Conceptual Design of Wind Farms Through Novel Multi Objective Swarm Optimization Syracuse University Syracuse University SURFACE SURFACE Dissertations ALL SURFACE May 2015 Conceptual Design of Wind Fa[.]
Overview of Wind Farm Development
Economic Aspect
The economic feasibility of a wind energy project depends on multiple critical factors that must be thoroughly analyzed Understanding the interrelation between these factors is essential to gain a comprehensive, quantitative insight into the challenges associated with wind farm design This holistic approach ensures more accurate assessments, leading to optimized, cost-effective wind energy solutions.
The economics of energy systems are primarily influenced by four key cost factors: capital cost, operation and maintenance cost, fuel cost, and external cost Fuel and external costs are particularly sensitive to the type of fuels used, impacting overall system economics Additionally, market and policy parameters—such as incentive programs, production tax credits, and discount or inflation rates—play a significant role in shaping the economic performance and viability of energy systems.
Key elements governing the economics of a wind energy project are listed below [6,7]:
• electricity production cost (or capacity factor);
Wind energy requires high initial investments, making it capital-intensive, but its upfront project costs are generally lower than those of most new conventional energy sources, positioning wind as a highly cost-effective clean energy technology The total installed capital cost for onshore and offshore wind projects is detailed in Table 1.1, highlighting the economic aspects of wind energy deployment Additionally, U.S wind energy prices have declined by approximately 90% since the early 1980s, driven by advancements in technology and manufacturing improvements domestically.
The Levelized Cost of Energy (LCOE) is the key metric used to evaluate and compare the economic viability of wind and other renewable energy projects It quantifies the total cost of building, operating, and maintaining a wind farm over its expected lifespan, expressed in dollars per kilowatt-hour ($/kWh) By discounting all financial flows to a common point in time, the LCOE provides a comprehensive measure for assessing renewable energy project's competitiveness and financial performance.
Table 1.1: Capital Cost Breakdown for Typical Onshore/Offshor Wind Energy Projects in 2011 [11]
1: Wind turbine costs generally include manufacture, transportation, and installation of the turbine rotor, blades, and gearbox.
2: Grid connection costs generally include cabling, substations, and buildings.
3: Construction costs generally include transportation and installation of the turbine rotor, tower, and foundation, as well as road access and infrastructures required for the construction.
4: Other capital costs generally include regulatory (e.g., consulting and permitting) costs, and costs of engineering development and monitoring systems. year [7,12] The widely used formula to calculate theLCOE of renewable energy is given by:
It = investment expenditures in the year t
M t = operation and maintenance expenditures in the year t
Ft = fuel expenditures in the year t
E t = electricity generation in the year t r = discount rate n = economic life of the system
The wind turbine represents the largest single cost component of a wind farm’s total installation expenses, with rotor blades, the tower, and gearbox collectively accounting for up to 60% of a turbine's cost Electricity production costs are highly dependent on wind resource availability; a 10% reduction in wind speed can lead to more than a 20% decrease in energy output due to the high sensitivity of energy generation to wind speed fluctuations Key planning activities—including site analysis, wind resource assessment, turbine selection, and farm layout design—significantly influence both project costs and financial viability Understanding how these interconnected factors impact the balance between economic performance and other objectives such as energy output, land use, and environmental impact is crucial for optimizing wind farm development.
Engineering Aspect
As wind flows across a turbine, the power available (P0) in the wind is given by
2ρAU ∞ 3 (1.2) where ρis the air density; Ais the rotor swept area; andU∞ is the incoming wind speed at hub height (assuming uniform velocity profile).
The power generated from the turbine is given by
P = (p1−p2)AV (1.3) wherep1 andp2 are the pressure immediately in front of and behind the turbine, respectively;
V is the velocity through the turbine.
Assuming the air flow is incompressible, from continuity equation and Bernoulli’s equa- tion, we have ρA∞U∞=ρAV =ρAdUd
(1.4) where U d is the downstream wind speed; A ∞ and A d represent the cross sectional area of the incoming wind flow and the downstream flow in the stream tube, respectively.
2(U∞+Ud) (1.5) which means that the velocity through the turbine is the mean of the upstream and down- stream velocities (in the stream tube).
Therefore, the turbine power coefficient, Cp, can be given by
The maximum power coefficient of a wind turbine is described by the formula 2(1−d)(1 +d) 2, where d equals Ud divided by U∞ It can be demonstrated that the turbine’s maximum efficiency occurs when Ud/U∞ equals 1/3 This highest possible efficiency, known as the Betz limit, represents the theoretical maximum power that a wind turbine can extract from the wind.
Effective wind energy extraction depends on engineering activities that directly influence project performance, encompassing key processes at the wind turbine, wind farm, and wind regime levels Optimizing these activities is essential for maximizing energy output and ensuring the overall success of the wind energy project.
Wind resource assessment is the primary activity in wind regime analysis, crucial for evaluating site potential from regional to micro-scale levels using numerical (wind atlas) and meteorological data Key steps include measuring on-site wind conditions such as speed, direction, temperature, and pressure; correlating data from meteorological towers and long-term weather stations; estimating wind speed at hub height through shear profiles; modeling wind condition distributions; and predicting energy production based on turbine power curves or wind farm models.
An accurate prediction of wind conditions can help procure funding, and therefore better analyze the project economics.
Wind turbine design is a crucial aspect of wind energy development, focusing on creating turbines that efficiently harness wind power This involves designing essential components such as blades, control systems, generators, towers, foundations, and cable connections to meet technical specifications Additionally, the design must adhere to economic and environmental standards, ensuring the turbines are cost-effective and environmentally sustainable Properly engineered turbines optimize energy extraction while complying with safety and regulatory requirements.
Wind farm planning activities are systematically integrated through strategic layout design, which involves arranging multiple turbines within the site While a typical wind farm consists of a group of turbines, the total power generated by the entire farm is often significantly less than the combined output of individual turbines operating independently in the same wind conditions This discrepancy highlights the importance of optimal placement to minimize wake effects and maximize overall efficiency.
In Eq.1.7,Pf arm represents the power generation of an N-turbine wind farm; whereas
Pˆ i represents the power generated by Turbine-i when operating independently under the same wind conditions This energy loss is primarily caused by wake effects that develop downstream of the turbines To reduce wake-induced energy losses, Wind Farm Layout Optimization (WFLO) is implemented, focusing on optimizing turbine placement, selecting appropriate turbine types, and configuring the site layout based on the assessed wind resource.
This research introduces a comprehensive framework at the wind farm level that considers multiple objectives in the conceptual design process By incorporating diverse stakeholder interests, including developers, investors, and landowners, the framework enables better understanding of tradeoffs involved in wind farm development This innovative approach helps optimize decision-making, ultimately improving the efficiency and sustainability of wind farm projects.
Environmental Aspect
When designing a wind farm, it is essential to consider factors related to environmental impact throughout all stages, from planning to operation While efforts to reduce environmental harm are important, they can sometimes negatively affect the wind farm's productivity Consequently, assessing the environmental impact in conjunction with economic viability and energy output early in the development process is crucial for creating a balanced and sustainable wind energy project.
Generally, the environmental impact of a wind farm involves noise impact, visual im- pact, impact on wildlife, and public concerns (e.g., participation of local landowners and social acceptance).
Wind turbines in operating often produce significant amount of noise Due to the features of the sound, most of the turbine noise is masked by the sound of the wind itself. However, the noise can still propagate along the direction of the wind and cause annoyance in local communities downstream from the wind farm Hence, proper siting of turbines and using noise insulating materials in the nacelle is required to restrict the noise to an acceptable level [16,17].
Utility-scale wind turbines are typically installed in exposed locations, making them highly visible and impacting the natural landscape's aesthetics To mitigate this visual impact, strategies such as installing fewer turbines at each site and utilizing larger, more efficient turbine models are employed These approaches emphasize the importance of optimal siting and careful selection of wind turbines to balance energy generation with visual considerations.
Wind turbines can negatively impact local wildlife by causing fatalities among birds and bats, destroying habitats, and disrupting the natural behaviors of fish and other species Effective site selection and precise turbine micro-siting are essential strategies to reduce these environmental impacts Recent studies indicate that larger turbines tend to result in fewer raptor fatalities compared to smaller ones, suggesting that optimal turbine configurations can further mitigate risks to birds, bats, and overall ecosystems.
Wind energy offers a clean alternative to conventional fossil fuel power plants, producing electricity without releasing pollutants or greenhouse gases Public concerns surrounding wind farms primarily include safety risks from blade movement, potential electromagnetic interference with local radar and telecommunication systems, shadow flicker effects, and perceived health impacts These issues are important considerations in the development and acceptance of wind energy projects.
Conceptual Design of Wind Farms
Wind Farm Development Process
Conceptual design is the initial phase of wind farm development, involving the planning of large-scale projects that may include hundreds of turbines Wind energy project development is typically divided into three stages: early planning, initial development, and construction During the early stage, comprehensive consideration of technical, socio-economic, permitting, legal, and environmental factors is essential The development process varies based on project-specific requirements and policies but generally follows a structured progression from planning to construction.
Wind farm planning involves multiple interconnected disciplines, especially during the early stages when assessing project feasibility is challenging due to limited information The approval and leasing of land plots are often uncertain, as landowners may be unwilling to participate, complicating conceptual design efforts Early-stage conceptual design is crucial, serving as a foundation to outline integrated ideas, concepts, and models despite transparency issues in the planning process These challenges often lead to delays, making wind farm development a time-consuming process that can span from a few months to several years.
Resource Land Grid Fatal flaw Competitors Assessment committee
Engage LO and secure land and servitudes Environmental studies Bird and bat monitoring Resource assessment Grid assessment Start permitting Investors EPC tender SED/ED
9 agreements Non-binding agreements Bid bonds
Complete permitting Due diligence Agree financing and equity terms Binding offers PPA signed
ED = economic development; FC = financial close; LO = landowner;
PPA = power purchase agreement; SED = socio-economic development
Figure 1.2: Timeframe of Wind Farm Development Process in South Africa(from a wind farm developer’s perspective) [21]
Role of Land Resource
Land usage is a critical factor in wind farm development, requiring developers to secure land with the most productive wind resources Expanding the land area for turbine installation can reduce wake-induced energy losses, thereby increasing overall energy output However, land is a limited resource with alternative human and natural uses, making site selection a complex process Key considerations for successful wind energy project siting include balancing resource productivity, minimizing environmental impact, and optimizing land use efficiency.
Leasing is a crucial step for wind farm developers, as they must secure land rights from landowners to proceed with their projects The willingness of landowners to participate in wind energy development largely depends on the compensation or incentives provided by developers Offering lease agreements is a common and standard method for compensating landowners, enabling developers to gain access to the land for the duration of the project while ensuring mutually beneficial arrangements.
For large wind farms, effective grid transmission planning must consider existing transmission lines, transformers, and infrastructure to ensure efficient power delivery Offshore wind farms, in particular, face significant challenges when establishing local cable connections due to site-specific factors and logistical complexities Additionally, the costs associated with cable installation and grid connection can be substantial, especially when the site is remote from major transmission lines, as high-voltage cables and transformers required for connection can be expensive investments.
Proper siting of wind energy projects is essential to minimize their environmental impact, including noise pollution and habitat loss for local wildlife Careful land use planning ensures that the project's footprint is optimized, reducing adverse effects on ecosystems and surrounding communities Effective siting strategies are crucial for sustainable wind energy development, addressing concerns related to land use and environmental preservation.
Land configuration plays a crucial role in wind turbine projects, encompassing factors such as land area, shape, site orientation, soil properties, and terrain The land area determines the total number of turbines that can be installed, while land shape and site orientation influence turbine arrangement and affect potential energy extraction from local wind resources Additionally, soil properties are essential for assessing land suitability and determining appropriate turbine foundation types to ensure stability and longevity of the wind turbines Proper consideration of these land configuration aspects is vital for optimizing wind farm efficiency and environmental compatibility.
After identifying sites with strong wind resources, developers should promptly consult with permitting authorities to secure the necessary permits and licenses for building wind power facilities, as requirements can vary by state Conducting thorough legal investigations early in the development process helps prevent unnecessary delays and ensures compliance with local regulations.
It is to be noted that, in the early stage of wind farm development, a substantial portion of the planning activities are land orientated, since land usage strongly impacts the economic, technical, and environmental aspects (objectives) of the project Hence, a carefully formulated land usage model is desired, which can appropriately reflect the environmental impact, landowner considerations, and land-based constraints on turbine installation.
Multi-Objective Mixed-Discrete Optimization Problems
Swarm-based Algorithms
Swarm-based algorithms, also known as Swarm Intelligence (SI), are inspired by natural behaviors observed in animals like schools of fish, flocks of birds, and ant colonies These algorithms mimic the collective actions of these groups, which are naturally used for efficient foraging, predator evasion, and colony relocation By emulating these biological processes, swarm-based algorithms offer effective solutions for complex optimization problems in various fields.
Swarm-based algorithms excel in solving complex, continuous search problems due to their inherent characteristics of decentralization, self-organization, and emergence These algorithms leverage exploration and exploitation capabilities to efficiently identify optimal solutions Popular examples include Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), and Artificial Bee Colony (ABC), each effectively navigating challenging search domains through collective intelligence.
Research Goals and Impact
Research Motivation
The quality of a wind energy project depends on key performance criteria influenced by various interconnected factors throughout the wind farm development process To ensure profitability, reliability, and community acceptance, it is crucial to balance socio-economic, technical, and environmental considerations Effective management of these factors enhances overall project success and sustainability.
However, owing to the lack of information on potential impacts in each aspect in wind farm development, several design alternatives often need to be considered to explore the bal- ance point between the concerned performance objectives More importantly, owing to the lack of decision-making transparency in wind farm planning, the evaluation of design alter- natives can be undesirably time-consuming As a result, before a wind energy project can be approved and proceed to construction, it might have gone through years of planning [21,31].
To enable wind farm developers and stakeholders to make more time-efficient decisions on the optimal project configuration, a systematic exploration of trade-offs among multiple objectives is essential, especially considering land resource availability early in planning A robust wind farm layout optimization (WFLO) tool must handle complex, nonlinear, high-dimensional, and constrained problems involving both continuous and discrete variables Therefore, implementing a powerful multi-objective mixed-discrete optimization solver is crucial for establishing a time-efficient and effective wind farm planning process.
Research Objectives
This research aims to develop a sensitivity-integrated approach to the conceptual design of wind farms, enhancing understanding of how various factors impact wind farm performance By leveraging this comprehensive insight, the study seeks to facilitate more informed and effective decision-making in wind farm development The specific research objectives focus on identifying key variables influencing performance and integrating sensitivity analysis to optimize design strategies, ultimately advancing wind energy projects with increased efficiency and reliability.
1.4.2.1 Analyzing the Sensitivity of Wind Farm Power Output to Key Factors The expected power generation (or energy production) is one of the most important considerations in planning a wind energy project Analytical wake models are generally used to estimate the wake-induced power losses, which is the major cause of wind farm inefficiency.
Understanding the relative impact of key natural and design factors is essential for accurate wind farm power estimation and high-quality project planning Currently, this understanding is lacking within the existing wind farm design paradigm To address this gap, a comprehensive sensitivity analysis (SA) is conducted to evaluate how factors such as incoming wind speed, the number of turbines, ambient turbulence, and land configuration influence maximum farm output potential Additionally, the study explores how different wake models affect the sensitivity analysis, providing critical insights for optimizing wind farm performance and planning.
1.4.2.2 Multi-Objective Wind Farm Design Framework
WFLO involves a multi-objective approach that balances conflicting performance goals such as maximizing energy production while minimizing land usage This research focuses on developing a comprehensive multi-objective framework for the conceptual design of wind farms, enabling optimization without restricting factors like land configuration or turbine selection The framework aims to enhance decision-making in wind farm planning by considering various trade-offs to achieve optimal, sustainable outcomes.
More specifically, we aim to explore how the tradeoffs between multiple objectives are related to site-scale decisions, such as installed capacity.
Land usage plays an important role at the early stage of wind farm planning Most of the early planning activities involve analysis and consideration directly related to land usage. However, in the state of the art in wind farm design, a wind farm is generally assumed to have a rectangular shape and fixed boundaries Such assumptions are unrealistic In practice, wind farm siting should explore the maximum energy potential of the candidate sites under different land resource availability Hence, this research aims to develop an optimal land usage model, to explore how optimal land shapes are related to site-scale decisions (e.g., installed capacity and unit land area), to landowner participation, and to the nature of the local wind resource.
1.4.2.4 Multi-Objective Mixed-Discrete Particle Swarm Optimization
This study aims to develop, test, and implement a multi-objective mixed-discrete PSO algorithm capable of addressing the complex characteristics of multi-objective WFLO, including highly nonlinear criteria, high-dimensional constrained design spaces, and mixed discrete and continuous variables, while preserving the computational efficiency of fundamental swarm dynamics Key advancements involve leveraging Pareto dominance-based search strategies utilizing local and global Pareto solutions to retain PSO’s natural dynamics, modifying leader selection mechanisms for effective multi-objective optimization, and introducing a novel multi-domain diversity preservation technique to prevent premature particle stagnation and ensure an even distribution of Pareto optimal solutions, thereby enhancing the algorithm's robustness and efficiency.
Research Impact
This dissertation develops a time-efficient, transparent decision-making platform for multi-objective wind farm development during the conceptual design phase, addressing a gap in existing literature Unlike traditional studies focused on single-objective optimization with fixed parameters such as turbine count and farm size, this research introduces an innovative approach that eliminates the need to preset these variables The proposed method integrates land usage considerations through a post-optimization land use model and employs a novel Pareto shifting technique to visualize tradeoffs between multiple objectives across different installed capacity scenarios This comprehensive framework enables more flexible and informed decision-making in early wind farm design.
Heuristic algorithms are suitable for solving WFLO problems Such problems are normally constrained, highly nonlinear, high dimensional, and multi-objective PSOhas been shown to be a powerful single objective optimization solver for continuous design variables.
This research focuses on enhancing Multi-Objective Particle Swarm Optimization (MOPSO) by addressing key limitations such as premature stagnation arising from loss of population diversity While PSO is renowned for its ease of implementation and rapid convergence, existing MOPSO versions often struggle with discrete design variables and maintaining dynamic search capabilities The newly developed MOPSO retains the fundamental dynamics of the basic PSO, ensuring its original advantages are preserved, and effectively tackles complex multi-objective optimization problems like those found in WFLO This improved MOPSO provides a reliable and efficient solution for complex multi-objective problems, offering a significant advancement in MOO solver capabilities.
This research introduces a novel Pareto shifting technique that enables the parameterization of tradeoffs between multiple objectives, with applications extending beyond wind farm design to complex engineering systems with variable design parameters The case study demonstrates the implementation process of this technique, showcasing how it integrates optimization and regression modeling for effective solutions Additionally, a multi-objective swarm-based strategy enhances the wind farm design process by providing time-efficient solutions to complex optimization challenges The innovative concepts, including multi-domain diversity preservation and a leader selection mechanism, not only benefit the wind energy sector but also contribute broadly to Swarm Intelligence algorithms and decision-making methods These advancements have significant implications for both academic research and practical engineering applications.
CHAPTER ONE Introduction and Technical Context
CHAPTER TWO Literature Survey and Research Needs
CHAPTER THREE Primary Performance Objectives in Wind
CHAPTER FIVE Multi-Objective Wind Farm Design
CHAPTER FOUR Identifying Key Natural & Design Factors
CHAPTER SIX Multi-Objective WFLO Considering Land Usage and Landowner Participation
CHAPTER SEVEN Developing Multi-Objective Mixed-
CHAPTER EIGHT Practical Application of MO-MDPSO
Concluding Remarks and Future WorkFigure 1.3: Thesis structure
Dissertation Outline
The Role of Wake Effects in Wind Farm Power Estimation
As wind flows across a turbine, the wind speed reduces and the turbulence intensity increases Thus, a wake is formed behind the turbine, which affects the performance of downstream turbines The wake not only progresses along the streamwise direction, it also
Table 2.1: Comparison of computation time of wake simulation for two turbines in line [32]
Wake model Computation time Model type
Actuator disk model [35] 25 seconds Actuator disk
Dynamic Wake Meandering model [36] 8 minutes Analytical+Actuator disk
SOWFA [37,38] 30 hours 3D CFD expands laterally As a result, downstream turbines that are not coaxially downstream can be also affected by upstream turbine wakes Collectively, this is called the wake effects. There are two major impacts of the wake effects on the entire wind farm: (i) it causes a deficiency in the overall energy output due to the velocity deficit in the wakes, and (ii) it causes a reduction of the turbine lifetime due to the additional turbulence induced structural loading Factors affecting the wake behavior can be classified into two categories: natural factors and design factors.
Natural factors affecting wind farm performance mainly include variations in wind conditions such as wind speed, wind shear, and ambient turbulence at the site, which cannot be controlled through design or optimization In contrast, design factors are determined by strategic decisions like turbine placement, rotor diameter, hub height, land layout, and the total number of turbines installed, allowing for optimization to enhance energy output and efficiency.
Understanding the factors that regulate turbine wake behavior is crucial, as they directly impact the overall quality and efficiency of a wind energy project Accurate wind farm power estimation depends on the precision of the wake models employed and the assumptions related to natural and design factors Therefore, selecting reliable wake models and thoroughly analyzing associated assumptions are essential for optimizing wind farm performance and ensuring reliable energy output predictions.
Analytical Wake Models
In the context of WFLO problems, the computational efficiency of a particular ana- lytical wake model often presents a higher priority compared to the specific applicability.
Analytical wake models are the most suitable choice for Wind Farm Layout Optimization (WFLO) problems due to their computational efficiency, as demonstrated in Table 2.1, which compares the computation times of various wake models for a two-turbine scenario These models, including the Jensen and Frandsen models, have been widely adopted by researchers for their effectiveness in WFLO Validation studies highlight the importance of comparing wake model predictions with test cases to identify limitations and establish application guidelines For instance, the Jensen model is reliable for long-term power predictions in small to medium-sized wind farms, but its accuracy diminishes when wind direction sectors are narrower than 10 degrees Moreover, the fidelity of wake model validation heavily depends on the quality and quantity of real wind farm data, such as high-resolution anemometer measurements.
Four popular analytical wake models are discussed in the following part: Sections 2.1.2
− 2.1.2 provide the mathematical description of each of these wake models.
The Jensen wake model, developed by Jensen [33] and further refined by Katic [34], is renowned as one of the most widely used analytical models for wind turbine wake analysis This model assumes that the wake behind a turbine expands linearly, meaning the velocity deficit depends solely on the downstream distance from the turbine The simplified assumption allows for straightforward calculations of wind flow disruptions, making the Jensen model a valuable tool in wind farm layout optimization and performance assessment.
The turbine thrust coefficient (CT) is a key parameter in analyzing wake behavior, with the wake decay constant (k) controlling how the wake dissipates by influencing the vertical wake width growth per unit length downstream The normalized downstream distance (s), defined as the ratio of the distance between two turbines to the turbine rotor diameter (D), is essential for understanding wake interactions in wind farm topology Wake growth (Dw) can be modeled based on these parameters to accurately predict the spatial development of turbine wakes, improving wind farm efficiency and optimizing turbine placement.
The recommended k values for onshore and offshore wind farms are 0.075 and 0.04, respec- tively [50].
The Frandsen model was initially designed to predict wind speed deficits in large offshore wind farms with rectangular layouts and array-like turbine configurations [51] It is based on the analysis of inner flow patterns, identifying three regimes of turbine wakes within a wind farm The first regime focuses on wake development, where the growth of wake size and velocity deficits are quantitatively modeled to enhance understanding of wind flow dynamics in offshore wind farm planning and optimization.
The initial wake speed deficit, represented by α, must be determined through experimental measurements The shape parameter k, set at 2, indicates a square root profile for wake expansion, as referenced in studies [51,52] The awake area refers to the effective influence zone of the wake relative to its current width at a specific location Additionally, the wake expansion parameter β is defined by the formula β = 1 + √, highlighting its dependence on the square root function for modeling wake growth and turbulence effects.
For the “±” sign in Eq.(2.4), the “+” applies to cases in which the induction factora≤0.5; while the “−” applies toa >0.5.
It is noted that the Eq.(2.5) uses an effective rotor diameter, Def f, to account for the near wake approximation, which is given by
The Larsen wake model was initially introduced in previous research and later incorporated into the European Wind Turbine Standards II (EWTS II), utilizing Prandtl’s mixing length theory to describe wake behavior Unlike the Jensen model, the Larsen model accounts for both the streamwise distance (x) downstream of a turbine and the radial distance (r) from the hub in its velocity deficit calculations This model assumes that wake flow is incompressible, stationary, and axisymmetric, providing a more comprehensive understanding of turbulence and energy distribution behind wind turbines.
The wake growth in the Larsen model is given by
In equations (2.7) and (2.8), the constant c₁ represents the non-dimensional mixing length, which is related to Prandtl’s mixing length, while x₀ indicates the turbine’s position relative to the reference coordinate system The methods for estimating these two constants are provided by reference [54], offering essential formulas for accurate modeling of flow and turbine behavior.
Here,R 9.5 represents the wake radius at a relative distance of 9.5 rotor diameters (9.5D) downstream from the turbine, which is defined based on an empirical equation expressed as
R9.5 = 0.5 [Rnb+min(H, Rnb)] (2.11) where Rnb is an empirical parameter related to the ambient turbulence at the hub height (Ia), as given by
The Ishihara model, developed using wind tunnel data from a scaled Mitsubishi wind turbine, effectively accounts for the influence of turbulence—both ambient and turbine-induced—on wake recovery Experimental evidence indicates that onshore wind farm sites experience faster wake recovery due to higher ambient turbulence levels, whereas offshore sites, characterized by lower ambient turbulence, rely more on turbine-induced turbulence for wake recovery Similar to the Larsen model, the Ishihara model predicts wake velocity as a function of streamwise (x) and radial (r) distances, assuming a Gaussian velocity profile, with the velocity deficit expressed by uf √CTU∞, highlighting its applicability in modeling wind turbine wake behavior under various atmospheric conditions.
(2.13) where the wake growth is formulated as
The parameter p, as defined in Equations (2.13) and (2.14), depends on two types of turbulence: ambient turbulence and turbine-induced turbulence It is expressed mathematically as p = k² (Iₐ + I_w), where Iₐ represents ambient turbulence and I_w denotes the turbulence generated by the turbine itself Understanding this relationship is crucial for accurately modeling turbulence effects in the system.
The turbine-induced turbulence can be expressed as
In Eqs.(2.13) − (2.16), the coefficients k1, k2, and k3 are respectively set to 0.27, 6.0, and0.004, as recommended in the literature [55,56].
The State of the Art in Wind Farm Layout Optimization
Overview of Wind Farm Layout Optimization Frameworks
Existing WFLO frameworks in the literature can be classified into two types: (i) the discrete model and (ii) the continuous model.
In discrete models for wind farm layout optimization, the site is divided into uniform grids that specify potential turbine locations, restricting turbine placement to these predefined points The WFLO (Wind Farm Layout Optimization) framework, as introduced by Mosetti et al [57], employs this discrete modeling approach, discretizing the wind farm into a 10 × grid structure to facilitate optimization.
Grady et al [58] enhanced Mosetti's framework by implementing an improved optimization algorithm, demonstrating advancements in wind farm layout optimization While some researchers assume an array-like layout for wind farms [59], focusing on optimizing lateral spacing between arrays, this approach limits turbine placement to predefined arrays, representing a discrete model Numerous wind farm layout optimization (WFLO) frameworks employ this discrete modeling approach, as documented in references [23, 40–42, 59–72], highlighting its significance in the field.
In continuous models, on the other hand, the location of turbines is not restricted to
Recent advancements in wind farm layout optimization (WFLO) have emphasized the benefits of continuous models, which allow turbines to be placed arbitrarily within the designated boundaries, potentially leading to more optimal designs Early studies by Ozturk and Norman enabled turbine placement in a continuous space, paving the way for subsequent models Kusiak and Song expanded upon this by developing a continuous framework based on the Lackner and Elkinton model, greatly enhancing the optimization process Building on these concepts, Chowdhury et al introduced the UWFLO framework, one of the most advanced solutions in the literature, which offers greater flexibility in turbine placement Unlike discrete models that limit potential turbine positions to predefined grids, continuous models are more adept at identifying the global optimum, a reason for their increasing popularity in recent years Numerous recent studies (Refs [76–83]) highlight the growing focus on continuous WFLO approaches, underscoring their importance in achieving efficient wind farm designs.
Performance Criteria in WFLO
Wind farm Annual Energy Production (AEP) is one of the most important performance criteria used to evaluate the quality of a wind energy project More than one third of the work reviewed in Ref [84] used AEP or wind farm power generation as the objective function.
A utility-scale wind farm, comprising multiple turbines, derives potential power from the available wind energy, which is calculated based on the wind's mass flow rate and kinetic energy The actual power produced by a turbine depends on the mechanical conversion of this available wind energy, influenced by the turbine's power coefficient (Cp), a complex factor affected by wind conditions such as speed and turbulence, as well as turbine design features like rotor diameter and tip speed ratio To evaluate a wind farm’s performance, two key metrics are used: wind farm efficiency (η), which measures the ratio of actual power output to the ideal power output in the absence of wake-related losses, and wind farm capacity factor (CF), reflecting the consistency of power generation relative to its maximum potential over time.
(2.18) where Pf arm is the actual power generated by the wind farm; and P0i is the ideal power generation of Turbine-i when operating as a standalone entity.
The wind farm capacity factor is given by
(2.19) where P N C is the nameplate capacity of the concerned wind farm.
In the early research projects, Mosetti et al [57] and Grady et al [58] considered wind farm energy production as the objective function Other reviewed work considering AEP or wind farm power generation can be found in Refs [23,39,40,42,43,60,63,64,67,68,71–73, 76–78,78–82,85,86].
Economic performance is a crucial criterion in WFLO, encompassing key metrics such as the Levelized Cost of Energy (LCOE), Net Present Value (NPV), Financial Balance (FB), and the overall operation and maintenance costs of the wind farm These indicators are essential for assessing the financial viability and sustainability of wind farm projects, ensuring optimal investment decisions and long-term profitability.
Research on economic performance can be found in Refs [41,43,58–60,62–67,70,71,
Other considerations in wind farm design include noise impact [72], land usage related considerations [23,82,88], landowner participation [41], risk management [87], and transmis- sion capacity [69].
Optimization Algorithms in WFLO
In this part, we discuss the algorithms and optimization solvers used to performWFLO.
Genetic Algorithms (GAs) are adaptive heuristic search algorithms inspired by natural selection and genetics, effectively exploring complex design spaces in WFLO problems They maintain a large population of random chromosomes, each representing a potential wind farm layout, which evolve over generations through selection and genetic operators like crossover and mutation During selection, each candidate solution is assigned a fitness value, determining its eligibility for reproduction, while the reproduction process creates new layouts by combining and mutating existing ones Due to their genetic characteristics, GAs can efficiently and effectively identify optimal or near-optimal wind farm configurations in initially unknown and complex environments Mosetti et al [57] pioneered the application of GAs for WFLO, and since then, their use in this field has significantly increased, as documented in subsequent studies [42,57].
Particle Swarm Optimization (PSO) is a population-based algorithm inspired by the social behavior of birds and fishes, used to solve complex optimization problems In PSO, candidate solutions are represented as particles moving within the design space, each with an assigned velocity guiding their movement toward the best solutions The algorithm updates each particle’s local best based on its personal experience and the global best through social exchange of information within the swarm In wind farm layout optimization (WFLO) problems, each particle corresponds to a potential layout, with the initial population generated randomly Particles are dynamically guided by local and global leaders to explore solutions that maximize wind farm performance efficiently.
Particle Swarm Optimization (PSO) faces a key challenge known as pre-stagnation, where the swarm prematurely converges to sub-optimal solutions This issue is primarily caused by a loss of diversity within the swarm during rapid convergence, limiting its ability to explore the problem space effectively Such premature convergence is especially problematic when dealing with complex, multimodal problems like Water-Flooding Loss Optimization (WFLO), where maintaining diversity is crucial for finding optimal solutions.
Relevant research usingPSOto solveWFLOproblems can be found in Refs [43,78,86].
Simulated Annealing Algorithm (SAA) is a metaheuristic technique for global optimization inspired by the cooling process of materials to reduce defects and minimize system energy Proposed by Kirkpatrick et al [90], SAA generates new solution points at each iteration based on a probability distribution influenced by temperature, allowing exploration of the solution space The algorithm accepts solutions that improve the objective function and, with a certain probability, accepts solutions that worsen it, facilitating escape from local minima An annealing schedule gradually decreases the temperature, guiding the algorithm toward convergence on an optimal solution.
Rivas et al [91] applied SAA to optimize turbine locations for a large offshore wind farm Bilbao and Alba [66] also appliedSAAin their work to maximize the wind farm annual profit.
Other algorithms used to solve WFLO problems include: Evolutionary Algorithms(EA) [39,61,71,72], Greedy Heuristic Algorithm [60,73], Mixed Integer Programming [68],Patter Search [40], Monte Carlo Simulation [62], and Ant Colony Algorithm [77].
Commercial Software
There are several commercial software programs used to optimize and design wind farms Below is a summary of the most widely used programs:
1 WAsP The Wind Atlas Analysis and Application Program (WAsP developed by the Risứ National Laboratory (www.wasp.dk), is considered the industry-standard software for bankable wind resource assessment and wind farm micro-siting WAsP provides dif- ferent analysis regarding the wind farm production, the wind power potential, the wind climate estimation, and micro-sitting Although it lacks an optimization tool for wind farm design, its powerful packages are normally incorporated by other WFLO frame- works (e.g., TOPFARM [92]) or software programs (e.g., WindPRO and WindFarmer).
2 WindSim (www.windsim.com) is a powerful wind farm design tool based on compu- tational fluid dynamics (CFD) that is mainly used for wind data analysis andWFLO. The wind flow modeling approach is based on a 3D Reynolds-Averaged Navier-Stokes (RANS) solver, which is complemented with different types of turbulence models (e.g., standard k−ε, RNG k−ε and the standard k−ω) The Park Optimizer module in WindSim can determine the areas where is not advisable for turbine placement due to poor resource or bad wind quality based on IEC criteria Hence, wind farm developers are able to identify the suitable positions for turbine installation.
3 Wind Farm(http://www.resoft.co.uk) developed by ReSoft is a general commer- cial system for wind farm development Its capabilities in wind farm design include: (i) WFLO for maximizing energy production or minimizing COE, subject to environ- mental (noise, visual impact, and shadow flicker) and physical (forests, trees, hedges, etc) constraints, (ii) long-term wind speed prediction, (iii) 3D visualizations of multiple wind farms and the landscape, and (iv) option to calcuate energy yields using multiple anemometers.
4 WindPRO(http://www.emd.dk/windpro) is a robust tool developed by EMD Inter- national A/S Several different modules are included in WindPRO for the simulation and quantification of the wind farm energy production In addition, it containts mod- ules for the electrical layout design and its optimization (including the quantification of power losses) and a robust financial balance model WindPro optimizes the wind farm layout using the AEP as a performance criterion while accounting for several environmental impacts (not accounted during the optimization procedure), including noise impact, visual impact, and shadow flicker effect The optimization framework is incorporated from the WAsP engine Different WFLO strategies are available in Wind- PRO: (i) a stochastic and gradual placement of turbines into the wind farm until the pre-specified number of turbines are all installed; (ii) an array-layout based strategy; (iii) an iterative addition of turbines into the available land plots; and (iv) minimizing the noise impact for fixed wind farm layouts.
5 WindFarmer(www.dnvgl.com/services/windfarmer-3766) developed by DNV-GL is a state-of-the-art software tool for designing, optimizing and analysing wind farms.
The optimization procedures in WindFarmer are based on greedy heuristics, which
Excessive shadow flicker caused by rotating blades can be considered a nuisance in wind energy projects To minimize environmental impacts, projects should implement measures to reduce shadow flicker, thereby optimizing energy production and financial returns Key environmental considerations include noise impact, visual impact, shadow flicker, and effects on local radar stations WindFarmer enables precise analysis of energy production by integrating the WAsP engine, which accounts for turbulence, terrain, and variable air density at each turbine, ensuring accurate assessments of project performance.
Multi-Objective Particle Swarm Optimization (MOPSO)
Overview of MOPSO
Evolutionary Algorithms (EAs) and Particle Swarm Optimization (PSO) are among the most popular nature-inspired algorithms for solving highly nonlinear optimization problems. EAs that are used for solving MOOproblems (known as MOEAs), include Vector Evaluated Genetic Algorithm (VEGA) developed by Schaffer [93,94], Non-dominated Sorting Genetic Algorithm II (NSGA-II) developed by Deb et al [95], Strength Pareto Evolutionary Algo- rithm (SPEA) [96,97], SPEA2 [98], Predator-Prey Evolutionary Strategy (PPES) [99], and Modified Predator Prey (MPP) [100] Some of these MOEAs are also capable of handling integer and discrete design variables, e.g., NSGA-II.
Particle Swarm Optimization (PSO) is renowned for its rapid convergence and straightforward implementation, especially in solving single-objective, unconstrained, continuous optimization problems Since 1999, researchers have increasingly focused on adapting PSO's core advantages to tackle Multi-Objective Optimization (MOO) problems Various multi-objective PSO (MOPSO) algorithms have been developed, with notable versions including early studies by Parsopoulos and Vrahatis, the approach by Coello et al., and subsequent dynamic adaptations An overview of MOPSO applications reported in literature highlights its expanding role across diverse optimization scenarios.
Figure 2.1: Publications of MOPSO by field of engineering applications [101]
Neighborhood PSO algorithm (DNPSO) [104,105], (iv) the Non-dominated Sorting PSO (NSPSO) developed by Li [106], and (v) the MOPSO that uses crowding distance (MOPSO- CD), developed by Raquel and Naval, Jr [107].
The numerous variants of MOPSO, developed over the past few decades, primarily focus on the search strategy in the multi-objective space Mechanisms have also been devel- oped to handle constraints and select individuals Unfortunately, there exists only a handful of studies in MOPSO where mixed-discrete variables are considered [108–114], and even fewer studies where diversity preservation is also considered [103,106,115,116].
Search Strategies in MOPSO
In many Multi-Objective Optimization (MOO) problems, selecting particles must balance multiple objectives, often utilizing strategies such as aggregating functions, single objective-based approaches, or Pareto dominance principles The aggregating function method is widely used in Particle Swarm Optimization (PSO) due to its straightforward implementation, with techniques like the weighted sum approach employed to combine multiple objectives into a single scalar function For example, Baumgartner et al applied the weighted sum approach to MOO problems using standard PSO as a single objective optimizer, while Parsopolous and Vrahatis tested various aggregating methods, including conventional, dynamic, and Bang-Bang weighted sums However, aggregating function strategies face notable limitations, such as difficulty in assigning appropriate weights, the need for objective scaling, poor representation of non-convex Pareto fronts, and high computational costs, since each run typically yields only one Pareto optimal solution, making them less popular compared to Multi-Objective Evolutionary Algorithms (MOEAs).
Single objective-based strategies optimize one objective at a time In the DNPSO algo- rithm proposed by Hu et al [104], bi-objective optimization problems were solved using the lexicographic ordering scheme This scheme compares a particle only with its two neighbors, where the performance of optimization is likely to be sensitive to the assigned ordering of importance of objectives [117] Similarly, in a multi-swarm variant of PSO called Vector Evaluated PSO (VEPSO) method, developed by Parsopoulos et al [120], the evaluation of each sub-swarm is based on one assigned objective (local search); while the global search depends on the information exchange between multiple sub-swarms It is noted that both lexicographic ordering scheme and the multi-swarm based approach are generally applicable for only bi-objective problems.
The MOPSO algorithm developed by Coello et al utilizes Pareto dominance to compare solutions and employs an external repository to store non-dominated solutions, with the search space divided into adaptively controlled hypercubes based on particle count Additionally, some MOPSO algorithms combine multiple strategies to efficiently explore the multi-objective search space For example, Ray and Liew proposed a “swarm metaphor” algorithm that incorporates non-dominance sorting within PSO and uses a probabilistic crowding radius to guide particle selection, enhancing diversity and convergence in multi-objective optimization.
Li [106] also applied the concept of non-dominance sorting The selection of individuals in this algorithm is based on two criteria, the niche count and the crowding distance.
In basic PSO, particles are compared based on objective function values, but for multi-objective problems, the Pareto dominance strategy uses non-dominance comparison to guide the search This paper's search strategy leverages the Pareto dominance principle, preserving the original PSO dynamics However, many existing MOPSO algorithms with this approach often fail to produce evenly distributed Pareto solutions, which is essential for assessing the quality of a multi-objective optimization (MOO) algorithm The primary reason for this issue is the loss of population diversity as the swarm converges to global Pareto solutions, resulting in incomplete coverage of the Pareto frontier To address this, we introduce a multi-domain diversity preservation technique that maintains population diversity during convergence, ensuring a more uniform and comprehensive distribution of Pareto optimal solutions.
Research Observations and Needs
Key Observations
Most research in Wind Farm Layout Optimization (WFLO) focuses on single-objective functions due to the inherent complexity of WFLO problems These challenges arise from the multidisciplinary nature of wind farm design, which involves evaluating performance objectives like power generation within complex constraints WFLO problems are characterized by high dimensionality, nonlinearity, multimodality, and a combination of continuous and discrete variables—such as turbine selection and land availability—making the optimization process highly complex and constrained.
Recent studies indicate that most research reports results based on predefined wind farm boundaries and installed capacities In real-world scenarios, the size of a wind farm and its capacity are typically constrained by factors such as maximum energy sales potential, land availability, and transmission infrastructure Relying on prescribed conditions can limit the range of feasible wind farm configurations, potentially restricting innovative layout options and impacting the overall effectiveness of wind energy projects.
Heuristic algorithms are widely preferred for solving WFLO problems because of their ability to efficiently explore complex, highly nonlinear, and high-dimensional design spaces Among these, Genetic Algorithms (GAs) and Particle Swarm Optimization (PSO) are the most popular, with GAs primarily suited for discrete models and PSO for continuous models Recent research shows increasing focus on continuous models, which avoid the limitations of discrete approaches—such as the restriction of turbine locations to predefined grid points—potentially leading to more globally optimal solutions However, discrete models are advantageous when land plot-based constraints are critical, as discretization makes the models less sensitive to turbine placement, with Chen and McDonald [41] highlighting this by considering landowner participation through discrete land plots.
To effectively solve WFLO problems, the multi-objective optimization (MOO) approach must be computationally efficient and robust due to the high computational cost associated with evaluating performance objectives and constraints Particle Swarm Optimization (PSO) emerges as a suitable technique for this purpose, given its efficiency and effectiveness However, many MOPSO variants struggle to preserve the core advantages of the original PSO algorithm, and their ability to handle mixed-discrete design variables remains underreported in existing literature.
Research Needs
2.4.2.1 Research Needs in Wind Farm Power Estimation
Understanding the complex relationship between wind farm power output and the factors influencing power estimation is crucial for effective wind farm analysis and optimization Key factors such as wind speed, atmospheric conditions, and turbine efficiency significantly impact energy production, highlighting the need for accurate modeling and data analysis Optimizing these variables can enhance power generation, making wind farms more efficient and cost-effective Addressing these interconnected elements is essential for maximizing performance and ensuring sustainable energy development.
1 What is the relative importance of each natural and design factor in the context of power output potential of a wind farm?
2 Which of these factors can be neglected and/or assumed to be practically fixed in the process of WFLO?
3 How does the impact of these factors on the wind farm power output vary under the use of different wake models?
Current WFLO literature lacks a comprehensive analysis of key factors influencing wind farm power estimation An extensive sensitivity analysis is essential to understand how variables such as incoming wind speed and inter-turbine spacing impact overall power output This study aims to evaluate the sensitivity of wind farm power predictions to critical farm-scale factors, considering different wake modeling approaches By exploring how these factors affect power output under various wake models, the research seeks to fill the existing knowledge gap and enhance the accuracy of wind farm performance assessments.
2.4.2.2 Research Needs in Wind Farm Design
Designing wind farms involves complex multi-objective challenges that require a comprehensive framework to evaluate various performance criteria A well-formulated multi-objective model considers key factors such as annual energy production, energy cost, and the environmental impact on surrounding areas This systematic approach enables balanced optimization of wind farm layouts by assessing constraints and performance metrics effectively Incorporating these criteria ensures sustainable and cost-efficient wind farm development, aligning operational goals with environmental considerations.
Developing flexible strategies for the WFLO (Wind Farm Layout Optimization) is essential to enable wind farm planning without defining specific boundaries or turbine counts This approach is especially critical during the conceptual design phase, where much of the project information remains uncertain Rigid assumptions about fixed wind farm sizes or capacity can lead to delays, highlighting the need for adaptable planning methods to streamline early-stage development.
To effectively address land use planning, it is essential to develop a comprehensive land usage model early in the process Such a model should account for land-based constraints and environmental impacts, facilitating informed decision-making and supporting sustainable development Incorporating land usage considerations at the initial planning stage ensures better integration of land management and planning activities, ultimately promoting more efficient and environmentally responsible land use.
2.4.2.3 Research Needs in the Multi-Objective Optimization Solver
This research emphasizes the importance of developing a multi-objective version of Particle Swarm Optimization (PSO) to efficiently solve Warehouse Functional Layout Optimization (WFLO) problems, given the urgent need for rapid convergence To effectively address the complex attributes inherent in multi-objective WFLO, the proposed PSO must incorporate significant modifications that preserve its core advantages while overcoming its tendency to stagnate prematurely Implementing these enhancements ensures that the optimized algorithm can deliver accurate, reliable solutions swiftly, making it highly suitable for tackling time-sensitive WFLO challenges.
Designing a utility-scale wind farm involves numerous continuous and discrete design variables, making it essential for the proposed MOPSO to effectively handle mixed-discrete variables An advanced multi-objective particle swarm optimization (MOPSO) tailored for this complexity can optimize the design process Incorporating capabilities to manage both types of variables ensures a comprehensive and efficient approach to wind farm development This adaptability is crucial for achieving optimal performance and cost-effectiveness in large-scale renewable energy projects.
A Novel Approach to the Conceptual
Primary Performance Objectives in Wind Farm Design
This chapter details the models used to evaluate key performance objectives of wind farms It explains how annual energy production is calculated using the Unrestricted Wind Farm Layout Optimization model, providing accurate estimates of energy output Additionally, the wind farm's cost of energy is assessed through the Wind Turbine Design Cost and Scaling model developed by the National Renewable Energy Laboratory, ensuring cost-effectiveness analysis Furthermore, a novel land usage model is introduced to quantify land requirements based on specific wind farm layouts, supporting sustainable site planning and optimization.
Annual Energy Production
Annual Energy Production (AEP) is a key performance metric in wind energy development, measuring the total energy generated by a wind farm over a year The energy production model used in this study is based on the advanced UWFLO framework developed by Chowdhury et al., which accurately quantifies wind farm power output considering turbine specifications, turbine placement, and incoming wind conditions A generalized power curve is employed to estimate individual turbine energy output, scaled to match the specific characteristics of commercial turbines via manufacturer data This model enables precise evaluation of turbine power generation, ensuring optimized wind farm performance.
0, if Uout < Ui orUi < Uin
(3.1) where Ui is the velocity immediately in front of Turbine-i Estimation of Ui accounts for wake merging scenarios and the possibility of partial wake-rotor overlap Uin, Uout, and
The turbine's cut-in, cut-out, and rated speeds are provided by the manufacturer, serving as essential parameters for operational performance The power curve is modeled using a polynomial function, denoted as Pn, which fits the generalized power output based on specific wind speeds This polynomial is derived from the observed power curve data of the “GE 1.5 MW xle” turbine, enabling accurate prediction of power generation under varying wind conditions.
This power generation model also allows for a variable induction factor According to the 1-D flow assumption [123,124], the induction factor aand the power coefficient, C p , can be related by
Cp = 4a(1−a) 2 (3.3) where the power coefficient itself can be expressed as a function of incoming wind speed and turbine characteristics, as given by
In Eq.(3.4),P0 represents the power available from the wind; andU∞ is the incoming wind speed at the hub height.
The solution to the non-linear equation, Eq (3.3), determines the induction factor for each turbine based on the estimated approaching wind conditions This approach enables an accurate calculation of the turbines' performance under varying wind scenarios Subsequently, the total power output of an N-turbine wind farm, denoted as P_farm(U_j, θ_j), can be effectively calculated by aggregating individual turbine contributions, facilitating optimized wind farm energy production.
Pi (3.5) where U j and θ j represent the j th wind condition defined by incoming wind speed U and wind direction θ Assuming the wind farm operates continuously throughout the year (all
365×24 hours), the AEP of this wind farm, Ef arm (in kWh/yr), can be expressed as
Ef arm = (365×24)PN p j=1Pf arm(U j , θ j )p(U j , θ j )∆U∆θ, where
In Eq 3.6, Umax represents the maximum possible wind speed in the current wind distribution; p(U j , θ j ) represents the probability of the occurrence of thej th wind condition.
This model incorporates wake effects by determining the effective wind speed immediately in front of each turbine (U_i), considering predicted wake growth, turbine locations, and features An influence matrix is developed to identify whether a turbine is within the wakes of upstream turbines for specific wind directions The velocity in front of each turbine is dynamically evaluated using a wake model, reflecting the order in which turbines encounter the wind The Katic model is employed to account for wake merging and partial wake-rotor overlap, allowing accurate calculation of velocity deficits when a turbine is influenced by multiple upstream wakes.
The velocity deficit in the wake of Turbine-k at the location of Turbine-i is represented by (u ki f) as defined by equation (3.7) The effective influence area of Turbine-k's wake on Turbine-i is denoted by A ki When Turbine-i is entirely within the wake of Turbine-k, A ki equals the total wake area, Ai If only part of Turbine-i overlaps with the wake, A ki is calculated as the intersection area between the two wakes using standard geometrical formulas Proper understanding of these parameters is essential for analyzing wake effects and optimizing turbine placement for enhanced efficiency.
Wind Farm Cost of Energy
Wind farm cost of energy (COE) is measured by the LCOE, which is given by
COE = F CR×ICC AEP +LRC +LLC +O&M (3.8) where
ICC − Initial Capital Cost ($/kWh)
LRC − Levelized Replacement Cost ($/kWh)
LLC − Land Lease Cost ($/kWh)
O&M − Operation and Maintenance Cost ($/kWh)
AEP − Annual Energy Production (kW)
The Wind Turbine Design Cost and Scaling (WTDCS) model, developed by the National Renewable Energy Laboratory, estimates key economic factors such as initial capital cost, levelized replacement cost, land lease cost, and annual operation and maintenance expenses The initial capital cost comprises the turbine system cost and balance of station cost, which are calculated based on parameters like turbine rated power, rotor diameter, hub height, and drive train type Key cost elements include the turbine's core components and installation expenses, essential for accurate project budgeting and financial planning.
– Mechanical brake, high-speed coupling, and associated components
• Control, safety system, and condition monitoring
This model utilizes turbines that are specifically designed as three-bladed, upwind, pitch-controlled units These turbines operate at variable speeds and feature active yaw control to optimize performance They are mounted on robust steel tubular towers, ensuring stability and durability.
This research calculates the Annual Energy Production (AEP) by integrating power generation across various wind conditions using sampling methods within the UWFLO framework [43] The AEP provides a comprehensive measure of expected energy output for wind turbines Additionally, the study determines the annual levelized replacement cost, offering insights into the economic aspects of wind energy investments [125] This approach ensures accurate assessment of both energy production and associated costs, supporting optimal decision-making in wind farm development.
The annual Levelized Replacement Cost (LRC) is calculated as $10.7 per kW multiplied by the turbine's rated power (Pr), as shown in the equation Annual LRC = $10.7/kW × Pr According to the report referenced in Ref [125], the land-based operation and maintenance costs, along with the annual land lease expenses, are modeled as linear functions of the annual energy production (AEP), amounting to $0.00108 per kWh and $0.007 per kWh, respectively Additionally, the fixed charge rate is consistently assumed to be 11.85%, impacting overall financial evaluations.
Land Usage
Land configuration plays a crucial role in wind energy development, encompassing factors such as land area, shape, and site orientation, which influence the optimization of wind farm layouts for maximum energy output The design aims to minimize wake-induced energy losses and enhance overall efficiency, but the maximum extractable energy varies significantly depending on the farm's land shape and boundaries Additionally, the size and ground properties of a site determine the number and type of turbines that can be installed, shaping the scale of the project In conventional Wind Farm Layout Optimization (WFLO), land area and installed capacity are predefined, meaning optimal layouts and potential energy production depend on these initial constraints During early development stages, wind farm boundaries are flexible and subject to planning, allowing adjustments to optimize turbine placement and energy yield.
Large utility-scale wind energy projects require extensive land areas due to the need for larger inter-turbine spacing to reduce wake-induced energy losses, making land availability a critical factor for energy production These projects often face permitting challenges, environmental concerns such as noise pollution and impacts on local wildlife, and issues related to landowner participation According to ISO-9613-2 standards, noise impact is primarily determined by the distance from turbines, while bird, raptor, and bat mortality rates correlate with the wind farm's capacity, which depends on land resources Consequently, minimizing the land footprint of wind farms is essential to reduce their environmental impact and community disturbance.
This research developed a wind farm land usage model that determines the land area occupied by turbines based on layout without preset farm boundaries The model uses the 2D convex hull to encapsulate all turbines, identified with the Graham scan algorithm Since wind farms are typically rectangular and land is leased similarly, the smallest bounding rectangle (SBR) enclosing all turbines is calculated using the rotating calipers algorithm To account for safety and operational clearances, a buffer zone equal to one rotor diameter is added to each side of the SBR The final land usage estimate is represented by the combination of the SBR and buffer zone, with the land area quantified as a function of turbine coordinates.
(3.10) where Aland and Sland represent the land area and the land shape of the wind farm; and (X~ N , ~Y N ) represents the turbine coordinates.
If the optimal layout, (X~ ∗ N , ~Y ∗ N ), is given, the optimal land area (A ∗ land ) and land shape (S land ∗ ) of the wind farm can be expressed as
It should be also noted that the land shape can be regulated by the smallest bounding circle, eclipse, triangle, or any other 2D convex polygon.
Figure 3.1: Illustration of the wind farm layout