Realistic wind farm design layout optimization with different wind turbines types
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Abstract
Seeking for an appropriate design of wind farm (WF) layout constitutes a complex task in a wind energy project. An optimization approach is seriously needed to deal with this complexity, especially with current trend of large WFs area with important number of wind turbines (WTs). The present paper investigates optimization study of realistic offshore WF design layout (hornsrev1). The main objective of the current study is to design WF area that maximizes the extraction of wind power with low cost. In the first step, an optimization model using genetic algorithm with continuous layout representation is developed to look for the optimal design as a function of WTs placement. The effectiveness of such a methodology is validated and compared with the reference and irregular layout of horsrev1 offshore WF. With the aim to analyze the impact of WTs types on WF objectives, four commercial WTs are considered in the second step. The results showed that designing WF with big WTs gives best design layout. In addition, it demonstrated that selecting WTs based uniquely on rotor diameter size is not always a good idea. It should includes as well the number of WTs that influence significantly the power production and WF cost.
Keywords
Wind energy project Design Wind farm layout Wind turbines placement Wake effect Optimization Genetic algorithmAbbreviations
 x
Wind turbines coordinate in xaxis (m)
 y
Wind turbines coordinate in yaxis (m)
 d_{sw}
Downstream distance between two wind turbines (m)
 d_{per}
Perpendicular distance between two wind turbines(m)
 D
Rotor diameter (m)
 R
Rotor radius (m)
 N
Total number of wind turbines
 N_{up}
Number of upstream wind turbines
 z_{h}
Height of wind turbines (m)
 V_{f}
Free incoming wind speed (m/s)
 V_{df}
Wind velocity deficit (m/s)
 \(\theta\)
Wind direction (°)
 C_{p}
Power coefficient
 WTs
Wind turbines
 WF
Wind farm
 WFDLO
Wind farm design layout optimization
 COE
Cost of energy
 η_{m}
Gearbox mechanical efficiency
 η_{g}
Generator efficiency
 D_{wk}
Wake diameter (m)
 C_{t}
Trust coefficient
 ƿ
Air intensity (kg/m^{3})
 α
Wake decay coefficient
 z_{0}
Surface roughness length (m)
 a
Induction factor
 A
Swept area of wind turbines (m^{2})
 A_{ov}
Overlap area (m^{2})
 C_{WF}
Wind farm cost ($)
 P_{WT}
Power produced by wind turbine (MW)
 P_{WF}
Power produced by wind farm (MW)
 η_{WF}
Wind farm efficiency (%)
 CF
Capacity factor of wind farm (%)
 P_{r}
Rated power of wind turbines (MW)
 V_{r}
Rated wind speed of wind turbines (m/s)
Introduction
The important interest and efforts devoted by government, energy production, industries and academic research to electricity production from renewable and clean energy with the maturity of existed technologies justify the biggest exploitation of wind energy over the recent years. For instance, the wind energy investments in Europe has received the biggest part of new renewable energy finance about 63% in 2018, up from 52% in 2017 [1]. As a result of this evolution, the design process becomes highly complex from the point of the significant energy capacity to be produced, which generally requires hundreds of wind turbines (WTs) to be installed over a limited area. At this stage, several conflicting objectives, mechanisms and constraints have been imposed while requiring a balance between them in order to ensure the viability of wind energy project.
Designing wind farm (WF) layout refers to find the optimal placement of each individual WT from others inside the specific WF boundaries. However, the quality and quantity of expected power produced by WF are generally reduced by various sources of losses in which wake effect is considered the most influencing one [2]. Many published works provide that wake interferences generated randomly by upstream turbines cause a significant reduction of wind speed and increase turbulence intensity [3, 4]. Consequently, it gives rise to maintenance cost and diminishes the power production of downstream turbines. In this regard and in order to mitigate the wake effect among each WTs placement, wind farm design layout optimization (WFDLO) remains the best strategy to maximize WF performances.
Up to now, this problem has received a big attention by scientific research which is justified by the huge numbers of studies that have been addressed in the literature. The main objective conducted by these works is developing numerical algorithms that maximize power/energy production (in other words decreases the wake effect) and minimize the cost while satisfying certain constraints. These algorithms are based on different optimization techniques in which heuristic methods widely used. These methods includes genetic algorithm [5, 6], evolutionary algorithm [7], particle swarm optimization algorithm [8] and among others methods that can found in detail in these references [2, 9, 10].
Before reviewing some works that have done in this context, it is important to note that there are two basic approaches to represent the WF layout using heuristic methods [11, 12]. The first proposed approach consists of discretizing WF area into equal square grids. The center of each square represents the possible placement of WTs indicated by binary variables (0 and 1). Whilst the second approach called the continuous representation assumed that WTs can be placed at any position within the specified WF boundaries. In the literature, discrete approach is widely used to describe WF layout. But using such a methodology limits the feasible solutions of WTs placement due to the predefined grids. Thus, using continuous approach sound more appropriate to explore all feasible positions of wind turbines within wind farm area.
Since the two works conducted by Mosetti et al. [13] and Grady et al. [14] to optimize WFDL using genetic algorithm with discrete approach, much studies have been developed. They focus on improving WF performances through several variables and using various optimization methods as mentioned before. The vast majority of studies are interested to optimize the cost per unit of power (COE) using turbines with different hub height. For instance, Chen et al. [15] proposed an optimization approach based on greedy algorithm to investigate the benefit of using WTs with different hub height (78 m and 50 m) rather than identical hub heights (78 m) considering the same cases study of Mosetti et al. [13]. The results obtained show a significant improvement in COE value. Note that this study gives importance only to the concept of using WTs with different hub height neglecting the sensitivity variation of wind speed and wake interactions with tower height. This aspect is then studied by MirHassani et al. [16] who developed a mathematical programming model using linearization technique and iterative method to evaluate power production under various conditions of wind speeds and directions. The numeral results showed better arguments compared with the results found in References [13, 15].
Other research studies attempted to investigate the influence of rotor diameter on the COE. Mustakerov and Borissova [17] optimize WTs placement for both square and rectangular area using combinatorial algorithm. In their study, they strived to optimize COE under two wind direction cases (uniform and predominant) as function of type and number of WTs. They concluded that installing WTs with big size is more beneficial than WTs with small size. This study suffers from the lack of appropriate modeling of wake effect and WF cost that have to be assumed as function of WTs size and number. Chowdhury et al. [18] confirmed that employing different diameters (case 2) with assumption of using uniform WT type for entire WF can improve the power output. They solved the problem using mixed discrete PSO algorithm. Meanwhile, in their last case study they showed that choosing different WTs type instead of identical ones to be installed in WF can enhance the capacity factor by 2%. In the same manner, Rahbari et al. [19] combine the quadratic assignment problem with genetic algorithm to found the optimal arrangement of WTs. They also proved that using different types of WTs achieved a high WF efficiency.

Considering WTs types (rotor diameter), number and placement choice as variables of optimization.

The cost of WF is estimated as a function of WT design variables to be more realistic.

The power production is optimized using genetic algorithm with continuous approach allowing the exploration of unlimited WF layouts.

The optimization study is based on real offshore WF Horns Rev1 obtained from the literature [20, 21].
Thereafter, the paper continues with presenting the basic models for WF power and cost calculation in “Wind farm modeling”. The optimization procedure and case study are, respectively, explained in detail in “Optimization methodology” and “Description of case study”. “Optimization results and discussions” discussed the optimization results of this current study. The last section summarized the conclusions and possible future research studies.
Wind farm modeling
Wake modeling
Wind speed passing through upstream WTs is modified by the phenomenon called wake effect. The growth of this effect is characterized by reduced wind speed and increased turbulence intensity in downwind region. Indeed WTs placed in wake region produce less energy and require high maintenance cost as compared with upstream WTs. Thus, modeling appropriately wake effect that plays a key role in determining WTs placement is a serious need to take into account during the WFDLO.
 For partial wake interactions, this inequality is verified:$$R_{\text{wk}}  R < d_{\text{per}} \le R_{\text{wk}} + R.$$(8)
 For total interaction level, this inequality is verified:$$R_{\text{wk}}  R \ge d_{\text{per}} .$$(11)

Incoming wind speed V_{f}.

Wind direction.

Trust coefficient C_{t}.

Wake decay coefficient α (in other words).

Interspace between turbines d_{sw} and d_{per}.

Rotor diameter of WT D.

Number of WTs N.
Power production modeling
In the present study, C_{EF} is assumed to be equal to 40%.
Cost modeling
Optimization methodology
Any optimization problem including WF design layout requires the definition of four essential elements: the design variables, the constraints, the objective function and optimization method. The formulation of these elements in the context of WF design layout is explained in subsections.
Design variables They consist of input parameters that can be varied to find the optimum solution. In our optimization study, consider these following design variables: position of each WT (x, y), WT types (diameter rotor) and number of WTs.
Optimization method In broad sense, optimization method is strongly dependent on the nature of optimization problem. It is well known that due to the nonlinear behavior of power production that has to be evaluated under various types of variables (design/natural) WF design optimization cannot be solved by traditional approach such as trial and error or deterministic methods. Thence evolutionary algorithms are widely used in a particular genetic algorithm (GA) [2, 9]. This can be justified by its ability to handle complex and nonlinear problems. Accordingly, we are interested in our study to use this method of optimization based on continuous layout approach in which WTs can be located at any position within WF area.

Step 1: Creation of initial population GA began with generating a random population of n WTs position with respect to the two aforementioned constraints.

Step 2: Evaluation of objective function WF layouts resulted from previous phase is done through objective function (Eq. 22)

Step 3: GA operators The first operator started to select individuals that will contribute in the next population generation. The selection probability permits selecting the best individuals from the current generation. Crossover operator aim is to exchange two couples of genes (position) to produce new design layout. As crossover function, mutation operator is activated randomly with a certain probability (which is a parameter of GA) to modify one gene (position) of individual to another random and allowable position.
 Step 4: Generation of new wind farm layout The population of WF layouts that results from applying GA operators produces new design solution that will replace the old population. All steps above are repeated to ensure the generation of new population of feasible design layout at each iteration of optimization process until reaching the maximum number of iterations. Genetic algorithm parameters used in our study are summarized in Table 1.Table 1
Defined parameters of genetic algorithm
Parameters
Values
Size of initial population
Selection pressure
Crossover probability
Mutation probability
Iterations number
150
3
0.25
0.75
400
Description of case study
Specific information of wind farm site and wake parameters
Site roughness Mean wind speed Wind direction Wake decay coefficient Air density  0.001 10.6 0 0.04 1.225 
It is worth to keep in mind that in the present study we investigate and compare different design layouts of Horns Rev offshore WF considering two principal case studies described below.
Case 1: comparison of three design layout of Horns Rev offshore wind farm
In this case, we considered three different design layouts of Horns Rev offshore WF: reference layout (which is regular), irregular layout and optimized layout. The three layouts are compared in terms of power production, capacity factor and WF efficiency considering only the WTs position as design variable and using the 80 reference WTs of Vestas 802MW (same WTs type). Note that interspace between WTs in the regular configuration (reference layout) is d_{sw} = 7D and d_{per} = 7D, whilst in irregular configuration the separation distance is equal to d_{sw} = 7D and d_{per} = 3.5D. Concerning the genetic algorithm used to obtain the third configuration, we use the data given in Table 1.
Case 2: Design layout optimization with four types of wind turbine
Optimization results and discussions
The present study is conducted based on Horns Rev offshore WF characteristics with assumption that all design layouts are optimized under the mean wind speed of 10.6 m/s and dominant wind direction of 0° [32]. Our purpose here is to investigate the impact of some effective inputs variables on power production and cost of WF considering the main cases study explained in previous section.
Seeking of how to place WTs inside the limited WF area constitutes a complex task during design process. Indeed, sitting WTs based on classical method cannot always gives a high performance, especially when WTs number is very important.
Results of power improvement
Layouts comparison  Irregular/reference  Optimized/reference  Optimized/irregular 

Power improvement (%)  57,890  92,679  22,033 
Comparison results of three wind farm design layouts
WF layouts  Reference  Irregular  Optimized 

P_{WF} (MW)  37.4  59.1  72.04 
CF (%)  23.3  36.93  45 
η (%)  31.89  50.39  88 
Optimization results of WFDL using four wind turbines types
WT types  V66  V80  V112  LW164 

P_{WF} (MW) CF (%) η (%)  47.20 30 88  71.68 45 87  107.12 67 94  94.23 59 99.81 
Cost per unit of power for optimized design layouts
V66  V80  V112  LW164  

C_{WF} (M$)  196.48  199.04  199.22  200 
C_{WF}/P_{WF} ($/W)  4.16  2.77  1.85  2.13 
Conclusion
In this paper, a new optimization study of realistic WF design layout was performed. The main objective is designing wind farm area under realistic conditions considering different WTs types. In the first step of proposed study, an optimization approach using genetic algorithm with continuous layout representation is conducted to demonstrate and validate the effectiveness and benefit of using such a methodology to seek for optimal WTs placements. Designing the WF layout with four commercial WTs is then investigated and compared in terms of various performance objectives in a second step.
The results show that using an optimization approach instead of designing WF area with traditional rules (regular or irregular layouts) leads to find the optimal design layout with high degree of power production. Otherwise, for a given WF area it figured out that a selection of specific WT type plays a key role. Designing an area based only on WT size is not always a good idea. Indeed, the power production, capacity factor, efficiency and cost per unit of power depend strongly on both number and size of WTs. Accordingly, it can be concluded that it is hard to make a choice in terms of power production and WF cost at the same time due to the contradictory aspect of both objectives.
In future studies, it is important to investigate the relationship between WF design layout and the compromise between power production and WF cost. The study will emphasize the need to include other design variables such as using WTs with different hub height. In addition, the study will be conducted under the variability of wind speed and direction of WF.
Notes
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