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Contents lists available at ScienceDirect

Expert Systems with Applications

journal homepage: www.elsevier .com/locate /eswa

Wind turbine selection for wind farm layout using multi-objectiveevolutionary algorithms

http://dx.doi.org/10.1016/j.eswa.2014.04.0440957-4174/� 2014 Published by Elsevier Ltd.

⇑ Corresponding author. Tel.: +34 950 214501; fax: +34 950 015491.E-mail addresses: pagilm@ual.es (F.G. Montoya), fmanzano@ual.es

(F. Manzano-Agugliaro), slm686@alboran.ual.es (S. López-Márquez), qhernandezuv.mx (Q. Hernández-Escobedo), cgil@ual.es (C. Gil).

Please cite this article in press as: Montoya, F. G., et al. Wind turbine selection for wind farm layout using multi-objective evolutionary algorithmsSystems with Applications (2014), http://dx.doi.org/10.1016/j.eswa.2014.04.044

Francisco G. Montoya a,⇑, Francisco Manzano-Agugliaro a, Sergio López-Márquez b,Quetzalcoatl Hernández-Escobedo c, Consolación Gil b

a Department of Engineering, University of Almería, 04120 Almería, Spainb Department of Informatics, University of Almería, 04120 Almería, Spainc Facultad de Ingenería, Universidad Veracruzana, Campus Coatzacoalcos, Coatzacoalcos, Mexico

a r t i c l e i n f o a b s t r a c t

26272829303132

Keywords:Multi-objectiveEvolutionary algorithmWind energyOptimizationWind turbineRenewable energy

3334353637383940414243444546

Wind energy has become the world’s fastest growing energy source. Although wind farm layout is a wellknown problem, its solution used to be heuristic, mainly based on the designer experience. A key insearch trend is to increase power production capacity over time. Furthermore the production of windenergy often involves uncertainties due to the stochastic nature of wind speeds. The addressed problemcontains a novel aspect with respect of other wind turbine selection problems in the context of wind farmdesign. The problem requires selecting two different wind turbine models (from a list of 26 items avail-able) to minimize the standard deviation of the energy produced throughout the day while maximizingthe total energy produced by the wind farm. The novelty of this new approach is based on the fact thatwind farms are usually built using a single model of wind turbine. This paper describes the usage ofmulti-objective evolutionary algorithms (MOEAs) in the context of power energy production, selectinga combination of two different models of wind turbine along with wind speeds distributed over differenttime spans of the day. Several MOEAs variants belonging to the most renowned and widely used algo-rithms such as SPEA2 NSGAII, PESA and msPEA have been investigated, tested and compared based onthe data gathered from Cancun (Mexico) throughout the year of 2008. We have demonstrated the pow-erful of MOEAs applied to wind turbine selection problem (WTS) and estimate the mean power and theassociated standard deviation considering the wind speed and the dynamics of the power curve of theturbines. Among them, the performance of PESA algorithm looks a little bit superior than the other threealgorithms. In conclusion, the use of MOEAs is technically feasible and opens new perspectives for assist-ing utility companies in developing wind farms.

� 2014 Published by Elsevier Ltd.

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1. Introduction

Energy is a vital input for social and economic development(Baños et al., 2011). Deployment of 100% renewable energy systemis technically and economically feasible in the future (Mathiesen,Lund, & Karlsson, 2011). The wind energy is one of the most pow-erful and profitable way to satisfy the demands of sustainabledevelopment (Sebitosi, 2008), while the production of wind energyhas grown 30% per year over the last 10 years (Pacala & Socolow,2004). It is worth noting that wind power has the lowest relativegreenhouse gas emissions, the least water consumption demands

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and the most favorable social impacts, but it requires more landand has relatively high costs (Hernández-Escobedo, Manzano-Agugliaro, & Zapata-Sierra, 2010). Some agencies (European WindEnergy Association and the German Aerospace Center) have drawnup scenarios where renewable energies, including wind farms,could supply 80% of Europe’s entire electricity demand by 2050.The National Renewable Energy Laboratory in the US assessedhow wind could supply 20% of the entire US electricity demandby 2030 DoE. Other study demonstrates that the wind electricitypotential in Canada is many times the current total electricitydemand (Harvey, 2013).

The results of wind energy resource studies depend on the qual-ity of the available wind energy data as well as on the assumptionsabout technology and available space (Manzano-Agugliaro,Alcayde, Montoya, Zapata-Sierra, & Gil, 2013). Therefore, suchstudies can only provide an approximation of the overall wind

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energy potential. Furthermore, it is important to consider that thewind energy potential can vary significantly for different regions(Hernandez-Escobedo, Manzano-Agugliaro, Gazquez-Parra, &Zapata-Sierra, 2011). It is worth noting that wind power has thelowest relative greenhouse gas emissions, the least water con-sumption demands and the most favorable social impacts, but itrequires more land and has relatively high costs (Hernández-Escobedo et al., 2010).

Meteorological stations save an enormous quantity of statisticaldata every 10 min. Among the information they record is the aver-age wind speed over the 10-min interval as well as the maximumwind speed and wind direction. Processing the data of a whole yearprovides important information about the wind regime of a givenarea (Alemán-Nava et al., 2014; Cancino-Solórzano & Xiberta-Bernat, 2009). Using these statistical data it is possible to calculatethe energy output that a certain type of wind turbine can producein the region as well as uptime/downtime average times(Hernández-Escobedo et al., 2010). Different models of wind tur-bine produce different amounts of energy depending on the windspeed (m/s) (Slootweg, De Haan, Polinder, & Kling, 2003).

The wind resource use fairly depends on the selected wind tur-bine. For every wind turbine model, the generated power (kW) canbe calculated using the provided power curve from the manufac-turer (Carrillo, Montaño, Cidrás, & Díaz-Dorado, 2013; Lydia,Kumar, Selvakumar, & Kumar, 2014). This way, different wind tur-bine models can be evaluated according to the characteristics ofthe wind for a specific region. Nowadays, the wind turbine selec-tion problem based on the specific wind regimen has become animportant task proved by the large number of examples found inthe specialized academic literature. In 2009, for the Kingdom ofBahrain, Jowder (2009) uses a classical method to compare 5 windturbines at 60 m height (Gamesa G58, Nordex N60, Nordex 70,Gamesa G80, and Nordex N80), determining that the most suitableturbine was Gamesa G58. Wind energy assessment of the São Joãodo Cariri (SJC) in Paraiba (PB) state situated in Brazilian northeastwas evaluated by de Araujo Lima and Filho (2012) using 3 differenttypes of wind turbine (Bonus Mk III, Vestas V27 and Bonus Mk III).Alimi, Maatallah, Dahmouni, and Nasrallah (2012) assess eightcommercial turbines at different hub heights for wind power gen-eration on the central coast of the gulf of Tunis (Anbonus MK III-30,V39-35, V82-0.9, Dewind 1250 kW, GE 1500 kW, Vestas V80,Repower (2000 kW) MM 70-65 and Nordex (2300 kW) N90-100).For the Niger Delta region, Adaramola, Oyewola, Ohunakin, andAkinnawonu (2014) evaluated the performance of four wind tur-bine models ranging from 35 to 500 kW (G-3120, P19-100, WES-30 and ZEUS 500), obtaining that the energy output from wind tur-bine G-3120 was the highest. In Saudi Arabia on 2014, Al-Hadhrami (2014) evaluated the energy output of 16 wind turbinesin the category of 1–3 kW, 5–10 kW, 15–20 kW and 50–80 kWrated powers, and the effect of hub height on energy output; thehighest percentage change in annual energy yield (AEY) wasobtained for an increase in hub height of 10 m from 20 to 30 m.Adaramola, Agelin-Chaab, and Paul (2014) assess the wind powergeneration along the coastal region of Ghana using 4 different windturbines (WES30, CF-100, Polaris 15–50, and Garbi150/28). Basedon the above mentioned references, a limited number of wind tur-bines has been evaluated on site in order to validate the energypossibilities of a region. Moreover, the combination of wind tur-bines for a wind farm has not been yet tested and there is no avail-able studies that permits the optimization of the standarddeviation for the average generated energy and the gross generatedpower.

This paper describes the usage of multi-objective optimizationproblems in the context of power energy production with theusage of 26 different wind turbines, selecting a combination oftwo of them respecting different wind speeds distributed over

Please cite this article in press as: Montoya, F. G., et al. Wind turbine selectionSystems with Applications (2014), http://dx.doi.org/10.1016/j.eswa.2014.04.044

different time spans of the day. To solve the addressed problemwe use different multi-objective evolutionary algorithms. The usedalgorithms are adaptations of four well-known MOEAs such as:NSGAII (Deb, Pratab, Agrawal, & Meyarivan, 2002), PESA (Corne,Knowles, & Oates, 2000), msPESA (Gil, Márquez, Baños, Montoya,& Gómez, 2007) and SPEA2 (Zitzler, Laumanns, & Thiele, 2001).Every implemented algorithm provides a solution set (called Par-eto Set) for the addressed problem. These algorithms have alreadybeen successfully used in other kinds of planning problems, e.g.greenhouse planning (Márquez et al., 2011), cartographic problems(Manzano-Agugliaro, San-Antonio-Gómez, López, Montoya, & Gil,2013), vehicle routing problems with time windows (Baños,Ortega, Gil, Fernández, & de Toro, 2013) or power systems optimi-zation (Montoya et al., 2010; Zavoianu et al., 2013).

The paper is organized as follows. Section 2 presents the relatedworks using EAs for wind farms layout. Section 3 presents theproblem definition. Section 4 summarises the implementedmulti-objective evolutionary algorithms. Section 5 shows the com-putational experiments with the proposed method and results.Finally, conclusions are given in Section 6.

2. Related works

Although wind park layout is a well known problem, its solu-tion used to be heuristic, mainly based on the designer experience(Khan & Rehman, 2013). Due to the complexity of the wind farmlayout design problem, traditional optimization approaches suchas linear programming, branch-and-bound, dynamic program-ming, or backtracking cannot be applied (Khan & Rehman, 2013).Optimal wind farm designing is the result of a process, due tothe non-differentiable nature of the problem; EAs are efficienttechniques to work out this kind of optimization problem (Mora,Barón, Santos, & Payán, 2007).

Multimegawatt wind-turbine systems, often organized in awind park, are the backbone of the power generation based onrenewable-energy systems (Liserre, Cardenas, Molinas, &Rodriguez, 2011). Therefore, there are places where it is not suit-able to place a certain model of wind turbine. One of the mostimportant factors when considering the design of wind farms isthe placement of the generators. As wind flows through the gener-ator field, it loses part of its energy. This effect is known as ‘‘wake’’,and it means that the location of an wind turbine affects nearbywind turbines as well. Evolutionary Algorithms have been success-fully used in the past (Kusiak & Zheng, 2010) to optimize the place-ment of wind turbines in order to minimize the effect of wake, in a2D grid (Emami & Noghreh, 2010; Grady, Hussaini, & Abdullah,2005). Minimizing wake is important in order to maximize theenergy production, which is one of the most important objectivesto attain (Kusiak & Song, 2010). For the sake of simplicity, as wellas for practical reasons, this study will consider that the wind tur-bines are placed in a straight line perpendicular to the direction ofthe strongest wind regime.

Mosetti, Poloni, and Diviacco (1994) proposed one of the firstoptimization approaches to wind turbine distribution at a givensite in order to extract the maximum energy for the minimuminstallation costs. This problem has been widely studied by meansof genetic algorithms, GA (Emami & Noghreh, 2010; Grady et al.,2005). A comprehensive survey covering the use of GA which spe-cifically looks at the research on different wind farm layout designproblems (Wind turbine height, rotor diameter, or wake decaymodel) is done by Khan and Rehman (2013). A combinatorial opti-mization model for wind turbines type and number choice andplacement considering the given wind park area shape and sizeis developed by Mustakerov and Borissova (2010) studding 24 tur-bine models. They state that the several wind park area conditions

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can be introduced into optimization tasks formulation as variablesrelations and restrictions. For the optimization of wind farm tur-bines layout using an evolutive algorithm, González, Rodriguez,Mora, Santos, and Payan (2010) use 4 wind turbines (although theydid not specify any model). Almost three fourth parts of the initialcost of a wind farm corresponds to the wind turbines (Junginger,Faaij, & Turkenburg, 2004). Another key in search trend is toincrease power production capacity over time by increasing rotordiameter (McKay, Carriveau, & Ting, 2011), however, there areoften legal limits to the maximum nameplate capacity of an indi-vidual turbine. Furthermore, the production of wind energy ofteninvolves uncertainties due to the stochastic nature of wind speeds(Hernández-Escobedo, Saldaña-Flores, Rodríguez-García, &Manzano-Agugliaro, 2014; Jin & Tian, 2010), so that the standarddeviation of the generated energy must be taken into account.Therefore, the optimization of generated power using differentwind turbine models with low standard deviation plays an impor-tant role in order to guarantee the highest reliability of power net-work. This gives the motivation to carry out the survey reported inthis paper.

Multi-objective evolutionary algorithms are known for their abil-ity to optimize several objective functions simultaneously to providea representative set of the Pareto front (Baños, Gil, Reca, & Martínez,2009; Benson & Sayin, 1997; Coello, Lamont, & Van Veldhuizen,2007; Miettinen, 1999). The goal of Pareto-based multi-objectivestrategies is to generate a front (set) of non-dominated solutions asan approximation to the true Pareto-optimal front (Alcayde et al.,2011). In last years most papers dealing with multi-objective opti-mization use the concept of Pareto-optimality comparing severalgenetic algorithms them self (Anagnostopoulos & Mamanis, 2011;Baños et al., 2013; Fernández, Gil, Baños, & Montoya, 2013;Gómez-Lorente, Triguero, Gil, & Estrella, 2012), or comparing withtraditional analysis (Dovgan, Javorski, Tušar, Gams, & Filipic, 2013;Sánchez, Montoya, Manzano-Agugliaro, & Gil, 2013).

3. Problem definition

3.1. Formulation

The problem of multiple wind turbine selection for wind farmlayout is addressed. Wind farms are usually built using a singlemodel of wind turbine, but for this experiment, the wind farm willbe planned with two different models. It is clear that there are twoobjectives of interest to optimize in this problem: maximizing thepower output of the wind farm and minimizing the average absolutedeviation of power generation through the day, allowing energy tobe produced in situations where using a single type of wind turbinewould imply ceasing production of energy at lower wind speeds.

� Maximize the total power output (Pp) by the wind farm

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where Pi is the power generated in a 10-min interval, and 144 isthe total number of 10-min intervals in 24 h. Note that maxi-mize power is the same as maximize the produced energy.� Minimize the average deviation of the power (PD) output

through the day

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where mðPÞ is the measure of central tendency, represented bythe median value of all the power outputs.

Subject to the following constraints:

cite this article in press as: Montoya, F. G., et al. Wind turbine selections with Applications (2014), http://dx.doi.org/10.1016/j.eswa.2014.04.044

� The maximum amount of wind turbines installed is 20, in orderto set an upper limit for energy generation, and to limit the run-times of the simulations, because of the size of the data sets inthis study.� Two different models of wind turbines are to be used from a list

of 26 available. This limit is chosen because the logistics of deal-ing with a number of wind turbine models for a certain windfarm increases with the number of different models used, espe-cially when using wind turbines manufactured by differentcompanies. Another downside of increasing the amount of dif-ferent models is that both their management and the trainingof specialized crew for maintenance operations become addi-tional expenses. The most powerful wind turbines in the datasample can ideally generate up to 2,500 kW of power. Thebehavior of the power generation of each wind turbine can bedescribed with a ‘‘power curve’’ graph and Fig. 1 shows thepower curve for 26 different wind turbine models in the rangeof wind speeds from 1 m/s to 6 m/s.Statistical data were obtained throughout 2008 for the region ofCancún in Mexico (Hernández-Escobedo et al., 2010). The aver-age wind speeds in the area were recorded over 10-min inter-vals through the day, starting at 0:00, making a total of 144intervals. Wind speeds were then averaged for the whole yearto calculate the energy each wind turbine in the wind farm pro-duces (Hernandez-Escobedo et al., 2011). Fig. 2 shows theyearly average wind speed. It is worth noting that the highestwind speeds are recorded at night.� All wind turbines will be placed in a straight line so as to receive

the maximum amount of wind according to the local windregime direction and speed (González-Longatt, Wall, & Terzija,2012; Migoya et al., 2007). With this design, there is no needto take into account factors such as the dispersion of windenergy through the wind farm due to wind wake, which mayaffect wind turbines behind the front line of wind (Adaramola& Krogstad, 2011). There are also studies which primarily aimto reduce installation cost and energy loss, and propose to opti-mize the electric power networks of such farms serve to electri-cally connect all the turbines in the farm back to a centralsubstation (Pemberton, Daly, & Ertugrul, 2013).

To solve the proposed problem, an approximation to the ParetoSet is considered as a solution to the multi-objective problem.

3.2. Concepts in multi-objective optimization

The use of multi-objective optimization as a tool to solve multi-objective problems (MOP) implies explaining some key conceptsthat are of invaluable importance. Without them it would be inac-curate to describe what a good approximation to the Pareto front isin terms of criteria such as closeness to the Pareto set, diversity,etc. (Coello, Lamont, & van Veldhuizen, 2007; Deb, 2002; Talbi,2009; Voorneveld, 2003).

Multi-objective optimization is the exploration of one or moredecision variables belonging to the function space, which simulta-neously satisfy all constraints to optimize an objective functionvector that maps the decision variables to two or more objectives.

minimize=maximizeðfkðsÞÞ;8k 2 ½1;K� ð3Þ

Each decision vector s ¼ fðs1; s2; ::; smÞg represents accuratenumerical qualities for a MOP. The set of all decision vectorsconstitutes the decision space. The set of decision vectors thatsimultaneously satisfies all the constraints is called feasible set(F). The objective function vector (f) maps the decision vectorsfrom the decision space into a K-dimensional objective spaceZ 2 RK ; z ¼ f ðsÞ; f ðsÞ ¼ f1ðsÞ; f2ðsÞ; . . . ; fKðsÞf g; z 2 Z; s 2 F.

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Fig. 1. Power curves of 26 wind turbine models.

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In order to compare the solutions of a given MOP with KP2objectives, instead of giving a scalar value to each solution, a par-tial order is defined according to Pareto-dominance relations, asdetailed below.

Order relation between decision vectors: Let s and s0 be two deci-sion vectors. The dominance relations in a minimization problemare:

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s dominates s0ðs � s0Þ iff

fkðsÞ < fkðs0Þ ^ f 0kðsÞ� f 0kðs0Þ; 8k0 – k 2 ½1;K�

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s; s0 are indifferent ðs � s0Þ iff

fkðsÞ < fkðs0Þ ^ f 0kðsÞ > f 0kðs0Þ; k0 – k 2 ½1;K�

(ð5Þ

Pareto-optimal solution: A solution s is called Pareto-optimal ifthere is no other s0 2 F, such that fðs0Þ < f(s). All the Pareto-optimalsolutions define the Pareto-optimal set, also called Pareto front.

Please cite this article in press as: Montoya, F. G., et al. Wind turbine selectionSystems with Applications (2014), http://dx.doi.org/10.1016/j.eswa.2014.04.044

Non-dominated solution: A solution s 2 F is non-dominatedwith respect to a set S02F if and only if 9= s0 2 S0, verifying thats0 � s.

To summarize these definitions, Fig. 3 shows the Pareto-dominance concept for a MOP with two objectives (maximizingf1 and minimizing f2). The filled circles represent non-dominatedsolutions, while the non-filled ones are dominated or indifferentsolutions. Fig. 3(a) shows the location of several solutions inrelation to the Pareto front, while Fig. 3(b) shows the relative dis-tribution of the solutions in reference to a certain solution s. Thereexist solutions that are worse (in both objectives) than s, better (inboth objectives) than s, and incomparable (better in one objectiveand worse in the other).

Obtaining a set of non-dominated solutions is not the onlyimportant objective when solving this kind of problem. Obtaininga wide and evenly distributed Pareto front is also of key impor-tance because such a set of solutions is more useful for the decisionmaking process.

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Fig. 3. Pareto-dominance relations in a two-objective problem.

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4. Implemented multi-objective evolutionary algorithms

Fig. 4 shows the flow diagram used for the proposed algorithms.The following MOEAs have been used to perform the experimentsneeded to gather the data used in this paper:

� NSGAII, Non-dominated Sorting Genetic Algorithm II (Deb et al.,2002). It makes use of a population as well as a temporal helperpopulation where it stores the descendant individuals. It thenjoins both populations and classifies them by using a fastnon-dominated sorting to separate the solutions into severalfronts, with a domination relationship between them. To gener-ate the next population, only the first fronts are kept, while theother solutions are disregarded. In this way, the populationholds the Pareto front and becomes the solution at the end ofthe procedure.

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425Fig. 4. Flow diagram for the proposed algorithms.

Please cite this article in press as: Montoya, F. G., et al. Wind turbine selectionSystems with Applications (2014), http://dx.doi.org/10.1016/j.eswa.2014.04.044

� PESA, Pareto Envelope-based Selection Algorithm (Corne et al.,2000). This MOEA uses a hypergrid for analyzing the densityinformation of the individuals. PESA keeps the non-dominatedindividuals in an archive, updating it each time a new solutionis inserted by removing the old solutions that become indiffer-ent or dominated by the new one. The archive holds the Paretofront, which becomes the solution at the end of the procedure.� SPEA2, Strength Pareto Evolutionary Algorithm (Zitzler et al.,

2001). SPEA2 uses a strength indicator in order to measurethe solution quality of the individuals stored in the archive. Atthe end of the procedure, the archive becomes the final solution,storing the generated Pareto front. The main operations in thisMOEA consist of generating the fitness of the solutions, calculat-ing the density information for each solution within the solu-tion set, and then truncating the archive once it becomes full,by removing the worst quality solutions in the densest areas.� msPESA, Mixed Spreading PESA (Gil et al., 2007). This MOEA is a

derivative of PESA that implements a different hypergrid policyallowing the grid resolution to increase without penalizing per-formance. In this case, the hypergrid has one dimension lessthan the PESA hypergrid, so the memory requirements aregreatly reduced for larger populations. The logic behind thisconsists of using the same number of cells in the grid as thereare solutions. Ideally this would mean that as the algorithmoptimizes the Pareto front, the solutions would end up evenlyspread alongside the front. On inserting a solution into thearchive, it performs a local search procedure in order to improvethe quality of the solution, or it even inserts more than one pos-sible solution. Inserting a new solution into the archive does notenforce a strong elitism, since all the solutions are kept, andthey are only removed when the archive is full. This increasesgenetic variety during the first iterations of the MOEA.

4.1. Representation of the population

The population is coded using the following class structure:

public class Mill

{public string name;public double[] powerRegime = new double[25];public double diameter;public double surface;

}

It can be noted that the generated power for every wind turbineis stored in the field ‘‘powerRegime’’. Thus, the average energy/power though a time period can be calculated easily using the fit-ness function. Moreover, there are two arrays millVarieties and mill-Configurations where the wind turbine models used by everyindividual and the model configuration for every individual genis stored, respectively (see Fig. 5).

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4.2. Fitness function

The generated output power for the 26 wind turbines have beenmathematically modeled through their power curve (see Fig. 6)using the equation for the logistic curve (Hernández-Escobedoet al., 2010),

Py ¼ky0erx

kþ y0 erx � 1ð Þ ð6Þ

where Py is the generated power (W), x is the wind speed (m=s), rthe rate of increase, y0 is an initial solution (m=s) and k is the capac-ity of the system. The values of the variables in the above equationwere adjusted using MatLab�software. The generated power iscoded inside the wind turbine object though the powerRegime field.So, this way it’s very easy to get the total generated power by theindividual (20 wind turbines) and also the averaged energy pro-duced in any time period.

4.3. Evolutionary operations

Because of the object representation for the individuals, specialoperators have been implemented. The properties of these objectshave been introduced in the Representation of the populationsection.

Mutation The coding of individuals has been implementedas showed in Fig. 7. It should be noted that everygen matches a wind turbine unit, having a total of20 genes and a maximum of 2 different models.

Fig. 5. Representation

Fig. 6. Power curve for a g

Please cite this article in press as: Montoya, F. G., et al. Wind turbine selectionSystems with Applications (2014), http://dx.doi.org/10.1016/j.eswa.2014.04.044

It carries out one of the following operations(There is a 60% probability of choosing the firstoption, 40% for the second one):

� Each wind turbine in the farm (in the list of 20 units, repre-senting a gene) has a 10% probability of being changed forthe alternative model.

� All the wind turbines of a given model in the solution arechanged for another model of wind turbine from the listof 26 different available models (except the 2 already pres-ent in the individual).

Mutation strategy is detailed in Figs. 8 and 9. It is clearly noted thatmutation can affect to only one gen (wind turbine) changing itsvalue to the alternative model already existing in the individual(see Fig. 8), or it can affect to all the occurrences of one existingmodel changing them to another different model available in thecomplete list of wind turbines (see Fig. 9).Crossover (1, 2) The crossover operation implemented works as

follows:The crossover strategy is detailed in Fig. 10. First,2 individuals (1 and 2) are selected for crossover,producing a new individual 10 (child). The processstarts with the cloning of the better fitness indi-vidual, that is, the individual with the best aver-age energy production. The cloned individualð10Þ is compared with the remaining individual(individual 2 in this case). If the models of indi-vidual 2 are better (supplying more energy/power) than of those in 10 then they are acquiredby 10. This comparison is made in an orderly way,

of an individual.

eneric wind turbine.

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Fig. 7. Coding of individuals.

Fig. 8. First strategy of mutation.

Fig. 9. Second strategy of mutation.

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i.e. if every individual has 2 model of wind tur-bines (10A, 10B and 2C, 2D), the procedure willinvolve 10A – 2C and 10B – 2D. If 2C is better than10A and/or 2D is better than 10B, then swappingwill take place (on condition that 2C or 2D arenot already present in 10). Finally, the last stepis to consider swap indexes of 2 and 10 individualswith a probability of 65% (keeping the existingmodels in 10).

All the constraints are enforced to meet the criteria. The cross-over and the mutation do consider the constraints exposed in theProblem definition section, then non-feasible solutions are avoidedby crossover and mutation operators.

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5. Computational experiments

In order to ascertain the quality of the results, each experimentis repeated 100 times. The experiments consist in running eachalgorithm once and saving their Pareto fronts. In practice, thismeans that for clarity of results, each algorithm is run 100 timesand the solutions it finds are saved on a file with its name. This willallow enough information to be collected about the experimentsand the obtained Pareto fronts. Through combining the collectivePareto fronts of the 100 independent runs for each algorithm, itis possible to build a reference Pareto front. The reference Paretofront is built by joining all 100 sets of solutions into a single solu-tion set and then applying Pareto domination in order to obtain a

Please cite this article in press as: Montoya, F. G., et al. Wind turbine selectionSystems with Applications (2014), http://dx.doi.org/10.1016/j.eswa.2014.04.044

single Pareto front. The configuration of the algorithms involvesperforming 90% crossover operations and 10% mutation opera-tions, with a population size of 100 individuals, for a total of15,000 objective function evaluations. These parameters have beenchoosed based on previous trials and have demonstrated very goodperformance (it is out the scope of this paper to show our tunningprocess). Initial population has been generated from randomindividuals.

Once the reference Pareto front is obtained for a given algo-rithm, it can be compared with the others by using a metric. Oneof the most used metrics is the coverage metric, that states howmuch a certain Pareto front dominates or is dominated by anotherfront. This metric is fully described in the following paragraphs.There are other two main metrics to measure the quality of thenon-dominated fronts obtained by a multi-objective algorithm:Hyper-volume (Hv) and set coverage (Cv) (Ak et al., 2013;Grosan, Oltean, & Dumitrescu, 2003). Hv is the only known indica-tor that reflects the Pareto dominance in the sense that, if anapproximation set weakly dominates other, this fact will bereflected in the values of Hv. We already have evaluated Hv andCv but, in our case, there is no sense to introduce hyper-volumemetric because of the similarity of all Pareto fronts obtained bythe four implemented algorithms.

To solve this problem multi-objective evolutionary algorithmsare suitable because of the conflicting nature of the proposedobjectives. Statistical data were taken every 10 min from a meteo-rological station in Cancun (Mexico) over the year 2008(Hernández-Escobedo et al., 2010), and the power outputs of 26different models of wind turbines have been considered. These

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Fig. 10. Crossover strategy.

Table 1Computation time required by the algorithms.

Algorithm Time (s)

NSGAII 56.05msPESA 26.47SPEA2 53.73PESA 49.45

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data have provided an accurate estimation of the power producedover a whole year, which allows us to know how well a certainwind turbine configuration performs.

To determine which Pareto front is the best one, the coveragemetric has been used to compare their quality:

Coverage of two sets ðCÞ : Let X;X0 be two solution sets. Func-tion C maps the sorted pair X;X0 tothe interval ½0;1� (see Eq. (7)). Thevalue CðX;X 0Þ ¼ 1 means that all thepoints (solutions) in X 0 are dominatedby at least one solution of X. The oppo-site value, CðX;X0Þ ¼ 0 means that nosolution in X0 is covered by any otherpoint in set X. It is important to notethat both CðX;X 0Þ and CðX 0;XÞ have tobe considered because they are notcomplementary values, nor are theynecessarily equal. X and X0 are thesolution sets produced by two differ-ent algorithms (or two different runsof the same algorithm).

Please cite this article in press as: Montoya, F. G., et al. Wind turbine selection for winSystems with Applications (2014), http://dx.doi.org/10.1016/j.eswa.2014.04.044

CðX;X0Þ :¼ ja0 2 X0;9a 2 X : a � a0j

jX 0jð7Þ

The computer used for the simulations is an Intel Core i5,2.3 GHz with 4 GB RAM and Intel HD Graphics 3000 video card.The computation time required by algorithms is detailed inTable 1.

The results for the coverage of the Pareto fronts shown in Fig. 11are given in Table 2, and it can be seen that the convergence is veryhigh for this dataset and problem, so all procedures are able to findgood solutions for the two objectives proposed. PESA is marginallythe best algorithm, finding several solutions belonging to the Par-

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Fig. 11. Pareto front of generated power vs. Unused Installed power, for a 20-unit wind farm built using 2 different models of wind turbines, obtained by combining theresults of the 100 independent runs for each algorithm.

Table 2Coverage metric, two-objective problem.

NSGAII SPEA2 PESA msPESA

NSGAII — 1.00 1.00 0.99SPEA2 0.98 — 1.00 0.99PESA 0.93 0.95 — 0.96msPESA 0.98 0.99 1.00 —

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eto front that are not present in any other algorithm. It is possibleto conclude that all the algorithms used in this study are useful tofind the Pareto-optimal solutions, so the results and methodsdeveloped for this study should be easily repeatable for any otherregion in the world.

Fig. 12. Solutions found within the final Pareto front, for

Please cite this article in press as: Montoya, F. G., et al. Wind turbine selectionSystems with Applications (2014), http://dx.doi.org/10.1016/j.eswa.2014.04.044

In Fig. 12 it is possible to see the power curves of the selectedgenerators for two extreme solutions found within the final Paretofront. In the first case, the algorithms found that a combination of18 K100 wind turbines and 2 LTW80 make up the most efficientcombination for producing the maximum amount of energy, whilethis combination shows the lowest possible average deviation forthat level of energy production, therefore increasing the odds ofobtaining a more easily predictable amount of energy, in line withthe energy requirement predictions that electrical networks mustmake in order to ensure a proper service. The second graph inFig. 12 shows the configuration with the lowest deviation. Thisconfiguration is also the one with the lowest energy productionand so it is unlikely to be the most profitable one, but it is includedhere only for the sake of completeness.

maximum energy production, minimum deviation.

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Designing a wind farm using different wind turbine models toreduce the difference in energy output while maximizing the totalenergy production by using evolutionary algorithms is a novelwork. As Fig. 11 shows, there is a strong convergence towardsthe Pareto front for each one of the algorithms used for evaluatingthe problem, using a total of 50,000 function evaluations for eachMOEA.

660661662663664665666667668669670671672673674675676677678679680681682683684685686687688689690691692693694695696697698699700701702703704705706707708709710711712713714715716717718719720721722723724Q4725726727728729730731732733734735736

6. Conclusions

The use of MOEAs to study multiple configurations of wind tur-bines in order to optimize energy production is useful to explore allthe possible viable alternatives, allowing a team of experts tochoose the configuration that best suits their needs. In this situa-tion, all the algorithms were able to produce a definite set of solu-tions, meaning that the best solutions to the problem were foundby using a combination of two different wind turbine models,and by varying the numbers of each type of model. All algorithmsperform well, as the coverage metric shows (see Table 2), wherethe fronts produced by all algorithms overlap for most solutionsdue to the high convergence for this instance of the problem.

The complexity of this problem increases with higher numbersof models of wind turbine. For two different models, it is possiblefor the procedures to obtain the most accurate results, generating adiscontinuous Pareto front because there is a discrete number ofdifferent wind turbines. The number of generators to install inthe field does not change the overall shape of the Pareto front,but merely stretches it. This happens because the overall propor-tion of generator models remains constant regardless of how manygenerators are to be installed.

We have demonstrated the powerful of multi-objective evolu-tionary algorithms to wind turbine selection and estimate themean power and the associated standard deviation consideringthe wind speed and the dynamics of the power curve of the tur-bines. Our method can potentially assist utility companies indeveloping robust distributed generation systems or deployingsmart grid systems.

The research reported in this paper has as main conclusion thatthe use of multi-objective optimization Algorithms opens new per-spectives for wind turbines selection in specific areas for WindFarms implementation.

The future work will try to dig into new versions of our imple-mented algorithms. For example, HVSEA version is on the road.Also, other considerations like digital elevation model (DEM) andenvironmental constraints will be taken into account.

Acknowledgments

This work has been financed by the Spanish Ministry of Innova-tion and Science (TIN2008-01117) and the Excellence Project ofJunta de Andalucía (P07-TIC02988), in part financed by the Euro-pean Regional Development Fund (ERDF).

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