A wind turbine evaluation model under a multi-criteria decision making environment

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A wind turbine evaluation model under a multi-criteria decision

making environment

Amy H.I. Lee

a

_{, Meng-Chan Hung}

b

_{, He-Yau Kang}

c,⇑

_{, W.L. Pearn}

b a

Department of Technology Management, Department of Industrial Management, Chung Hua University, Hsinchu, Taiwan b

Department of Industrial Engineering and Management, National Chiao Tung University, Hsinchu, Taiwan c

Department of Industrial Engineering and Management, National Chin-Yi University of Technology, Taichung, Taiwan

a r t i c l e

i n f o

Article history: Received 3 January 2012

Received in revised form 24 February 2012 Accepted 15 March 2012

Available online 27 September 2012

Keywords: Wind turbine Evaluation

Fuzzy analytic network process (FANP) Interpretive structural modeling (ISM)

a b s t r a c t

Due to the impacts of fossil and nuclear energy on the security, economics, and environment in the world, the demand of alternative energy resources is expanding consistently and tremendously in recent years. Wind energy production, with its safe and environmental characteristics, has become the fastest growing renewable energy source in the world. The construction of new wind farms and the installation of new wind turbines are important processes in order to provide a long-term energy production. In this research, a comprehensive evaluation model, which incorporates interpretive structural modeling (ISM) and fuzzy analytic network process (FANP), is constructed to select suitable turbines when devel-oping a wind farm. A case study is carried out in Taiwan in evaluating the expected performance of sev-eral potential types of wind turbines, and experts in a wind farm are invited to contribute their expertise in determining the importance of the factors of the wind turbine evaluation and in rating the perfor-mance of the turbines with respect to each factor. The most suitable turbines for installation can ﬁnally be generated after the calculations. The results can be references for decision makers in selecting the most appropriate wind turbines.

1. Introduction

Global warming and climate change have increased the con-sciousness of human beings in preserving the world and have shifted the focus of industrial development towards low-carbon renewable energy. Commercial wind farms currently operate in around 80 countries, and there are many benefits for both devel-oped and developing countries to build wind farms. These benefits include increased energy security, stable power prices, economic development to attract investment and to create jobs, reduced dependence on imported fuels, improved air quality, and CO2 emis-sions reductions[1]. To generate electricity, a wind farm incurs three major types of costs: capital costs, running costs and financ-ing cost. The capital costs include all the costs of buildfinanc-ing the power plant and connecting it to the grid; the running costs in-clude the operation and maintenance of the wind farm; and the financing cost is the cost of acquiring the necessary funds for con-structing and running a wind farm. The capital cost is very high, between 75% and 90% of the total for onshore projects, and wind turbines amount to 64% of total capital cost for a typical 5 MW on-shore project[2]. Fortunately, the capital cost of producing wind turbines has fallen steadily over the past two decades because of

advanced manufacturing techniques and mass production and automation [3]. Nevertheless, the selection of appropriate wind turbines is of extremely high importance as the costs of the wind turbines make up the majority of the total cost for a wind farm pro-ject. In addition, the suitability of the wind turbines for a particular location may affect the capacity factor of the wind turbines.

The evaluation and selection of renewable energy alternatives is a criteria decision making (MCDM) problem because multi-ple criteria, some may even be in conﬂict, must be taken into con-sideration at the same time. MCDM methods, such as analytical hierarchy process (AHP), analytic network process (ANP), prefer-ence ranking organization method for enrichment of evaluations (PROMETHEE), multi-attribute utility theory (MAUT), technique for order preference by similarity to the ideal solution (TOPSIS), multi-objective decision making (MODM), VlšeKriterijumska Opti-mizacija I Kompromisno Resenje (VIKOR) and ELimination Et Choix Traduisant la REalité (ELECTRE), have been used in the evaluation of renewable energy projects[4,5]. Past applications of MCDM on renewable energy include renewable energy project planning, wind farm projects, solar energy projects, geothermal projects and hydro-site selection, etc.[5]. Wang et al.[6]did a very compre-hensive review on multi-criteria decision analysis aid in sustain-able energy decision-making. Methods in different stages of MCDM for sustainable energy were reviewed, including criteria selection, criteria weighting, evaluation and ﬁnal aggregation.

http://dx.doi.org/10.1016/j.enconman.2012.03.029

⇑ Corresponding author. Tel.: +886 4 23924505x7624; fax: +886 4 23934620. E-mail address:[email protected](H.-Y. Kang).

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Energy Conversion and Management

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Kahraman et al. [4] and San Cristóbal [5] also reviewed some works.

Some recent studies of decision-making in energy are reviewed

here. Pilavachi et al. [7] proposed a MCDM method with an

agglomeration function based on the statistical evaluation of weight factors to calculate sustainability indices for several com-bined heat and power (CHP) systems. Patlitzianas et al. [8] pre-sented an integrated MCDM approach, based on ordered weighted average, to integrate qualitative judgments on many opportunities and threats factors for assessing the environment of renewable energy producers in EU accession member states. Af-gan et al. [9] applied ASPID to calculate the priority ratings amongst selected alternative options of gas transport systems in Southeast and Central Europe. Önüt et al.[10] adopted the ANP to evaluate the most suitable energy resources for the manufactur-ing industry in Turkey. Nobre et al.[11]used a geo-spatial multi-criteria analysis methodology, based on geographic information systems (GIS) technology, to identify the best location for deploy-ing a wave energy farm. Lee et al.[12]presented a MCDM method, with the incorporation of AHP and the beneﬁts, opportunities, costs and risks (BOCR) concept, to help select a suitable wind farm project. Kolios et al.[13]provided a systematic methodology based on the TOPSIS for classiﬁcation and evaluation of different avail-able offshore wind turbine support structures. Lee[14]evaluated and ranked the energy performance of buildings from the perspec-tive of multiple objecperspec-tive outputs by applying fuzzy measure and fuzzy integral, a multiple attribute decision-making approach. San Cristóbal[5]applied the AHP to obtain the relative importance weights of attributes and used the VIKOR method to select the most suitable renewable energy project in Spain.

Due to vagueness, ambiguity and subjectivity of human judg-ment in many decision making problems, the fuzzy set theory can be adopted to express the linguistic terms using membership functions[4,15]. Kahraman et al.[4]applied two MCDM methodol-ogies for selecting the best renewable energy alternative in Turkey: fuzzy analytic hierarchy process (FAHP) and fuzzy axiomatic de-sign (FAD). A comparative analysis of the case found that both methodologies led to the same outcome. Chen et al.[16]devised a FAHP approach associated with the BOCR concept to evaluate so-lar-wind power generation projects. Kaya and Kahraman[15]

con-structed an integrated VIKOR-AHP methodology with the

application of the fuzzy logic, to the selection of the best renewable energy policy ﬁrst and to the selection of the energy production site next. Lee et al.[17]developed a conceptual model for product strategy in the solar cell power industry, and interpretive struc-tural modeling (ISM), FANP and the BOCR concept are integrated to analyze suitable strategic products.

The topic of renewable energy evaluation is getting more atten-tion these days; however, the uses of MCDM methodologies with the consideration of imprecise and fuzzy information to tackle the complex problem are rather limited. Since the construction of wind farm is a complicated task and the selection of the most appropriate wind turbines is essential for the future operation of the wind farm, a systematic MCDM model for evaluating different wind turbine systems is necessary for making the correct selection decision. In the authors’ understanding, this paper is the ﬁrst one that examines the interrelationship of the criteria in the decision making process by adopting interpretive structural modeling (ISM) and fuzzy analytic network process (FANP) to evaluate differ-ent wind turbine systems. Based on the evaluation results, the ﬁrm can select the most appropriate wind turbine system to be con-structed in its new wind farm.

The rest of this paper is organized as follows. Section2brieﬂy introduces the research methods. In Section 3, an integrated MCDM model is constructed. In Section4, the model is applied to

a case study to evaluate wind turbine systems. Some concluding remarks are made in the last section.

2. Research methods

2.1. Interpretive structural modeling (ISM)

Interpretive structural modeling (ISM) was proposed by War-ﬁeld in 1974 to be applied in analyzing complex situations and putting together a course of action for solving a problem[18–20]. A question such as ‘‘Does criterion xiaffect criterion xj?’’ is asked, and

p

ij= 1 if the answer is yes,

p

ij= 0 otherwise. A binary matrix, called relation matrix, can then be prepared[21]. A reachability matrix is calculated next to consider transitivity. By applying the operators of the Boolean multiplication and addition, a ﬁnal reach-ability matrix, which can reﬂect the convergence of the relation-ship among the elements, is obtained, and a map of the complex relationships among elements can be depicted.

Since its introduction, the ISM has been applied in various ﬁelds. For example, Feng et al. [22] integrated factor analysis, ISM, Markov chain, fuzzy integral and the simple additive weighted method, and constructed a hybrid fuzzy integral deci-sion-making model for selecting locations of high-tech manufac-turing centers. Lee et al. [23] examined the interrelationship among the critical factors for technology transfer of new equip-ment in high technology industry using the ISM and applied the FANP to evaluate the technology transfer performance of equip-ment suppliers. Chen et al.[24]developed a decision-support

sys-tem framework for adjudicating construction industry

occupational accidents using case-based reasoning (CBR) with a nearest-neighbor retrieval (NNR) search mechanism. ISM was then used to build a three-layer hierarchy structure and to classify prob-lem attributes into four aspect subsets. Lin et al.[25]proposed a hybrid method to cope with the problem of different dimensions’ interdependence and feedback in vendor selection problem. The interrelationships amongst dimensions are distinguished by apply-ing the ISM, and the weightapply-ings of each dimension are derived using the ANP. Chen and Wu[26]presented a systematic proce-dure to evaluate an automobile manufacturer-distributor partner-ship with two phases. In the first phase, ISM is used to sort system variables into groups of various characteristics and to develop a hierarchic/network model of the partnership. In the second phase, AHP/ANP is applied to evaluate partnerships. Lee et al.[27] devel-oped a three-stage user interface design approach. Quality function deployment (QFD) was used to confirm the user’s design demand; ISM was employed to construct a clear hierarchical structure; and the impact matrix cross-reference multiplication applied to a clas-sification (MICMAC) was adopted to analyze the effect and depen-dence among the overall design components.

2.2. Analytic network process (ANP)

Analytic network process (ANP), introduced by Saaty, is a gener-alization of analytic hierarchy process (AHP). It is a multi-criteria decision support methodology to decompose a complex problem into a network when the relationships among clusters (elements) are not easily represented as higher or lower, dominated or being dominated, directly or indirectly[17,28,29]. After evaluating the importance of the clusters (elements) and inter-relationship among them, a ‘‘supermatrix’’ is formed. A weighted supermatrix is generated next to ensure column stochastic; that is, the sum of the elements in each column is equal to one[28]. Finally, a limit supermatrix is calculated for convergence and to obtain ﬁnal solu-tions. ANP has been applied successfully in various ﬁelds in recent years. A good decision-marking model needs to tolerate vagueness

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or ambiguity; thus, fuzzy set theory can be incorporated with the conventional ANP, termed FANP.

Some recent works of FANP are reviewed here. Onut et al.[30] designed a FANP-based approach for selecting container port from production ﬁrms’ perspective for sea transportation. Liou et al.[31] combined fuzzy preference programming and the ANP to form a model for selecting strategic alliance partners in the airline indus-try. Sevkli et al.[32] developed a FANP-based strengths, weak-nesses, opportunities and threats (SWOT) analysis to evaluate alternative strategies for the airline industry. Özgen and Tanyas [33] formulated a FANP-based decision-making model for joint selection of customs broker agencies and international road trans-portation ﬁrms. Yucel et al.[34]developed a predictive risk assess-ment model for a hospital information system (HIS) by applying ANP, reality-design gap evaluation and fuzzy inference system. Büyüközkan and Çifçi[35]developed a supplier selection approach based on sustainability principles using FANP under a multi-person decision-making schema with incomplete preference relations. Vi-nodh et al.[36]applied FANP for the supplier selection process in a manufacturing organization for sustaining in the global markets. Kang et al.[37]proposed a FANP model to evaluate various aspects of suppliers with the consideration of multiple decision makers, and a sensitivity analysis was conducted to examine the robust-ness of the outcomes. Kang[38]proposed a MCDM approach, by incorporating FANP, fuzzy Delphi method (FDM), constraint pro-gramming (CP) and BOCR, for capacity allocation problem in semi-conductor fabrication. Lee and Lin[39]constructed an integrated fuzzy QFD framework for new product development, with FDM to select the critical factors, fuzzy ISM to determine the relation-ships among the critical factors, and QFD and FANP to calculate the priorities of the critical factors.

3. Proposed model for evaluating wind turbines

A systematic ISM-FANP model is proposed here to help evaluate the expected performance of various types of wind turbines. The proposed steps are as follows:

Stage I: Construct a wind turbine evaluation network.

Step 1. Form a committee of experts in a wind farm company to deﬁne the wind turbine evaluation problem. Step 2. Decompose the wind turbine evaluation problem into a

network. A sample network is as depicted inFig. 1. Stage II: Determine the relationships among sub-criteria by ISM.

Step 3. Construct adjacency matrix (i.e., relation matrix) for the sub-criteria under each criterion. For each criterion Ci, establish relation matrix Di, using the sub-criteria iden-tiﬁed in Step 2, to show the contextual relationship among the sub-criteria. Experts, through a question-naire or the Delphi method, are invited to identify the contextual relationship between any two sub-criteria, and the associated direction of the relation. The relation matrix Diis presented as follows:

ð1Þ

where

p

ipq denotes the relation between sub-criteria SCip and SCiq under criterion i, and

p

ipq= 1 if SCiq is reachable from SCip; otherwise,

p

ipq= 0.

Step 4. Develop initial reachability matrix for each criterion and check for transitivity. The initial reachability matrix Riis calculated by adding Diwith the unit matrix I:

Ri¼ Diþ I ð2Þ

Step 5. Develop ﬁnal reachability matrix R

i for each criterion i. Under the operators of the Boolean multiplication and addition, a convergence can be met:

R i ¼ R l i¼ R lþ1 i ; l > 1 ð3Þ ð4Þ where

p

ipq denotes the impact of sub-criterion SCp to sub-criterion SCqunder criterion i.

Step 6. Construct a sub-network for each criterion based on the ﬁnal reachability matrix for the criterion.

Stage III: Calculate the priorities of wind turbine systems using FANP.

Step 7. Prepare a questionnaire to collect experts’ opinions based on the network. Experts are asked to pairwise compare the importance of the criteria, the importance of the sub-criteria with respect to the same upper-level criterion, and the interdependence among the sub-cri-teria under the same upper-level criterion, using seven different linguistic terms, as listed inTable 1. The lin-guistic variables of pairwise comparison of each part of the questionnaire from each expert are transformed into trapezoid fuzzy numbers. Experts are also asked to determine the performance of each alternative with respect to each sub-criterion by a seven-step scale, as shown inTable 2.

Step 8. Employ geometric average approach to aggregate

experts’ responses and calculate synthetic trapezoid fuzzy numbers. For instance, the synthetic trapezoid fuzzy number for the relative importance between cri-terion i and cricri-terion j is calculated as follows: ~

rij¼ ð~aij1 ~aij2 . . . ~aijkÞ 1=k

ð5Þ where ~aijkis the pairwise comparison value between cri-terion i and j determined by expert k.

Step 9. Calculate aggregated crisp pairwise comparison matri-ces. Defuzzify each fuzzy number into a crisp number using Yager[40] ranking method. For example, fuzzy number ~rij is deffuziﬁed into a crisp number rij as follows: rij¼ Z 1 0 1 2 ð~rijÞ L aþ ð~rijÞUa d

a

ð6Þ

The

a

-cuts of the fuzzy numbers are shown inTable 3. The aggregated pairwise comparison matrix for the criteria is:

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W21¼ 1 r12 r1j 1=r12 1 r2j .. . .. . 1 .. . .. . .. . 1 rij .. . .. . .. . 1=rij 1 1 1=r1j 1=r2j 1 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 ð7Þ

The aggregated pairwise comparison matrices for the sub-criteria with respect to the same upper-level crite-rion and for the interdependence among the sub-criteria

under the same upper-level criterion are obtained in the same way.

Step 10. Determine the priorities of the criteria, sub-criteria, and interdependence among sub-criteria. For instance, the priority vector for the aggregated comparison matrix for the criteria is derived as follows:

W21 w21¼ kmax w21 ð8Þ

where W21is the aggregated comparison matrix for the criteria, w21is the eigenvector, and kmaxis the largest eigenvalue of W21.

Step 11. Examine the consistency property of the aggregated comparison matrices. The consistency index (CI) and consistency ratio (CR) are deﬁned as[28,41]:

CI ¼kmax n

n 1 ð9Þ

CR ¼CI

RI ð10Þ

where n is the number of items being compared in the matrix, and RI is random index. As suggested by Saaty [41], RI is 0.00 for a 2 2 matrix, 0.58 for a 3 3 matrix, 0.90 for a 4 4 matrix, 1.12 for a 5 5 matrix, and 1.24 for a 6 6 matrix, etc. When a calculated CR value ex-ceeds the threshold, it is an indication of inconsistent judgment. The experts are asked to revise the part of the questionnaire, and the calculations in Steps 7–10 are done again.

21

w

32

W

43

W

33

W

Criterion C1 Sub-criterion SC11

Wind turbine evaluation problem

Wind turbine A1

Goal

Criteria

Sub-Criteria

Alternatives

Criterion C2 Criterion C3 Criterion C4 Sub-criterion SC12 Sub-criterion SC21 Sub-criterion SC22 Sub-criterion SC31 Sub-criterion SC32 Sub-criterion SC41 Sub-criterion SC42 Wind turbine A2 Wind turbine A3 Wind turbine A4

Fig. 1. The network.

Table 1

Membership function of fuzzy numbers for relative importance.

Linguistic variable

Positive trapezoidal fuzzy numbers

Positive reciprocal trapezoidal fuzzy numbers Extremely high (EH) (7.5, 8.5, 9, 9) (91_{, 9}1_{, 8.5}1_{, 7.5}1₎ Very high (VH) (6.5, 7.5, 7.5, 8.5) (8.51_{, 7.5}1_{, 7.5}1_{, 6.5}1₎ High (H) (5, 5.75, 6.75, 7.5) (7.51 , 6.751 , 5.751 , 5.51 ) Medium high (M) (4, 5, 5, 6) (61 , 51 , 51 , 41 ) Moderately high (MH) (2.5, 3.25, 4.25, 5) (51_{, 4.25}1_{, 3.25}1_{, 2.5}1₎ Little high (LH) (1.5, 2.5, 2.5, 3.5) (3.51_{, 2.5}1_{, 2.5}1_{, 1.5}1₎ Equal (E) (1, 1, 1.5, 2.5) (2.51_{, 1.5}1_{, 1, 1)}

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Step 12. Determine the priorities of the alternatives with respect to each sub-criterion. Based on the collected experts’ opinions, the membership function of fuzzy numbers for ranking onTable 2, the synthetic trapezoid fuzzy number for the expected performance of an alternative is calculated as follows:

~

gipv¼ ð~fipv1 ~fipv2 . . . ~fipvkÞ 1=k

ð11Þ where ~fipvkis the expected performance of alternative

v

under sub-criterion p of criterion i determined by expert k. Defuzzify each fuzzy number into a crisp number using Yager[40]ranking method, and normalize the pri-orities of alternatives with respect to each sub-criterion. Quantitative performance indicators can also be used for evaluating the alternatives. Quantitative data is trans-formed into values between zero and one by member-ship functions, where ‘‘1’’ represents the best outcome and ‘‘0’’ represents the worst outcome. For a sub-crite-rion that is better with a bigger value, its membership function is as follows: gipv¼ fipv f ip = fþ ip f ip ; f ip 6fipv6f þ ip 1; fipvPf þ ip 8 < : ð12Þ

For a sub-criterion that is better with a smaller value, its membership function is as follows:

gipv¼ fþ ip fipv = fþ ip f ip ; f ip 6fipv6f þ ip 1; fipv6f ip 8 < : ð13Þ where fþ

ip is the largest possible value of sub-criterion p of criterion i, f

ip is the smallest possible value of a sub-criterion p of sub-criterion i, fipv is the value of alternative

v

under sub-criterion p of criterion i.

Step 13. Form an unweighted supermatrix. Based on the priori-ties obtained from Steps 11 and 12, an unweighted supermatrix is formed, as depicted inFig. 2.

Step 14. Calculate a weighted supermatrix. To ensure column stochastic, the unweighted supermatrix must be trans-formed into a weighted supermatrix[28,42].

Step 15. Calculate the limit supermatrix and obtain the ﬁnal pri-orities of the alternatives. By taking the weighted supermatrix to powers, the supermatrix can converge into a stable supermatrix, called the limit supermatrix. The ﬁnal priorities of the alternatives are shown in the alternative-to-goal column of the limit supermatrix. 4. Case study

Taiwan depends heavily on imported fossil fuels, with an im-port of 98% of its fuel requirements. Facing the problems caused by increasing energy consumption and scarcer global fuel energy, Taiwan is encountering energy shortages, escalating fuel price, pol-lution emission and environmental issues. The government had introduced a feed-in tariff in 2009 and set a target for renewable energy to meet 10% of the electricity supply by 2010[1]. Because of its unique geographic characteristics, Taiwan can develop wind farms in various places, especially on its western coast and offshore in the island. During 2010, Taiwan installed 83 MW of new wind power, and its capacity has increased to a total of 519 MW, expect-ing to meet 80% of renewable energy production[43]. However, the development of wind power needs to consider important as-pects such as political issues, technologies, costs and societal envi-ronments, and the guaranteed purchase price must be high enough to encourage investment. In addition, the construction of wind farm can be a complicated task, and the selection of the most appropriate wind turbines is essential for the future operation of the wind farm. To be precise, wind turbine evaluation problem is a MCDM problem which involves the assessments of different fac-tors under an uncertain environment. Thus, the proposed model is used to help a wind farm evaluate the expected performance of dif-ferent types of wind turbines.

Stage I: Construct a wind turbine evaluation network.

With literature review and interview with the manage-ment in the anonymous firm, the network is con-structed, as shown in Fig. 3. There are four criteria, namely, machine characteristics, economic aspects, environmental issues and technical levels. Under each criterion, there are criteria. The criteria and sub-criteria are defined inTable 4. To keep anonymousness, the four wind turbines under evaluation are identified as A1, A2, A3and A4, and their specifications are listed inTable 5.

Stage II: Determine the relationships among sub-criteria by ISM. A committee of ﬁve experts in the ﬁrm was formed. These experts included one senior manager and two managers from the operations department, and one senior manager and one manger from the engineering department. The experts were asked to determine

whether there are interrelationships among the

Table 2

Membership function of fuzzy numbers for ranking.

Linguistic variable Positive trapezoidal fuzzy numbers

Very good (VG) (0.75, 0.9, 0.9, 0.9) Good (G) (0.65, 0.7, 0.8, 0.85) Medium good (MG) (0.45, 0.6, 0.6, 0.75) Fair (F) (0.35, 0.4, 0.5, 0.55) Medium poor (MP) (0.15, 0.3, 0.3, 0.45) Poor (P) (0.05, 0.1, 0.2, 0.25) Very poor (VP) (0, 0, 0, 0.15) Table 3

a-cuts of fuzzy numbers.

~ a ð~aÞLa ð~aÞUa ~ aEH¼ ð7:5; 8:5; 9; 9ÞLR ð~aEHÞaL¼ 7:5 þa ð~aEHÞUa¼ 9 ~ aVH¼ ð6:5; 7:5; 7:5; 8:5ÞLR ð~aVHÞLa¼ 6:5 þa ð~aVHÞUa¼ 8:5 a ~ aH¼ ð5; 5:75; 6:75; 7:5ÞLR ð~aHÞLa¼ 5 þ 0:75a ð~aHÞUa¼ 7:5 0:75a ~ aM¼ ð4; 5; 5; 6ÞLR ð~aMÞLa¼ 4 þa ð~aMÞUa¼ 6 a ~ aMH¼ ð2:5; 3:25; 4:25; 5ÞLR ð~aMHÞLa¼ 2:5 þ 0:75a ð~aMHÞUa¼ 5 0:75a ~ aLH¼ ð1:5; 2:5; 2:5; 3:5ÞLR ð~aLHÞLa¼ 1:5 þa ð~aLHÞUa¼ 3:5 a ~ aE¼ ð1; 1; 1:5; 2:5ÞLR ð~aEÞaL¼ 1 ð~aEÞUa¼ 2:5 a 43

Goal Criteria Sub-criteria Alternatives

Goal Criteria Sub-criteria Alternatives 21 33 32 I W W W I w ⎤ ⎡ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ _⎦ ⎣

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sub-criteria in a meeting so that a consensus could be met. For example, an adjacency matrix (relation matrix) for the sub-criteria under criterion machine characteris-tics was formed after discussion, as follows:

The initial reachability matrix R1for the sub-criteria un-der criterion machine characteristics is calculated:

R1¼ D1þ I ¼ 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 2 6 6 6 4 3 7 7 7 5þ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 2 6 6 6 4 3 7 7 7 5¼ 1 0 1 1 0 1 0 0 1 0 1 1 1 0 1 1 2 6 6 6 4 3 7 7 7 5

The ﬁnal reachability matrix R1for the sub-criteria un-der criterion machine characteristics is:

R 1¼ R 2 1¼ R 3 1¼ 1 0 1 1 0 1 0 0 1 0 1 1 1 0 1 1 2 6 6 6 4 3 7 7 7 5 Based on R

1, the interrelationship among the four sub-criteria can be depicted as in Fig. 4(1). According to the experts’ opinions through ISM analysis, SC11, SC13, SC14 are mutually interrelated. This can be seen from the double-sided arrows among these three criteria. For example, while system conversion rate (SC11) had an effect on utilization rate (SC13) and construction reli-ability (SC14), the sub-criterion was also affected by these two sub-criteria. In addition, SC12is independent. The interrelationships among sub-criteria under the other three criteria are also shown inFig. 4(2)–(4). Stage III: Calculate the priorities of wind turbine systems using

FANP.

Based on the network inFig. 3and the interrelationship among sub-criteria under each criterion in Fig. 4, a questionnaire using seven different linguistic terms from Table 1 was prepared to pairwise compare the importance of the criteria, the importance of the sub-criteria with respect to the same upper-level criterion, and the interdependence among the sub-criteria under the same upper-level criterion. For the performance evaluation of the alternatives with respect to each sub-criterion, the seven different linguistic terms from

Table 2 were used. The ﬁve experts in the committee were invited to ﬁll out the questionnaire. Geometric average approach was used to aggregate experts’ responses. For example, the pairwise comparison between machine characteristics (C1) and economic aspects (C2) by the experts are (1, 1, 1.5, 2.5), (3.51_, 2.51_{, 2.5}1_{, 1.5}1_), _{(1, 1, 1.5, 2.5),} _(3.51_{, 2.5}1_{, 2.5}1_, 1.51_{) and (1.5, 2.5, 2.5, 3.5). The aggregated trapezoid} fuzzy number is: ~r12¼ ðð13:51_13:51_1:5Þ1=5

; ð12:5112:512:5Þ1=5;ð1:52:511:52:51 2:5Þ1=5_;

ð2:5 1:51 2:5 1:51 3:5Þ1=5Þ ¼ ð0:657; 0:833;0:979;1:576Þ:

The fuzzy aggregated pairwise comparison matrix for the criteria is:

The Yager ranking method is applied next to prepare a defuzzified comparison matrix. For example, with the synthetic trapezoid fuzzy number for the comparison between C1 and C2 of (0.657, 0.833, 0.979, 1.576), the defuzzified comparison between C1 and C2 is 1.011. The defuzzified aggregated pairwise comparison matrix is:

The priority vector and kmaxof the defuzziﬁed aggregated pairwise comparison matrix for the criteria are calculated:

The consistency test is performed by calculating CI and CR: CI ¼kmax n n 1 ¼ 4:0542 4 4 1 ¼ 0:0181; and CR ¼CI RI¼ 0:0181 0:90 ¼ 0:0201:

Since CR is less than 0.1, the experts’ judgment is consistent. If the consistency test fails, the experts are asked to ﬁll out the speciﬁc part of the questionnaire again.

Priority vectors for the importance of the sub-criteria with re-spect to the same upper-level criterion, and the interdependence

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21

w

32

W

43

W

33

W

Wind turbine evaluation problem

Goal Criteria Sub-Criteria Alternatives

Economic aspects (C2) Environmental issues (C3) Technical levels (C4) Wind turbine operation (SC12)

Net present value (SC21) Capital costs (SC22) Land use (SC31) Aesthetics (SC32) Satisfaction level of supplier (SC41) Integration capability of system (SC42) Wind turbine A2 Wind turbine A3 Wind turbine A4 R&D capability of supplier (SC42)

Noise and waste pollution (SC33) Operation and maintenance costs (SC23) Utilization rate (SC13) Construction reliability (SC14) System conversion rate (SC11) Machine characteristics (C1) Ecological impact (SC34) Wind turbine A1

Fig. 3. The network for the case.

Table 4

Deﬁnitions of the criteria and sub-criteria.

Criteria Sub-criteria Deﬁnition

Machine characteristics (C1)

System conversion rate (SC11)

The rate to convert wind’s energy into electricity. A low start up wind speed and a maximum generating power are preferred

Wind turbine operation (SC12)

Easiness in operating the wind turbines

Utilization rate (SC13) The normal utilization rate of the wind turbine system after deducting system breakdowns and equipment malfunctions, etc.

Construction reliability (SC14)

The physical strength, safety and reliability of the wind turbine system

Economic aspects (C2)

Net present value (NPV) (SC21)

The total present value of a time series of cash ﬂows generated from the operation of wind turbines, considering the operation life of wind turbines, bank ﬁnancing terms, buy-back price of electricity, etc.

Capital costs (SC22) The cost of wind turbines and connections in constructing the wind turbine system Operation and

maintenance costs (SC23)

Day-to-day operation costs and maintenance costs incurred in operating the wind turbine system

Environmental issues (C3)

Land use (SC31) The geographic area and the size of land required for constructing wind turbines with different destructive impacts to the environment

Aesthetics (SC32) The aesthetics of the area being diminished Noise and waste pollution

(SC33)

The noise, interference with radio and television signals, shadow ﬂicker and waste from the operation of wind turbines, which have negative impacts on the people and may damage the environment

Ecological impact (SC34) The impact of wind turbines and buildings to the ecology, such as the collision of birds and bats and the harmful impacts on wildlife

Technical levels (C4)

Satisfaction level of supplier (SC41)

Technology and parts support of supplier

Integration capability of system (SC42)

The integration of hardware and software of the wind turbine system, including equipment, parts, personnel and supervisory control and data acquisition (SCADA) system, etc.

R&D capability of supplier (SC43)

R&D level and improvements that can be achieved by the supplier, including incremental improvement and radical innovation

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among the sub-criteria under the same upper-level criterion are calculated in a similar way. For the performance of the alternatives, geometric average method is adopted to aggregate experts’ opin-ions, Yager [40] ranking method is used to obtain crisp values, and normalization is applied to calculate the priorities of alterna-tives with respect to each sub-criterion. For instance, the expected performance of wind turbine A1under system conversion rate (SC11) is evaluated by the ﬁve experts as: fair, medium poor, poor, med-ium poor and medmed-ium poor. The fuzzy numbers are (0.35,0.4,0.5, 0.55), (0.15,0.3,0.3,0.45), (0.05,0.1,0.2,0.25), (0.15,0.3,0.3,0.45) and (0.15,0.3,0.3,0.45). The aggregated trapezoid fuzzy number is (0.143,0.255,0.306,0.416) = ((0.35 0.15 0.05 0.15 0.15)1/5_, (0.4 0.3 0.1 0.3 0.3)1/5_{, (0.5 0.3 0.2 0.3} _0.3)1/5_, (0.55 0.45 0.25 0.45 0.45)1/5_{). After defuzziﬁcation, the} priority of wind turbine A1under system conversion rate (SC11) is 0.2801. Similar calculations are performed to obtain the priorities

of A2, A3 and A4 under system conversion rate (SC11), which are 0.5131, 0.4376 and 0.6002, respectively. After normalization, the priorities of A1, A2, A3and A4under system conversion rate (SC1) are 0.1530, 0.2802, 0.2390 and 0.3278, respectively. The priorities of A1, A2, A3and A4under the other sub-criteria are calculated in the same way.

To obtain global priorities in a system with interdependent inﬂuences, the local priority vectors were entered in the appropri-ate columns of the unweighted supermatrix[28]. For example, the priorities of the criteria (C1–C4) with respect to the goal are 0.3219, 0.3895, 0.1883, and 0.1003, respectively. They are entered into the (2, 1) block of the unweighted supermatrix inTable A1in Appendix A. The (3, 2) block shows the priorities of sub-criteria with respect to the criteria when the interrelationship among sub-criteria was not considered. The interrelationships among sub-criteria are de-picted in the (3, 3) block. Each zero entry in the supermatrix

Table 5

Speciﬁcations of the four wind turbines.

Wind turbine A1 A2 A3 A4

Location of manufacturer Netherlands Denmark Spain Germany

Model Z-72 V-80 G-80 E-70

Rated power (MW) 2.0 2.0 2.0 2.3

Generator Direct-drive annular generator Asynchronous generator Asynchronous generator Direct-drive annular generator

Rotor – Doubly-fed machine Doubly-fed machine –

Gearbox Gearless Parallel Parallel Gearless

Voltage (V) 690 690 690 400

Hub height (m) 65 67 67 65

Rotor diameter (m) 70.64 80 80 71

Swept area (m2₎ ₃₆₉₆ ₅₀₂₇ ₅₀₂₆ ₃₉₅₉

Rotational speed (rpm) 22.5 9–19 10.8–22.8 6–21.5

Cut-in wind speed (m/s) 3 4 4 2

Cut-out wind speed (m/s) 25 25 25 35

Nominal wind speed (m/s) 13 15 15 12

Maximum wind speed (m/s) 70 70 70 70

Design life time (years) 20 20 20 20

System conversion rate (SC11) Wind turbine operation (SC12) Construction reliability (SC14) Utilization rate (SC13)

(1) Machine characteristics

Net present value (SC21) Capital costs (SC22) Operation and maintenance costs (SC23)

(2) Economic aspects

Land use (SC31) Aesthetics (SC32)

Ecological impact (SC34) Noise and waste pollution (SC33)

(3) Environmental issues

Satisfaction level of supplier (SC41) Integration capability of system (SC42) R&D capability of supplier (SC₄₃)

(4) Technical levels

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implies that there is no relationship between the two elements. The performance of wind turbines with respect to each sub-crite-rion is shown in the (4, 3) block. For example, the priorities of the

four types of wind turbines under system conversion rate (SC11), that is, 0.1530, 0.2802, 0.2390 and 0.3278 respectively, can be found in the ﬁrst column of the (4, 3) block.

0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 A1 A2 A3 A4 0.0 0.1 0.2 0.3 0.4 0.5 A1 A2 A3 A4

(1) Priority changes in machine characteristics

(C

1

)

(2) Priority changes in economic aspects (C

2

)

0.0 0.1 0.2 0.3 0.4 0.5 A1 A2 A3 A4 0.0 0.1 0.2 0.3 0.4 0.5 A1 A2 A3 A4

(3) Priority changes in environmental issues (C

3

)

(4) Priority changes in technical levels (C

4

)

C₁ C₂

C₃ C₄

Priority Priority

Fig. 5. Sensitivity analysis.

Table 6

Priorities of criteria and sub-criteria.

Criteria/sub-criteria Criterion priorities Sub-criterion priorities Integrated priorities Integrated ranking Machine characteristics (C1) 0.3219

System conversion rate (SC11) 0.3937 0.1267 2

Wind turbine operation (SC12) 0.3622 0.1166 4

Utilization rate (SC13) 0.1438 0.0463 9

Construction reliability (SC14) 0.1003 0.0323 11

Economic aspects (C2) 0.3895

Net present value (NPV) (SC21) 0.5604 0.2183 1

Capital costs (SC22) 0.3104 0.1209 3

Operation and maintenance costs (SC23) 0.1291 0.0503 8

Environmental issues (C3) 0.1883

Land use (SC31) 0.3936 0.0741 5

Aesthetics (SC32) 0.2990 0.0563 7

Noise and waste pollution (SC33) 0.1671 0.0315 12

Ecological impact (SC34) 0.1404 0.0264 13

Technical levels (C4) 0.1003

Satisfaction level of supplier (SC41) 0.5376 0.0539 6

Integration capability of system (SC42) 0.3316 0.0333 10

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To make the matrix stochastic, a weighted supermatrix is formed, as shown in Table A2. Finally, by taking the weighted supermatrix to a large power, a limit supermatrix is obtained, as shown inTable A3. The priorities of the alternatives can be seen from the (4, 1) block of the limit supermatrix. That is, the priorities for wind turbines A1, A2, A3and A4are 0.1657, 0.2926, 0.2400 and 0.3016, respectively. Thus, A4performs the best with the highest priority, followed by A2, A3and A1.

The importance of criteria and sub-criteria in making the wind turbine selection decision should be understood by the manage-ment.Table 6shows the relative priorities of criteria and sub-cri-teria. Economic aspects (C2), with a priority of 0.3895, is the most important criterion, followed by machine characteristics (C1), with a priority of 0.3219. The priorities of sub-criteria under the same upper-level criterion can be compared too. For example, under the machine characteristics (C1) criterion, the most important sub-criterion, out of a total of four sub-criteria, is system conversion rate, with a priority of 0.3937. This means that the major machine characteristics concern for selecting wind turbines is the system conversion rate for the power generated. The second and third sub-criteria are wind turbine operation (0.3622) and utilization rate

(0.1438). Table 6 also shows the integrated priorities of

sub-criteria, and their respective rankings. Among all the factors, net present value (SC21), with an integrated priority of 0.2183 in the network, is the most important concern in selecting the wind turbines. Other important factors include system conversion rate (SC11), capital costs (SC22), wind turbine operation (SC12), and land use (SC31).

To examine the robustness of the outcomes, a sensitivity analy-sis is carried out next by changing the priorities of the criteria, and the results are shown inFig. 5.Fig. 5(1)–(4) show the sensitivity analysis graphs when the priority of machine characteristics (C1), economic aspects (C2), environmental issues (C3) and technical levels (C4) changes, respectively. Depending on the changes of the prior-ities of the criteria, the best wind turbine system may change as a result. As shown inFig. 5(1) and (3), no matter how much the pri-ority of C1or C3changes, the ranking of the four alternatives re-mains the same. While the original best alternative is wind turbine A4, A2may become the best alternative when C2increases from 0.3895 to 0.695, as shown inFig. 5(2). The same applies when C4increases from 0.1003 to 0.425. Nevertheless, the likelihood that C2or C4has such a big change is small. Therefore, the current solu-tion is rather robust.

5. Conclusions and discussions

While energy is being one of the most important sources for economic development and fossil fuels keeps depleting exponen-tially, renewable energy has been recognized as the last resort for future economic development. Wind energy is expected to be the most promising renewable energy source, and the construction of wind farms is the elementary step for a long-term operation. This study is a continuation of Kang et al.[44], in which a compre-hensive evaluation model was constructed to select a suitable loca-tion for developing a wind farm. In Kang et al.[44], the model incorporated ISM and FANP to evaluate the beneﬁts, opportunities, costs and risks aspects of different wind farm locations. After the wind farm location is determined, the selection of the most suit-able wind turbine system is a next important issue. It is also a MCDM problem that requires multiple decision makers being in-volved in the process. In this research, a decision analysis model in selecting the most suitable type of wind turbines is thus pro-posed. The factors for achieving the goal are listed ﬁrst through lit-erature review and interview with experts, and they are used to construct a network with four major criteria, namely, machine Table

A1 Unweighted supermatrix. Goal C1 C2 C3 C4 SC 11 SC 12 SC 13 SC 14 SC 21 SC 22 SC 23 SC 31 SC 32 SC 33 SC 34 SC 41 SC 42 SC 43 A1 A2 A3 A4 Goal 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C1 0.3219 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C2 0.3895 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C3 0.1883 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C4 0.1003 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SC 11 0 0.3937 0 0 0 0.5878 0 0.6837 0.6495 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SC 12 0 0.3622 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SC 13 0 0.1438 0 0 0 0.2522 0 0.1933 0.2122 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SC 14 0 0.1003 0 0 0 0.1600 0 0.1231 0.1384 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SC 21 0 0 0.5604 0 0 0 0 0 0 0.6146 0.5620 0.5949 0 0 0 0 0 0 0 0 0 0 0 SC 22 0 0 0.3104 0 0 0 0 0 0 0.2824 0.3381 0.2679 0 0 0 0 0 0 0 0 0 0 0 SC 23 0 0 0.1291 0 0 0 0 0 0 0.1030 0.0999 0.1373 0 0 0 0 0 0 0 0 0 0 0 SC 31 0 0 0 0.3936 0 0 0 0 0 0 0 0 0.4115 0.3332 0.4236 0.3437 0 0 0 0 0 0 0 SC 32 0 0 0 0.2990 0 0 0 0 0 0 0 0 0.2179 0.3622 0.2926 0.3402 0 0 0 0 0 0 0 SC 33 0 0 0 0.1671 0 0 0 0 0 0 0 0 0.2631 0.1703 0.1756 0.1817 0 0 0 0 0 0 0 SC 34 0 0 0 0.1404 0 0 0 0 0 0 0 0 0.1075 0.1344 0.1082 0.1343 0 0 0 SC 41 0 0 0 0 0.5376 0 0 0 0 0 0 0 0 0 0 0 0.5904 0.6288 0.5542 0 0 0 0 SC 42 0 0 0 0 0.3316 0 0 0 0 0 0 0 0 0 0 0 0.3074 0.2832 0.3483 0 0 0 0 SC 43 0 0 0 0 0.1308 0 0 0 0 0 0 0 0 0 0 0 0.1023 0.0880 0.0975 0 0 0 0 A1 0 0 0 0 0 0.1530 0.1709 0.1676 0.1540 0.1596 0.1603 0.1862 0.2059 0.1625 0.1670 0.1557 0.1786 0.1603 0.0999 1 0 0 0 A2 0 0 0 0 0 0.2802 0.3293 0.2521 0.2601 0.2894 0.3246 0.2629 0.2696 0.2882 0.2744 0.2630 0.3357 0.2700 0.3046 0 1 0 0 A3 0 0 0 0 0 0.2390 0.2024 0.2670 0.2601 0.2693 0.2263 0.2343 0.2475 0.1866 0.2509 0.2786 0.2236 0.2481 0.2084 0 0 1 0 A4 0 0 0 0 0 0.3278 0.2974 0.3132 0.3258 0.2816 0.2888 0.3167 0.2770 0.3627 0.3077 0.3027 0.2622 0.3217 0.3871 0 0 0 1

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Weighted supermatrix. Goal C1 C2 C3 C4 SC11 SC12 SC13 SC14 SC21 SC22 SC23 SC31 SC32 SC33 SC34 SC41 SC42 SC43 A1 A2 A3 A4 Goal 0.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C1 0.1609 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C2 0.1947 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C3 0.0942 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C4 0.0501 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SC11 0 0.3937 0 0 0 0.2939 0 0.3418 0.3248 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SC12 0 0.3622 0 0 0 0 0.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SC13 0 0.1438 0 0 0 0.1261 0 0.0966 0.1061 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SC14 0 0.1003 0 0 0 0.0800 0 0.0615 0.0692 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SC21 0 0 0.5604 0 0 0 0 0 0 0.3073 0.2810 0.2974 0 0 0 0 0 0 0 0 0 0 0 SC22 0 0 0.3104 0 0 0 0 0 0 0.1412 0.1690 0.1339 0 0 0 0 0 0 0 0 0 0 0 SC23 0 0 0.1291 0 0 0 0 0 0 0.0515 0.0500 0.0686 0 0 0 0 0 0 0 0 0 0 0 SC31 0 0 0 0.3936 0 0 0 0 0 0 0 0 0.2058 0.1666 0.2118 0.1719 0 0 0 0 0 0 0 SC32 0 0 0 0.2990 0 0 0 0 0 0 0 0 0.1090 0.1811 0.1463 0.1701 0 0 0 0 0 0 0 SC33 0 0 0 0.1671 0 0 0 0 0 0 0 0 0.1315 0.0851 0.0878 0.0909 0 0 0 0 0 0 0 SC34 0 0 0 0.1404 0 0 0 0 0 0 0 0 0.0537 0.0672 0.0541 0.0671 0 0 0 0 0 0 0 SC41 0 0 0 0 0.5376 0 0 0 0 0 0 0 0 0 0 0 0.2952 0.3144 0.2771 0 0 0 0 SC42 0 0 0 0 0.3316 0 0 0 0 0 0 0 0 0 0 0 0.1537 0.1416 0.1741 0 0 0 0 SC43 0 0 0 0 0.1308 0 0 0 0 0 0 0 0 0 0 0 0.0511 0.0440 0.0488 0 0 0 0 A1 0 0 0 0 0 0.0765 0.0854 0.0838 0.0770 0.0798 0.0801 0.0931 0.1030 0.0812 0.0835 0.0779 0.0893 0.0801 0.0500 1 0 0 0 A2 0 0 0 0 0 0.1401 0.1647 0.1261 0.1300 0.1447 0.1623 0.1314 0.1348 0.1441 0.1372 0.1315 0.1678 0.1350 0.1523 0 1 0 0 A3 0 0 0 0 0 0.1195 0.1012 0.1335 0.1300 0.1347 0.1132 0.1171 0.1238 0.0933 0.1254 0.1393 0.1118 0.1240 0.1042 0 0 1 0 A4 0 0 0 0 0 0.1639 0.1487 0.1566 0.1629 0.1408 0.1444 0.1583 0.1385 0.1814 0.1539 0.1513 0.1311 0.1608 0.1935 0 0 0 1 Table A3 Limit supermatrix. Goal C1 C2 C3 C4 SC11 SC12 SC13 SC14 SC21 SC22 SC23 SC31 SC32 SC33 SC34 SC41 SC42 SC43 A1 A2 A3 A4 Goal 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SC11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SC12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SC13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SC14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SC21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SC22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SC23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SC31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SC32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SC33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SC34 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SC41 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SC42 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SC43 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1 0.1657 0.1617 0.1629 0.1793 0.1638 0.1548 0.1708 0.1619 0.1552 0.1611 0.1614 0.1746 0.1931 0.1702 0.1736 0.167 0.1719 0.1631 0.1325 1 0 0 0 A2 0.2926 0.2920 0.2969 0.2752 0.3112 0.2753 0.3294 0.2618 0.2656 0.2931 0.3112 0.2794 0.2721 0.282 0.2748 0.2693 0.3240 0.2917 0.3079 0 1 0 0 A3 0.2400 0.2319 0.2522 0.2343 0.2296 0.2440 0.2024 0.2574 0.2541 0.2613 0.2392 0.2436 0.242 0.2093 0.2424 0.2557 0.2266 0.2387 0.2192 0 0 1 0 A4 0.3016 0.3145 0.2879 0.3114 0.2953 0.3259 0.2974 0.3188 0.3251 0.2845 0.2881 0.3022 0.2929 0.3385 0.3093 0.308 0.2775 0.3064 0.3404 0 0 0 1 A.H.I. Lee et al. /Energy Conversion and Management 64 (2012) 289–300 299

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characteristics, economic aspects, environmental issues and tech-nical levels, and various sub-criteria. By adopting interpretive structural modeling, the interrelationships among sub-criteria un-der each criterion are determined. After questionnaires are ﬁlled out by decision makers, fuzzy analytic network process is used to calculate the importance of the criteria and the sub-criteria and to evaluate the expected overall performance of the wind turbines. With the implementation of the model, the most suitable type of wind turbines can be selected for constructing the wind farm. The model can also be adjusted as required to help evaluate other renewable energy equipment.

In the case study, economic aspects (C2) is the most important criterion, followed by machine characteristics (C1). Under the eco-nomic aspects (C2), net present value is the most important objective of the experts, followed by the reduction of Capital costs. This means that the financial return is the most important factor in selecting wind turbines. Such outcome is in accord with the fact why governments in many countries need to provide favorable support schemes, financial incentives, adequate grid infrastructure and access to financing to wind farm operators. Under the machine characteristics (C1), system conversion rate is the highest concern, followed by the easiness in operating the wind turbines. The geo-graphic area and the size of land are also important concerns in constructing wind turbines in order to prevent destructive impacts to the environment. Needless to say, technology and parts support provided by suppliers is important for running the wind farm smoothly, and the selection of a credible supplier for long-term cooperation is essential. Although the results may be case specific, the proposed model can be tailored and applied by other wind farms in different locations or countries as a reference when select-ing the most appropriate wind turbines.

Acknowledgement

This work was supported in part by the National Science Coun-cil in Taiwan under Grant NSC 100-2221-E-167-014-MY3. Appendix A

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