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

By inergency On Mar 22, 2024

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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).

$P (v) = \{\begin{matrix} 0 i f V < V_{c u t - i n} \\ λ v + η i f V_{c u t - i n} < V < V_{r a t e} \\ P_{r a t e} i f V_{r a t e} < V < V_{c u t - o u t} \end{matrix}$

(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].

$A E P = 8760 \int_{A} p (θ) \int_{V} p_{v} (v; c_{i}; k_{i} | θ) η (v)$

(2)

where c and k denote the scale and shape parameters within the Weibull distribution, characterizing the wind resource’s intricate nature, while $η (v)$ is the power curve, and $p (θ)$ and $p_{v} (v; c_{i}; k_{i} | θ)$ 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 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.

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.

$v_{j}^{'} = v_{j} [1 -| \sum_{i = 1}^{n}| (1 - \sqrt{1 - C_{T}}) {(\frac{r_{i}}{r_{i} + k {d y}_{i j}})}^{2} \frac{A_{s}}{A_{j}}]$

(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).

$\begin{matrix} A_{s} = {r_{w}}^{2} \cos^{- 1} & (\frac{{d x}_{i j}^{2} + {r_{w}}^{2} + {∆ h}^{2} - {r_{j}}^{2}}{2 r_{w} \sqrt{{∆ h}^{2} + {d x}_{i j}^{2}}}) \\ + {r_{j}}^{2} \cos^{- 1} (\frac{{d x}_{i j}^{2} + {r_{j}}^{2} + {∆ h}^{2} - {r_{w}}^{2}}{2 r_{j} \sqrt{{∆ h}^{2} + {d x}_{i j}^{2}}}) \\ - r_{w} \sqrt{{∆ h}^{2} + {d y}_{i j}^{2}} . \sin (\cos^{- 1} \frac{{d x}_{i j}^{2} + {r_{w}}^{2} + {∆ h}^{2} - {r_{j}}^{2}}{2 r_{w} \sqrt{{∆ h}^{2} + {d x}_{i j}^{2}}}) \end{matrix}$

(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]:

$[\begin{matrix} x_{i}^{'} \\ y_{i}^{'} \end{matrix}] = [\begin{matrix} \cos θ \end{matrix}| - s i n θ| \sin θ] \cos θ [\begin{matrix} x_{i} \\ y_{i} \end{matrix}]$

(6)

${d x}_{i j} = x_{i}^{'} - x_{j}^{'} {d y}_{i j} = y_{i}^{'} - y_{j}^{'}$

(7)

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

${d x}_{i j} < 0 & |{d x}_{i j}| - \frac{D_{j}}{2} < \frac{D_{w a k e, i j}}{2}$

(8)

where

$D_{w a k e, i j} = 2 (k {d y}_{i j} + r_{j})$

(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:

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} = [x_{1} + x_{2} + \dots + x_{M}]

, 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):

–: 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 $[x_{1} + x_{2} + \dots + x_{M}]$ , 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 $1 \leq k \leq M - 1$ . 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).

${E C P}_{n e w} = {E C P}_{1} + β \times ({E C P}_{b e s t} - {E C P}_{1}) + β \times ({E C P}_{1} - {E C P}_{2})$

(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.

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 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 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 and Table 10 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 and Table 12 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, Table 14 and Table 15 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 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.

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