emulate the corresponding natural processes.

Furthermore, by adhering to the principles of the No Free Lunch (NFL) theorem [47], which asserts that no single algorithm universally outperforms in solving all optimization problems, there has been a proliferation of new metaheuristic approaches dedicated to addressing complex optimization problems including WFLO. One such instance is the Electric Charged Particles Optimization (ECPO) [48], a new metaheuristic algorithm inspired by physics-related phenomena. ECPO simulates the optimization process by replicating interactions among electric charged particles (ECP). Notably, this algorithm has been employed in optimizing wind farm layouts in [49,50].

Exploration and exploration capabilities are two essential components in metaheuristic algorithms that help to balance the search process and improve the performance of the algorithm. Exploitation focuses on intensifying the search around the current promising solution to refine the best solution. In another way, the exploration involves diversifying the search across different regions around the solution spaces to prevent the algorithm from getting stuck in local optima and to broaden the span of the search area.

The exploration capability of the algorithm is essential to solving the WFLO problem with many constraints, such as the coordinate-based WFLO problem. In a grid-based WFLO problem, the wind turbine is located in the middle of the grid, where the distance between two midpoints of adjacent gridsis usually specified as the minimum allowable distance between two adjacent WTs. In this case, the distance constraint is automatically fulfilled. In another way, in a coordinate-based WFLO problem, WTs can be located in all wind farm areas based on the defined coordinates. So, the distance constraint is essential to ensure that the distance between two adjacent WTs is greater than the allowable distance.

The original ECPO encountered challenges in solving a coordinate-based WFLO, as shown in this study. Due to its limitation in exploration capability, the solution obtained from this algorithm tends to be stuck in the constraints area. To address this limitation, a refined version of ECPO, named MECPO, is developed to enhance the exploration capability of the original ECPO algorithm. This enhancement involves adding two additional steps to the original ECPO algorithm: “ionization” and “electron exchange”. Both steps are inspired by chemical phenomena, specifically mimicking chemical reactions, as observed in previous research [51,52,53].

In the original ECPO, the initial population comprises ECPs that interact with each other, giving rise to new ECPs. In MECPO, the initial population is represented by atoms, which undergo two new steps, “ionization” and “electron exchange”, to transform a population of atoms into a population of ions. These steps mimic the ionic process observed in chemical phenomena. Consequently, the ions resulting from these steps act as a population of ECPs that undergo the interaction step, following the original ECPO algorithm. Including these two new steps will increase the exploration capability of the algorithm by presenting new sets of search regions that are present by adding new electrons in the ionization step and exchanging electrons in the electron exchange steps. Figure 3 visually represents the three main steps of the MECPO algorithm that mimic the ionic process: ionization, electron exchange, and interaction.

The detailed process of MECPO is detailed in the following steps:

-

Initialization

The initiation of the MECPO algorithm involves randomly creating a population of atoms within the designated search space. Subsequently, a comprehensive evaluation ensues, appraising each atom based on its objective function performance. Following this assessment, the performance of each atom will be sorted to find the best atom.

-

Ionization

Once all the atoms are created, the next step involves transforming these atoms into ions by modifying the number of electrons within the atom population by adding a number of electrons from electron sources. Assuming that atoms are represented as a vector of electrons, $x_i=\left[x_1+x_2+\dots +x_M\right]$, where i = 1, 2, …, M, and ‘M’ is the number of electrons in an atom. Each value of the electron $x_i$ is added by a random number ‘p’ based on a normal distribution. Mathematically, the modification of an electron in an atom can be expressed as shown in Equation (10):

$$x_i^{\prime }=x_i+p$$

(10)

-

Electron exchange

This process draws inspiration from a redox reaction, transferring electrons between ions to create novel ions, thereby expanding the algorithm’s search space. Here, we assume that the two ions are represented by ‘P’ and ‘Q’. Both ion populations consist of vectors of electrons $\left[x_1+x_2+\dots +x_M\right]$, with ‘M’ representing the number of electrons in each ion. Initially, two ions are randomly selected from the population. The electron exchange occurs following these steps:

• The first ‘k’ electrons are extracted from the ion ‘P’, where ‘k’ is a randomly generated integer, where $1 \le k \le M-1$. These ‘k’ electrons are combined with the remaining ‘M-k’ electrons from the ion ‘Q’ to create a new ion.
• The first ‘k’ electrons from ion ‘Q’ are paired with the remaining ‘M-k’ electrons from ion ‘P’ to form another new ion.

These new ions then become ECPs and proceed through the subsequent stages in the original ECPO algorithm.

-

Interaction

In this process, each ECP will interact with the best ECP and with one other ECP simultaneously to make a new ECP. Mathematically, this interaction can be expressed as Equation (11).

$${ECP}_{new}={ECP}_1+\beta \times \left({ECP}_{best}-{ECP}_1\right)+\beta \times \left({ECP}_1-{ECP}_2\right)$$

(11)

-

Bound check

The news ECPs created in the previous process are checked to determine whether they are inside the search space or not. The ECPs located outside the search spaces will be bound back inside the search space.

Figure 4 depicts the flowchart outlining the MECPO algorithm. The optimization process commences with initialization, generating a population termed ‘atoms’. This initial population comprises vectors of decision variables, denoted as electrons. In the context of the WFLO problem, these electrons represent parameters such as the WT position, diameter, or hub height. Subsequently, this initial population undergoes an evaluation based on the objective and constraint functions. In this study, the wind farm’s AEP serves as the sole objective function, while constraints encompass the wind farm boundary, minimum distance between the adjacent turbines, and land obstacles. A penalty function is incorporated into the objective function if any constraint is violated. The population’s objective functions are then sorted from the highest to lowest values.

Following initialization, the population of atoms undergoes an ionization process. During this phase, each atom’s electron undergoes modification by a random number derived from a normal distribution. This step broadens the span of decision variables, bolstering the optimization process’s exploration capability. Atoms that undergo ionization are termed ions. These ions subsequently engage in an electron exchange process. Here, pairs of atoms exchange electrons, birthing new ions termed ECPs. The objective functions of all ECPs are evaluated and sorted, augmenting the algorithm’s exploration capability. The subsequent step involves interaction, wherein each ECP interacts with the best ECP and another randomly chosen ECP to generate a new ECP. This step is essential in the exploitation capability of the algorithm. The three steps (ionization, electron exchange and interaction) are run repeatedly based on the number of iterations to find the best-defined objective function.

4. Methodology

4.1. Problem Formulation

The main challenge in layout optimization lies in designing a wind farm layout that optimizes specific objectives while adhering to various constraints and design requirements. This task involves the manipulation of multiple variables, commonly used as objective functions in optimization problems. In this study, the primary objective of the optimization process is to maximize AEP. These objectives can be formally expressed as follows:

$$\max \left(\sum _{i=i}^{N}AEP(x_i,y_i,D_i, H_i) \right)$$

(12)

while the constraints on the optimization process are set as follows:

$$\begin{gathered} x_{min} \le x_i\le x_{max} \\ {y}_{min} \le y_i\le y_{max} \end{gathered}$$

(13)

$$\sqrt{{\left(x_i-x_j\right)}^2+{\left(y_i-y_j\right)}^2}\ge 5 D_i, i\ne j \in \left[1,n\right]$$

(14)

$$\forall i \in \left[1n\right], x_i\notin {\left[x_{O_L},x_{O_U}\right]}_o{y}_i\notin {\left[y_{O_L},y_{O_U}\right]}_o O=1, 2,\dots Oi$$

(15)

4.2. Research Flowchart

Figure 5 illustrates the framework employed in this research. This study begins by processing the land’s geographical and meteorological data using WAsP map editor and WAsP climate analysis, respectively. These data are inputted in WAsP and CFD modules to develop a wind resource map. This resource map is a composite of various grids, each dynamically adjustable in size to meet specific accuracy requirements precisely. This map presents wind energy indicators such as the Weibull k and c factors, wind speed direction (θ), and frequency (ω) for all respective areas by considering the terrain and landscape characteristics of the land. These indicators are pivotal in informing the wind farm design process, facilitating the strategic placement of WTs based on the data derived from the wind resource map. The data from the wind resource map are then derived to model the land and wind resource characteristics in the optimization process using Matlab software (https://ww2.mathworks.cn/products/matlab.html, accessed on 14 March 2024).

The optimization process is initiated by configuring the terrain conditions and dimensions within Matlab and synchronizing the grid size with the WAsP wind resource map. Simultaneously, all wind resource indicators are extracted from the wind resource map, and the chosen wind turbine type is modeled within the optimization problem. All of these parameters are used to calculate the AEP of the wind farm based on the position of each WT in the wind farm. In the next step, the MECPO algorithm is used to adjust the positions of the WTs to find the best uniform wind farm layout with the highest AEP. Furthermore, the best uniform wind farm layout is used as the reference design to optimize the non-uniform wind farm by using the WT type, hub height, and blade diameter as the decision variables.

4.3. Wind Farm Site Selection

Selecting an appropriate site for a wind farm involves a comprehensive evaluation of various criteria, primarily focusing on factors such as the wind speed and geographical conditions. This study uses the Global Wind Atlas (GWA) map [54] to identify the potential locations with high potential for wind energy in the South Sulawesi region, Indonesia. Based on the initial previews, most of these high-potential areas are inland, featuring diverse terrains and distinctive landscape characteristics. Furthermore, the high wind potential areas are investigated using Google Earth to consider existing facilities, geographical conditions, and availability, such as road access, proximity to the nearest power station, and distance to urban centers. A comprehensive analysis of these aspects reveals 16 locations with the potential to host wind farms, as illustrated in Figure 6, where the red markers denote the specific areas. The geographical details of each location are outlined in

Table 2. Geographical data for each potential area.

No.	Coordinate	Area	Distance to Nearest Power Substation (km)	Distance to Nearest Road (km)	Distance to the Nearest City (km)
1	−5.601977, 119.812088	11008 Ha	0.71 Km	0.36 Km	5.97 Km
2	−4.819707, 119.792862	39.92 Ha	20.6 km	0.19 km	0.25 Km
3	−4.571634, 119.788055	195 Ha	25.85 km	9.47 km	9.18 km
4	−4.868627, 119.820671	269.42 Ha	24.30 km	7.3 km	0.54 km
5	−5.111804, 119.937401	51.68 Ha	35 km	6.03 km	8.61 km
6	−5.148392, 119.890366	142.28 Ha	34.7 km	0.34 km	0.34 km
7	−5.051617, 119.862213	46.49 Ha	32.48 km	8.33 km	8.33 km
8	−4.999547, 119.80638	196.04 Ha	23 km	1.17 km	3.2 km
9	−4.976375, 119.84127	113 Ha	27.45 km	0.1 km	0.1 km
10	−4.924042, 119.785652	248 Ha	19.51 km	0.38 km	0.38 km
11	−5.114198, 119.884529	267 Ha	29.19 km	0.39 km	0.32 km
12	−4.518928, 119.809685	55.6 Ha	24.23 km	1.38 km	1.4 km
13	−4.310465, 119.828911	31.06 Ha	11.42 km	0.14 km	0.17 km
14	−4.255687, 119.709778	28.82 Ha	8.41 km	0.31 km	0.32 km
15	−4.042015, 119.793549	954 Ha	11.35 km	0.27 km	3 km
16	−4.023693, 119.734841	1891 Ha	10.56 km	5.43 km	8 km

, providing valuable insights for further assessment and planning.

Utilizing the reanalysis data obtained from SoDa MERRA2 [55], a comprehensive assessment of the wind resources across all sites was conducted, employing the Weibull distribution to characterize the wind distribution patterns.

Table 3. Wind characteristics for each potential location.

Location	k	c	WPD	Wind Power Class
1	1.98	7.7	578	4
2	1.34	8	780	5
3	1.71	7.1	701	5
4	1.71	6.6	465	3
5	1.49	7.1	562	4
6	1.7	6.8	482	3
7	1.72	7.1	727	5
8	1.49	6.9	926	6
9	1.72	6.88	1142	6
10	2.02	7.2	736	5
11	1.65	6.7	310	2
12	1.74	6.8	701	5
13	1.61	6.6	261	2
14	1.54	7.3	520	4
15	2.11	7.1	471	3
16	1.94	8.4	942	6

provides insights into each location’s wind characteristics and power density, revealing that nearly all locations fall within or above the Class 3 wind category.

This study selects three specific locations (locations 1, 15, and 16) to establish an onshore wind farm. These selected locations are denoted as Site 1, Site 2, and Site 3. Site 1 is situated in the southern part of the area and boasts a predominantly flat terrain, while Sites 2 and 3, located in the northern region, feature complex terrains. Maintaining uniformity, each site adheres to a standardized size and shape, measuring 4 km in length and 2 km in width in a rectangular configuration.

Figure 7 and Figure 8 visually depict the boundaries of each site, demarcating the precise areas within which WTs can be strategically positioned. As illustrated in the figures, the rectangular boundary lines serve as construction boundaries, ensuring the optimal placements of the WTs.

The terrain characteristics of the designated sites are illustrated in Figure 7. Within this representation, it is evident that Site 1 exhibits a relatively flat terrain characterized by a slope index of less than 5 degrees. In contrast, Site 2 features a moderate terrain, predominantly comprising areas with slopes ranging between 8 and 14 degrees. Meanwhile, Site 3 can be classified as having a complex terrain, encompassing regions with slopes exceeding 33 degrees.

Figure 8 offers a detailed insight into the landscape characteristics of the three sites. Site 1 is predominantly marked by agricultural land use, interspersed with residential areas. Site 2 primarily comprises grasslands, with approximately two-thirds of certain regions designated for agriculture and a few areas covered by forests. Site 3 is predominantly forested, with only limited sections featuring grasslands and agricultural use. Each site is earmarked for the installation of 20 WTs. Additionally, Figure 9 presents the wind rose diagram for a specific point within each site, providing a comprehensive overview of the prevailing wind directions.

The wind distribution in specific locations can exhibit notable variations in a complex terrain. This study divides the designated sites into 50 grids measuring 400 m × 400 m. The wind data for each grid are obtained from WAsP CFD, ensuring a thorough understanding of the terrain’s impact. The gross power output is illustrated in Figure 10, employing a WT with the characteristics outlined in

Table 4. Wind turbine parameters.

Parameter	Value	Unit
Prated	2	MW
Vcut-in	3	m/s
Vrated	9	m/s
Vcut-off	25	m/s
Blade diameter	116	m
Hub height	80	m
Thrust coefficient	0.87

. This figure visually depicts the generated power across the diverse grids within the respective sites. It is essential to emphasize that gross power represents the power produced by the WT in the respective grid, excluding the wake effect. Therefore, the optimization task involves identifying the optimal combination of WT positions at each site to achieve the highest net AEP.

4.4. Wind Turbine Selection

Many commercial WTs are available in the market. Their power rates and blade diameters usually specify the turbine. For example, WT WD103-1200 is a WT with a 2000 kW power rating and 103 m blade diameter.

Table 5. Wind characteristics and dimensions of various commercial types of wind turbines.

WT Code	Brand	Vi	Vr	Vo	Prate	D	Hmin	Hmax
WT1	UP86	2.5	10.5	25	1500	86	65	80
WT2	GW82/1500	3	11	25	1500	82.3	70	100
WT3	LTW90/1500	3	1011.5	25	1500	90.3	80	80
WT4	SG1700.100	3	10	20	1700	100	100	100
WT5	WD103-2000	2.5	10	20	2000	103	80	100
WT6	H93-2000	2.5	11	25	2000	92.8	70	80
WT7	TZ2000/116	3	9	25	2000	116	70	90
WT8	WT2000df/113	3	9.5	20	2000	113	90	100
WT9	XE93-2000	3	10.5	25	2000	93.4	65	80
WT10	HJWT2000/87	3	11	25	2000	87	85	85
WT11	SG2.1-114	1.5	9	25	2100	114	68	153
WT12	AGW110/2.1	2.5	11	20	2100	110	80	120
WT13	U120	3	9.8	22	2300	120	100	100
WT14	G114/2500	2.5	11	24	2500	114	80	140
WT15	WD103-2500	2.5	11	25	2500	103	80	100
WT16	TZ2500/122	3	9.3	25	2500	122	90	90
WT17	SG2500.131 DD	3	10	20	2500	131	120	120
WT18	Vensys 121	3	11	22	2500	121	90	90
WT19	SG2700.116 DD	3	10.5	24	2700	116	100	100
WT20	WT3000df/140	3	9.5	20	3000	140	100	110
WT21	GW140/3400	2	10.5	20	3400	140	100	120
WT22	V136/3450	2.5	11	22	3450	136	112	166
WT23	Vensys 136	2.5	11.5	22	3500	136	81.7	161.2
WT24	SWT-3.6-130	2.5	13	25	3600	130	85	165
WT25	XD140-4000	3	10.5	25	4000	140	100	140
WT26	V150/4200	3	9.9	22.5	4200	150	105	166
WT27	AGW147/4.2	3	11	20	4200	147	120	120
WT28	U151	3	10.2	25	4300	151	95	125

provides a comprehensive overview of various WT types [56], offering key parameters for each turbine. These parameters include the power curve, WT dimensions, rotor diameter, and hub height range, uniquely defining each WT.

This study chose some WTs by considering their power rates and blade diameters. The first group of WTs chosen is those with the same power rate but differences in other parameters. This classification determines six types of WTs (WT5–WT10) with a 2000 kW power rate. The second group consists of WTs with the same power rate and same power curve (WT14 and WT15). In this group, the WT blade diameter is the only variable, so the effect of the WT blade diameter can be analyzed.

4.5. Compared Algorithms and Parameters Setting

Three well-known algorithms are used to compare the performances of the proposed algorithm: the GA, the ICA, and the BBO. The GA is a metaheuristic algorithm inspired by natural selection and genetics. This algorithm consists of three main steps: selection, crossover, and mutation. The ICA is the population-based algorithm inspired by the concept of imperialism. In this algorithm, a more powerful individual called an empire will dominate and control the region of the solution space. The steps in this algorithm consist of imperialist competition, assimilation, and revolution. The BBO is also a population-based algorithm inspired by species distributions in various environments over time. This algorithm consists of four steps: migration, mutation, selection, and replacement. The pseudocodes of the proposed is shown in Algorithm 1 and the pseudocode of comparison algorithm are shown in Algorithms 2–4.

Algorithm 1 MECPO
1	Inputs	Objective function (ObjFunc), dimension of the problem (nVar), number of atoms (nA), lower boundary (lb), upper boundary (ub), ionization coefficient (nIon), exchange coefficient (nE), number of interacting ions (nInt), and maximum iteration (maxIt)
2	Outputs	Best ECP, Best Cost
3	Initialization the Atom	for i = 1: nA
			Atom(i) = rand (lb, ub, nVar)
			Cost (i) = evaluate (Atom (i))
		end for
4	Main Algorithm	for i = 1: maxIt
			Ionization (nIon)
			ElectronExchange (nE)
			IonInteraction (nInt)
			Bound Check ( )
		end for

Algortihm 2 GA
1	Inputs	Objective function (ObjFunc), dimension of the problem (nVar), number of populations (nPop), lower boundary (lb), upper boundary (ub), crossover percentage (pC), mutation percentage (pM), mutation rate (mu), and maximum iteration (maxIt)
2	Outputs	Best Pop, Best Cost
3	Initialization population	for i = 1: nPop
			Population(i) = rand (lb, ub, nVar)
			Cost (i) = evaluate (Population (i))
		end for
4	Main Algorithm	for i = 1: maxIt
			Crossover (pC)
			Mutation (pM,mu)
			Bound Check ( )
		end for

Algorithm 3 ICA
1	Inputs	Objective function (ObjFunc), dimension of the problem (nVar), number of populations (nPop), keep rate (rK), lower boundary (lb), upper boundary (ub), selection pressure (alpha), assimilation coefficient (beta), revolution probability (PRev), colonies mean cost coefficient (zeta), and maximum iteration (maxIt)
2	Outputs	Best Empire, Best Cost
3	Initialization population	for i = 1: nPop
			Emp(i) = rand (lb, ub, nVar)
			Cost (i) = evaluate (Emp (i))
		end for
4	Main Algorithm	for i = 1: maxIt
			AssimilateColonies (beta, zeta)
			DoRevolution (pRev, nEmp)
			IntraEmpireCompetition (nEmp)
			InterEmpireCompetition (alpha)
			Bound Check ( )
		end for

Algorithm 4 BBO
1	Inputs	Objective function (ObjFunc), dimension of the problem (nVar), number of habitats (nH), lower boundary (lb), upper boundary (ub), keep rate (rK), migration rate (alpha), mutation rate (rMu), and maximum iteration (maxIt)
2	Outputs	Best Habitat, Best Cost
3	Initialization population	for i = 1: nH
			Habitat(i) = rand (lb, ub, nVar)
			Cost (i) = evaluate (Habitat (i))
		end for
4	Main Algorithm	for i = 1: maxIt
			Migration (alpha)
			Mutation (rMu)
			Bound Check ( )
		end for

In this study, all the algorithms were set using the same parameters, with 200 maximum iterations and 50 populations. The detailed setting parameters for each algorithm are shown in

Table 6. Parameter settings for the compared algorithms [57].

MECPO		GA		ICA		BBO
Ion interaction coefficient	5	Crossover percentage	0.7	Number of empires	10	Keep rate	0.2
Ion exchange coefficient	0.5	Mutation percentage	0.4	Selection pressure	1	Alpha	0.9
Ion ionization coefficient	0.5	Mutation rate	0.02	Assimilation coefficient	1.5	Mutation rate	0.1
				Revolution probability	0.1
				Revolution rate	0.1
				Colonies mean cost coefficient	0.2

.

5. Results and Discussion

Wind farms can be planned with either uniform or non-uniform configurations, depending on whether the turbines are identical or varied. A wind farm is termed uniform when all turbines are identical, simplifying the optimization process to focus solely on the turbine positioning. Conversely, non-uniform wind farms introduce additional decision variables such as the WT type, hub height, or blade diameter.

In this study, the initial phase begins with optimizing a uniform wind farm layout, where turbine positioning is the sole decision variable. The optimal layout obtained from uniform WFLO is used as the reference design for optimizing the respective non-uniform wind farms. Subsequently, for non-uniform designs, turbine locations are fixed based on the best layout from the uniform design phase. The decision variables include the turbine type, hub height, and diameter, allowing for a more comprehensive exploration of the design possibilities.

5.1. Uniform Wind Farm Layout Optimization

In this study, two different scenarios are considered. In the first scenario, six specific WT types (WT5–WT10) are selected, sharing identical power rates but varying wind power curve profiles and rotor diameters. In the second scenario, two WT types (WT14 and WT15) with the same power rate and power curve profile are chosen, differing only in their rotor diameter.

For both scenarios, 20 WTs are optimized within each site’s wind farm framework, enabling a thorough comparative performance analysis. To maintain consistency, a uniform hub height of 85 m is set for all WTs, a value carefully selected based on the hub height range available for each WT type, as detailed in Table 5.

Table 7. Performance comparison among selected WT types for the first scenario.

Site	WT Type	Net AEP (GWh)		Gross AEP (GWh)		Wake Index (%)
		Mean	SD	Mean	SD	Mean	SD
Site 1	WT5	253.411	1.119	266.156	0.652	4.789	0.254
	WT6	241.174	1.247	252.822	1.405	4.607	0.150
	WT7	260.772	0.705	274.773	0.791	5.095	0.148
	WT8	252.824	1.785	267.504	1.886	5.487	0.329
	WT9	243.107	0.959	255.147	0.546	4.719	0.329
	WT10	237.342	0.779	248.344	0.606	4.430	0.167
Site 2	WT5	212.447	1.422	229.265	2.712	7.331	0.585
	WT6	199.894	2.109	214.069	3.321	6.613	0.925
	WT7	219.137	1.976	237.145	2.000	7.594	0.126
	WT8	211.138	3.209	230.381	2.479	8.356	0.455
	WT9	199.923	0.838	214.782	0.908	6.918	0.288
	WT10	193.875	4.065	207.037	3.662	6.362	0.402
Site 3	WT5	287.977	1.374	295.737	1.280	2.624	0.174
	WT6	279.293	1.664	286.815	1.197	2.623	0.206
	WT7	292.991	1.692	302.063	1.356	3.004	0.156
	WT8	287.836	1.303	297.217	0.718	3.157	0.220
	WT9	280.857	0.764	288.511	0.360	2.653	0.152
	WT10	276.061	1.619	283.088	1.284	2.483	0.178

illustrates the performance comparison of each selected WT for the first scenario. WT7 emerges as the frontrunner, generating the highest gross and net AEPs across all sites. This outcome is driven by the favorable impacts of lower rate speeds V_rate on the energy production, although WT7 boasts a larger rotor diameter, contributing to a higher wake index.

Table 8. Performance comparison for the second scenario.

Site	WT Type	Net AEP (GWh)		Gross AEP (GWh)		Wake Index (%)
		Mean	SD	Mean	SD	Mean	SD
Site 1	WT14	296.517	1.190	315.760	1.174	6.094	0.064
	WT15	299.577	1.053	316.443	1.108	5.330	0.249
Site 2	WT14	246.947	2.221	270.079	1.737	8.566	0.320
	WT15	249.651	2.046	270.613	0.899	7.747	0.551
Site 3	WT14	344.407	1.655	357.364	1.263	3.626	0.203
	WT15	347.220	1.518	357.988	1.361	3.008	0.113

presents a performance comparison for the second scenario. Notably, WTs with a smaller rotor diameter (WT15) consistently exhibit a higher net AEP and lower wake index across all sites. The gross AEP remains nearly identical for both WT types due to the same power rate and wind speed characteristic for both WTs. These findings underscore the pivotal role of the rotor diameter in shaping the wake index, while the WT’s power curve significantly influences the gross AEP. It becomes evident that the interplay between these WT parameters is crucial in determining the net AEP for each wind farm.

Each case is simulated eight times to address the inherent stochasticity of the metaheuristic algorithm. The wind farm layout with the highest net AEP value from these runs is used as the reference design for optimizing the non-uniform wind farm layout. The optimal layouts for both scenarios are visually represented in Figure 11 and Figure 12, showcasing the differences between the traditional and optimal layouts for each site.

Table 9. Results comparison for traditional and optimal layouts for the first scenario.

Site	Parameter	Traditional Layout	Optimal Layout
Site 1	Gross AEP (GWh)	276.16	274.72
	Net AEP (GWh)	249.67	258.684
	Wake index (%)	9.59	5.84
Site 2	Gross AEP (GWh)	248.87	238.087
	Net AEP (GWh)	209.51	218.718
	Wake index (%)	15.81	8.14
Site 3	Gross AEP (GWh)	305.068	303.195
	Net AEP (GWh)	292.111	293.977
	Wake index (%)	4.25	3.04

and

Table 10. Results comparison for traditional and optimal layouts for the second scenario.

Site	Parameter	Traditional Layout	Optimal Layout
Site 1	Gross AEP (GWh)	318.3	316.957
	Net AEP (GWh)	287.249	299.369
	Wake index (%)	9.75	5.55
Site 2	Gross AEP (GWh)	281.92	269.55
	Net AEP (GWh)	239.492	246.736
	Wake index (%)	9.12	8.46
site 3	Gross AEP (GWh)	362.769	360.159
	Net AEP (GWh)	346.77	349.216
	Wake index (%)	4.35	3.118

show the result comparison between the traditional and optimal layout for the first and second scenario. In the traditional layout, the WT positions are determined by selecting the grid with the highest wind power based on the power distribution depicted in Figure 10. Notably, the traditional approach may yield a higher gross AEP, but it is accompanied by a higher wake index, resulting in a lower net AEP than the optimized layout. This observation highlights that the optimal layout effectively enhances the net AEP by minimizing the wake effects within the wind farm.

5.2. Non-Uniform Wind Farm Design Optimization

As highlighted in the preceding sections, the wake effect is influenced by the WT blade diameter, whereas the wind farm’s gross AEP is contingent upon the power curve profile of the WT. In the first scenario, the WT with lower V_rated values (WT7) demonstrates higher net and gross AEPs despite generating a more substantial wake effect attributable to its larger blade diameter. Conversely, in the second scenario, where WTs exhibit identical wind power curve profiles, the WT with a smaller blade diameter produces the least pronounced wake effect, resulting in a higher net AEP.

Subsequently, an in-depth analysis of the non-uniform wind farms is planned, with optimal uniform wind farm layouts with WT7 and WT15 selected as the reference. This section delves into the study of various non-uniform wind farm cases, which can be described as follows:

• Case I: Wind farm featuring the same WT type but varying hub heights using WT7;
• Case II: Wind farm with the same hub height but diverse WTs type, encompassing various wind power curves and blade diameters;
• Case III: Wind farm with the same WT type but varying hub heights using WT15;
• Case IV: Wind farm maintains uniform hub heights and wind power curve profiles while incorporating variable blade diameters.

The optimization process for non-uniform wind farms follows the initial layout optimization conducted for the uniform wind farms. The optimal layout obtained from the uniform wind farm serves as the baseline for the subsequent non-uniform optimization. During the non-uniform optimization, the layout remains constant, while other parameters, such as the hub height, WT type, and blade diameter, become decision variables based on specific cases. The superiority of a non-uniform wind farm design is determined by the improved performance of its objective function compared to the reference uniform wind farm. If the objective function remains identical to the reference uniform wind farm, it indicates that the uniform wind farm is better than its counterpart non-uniform design.

Table 11. Performance comparison for Cases I and II.

Indicator	Site 1			Site 2			Site 3
	Uniform	Non-Uniform		Uniform	Non-Uniform		Uniform	Non-Uniform
		Hub Height (Case I)	WT Type (Case II)		Hub Height (Case I)	WT Type (Case II)		Hub Height (Case I)	WT Type (Case II)
Net AEP	258.684	259.086	258.684	218.718	219.207	218.718	293.977	294.298	293.977
SD net AEP	-	0.008	0.000	-	0.012	0.156	-	0.006	0.125
Gross AEP	274.72	274.729	274.729	238.087	238.087	238.087	303.195	303.195	303.195
SD gross AEP	-	0.000	0.000	-	0.000	0.226	-	0.000	0.131
Wake index	5.84	5.694	5.840	8.135	7.930	8.030	3.040	2.935	3.038
SD wake index	-	0.003	0.000	-	0.005	0.036	-	0.002	0.001

and

Table 12. Performance comparison for Cases III and IV.

Indicator	Site 1			Site 2			Site 3
	Uniform	Non-Uniform		Uniform	Non-Uniform		Uniform	Non-Uniform
		Hub Height (Case III)	WT Type (Case IV)		Hub Height (Case III)	WT Type (Case IV)		Hub Height (Case III)	WT Type (Case IV)
Net AEP	299.369	299.588	299.369	246.736	247.087	246.736	349.216	349.351	349.216
SD net AEP	-	0.009	0.000	-	0.014	0.023	-	0.007	0.000
Gross AEP	316.957	316.957	316.957	269.550	269.550	269.550	360.159	360.159	360.159
SD gross AEP	-	0.000	0.000	-	0.000	0.000	-	0.000	0.000
Wake index	5.549	5.480	5.549	8.460	8.333	8.460	3.118	3.001	3.118
SD wake index	-	0.003	0.000	-	0.005	0.008	-	0.002	0.000

present a comprehensive performance comparison for all non-uniform wind farm layouts. The findings reveal a net AEP increase exclusively for Cases I and III, where the sole variable is the hub height. In contrast, for Cases II and IV, the optimal layout is achieved when the wind farm features the same type of WT. For case II, with several WT types with different power curves set as the design variables, the best objective is when all the WT types are WT7, which has the highest gross AEP. Even though this type of design also produces the highest wake effect due to the largest rotor diameter size, the optimization still tends to choose this type of WT, because the impact of the gross AEP is more significant than the effect of wake effect reduction. The interesting result is that in Case IV, with the rotor diameter being the only decision variable, the result shows that a uniform diameter for WTs is better than a non-uniform one. All the results show that the non-uniform wind farm outperforms the uniform one only if the varied hub heights are used with the same types of WT (Case I and III). Visual representations of the optimal wind farm layouts for Cases I and III can be found in Figure 13 and Figure 14.

5.3. Performance Comparison

Three well-known metaheuristic algorithms are used to compare the performance of proposed MECPO algorithm. All algorithms are used to optimize the uniform wind farms using WT7 for all three sites.

Table 13. Performance comparison for Site 1.

Algorithm	AEP (GWh)		AEPG (GWh)		Wake Index (%)		SR (%)
	Mean	SD	Mean	SD	Mean	SD
MECPO	257.919	2.007	272.999	1.519	5.525	0.265	100.00
GA	231.155	0.000	251.332	0.000	8.028	0.000	12.50
ICA	251.437	3.665	268.337	3.976	6.298	0.254	75.00
BBO	246.896	5.217	265.809	4.433	7.120	0.648	62.50

,

Table 14. Performance comparison for Site 2.

Algorithm	AEP (GWh)		AEPG (GWh)		Wake Index (%)		SR (%)
	Mean	SD	Mean	SD	Mean	SD
MECPO	217.354	2.083	236.956	2.158	8.271	0.545	100.00
GA	197.043	2.793	222.437	3.377	11.412	0.798	50.00
ICA	210.163	2.342	229.578	2.672	8.455	0.505	100.00
BBO	206.773	3.635	229.294	2.770	9.826	0.695	75.00

and

Table 15. Performance comparison for Site 3.

Algorithm	AEP (GWh)		AEPG (GWh)		Wake Index (%)		SR (%)
	Mean	SD	Mean	SD	Mean	SD
MECPO	291.949	0.949	301.391	0.689	3.133	0.203	100.00
GA	278.212	0.040	291.132	0.912	4.437	0.287	37.50
ICA	287.487	2.153	297.591	2.133	3.395	0.207	100.00
BBO	282.212	3.417	294.258	2.679	4.095	0.361	50.00

show the algorithm performances for all sites.

The presented table unequivocally demonstrates the superior performance of the MECPO algorithm in comparison to three widely recognized algorithms, namely GA, ICA, and BBO, across all examined sites. Notably, MECPO exhibits an outstanding 100% success rate for all sites, underscoring its efficacy in consistently identifying solutions that satisfy all imposed constraints in each of the eight simulation instances. This achievement underscores the enhanced exploration capability inherent in the MECPO algorithm, surpassing that of its counterparts.

The heightened exploration capability of MECPO Is attributed to incorporating two pivotal steps: ionization and electron exchange. These steps contribute to a broader spectrum of solution spaces in each iteration, introducing a new set of searching regions and reconfiguring existing ones. As a result, MECPO not only outshines other algorithms in terms of success rates but also showcases an extended reach in its exploration of the solution space.

Furthermore, the optimization of success simulations reveals that MECPO consistently achieves the highest AEP across all sites, indicating its superior exploitation capability. This proficiency is rooted in the interaction step of the algorithm, wherein the population engages with the best-performing subset to further refine the objective function. The confluence of these three pivotal steps within the MECPO algorithm has proven to strike a delicate balance between exploration and exploitation. In summary, the comprehensive analysis affirms the MECPO algorithm as a robust and versatile optimization tool, showcasing its prowess in handling diverse scenarios and outperforming its counterparts.

5.4. Analysis of the Effects of Terrain and Landscape Characteristic

Each site examined in this study exhibits distinct terrain and landscape characteristics. Site 1, characterized by a flat terrain, predominantly comprises agricultural areas featuring a mediated value roughness length (Z₀ = 0.05). Site 2, predominantly grasslands, is categorized as semi-complex terrain with a notably lower roughness length of approximately 0.008. In contrast, Site 3 is classified as a complex terrain with an elevated topography. This site is primarily covered by a forested area, boasting a considerably higher roughness length of 0.8.

Table 16. Comparison of terrain effects on AEP.

Site	Slope	Dominant Z0	Gross AEP (GWh)		Wake Effect (GWh)		Net AEP (GWh)
			Mean	SD	Mean	SD	Mean	SD
Site 1	<50	0.05	272.274	1.323	16.810	0.908	255.464	1.619
Site 2	80–140	0.008	235.301	3.580	21.482	2.727	213.819	3.332
Site 3	>330	0.8	298.812	2.158	10.478	0.837	288.334	2.822

provides a comparative performance analysis of each site based on the wind farm’s energy production. Site 3 has the highest wind speed resources, yielding a superior gross AEP. Additionally, Site 3 exhibits the lowest wake effect, attributed to its elevated roughness length.

From a terrain perspective, the elevation index and slope play pivotal roles in shaping the wind dynamics. The locations with a higher elevation index exhibit higher wind speeds, leading to a higher gross AEP. Similarly, the slope index induces a similar effect, with sites boasting higher slope indexes experiencing heightened wind speeds due to air acceleration as it descends from elevated to lower terrains. Table 16 highlights that Site 3 has the highest gross AEP, attributed to its elevated elevation and substantial slope index compared to the other two sites.

A site’s landscape characteristics significantly influence the wake effect within a wind farm. Varied landscapes contribute to distinct roughness lengths (Z₀), impacting the wake expansion parameter (k). Higher roughness lengths result in a diminished wake expansion, translating to a reduced influence on downwind turbines. Consequently, sites with higher roughness lengths, exemplified by Site 3 in Table 16, exhibit a diminished wake effect, leading to a higher net AEP. In essence, the interplay of the elevation, slope, and roughness length characteristics shapes the wind farms’ overall AEP.

6. Conclusions

Optimizing the layout of a wind farm is an essential step in designing an optimal wind farm design. Reducing the wake will increase the total energy produced by a wind farm. Besides the positions of WTs, the types of WTs can also be optimized to reduce the wake effect. In this research, a new metaheuristic algorithm called MECPO is developed to optimize both the WT position and type. The terrain and landscape characteristics are considered in the optimization to increase the accuracy of the result. Three sites with different terrain and landscape characteristics are used to test the algorithm’s performance. A single-objective WFLO is implemented to optimize the wind farm’s AEP. Several cases of non-uniform wind farms are simulated and compared with their uniform counterparts. The cases involve different decision variables, including the hub height, rotor diameter, and WT type. The optimization problem is set in the series system, with the non-uniform variables optimized after the layout optimization achieves the best result. The uniform wind farm is the reference layout to compare the non-uniform case’s performance. The result shows that the non-uniform wind farm is only better in the variable hub height when using the same type of WT. In terms of the algorithm performance, the proposed algorithm shows an excellent performance by outperforming the GA, CA, and BBO and has a 100% success rate for all the cases. Furthermore, Site 3, with a higher elevation, slope index, and mainly a higher roughness length, results in a lower wake effect and higher AEP than the two other sites with a lower elevation, slope index, and roughness length.