# External Economies Evaluation of Wind Power Engineering Project Based on Analytic Hierarchy Process and Matter-Element Extension Model

Authors: Hong-ze Li; Sen Guo
Journal: Mathematical Problems in Engineering
 (2013)

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## Abstract

The external economies of wind power engineering project may affect the operational efficiency of wind power enterprises and sustainable development of wind power industry. In order to ensure that the wind power engineering project is constructed and developed in a scientific manner, a reasonable external economies evaluation needs to be performed. Considering the interaction relationship of the evaluation indices and the ambiguity and uncertainty inherent, a hybrid model of external economies evaluation designed to be applied to wind power engineering project was put forward based on the analytic hierarchy process (AHP) and matter-element extension model in this paper. The AHP was used to determine the weights of indices, and the matter-element extension model was used to deduce final ranking. Taking a wind power engineering project in Inner Mongolia city as an example, the external economies evaluation is performed by employing this hybrid model. The result shows that the external economies of this wind power engineering project are belonged to the “strongest” level, and “the degree of increasing region GDP,” “the degree of reducing pollution gas emissions,” and “the degree of energy conservation” are the sensitive indices.


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## Body

## 1. Introduction

With the development of human society, the important role of energy in people’s daily lives is becoming increasingly prominent. Nowadays, the energy supply shortage and environmental pollution issues make exploiting and utilizing renewable energy as the focus of worldwide concerns [1]. As a kind of renewable energy, wind energy has the advantages of having huge reserves and wide distribution and being renewable and pollution-free [2]. In recent years, the installed capacity of wind power in China has been growing rapidly, just as shown in Figure 1, of which the cumulative installed capacity has increased from 0.3 GW in 2000 to 75.3 GW in 2012. In 2010, the cumulative installed capacity of wind power in China reached 41.827 GW with the annual installed capacity of 16 GW, and China surpassed the United States and ranked the first in terms of cumulative installed capacity of wind power at this year [3]. However, due to the continued growth momentum and the negative impact of large-scale wind power accessing grid, the ratio of annual installed capacity in cumulative installed capacity has shown downward trend in the recent years, and the ratio has declined to 17.21% in 2012 from 53.49% in 2009. In 2007, the ratio of annual installed capacity in cumulative installed capacity reached the top, which is 56.45%.Figure 1
Wind power installed capacity in China: 2000–2012.  Data source: Chinese Wind Energy Association (CWEA).External economies are benefits that are created when an activity is conducted by a company or other types of entity, with those benefits enjoyed by others who are not connected with that entity. The entity that is actually managing the activity does not receive the external economies, although the creation of these benefits for outsiders usually has no negative impact on that entity [4]. Wind power engineering projects have external economies which may affect the construction of wind farm, the sustainable development of wind power industry, and even the national energy security [5]. In order to promote the reasonable construction of wind farm and sustainable development of wind power industry, the scientific and effective evaluation on external economies of wind power engineering project is necessary. Therefore, the use of certain models to evaluate the external economies of wind power engineering project is particularly important.Some studies have been conducted on the wind power project in the past few years. Zhao et al. [6] analyzed and identified the success factors contributing towards the success of Build-Operate-Transfer (BOT) wind power projects by using an extensive literature survey. Bolinger and Wiser [7] discussed the limitations of incentives in supporting farmer- or community-owned wind projects, described four ownership structures that potentially overcome the limitations, and conducted comparative financial analysis on the four structures. Agterbosch et al. [8] explored the relative importance of social and institutional conditions and their interdependencies in the operational process of planning wind power scheme. In order to avoid the blindness of the current wind power integration decision-making, Liu et al. [9] used the improved fuzzy AHP method to evaluate the wind power integration projects by constructing complete index system considering the characteristics of the wind power integration. Coleman and Provol [10] explained the wind power projects involving many factors that require sophisticated financial analysis tools for a complete project assessment, and it systematically analyzed the economic risks in wind power projects in the USA in terms of risk management and risk allocation. Valentine [11] contributed to economically optimize wind power projects from the fields of energy economics, wind power engineering, aerodynamics, geography, and climate science, which identified the critical factors that influence the economic optimization of wind power projects. Zheng et al. [12] analyzed the main influence of wind power projects on environment including noise, waste water, solid waste, lighting, electromagnetic radiation, ecology, and some control measures were also put forward. Kongnam et al. [13] proposed a solution procedure to determine the optimum generation capacity of a wind park by decision analysis techniques which can overcome the uncertainty problem and refine the investment plan of wind power projects. To analyze the land use issues and constraints for the development of new wind energy projects, Grassi et al. [14] estimated the average Annual Energy Production (AEP) with a GIS customized tool, based on physical factors, wind resource distribution, and technical specifications of the large-scale wind turbines. Georgiou et al. [15] presented a stepwise evaluation procedure for assessing the attractiveness of different developing countries to host projects on clean technologies in the framework of the clean development mechanism (CDM) of the Kyoto Protocol (KP) based on multicriteria analysis and ELECTRE III method, and it also highlighted the most critical factors influencing the economic return of wind energy projects. However, it is very regretful to find that the external economies of wind power project have rarely been studied. Therefore, the external economies of wind power engineering project urgently require to be researched, namely, into how to establish a comprehensive and appropriate method to evaluate the external economies of wind power engineering project.Analytic Hierarchy Process (AHP), developed by Saaty (1980), is a subjective tool for determining the relative importance of a set of activities in a multicriteria decision-making (MCDM) problem [16], which has been widely used for solving complex problems, such as project decision-making, economic effectiveness analysis, test-sheet composition [17], and so forth. Matter-element extension model, established and developed by Chinese scholars Cai et al. in 1983, can analyze qualitatively and quantitatively the contradiction problem based on the formalized logic tools [18, 19]. This model has the convenient advantage that it quantifies the qualitative indices, and it has been used in many fields, including the performance evaluation of ERP project [20] and risk assessment of urban network planning [21]. In this paper, a hybrid evaluation model of external economies of wind power engineering project based on AHP and matter-element extension model is put forward: AHP is used to determine the weights of the evaluation indices; the matter-element extension model is used to deduce final ranking through the weights and the values of external economies evaluation indices.This paper comprises the following: Section2 introduces the basic theory regarding AHP for determining the weights of evaluation indices and the matter-element extension model, and then the hybrid evaluation model is introduced. Taking a specific wind power engineering project in China as an example, the evaluation index system of external economies of wind power engineering project is built, and the external economies evaluation based on this hybrid evaluation model is performed in Section 3; Section 4 concludes this paper.


## 2. The Hybrid Evaluation Model

### 2.1. Basic Theory of AHP for Determining the Weights of Evaluation Indices

AHP is a practical multicriteria decision-making (MCDM) method combining qualitative and quantitative analysis, which is also a compact and efficient tool for solving complex system problems based on the use of pairwise comparisons [22].There are mainly four steps in using AHP for determining the weights of evaluation indices.Step  1 (build the hierarchical structure model). According to the overall goal and characteristic of multicriteria decision-making problem, the complex determination of index weight is decomposed and framed as a bottom-up hierarchical structure, in which the goal, criteria, and subcriteria (index) are arranged similar to a family tree, just as shown in Figure 2.Figure 2
The hierarchical structure model of AHP for determining the index weight.Step  2 (construct the judgment matrix). The (n_n) evaluation matrix B in which every element bij(i,j=1,2,...,n) is the quotient of weights of the criteria is called comparison judgment matrix, referred to as judgment matrix, as shown in (1):
(1)B=[b11b12⋯b1nb21b22⋯b2n⋯⋯⋯⋯bn1bn2⋯bnn]bij>0,bii=1,bij=1bji.The judgment matrix demonstrates the comparison of relative importance between the elements in the same level for a certain element of the upper level. The value ofbij can be obtained by pairwise comparison using a standardized comparison scale of nine levels (see Table 1).Table 1
Nine-point comparison scale.
Scale of importance
Definition
Explanation
1
Equally important
Two elements contribute equally
3
Moderately more important
One element is slightly favoured over another
5
Strongly more important
One element is strongly favoured over another
7
Very strongly more important
An element is very strongly favoured over another
9
Extremely more important
One element is most favoured over another
2, 4, 6, 8
Intermediate value
Adjacent to the two odd number scalesStep  3(calculate the local weights and consistency test). In this step, the mathematical process commences to normalize and find the relative weights for each matrix. According to (2), the relative weight of the index can be given by the right eigenvector (w) corresponding to the largest eigenvalue (λmax) as
(2)Bw=λmaxw.By the same way, the weights of all the parent nodes above the indices, that is, the weights of criteria, can be calculated.It should be consistent in the preference ratings given in the pairwise comparison matrix when using AHP. Therefore, the consistency test must be performed. The consistency is defined by the relation between the entries ofB:bij×bjk=bik. That is, if bij represents the importance of index i over index j and bjk represents the importance of index j over index k, bij×bjk must be equal to bik, where bik represents the importance of index i over index k. For each criteria, the consistency ratio (CR) is measured by the ratio of the consistency index (CI) to the random index (RI):
(3)CR=CIRI.The CI is(4)CI=(λmax-n)(n-1).The value of RI is listed in Table2.Table 2
Random index (RI).
Matrix
Size (n)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
RI
0
0
0.58
0.9
1.12
1.24
1.32
1.41
1.45
1.49
1.51
1.54
1.56
1.57
1.58The number 0.1 is the accepted upper limit for CR.CR≤0.1 implies a satisfactory degree of consistency in the pairwise comparison matrix, but if CR exceeds this value, serious inconsistency might exist and the evaluation procedure has to be repeated to improve the consistency [23].Step  4(calculate the global weights). After the CR of each of the pairwise comparison judgment matrices is equal to or less than 0.1, the global weights can then be determined for the indices by multiplying local weights of the indices with weights of all the parent nodes above it. The sum of global weights satisfies
(5)∑i=1nwi=1.


### 2.2. Basic Theory of Matter-Element Extension Model

Matter-element extension model is a formalized model which studies extension possibility and extension law of things. Matter-element extension model is composed of objects, characteristics, and values based on certain characteristics. Things in the name ofP, characteristics c, and value vare called the three elements of matter-element R. The basic element uses an ordered triple R=(P,c,v) composed of P,c,v to describe things, which is also called matter-element.Suppose objectP can be described by n characteristics c1,c2,…,cn and the corresponding values v1,v2,…,vn. Then, the matter-element R can be called n-dimensional matter-element, denoted as
(6)R=(P,C,V)=[R1R2⋯Rn]=[Pc1v1c2v2⋯⋯cnvn],
where C=[c1,c2,…,cn]T is the eigenvector, V=[v1,v2,…,vn]T is the corresponding value of the eigenvector C, and Ri is called the submatter-element of R, i=1,2,…,n.The basic steps of matter-element extension model are as follows.Step  1 (determine the classical field matter-element and the controlled field matter-element). Suppose the classical field matter-element as
(7)R0j=(P0j,Ci,V0j)=[P0jc1v01jc2v02j⋯⋯cnv0nj]=[P0jc1〈a01j,b01j〉c2〈a02j,b02j〉⋯⋯cn〈a0nj,b0nj〉],
where P0j represents the jth grade, Ci is n different characteristics of P0j, V01j is the corresponding value range of P0j and about Ci, respectively; v0ij=〈a0ij,b0ij〉(i=1,2,…,n, j=1,2,…,m), namely, the classical field.Suppose the controlled field matter-element as(8)Rp=(P,C,Vp)=[Pc1vp1c2vp2⋯⋯cnvpn]=[Pc1〈ap1,bp1〉c2〈ap2,bp2〉⋯⋯cn〈apn,bpn〉],
where P represents all the grades of objects to be evaluated and Vp is the value range of P about C;  vpi=〈api,bpi〉(i=1,2,…,n), namely, the controlled field.Step  2 (determine the matter-element to be evaluated). Suppose the matter-element to be evaluated as
(9)R0=(P0,C,V)=[Pc1v1c2v2⋯⋯cnvn],
where P0 is the matter-element to be evaluated and  vi  is the detected concrete data of P0 about ci, respectively,  i=1,2,…,n.Step  3 (establish the correlation function and calculate its value).  The correlation function is used to characterize the extension set that is the set used to describe the transformation from the things that do not have certain properties to other things that have properties. The value range of correlation function is (-∞,+∞). The correlation function value of each index of matter-element to be evaluated with each level can be calculated according to
(10)Kj(vi)={-ρ(vi,v0ij)|v0ij|,vi∈v0ijρ(vi,v0ij)ρ(vi,vpj)-ρ(vi,v0ij),vi∉v0ij,
where Kj(vi) represents the correlation function value of the ith index related to the jth level; ρ(vi,v0ij) represents the distance of the matter-element to be evaluated of the ith index related to the corresponding classical field,
(11)ρ(vi,v0ij)=|vi-12(a0ij+b0ij)|-12(b0ij-a0ij)|v0ij| represents the value range of classical field of the ith index related to the jth level; ρ(vi,vpj) represents the distance of the matter-element to be evaluated of the ith index related to the controlled field,
(12)ρ(vi,vpj)=|vi-12(api+bpi)|-12(bpi-api)vi∈v0ij indicates that the value of the ith index is in the classical field of the jth level.Step  4 (determine the index weight). Selecting the appropriate method to calculate the weight of the evaluation index is quite important for the feasibility and quality of a comprehensive evaluation. The evaluation index system of external economies of wind power engineering project has several levels and many factors within each level, and there exists the interaction relationship between the evaluation indices, so the AHP is selected to be used for determining the index weight in this paper.Step  5 (calculate the correlation degree and rating). The correlation degree of the matter-element to be evaluated with all grades is calculated by
(13)Kj(P0)=∑i=1nwiKj(vi),
where Kj(P0) is the correlation degree of the jth level, wi is the weight of the ith index, and Kj(vi) is the value of correlation function.SupposeKj*(P0)=max{Kj(P0)}(j=1,2,…,m); then the matter-element to be evaluated P0 belonged to the j*th level.Suppose(14)K¯j(p0)=Kj(p0)-minKj(p0)maxKj(p0)-minKj(p0),
where Kj(P0) represents the correlation degree of the jth level; minKj(p0) represents the minimum of correlation degrees in all levels; maxKj(p0) represents the maximum of correlation degrees in all levels; j=1,2,…,m. Consider(15)j*=∑j=1mjK¯j(p0)∑j=1mK¯j(p0),
where j* is the external economies level variable eigenvalue of p0. The attributive degree of the matter-element to be evaluated tending to adjacent levels can be judged from  j*.


### 2.3. The Theory of the Hybrid Evaluation Model

The hybrid evaluation model of wind power engineering project is established based on AHP and matter-element extension model in this paper. The evaluation procedure is shown in Figure3.Figure 3
Evaluation procedure of the proposed hybrid evaluation model.


## 2.1. Basic Theory of AHP for Determining the Weights of Evaluation Indices

AHP is a practical multicriteria decision-making (MCDM) method combining qualitative and quantitative analysis, which is also a compact and efficient tool for solving complex system problems based on the use of pairwise comparisons [22].There are mainly four steps in using AHP for determining the weights of evaluation indices.Step  1 (build the hierarchical structure model). According to the overall goal and characteristic of multicriteria decision-making problem, the complex determination of index weight is decomposed and framed as a bottom-up hierarchical structure, in which the goal, criteria, and subcriteria (index) are arranged similar to a family tree, just as shown in Figure 2.Figure 2
The hierarchical structure model of AHP for determining the index weight.Step  2 (construct the judgment matrix). The (n_n) evaluation matrix B in which every element bij(i,j=1,2,...,n) is the quotient of weights of the criteria is called comparison judgment matrix, referred to as judgment matrix, as shown in (1):
(1)B=[b11b12⋯b1nb21b22⋯b2n⋯⋯⋯⋯bn1bn2⋯bnn]bij>0,bii=1,bij=1bji.The judgment matrix demonstrates the comparison of relative importance between the elements in the same level for a certain element of the upper level. The value ofbij can be obtained by pairwise comparison using a standardized comparison scale of nine levels (see Table 1).Table 1
Nine-point comparison scale.
Scale of importance
Definition
Explanation
1
Equally important
Two elements contribute equally
3
Moderately more important
One element is slightly favoured over another
5
Strongly more important
One element is strongly favoured over another
7
Very strongly more important
An element is very strongly favoured over another
9
Extremely more important
One element is most favoured over another
2, 4, 6, 8
Intermediate value
Adjacent to the two odd number scalesStep  3(calculate the local weights and consistency test). In this step, the mathematical process commences to normalize and find the relative weights for each matrix. According to (2), the relative weight of the index can be given by the right eigenvector (w) corresponding to the largest eigenvalue (λmax) as
(2)Bw=λmaxw.By the same way, the weights of all the parent nodes above the indices, that is, the weights of criteria, can be calculated.It should be consistent in the preference ratings given in the pairwise comparison matrix when using AHP. Therefore, the consistency test must be performed. The consistency is defined by the relation between the entries ofB:bij×bjk=bik. That is, if bij represents the importance of index i over index j and bjk represents the importance of index j over index k, bij×bjk must be equal to bik, where bik represents the importance of index i over index k. For each criteria, the consistency ratio (CR) is measured by the ratio of the consistency index (CI) to the random index (RI):
(3)CR=CIRI.The CI is(4)CI=(λmax-n)(n-1).The value of RI is listed in Table2.Table 2
Random index (RI).
Matrix
Size (n)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
RI
0
0
0.58
0.9
1.12
1.24
1.32
1.41
1.45
1.49
1.51
1.54
1.56
1.57
1.58The number 0.1 is the accepted upper limit for CR.CR≤0.1 implies a satisfactory degree of consistency in the pairwise comparison matrix, but if CR exceeds this value, serious inconsistency might exist and the evaluation procedure has to be repeated to improve the consistency [23].Step  4(calculate the global weights). After the CR of each of the pairwise comparison judgment matrices is equal to or less than 0.1, the global weights can then be determined for the indices by multiplying local weights of the indices with weights of all the parent nodes above it. The sum of global weights satisfies
(5)∑i=1nwi=1.


## 2.2. Basic Theory of Matter-Element Extension Model

Matter-element extension model is a formalized model which studies extension possibility and extension law of things. Matter-element extension model is composed of objects, characteristics, and values based on certain characteristics. Things in the name ofP, characteristics c, and value vare called the three elements of matter-element R. The basic element uses an ordered triple R=(P,c,v) composed of P,c,v to describe things, which is also called matter-element.Suppose objectP can be described by n characteristics c1,c2,…,cn and the corresponding values v1,v2,…,vn. Then, the matter-element R can be called n-dimensional matter-element, denoted as
(6)R=(P,C,V)=[R1R2⋯Rn]=[Pc1v1c2v2⋯⋯cnvn],
where C=[c1,c2,…,cn]T is the eigenvector, V=[v1,v2,…,vn]T is the corresponding value of the eigenvector C, and Ri is called the submatter-element of R, i=1,2,…,n.The basic steps of matter-element extension model are as follows.Step  1 (determine the classical field matter-element and the controlled field matter-element). Suppose the classical field matter-element as
(7)R0j=(P0j,Ci,V0j)=[P0jc1v01jc2v02j⋯⋯cnv0nj]=[P0jc1〈a01j,b01j〉c2〈a02j,b02j〉⋯⋯cn〈a0nj,b0nj〉],
where P0j represents the jth grade, Ci is n different characteristics of P0j, V01j is the corresponding value range of P0j and about Ci, respectively; v0ij=〈a0ij,b0ij〉(i=1,2,…,n, j=1,2,…,m), namely, the classical field.Suppose the controlled field matter-element as(8)Rp=(P,C,Vp)=[Pc1vp1c2vp2⋯⋯cnvpn]=[Pc1〈ap1,bp1〉c2〈ap2,bp2〉⋯⋯cn〈apn,bpn〉],
where P represents all the grades of objects to be evaluated and Vp is the value range of P about C;  vpi=〈api,bpi〉(i=1,2,…,n), namely, the controlled field.Step  2 (determine the matter-element to be evaluated). Suppose the matter-element to be evaluated as
(9)R0=(P0,C,V)=[Pc1v1c2v2⋯⋯cnvn],
where P0 is the matter-element to be evaluated and  vi  is the detected concrete data of P0 about ci, respectively,  i=1,2,…,n.Step  3 (establish the correlation function and calculate its value).  The correlation function is used to characterize the extension set that is the set used to describe the transformation from the things that do not have certain properties to other things that have properties. The value range of correlation function is (-∞,+∞). The correlation function value of each index of matter-element to be evaluated with each level can be calculated according to
(10)Kj(vi)={-ρ(vi,v0ij)|v0ij|,vi∈v0ijρ(vi,v0ij)ρ(vi,vpj)-ρ(vi,v0ij),vi∉v0ij,
where Kj(vi) represents the correlation function value of the ith index related to the jth level; ρ(vi,v0ij) represents the distance of the matter-element to be evaluated of the ith index related to the corresponding classical field,
(11)ρ(vi,v0ij)=|vi-12(a0ij+b0ij)|-12(b0ij-a0ij)|v0ij| represents the value range of classical field of the ith index related to the jth level; ρ(vi,vpj) represents the distance of the matter-element to be evaluated of the ith index related to the controlled field,
(12)ρ(vi,vpj)=|vi-12(api+bpi)|-12(bpi-api)vi∈v0ij indicates that the value of the ith index is in the classical field of the jth level.Step  4 (determine the index weight). Selecting the appropriate method to calculate the weight of the evaluation index is quite important for the feasibility and quality of a comprehensive evaluation. The evaluation index system of external economies of wind power engineering project has several levels and many factors within each level, and there exists the interaction relationship between the evaluation indices, so the AHP is selected to be used for determining the index weight in this paper.Step  5 (calculate the correlation degree and rating). The correlation degree of the matter-element to be evaluated with all grades is calculated by
(13)Kj(P0)=∑i=1nwiKj(vi),
where Kj(P0) is the correlation degree of the jth level, wi is the weight of the ith index, and Kj(vi) is the value of correlation function.SupposeKj*(P0)=max{Kj(P0)}(j=1,2,…,m); then the matter-element to be evaluated P0 belonged to the j*th level.Suppose(14)K¯j(p0)=Kj(p0)-minKj(p0)maxKj(p0)-minKj(p0),
where Kj(P0) represents the correlation degree of the jth level; minKj(p0) represents the minimum of correlation degrees in all levels; maxKj(p0) represents the maximum of correlation degrees in all levels; j=1,2,…,m. Consider(15)j*=∑j=1mjK¯j(p0)∑j=1mK¯j(p0),
where j* is the external economies level variable eigenvalue of p0. The attributive degree of the matter-element to be evaluated tending to adjacent levels can be judged from  j*.


## 2.3. The Theory of the Hybrid Evaluation Model

The hybrid evaluation model of wind power engineering project is established based on AHP and matter-element extension model in this paper. The evaluation procedure is shown in Figure3.Figure 3
Evaluation procedure of the proposed hybrid evaluation model.


## 3. Case Study

In this paper, a wind power engineering project in Inner Mongolia city is taken as an example. Firstly, the evaluation index system of external economies of wind power engineering project is built, and then an evaluation on the external economies of wind power engineering project in Inner Mongolia city is carried out by employing this proposed hybrid evaluation model.There exists a wind power project being constructed by China Datang Corporation in Inner Mongolia city, which is comprised of 58 wind turbines with the capacity of 850 kW and the corresponding ancillary facilities. At the same period, a 220 kV wind farm center transformer substation is building, and the total investment is 538 million Yuan. In order to identify the external economies of this wind power engineering project, the evaluation is performed, and the detailed evaluation procedure is as follows.


### 3.1. Build the Evaluation Index System

Questionnaires, which are formed based on the related literature and the reality of wind power engineering project, were dispatched to experts in the field of wind power. The external economies evaluation index system was obtained by analyzing the result of questionnaires, which are divided into economic benefit, social benefit, and environmental benefit. The external economies evaluation index system is shown in Figure4. Of which, C1, C3, and C5 are qualitative indices, and the others are quantitative indices. All of the indices are the greatest-type index.Figure 4
External economies evaluation index system of wind power engineering project.


### 3.2. Divide the Index System to Be Evaluated intoj Grades

In this paper, the external economies of wind power engineering project are divided into five grades: strongest, stronger, general, weaker, and extremely weak.


### 3.3. Construct the Matter-Element Evaluation Model

#### 3.3.1. Establish the Classical Field

Qualitative indices in the evaluation index system use a 10-point scale with a scoring system devised by experts, and the classical field values are 0–2, 2–4, 4–6, 6–8, and 8–10, successively. For the quantitative indices, the classical field values are set to 0–100% by experts, and this range was divided into five classical domains which are successively, 0–20%, 20–40%, 40–60%, 60–80%, and 80–100%.


#### 3.3.2. Establish the Controlled Field

The controlled field of each index is the sum of the classical field value.


#### 3.3.3. Establish the Matter-Element to Be Evaluated

The specific value of the matter-element to be evaluatedR0 is composed of two parts: one part is the value of qualitative index, which can be obtained through statistical analysis of the survey results made by wind experts, enterprise managers, wind enterprise customers, and local residents; the other part is the value of quantitative index, which can be obtained by practical calculations.The values of classical fieldsR01, R02, R03, R04 and R05, controlled field Rp, and the matter-element to be evaluated R0 are as follows:
(16)R01=[P01c1(0,2)c2(0%,20%)c3(0,2)c4(0%,20%)c5(0,2)c6(0%,20%)c7(0%,20%)c8(0%,20%)c9(0%,20%)c10(0%,20%)],R02=[P02c1(2,4)c2(20%,40%)c3(2,4)c4(20%,40%)c5(2,4)c6(20%,40%)c7(20%,40%)c8(20%,40%)c9(20%,40%)c10(20%,40%)],R03=[P03c1(4,6)c2(40%,60%)c3(4,6)c4(40%,60%)c5(4,6)c6(40%,60%)c7(40%,60%)c8(40%,60%)c9(40%,60%)c10(40%,60%)],R04=[P04c1(6,8)c2(60%,80%)c3(6,8)c4(60%,80%)c5(6,8)c6(60%,80%)c7(60%,80%)c8(60%,80%)c9(60%,80%)c10(60%,80%)],R05=[P05c1(8,10)c2(80%,100%)c3(8,10)c4(80%,100%)c5(8,10)c6(80%,100%)c7(80%,100%)c8(80%,100%)c9(80%,100%)c10(80%,100%)],Rp=[Pc1(0,10)c2(0%,100%)c3(0,10)c4(0%,100%)c5(0,10)c6(0%,100%)c7(0%,100%)c8(0%,100%)c9(0%,100%)c10(0%,100%)],R0=[P0c16.91c287%c36.56c482%c56.2c689%c788%c891%c983%c1074%],
where R01, R02, R03, R04, and R05 represent the classical field; Rp represents the controlled field; R0 represents the matter-element to be evaluated; P01 represents the extremely weak external economies grade, P02 represents weaker grade, P03 represents general grade, P04 represents stronger grade, and P05 represents the strongest grade.


### 3.4. Calculate the Correlation Function Value

The correlation function value can be calculated according to (10), of which the result is listed in Table 3.Table 3
The calculation result of correlation function value.
Index
Extremely weak
Weaker
General
Stronger
Strongest
K
1
(
v
i
)
K
2
(
v
i
)
K
3
(
v
i
)
K
4
(
v
i
)
K
5
(
v
i
)
C1
−0.61375
−0.485
−0.2275
0.455
−0.26077
C2
−0.8375
−0.78333
−0.675
−0.35
0.35
C3
−0.57
−0.42667
−0.14
0.28
−0.29508
C4
−0.775
−0.7
−0.55
−0.1
0.1
C5
−0.525
−0.36667
−0.05
0.1
−0.32143
C6
−0.8625
−0.81667
−0.725
−0.45
0.45
C7
−0.85
−0.8
−0.7
−0.4
0.4
C8
−0.8875
−0.85
−0.775
−0.55
0.45
C9
−0.7875
−0.71667
−0.575
−0.15
0.15
C10
−0.675
−0.56667
−0.35
0.3
0.010256


### 3.5. Determine the Index Weight

#### 3.5.1. Build the Hierarchical Structure Model

The AHP hierarchical structure model for external economies evaluation of wind power engineering project is shown in Figure5. The goal of our problem is to evaluate the external economies of wind power engineering project, which is placed on the first level of the hierarchy. Three factors, namely, economic benefit, social benefit, and environmental benefit, are identified to achieve this goal, which form the second level of the hierarchy, namely, criteria. The third level of the hierarchy consists of 10 indices, and the economic benefit, social benefit, and environmental benefit include 4 indices, 2 indices, and 4 indices, respectively.Figure 5
Hierarchical structure of external economies evaluation of wind power engineering project.


#### 3.5.2. Construct the Judgment Matrix

The pairwise comparison judgment matrices obtained from wind experts in the data collection and measurement phase are combined using the geometric mean approach at each hierarchy level to obtain the corresponding consensus pairwise comparison judgment matrices through using a standardized comparison scale of nine levels. The results of pairwise comparison judgment matrices are listed in Table4.Table 4
Pairwise comparison judgment matrices, local weight, and CR.
Goal
Economic benefit
Social benefit
Environmental benefit
Weight
Economic benefit
1.0000
2.3000
0.5556
0.3140
Social benefit
0.4348
1.0000
0.2703
0.1417
Environmental benefit
1.8000
3.7000
1.0000
0.5443
CR = 0.0012
Economic benefit
C1
C2
C3
C4
Local weight
C1
1.0000
0.4167
1.9000
3.2000
0.2257
C2
2.4000
1.0000
3.9000
5.7000
0.6232
C3
0.5263
0.2564
1.0000
1.4000
0.0950
C4
0.3125
0.1754
0.7143
1.0000
0.0561
CR = 0.0827
Social benefit
C5
C6
Local weight
C5
1.0000
1.3000
0.5436
C6
0.7692
1.0000
0.4564
CR = 0.0000
Environmental benefit
C7
C8
C9
C10
Local weight
C7
1.0000
3.2000
3.5000
1.4000
0.4877
C8
0.3125
1.0000
1.5000
0.4348
0.1147
C9
0.2857
0.6667
1.0000
0.3846
0.0815
C10
0.7143
2.3000
2.6000
1.0000
0.3161
CR = 0.0541


#### 3.5.3. Calculate the Local Weight and Consistency Test

After the pairwise comparison judgment matrices are constructed, they are then translated into the corresponding largest eigenvalue problem and further to find the normalized and unique priority weight for each index. According to (2)–(4), the local weight of each index and the CR of pairwise comparison judgment matrices can be obtained, just as shown in Table 4. It can be seen that the CR of each of the pairwise comparison judgment matrices is well below the rule-of-thumb value of CR equal to 0.1. This clearly implies that the wind experts are consistent in the preference ratings given in the pairwise comparison matrix.


#### 3.5.4. Calculating the Global Weight

By calculation, the global weight of each index is listed in Table5.Table 5
The global weight of each index.
Criteria
Weight
Index
Local weight
Global weight
Economic benefit (B1)
0.3140
C1
0.2257
0.071
C2
0.6232
0.196
C3
0.0950
0.030
C4
0.0561
0.018
Social benefit (B2)
0.1417
C5
0.5436
0.077
C6
0.4564
0.065
Environmental benefit (B3)
0.5443
C7
0.4877
0.265
C8
0.1147
0.062
C9
0.0815
0.044
C10
0.3161
0.172


### 3.6. Calculate the Correlation Degree and Rating

The correlation degree value of each grade is as follows:(17)K1(P0)=∑i=110wiK1(vi)=-0.766,K2(P0)=∑i=110wiK2(vi)=-0.688,K3(P0)=∑i=110wiK3(vi)=-0.533,K4(P0)=∑i=110wiK4(vi)=-0.146,K5(P0)=∑i=110wiK5(vi)=0.190.SinceK5(P0)=max{Kj(P0)}(j=1,2,3,4,5), it is shown that the external economies of this wind power engineering project belongs to “strongest” grade.


### 3.7. Sensitivity Analysis

Sensitivity analysis is performed according to the external economies index system of wind power engineering project. The valuej* represents the external economies level deflection degree to its adjacent levels. We use j*∈(0,1),(1,2),(2,3),(3,4) and (4,5) to represent the external economies level “extremely weak,” “weaker,” “general,” “stronger,” and “strongest,” respectively. For example, if j*=3.2, it shows that the external economies level belongs to “stronger” but closer to the “general” level more; if j*=3.7, it shows that the external economies level belongs to “stronger” but closer to the “strongest” level more. In this paper, by calculation, j*=4.3∈(4,5), the external economies level belongs to “strongest” but closer to the “stronger” level more.


#### 3.7.1. Sensitivity Analysis on Index Weight

The result of sensitivity analysis is shown in Figure6 when the weights of external economies indices are changed by ±0.1, ±0.2, ±0.3, ±0.4, ±0.5.Figure 6
Sensitivity analysis result on the index weight.As we can see from Figure6, whatever the weights of all the indices fluctuate, the value of j* remains in the scope of (4.25, 4.35), so they have a really general effect on the evaluation result and it can be said that their sensitivity is general. In detail, with the weights of external economies indices C2, C6, C7, and C8 increasing, the “strongest” level of external economies is enhanced gradually and the weight of C7 is the most sensitive. With the weights of external economies indices C1, C3, C5, and C10 increasing, the external economies level has the trend of deviating from the “strongest” level to “stronger” level gradually and the weight of C10 is the most sensitive factor. The weights changes of external economies indices C4, C9 have little effect on the external economies level, so their sensitivities are weak.


#### 3.7.2. Sensitivity Analysis on the Index Scoring

The sensitivity analysis result is shown in Figure7 when the index scoring values are changed by ±0.1, ±0.2, ±0.3, ±0.4, ±0.5.Figure 7
Sensitivity analysis result on the index scoring.As we can see from Figure7, with the scoring values of external economies indices C2, C6, and C7 decreasing, the external economies level deviates from the “strongest” level to “stronger” level gradually, which indicates that these indices have a significant impact and the sensitivity is relatively stronger, and the C7 scoring is the most sensitive. The external economies indices C1, C3, C4, C5, C8, C9, and C10 have very little effect on the evaluation result, which indicates that the sensitivity is not strong. The external economies level in this wind power engineering project lies between “strongest” and “stronger,” and as the index scoring value decreases, the degree of external economies level will change from “strongest” level to “stronger” level gradually.From the above two sensitivity analysis, it can safely draw the conclusion that C2, C7, and C10 are the sensitive indices in the external economies evaluation of wind power engineering project, namely, “the degree of increasing region GDP,” “the degree of reducing pollution gas emissions,” and “the degree of energy conservation.” In the construction and management process of the wind power engineering project, these factors should be focused and analyzed mainly in order to enhance the project external economies and reduce the obstacles of wind power project construction.


## 3.1. Build the Evaluation Index System

Questionnaires, which are formed based on the related literature and the reality of wind power engineering project, were dispatched to experts in the field of wind power. The external economies evaluation index system was obtained by analyzing the result of questionnaires, which are divided into economic benefit, social benefit, and environmental benefit. The external economies evaluation index system is shown in Figure4. Of which, C1, C3, and C5 are qualitative indices, and the others are quantitative indices. All of the indices are the greatest-type index.Figure 4
External economies evaluation index system of wind power engineering project.


## 3.2. Divide the Index System to Be Evaluated intoj Grades

In this paper, the external economies of wind power engineering project are divided into five grades: strongest, stronger, general, weaker, and extremely weak.


## 3.3. Construct the Matter-Element Evaluation Model

### 3.3.1. Establish the Classical Field

Qualitative indices in the evaluation index system use a 10-point scale with a scoring system devised by experts, and the classical field values are 0–2, 2–4, 4–6, 6–8, and 8–10, successively. For the quantitative indices, the classical field values are set to 0–100% by experts, and this range was divided into five classical domains which are successively, 0–20%, 20–40%, 40–60%, 60–80%, and 80–100%.


### 3.3.2. Establish the Controlled Field

The controlled field of each index is the sum of the classical field value.


### 3.3.3. Establish the Matter-Element to Be Evaluated

The specific value of the matter-element to be evaluatedR0 is composed of two parts: one part is the value of qualitative index, which can be obtained through statistical analysis of the survey results made by wind experts, enterprise managers, wind enterprise customers, and local residents; the other part is the value of quantitative index, which can be obtained by practical calculations.The values of classical fieldsR01, R02, R03, R04 and R05, controlled field Rp, and the matter-element to be evaluated R0 are as follows:
(16)R01=[P01c1(0,2)c2(0%,20%)c3(0,2)c4(0%,20%)c5(0,2)c6(0%,20%)c7(0%,20%)c8(0%,20%)c9(0%,20%)c10(0%,20%)],R02=[P02c1(2,4)c2(20%,40%)c3(2,4)c4(20%,40%)c5(2,4)c6(20%,40%)c7(20%,40%)c8(20%,40%)c9(20%,40%)c10(20%,40%)],R03=[P03c1(4,6)c2(40%,60%)c3(4,6)c4(40%,60%)c5(4,6)c6(40%,60%)c7(40%,60%)c8(40%,60%)c9(40%,60%)c10(40%,60%)],R04=[P04c1(6,8)c2(60%,80%)c3(6,8)c4(60%,80%)c5(6,8)c6(60%,80%)c7(60%,80%)c8(60%,80%)c9(60%,80%)c10(60%,80%)],R05=[P05c1(8,10)c2(80%,100%)c3(8,10)c4(80%,100%)c5(8,10)c6(80%,100%)c7(80%,100%)c8(80%,100%)c9(80%,100%)c10(80%,100%)],Rp=[Pc1(0,10)c2(0%,100%)c3(0,10)c4(0%,100%)c5(0,10)c6(0%,100%)c7(0%,100%)c8(0%,100%)c9(0%,100%)c10(0%,100%)],R0=[P0c16.91c287%c36.56c482%c56.2c689%c788%c891%c983%c1074%],
where R01, R02, R03, R04, and R05 represent the classical field; Rp represents the controlled field; R0 represents the matter-element to be evaluated; P01 represents the extremely weak external economies grade, P02 represents weaker grade, P03 represents general grade, P04 represents stronger grade, and P05 represents the strongest grade.


## 3.3.1. Establish the Classical Field

Qualitative indices in the evaluation index system use a 10-point scale with a scoring system devised by experts, and the classical field values are 0–2, 2–4, 4–6, 6–8, and 8–10, successively. For the quantitative indices, the classical field values are set to 0–100% by experts, and this range was divided into five classical domains which are successively, 0–20%, 20–40%, 40–60%, 60–80%, and 80–100%.


## 3.3.2. Establish the Controlled Field

The controlled field of each index is the sum of the classical field value.


## 3.3.3. Establish the Matter-Element to Be Evaluated

The specific value of the matter-element to be evaluatedR0 is composed of two parts: one part is the value of qualitative index, which can be obtained through statistical analysis of the survey results made by wind experts, enterprise managers, wind enterprise customers, and local residents; the other part is the value of quantitative index, which can be obtained by practical calculations.The values of classical fieldsR01, R02, R03, R04 and R05, controlled field Rp, and the matter-element to be evaluated R0 are as follows:
(16)R01=[P01c1(0,2)c2(0%,20%)c3(0,2)c4(0%,20%)c5(0,2)c6(0%,20%)c7(0%,20%)c8(0%,20%)c9(0%,20%)c10(0%,20%)],R02=[P02c1(2,4)c2(20%,40%)c3(2,4)c4(20%,40%)c5(2,4)c6(20%,40%)c7(20%,40%)c8(20%,40%)c9(20%,40%)c10(20%,40%)],R03=[P03c1(4,6)c2(40%,60%)c3(4,6)c4(40%,60%)c5(4,6)c6(40%,60%)c7(40%,60%)c8(40%,60%)c9(40%,60%)c10(40%,60%)],R04=[P04c1(6,8)c2(60%,80%)c3(6,8)c4(60%,80%)c5(6,8)c6(60%,80%)c7(60%,80%)c8(60%,80%)c9(60%,80%)c10(60%,80%)],R05=[P05c1(8,10)c2(80%,100%)c3(8,10)c4(80%,100%)c5(8,10)c6(80%,100%)c7(80%,100%)c8(80%,100%)c9(80%,100%)c10(80%,100%)],Rp=[Pc1(0,10)c2(0%,100%)c3(0,10)c4(0%,100%)c5(0,10)c6(0%,100%)c7(0%,100%)c8(0%,100%)c9(0%,100%)c10(0%,100%)],R0=[P0c16.91c287%c36.56c482%c56.2c689%c788%c891%c983%c1074%],
where R01, R02, R03, R04, and R05 represent the classical field; Rp represents the controlled field; R0 represents the matter-element to be evaluated; P01 represents the extremely weak external economies grade, P02 represents weaker grade, P03 represents general grade, P04 represents stronger grade, and P05 represents the strongest grade.


## 3.4. Calculate the Correlation Function Value

The correlation function value can be calculated according to (10), of which the result is listed in Table 3.Table 3
The calculation result of correlation function value.
Index
Extremely weak
Weaker
General
Stronger
Strongest
K
1
(
v
i
)
K
2
(
v
i
)
K
3
(
v
i
)
K
4
(
v
i
)
K
5
(
v
i
)
C1
−0.61375
−0.485
−0.2275
0.455
−0.26077
C2
−0.8375
−0.78333
−0.675
−0.35
0.35
C3
−0.57
−0.42667
−0.14
0.28
−0.29508
C4
−0.775
−0.7
−0.55
−0.1
0.1
C5
−0.525
−0.36667
−0.05
0.1
−0.32143
C6
−0.8625
−0.81667
−0.725
−0.45
0.45
C7
−0.85
−0.8
−0.7
−0.4
0.4
C8
−0.8875
−0.85
−0.775
−0.55
0.45
C9
−0.7875
−0.71667
−0.575
−0.15
0.15
C10
−0.675
−0.56667
−0.35
0.3
0.010256


## 3.5. Determine the Index Weight

### 3.5.1. Build the Hierarchical Structure Model

The AHP hierarchical structure model for external economies evaluation of wind power engineering project is shown in Figure5. The goal of our problem is to evaluate the external economies of wind power engineering project, which is placed on the first level of the hierarchy. Three factors, namely, economic benefit, social benefit, and environmental benefit, are identified to achieve this goal, which form the second level of the hierarchy, namely, criteria. The third level of the hierarchy consists of 10 indices, and the economic benefit, social benefit, and environmental benefit include 4 indices, 2 indices, and 4 indices, respectively.Figure 5
Hierarchical structure of external economies evaluation of wind power engineering project.


### 3.5.2. Construct the Judgment Matrix

The pairwise comparison judgment matrices obtained from wind experts in the data collection and measurement phase are combined using the geometric mean approach at each hierarchy level to obtain the corresponding consensus pairwise comparison judgment matrices through using a standardized comparison scale of nine levels. The results of pairwise comparison judgment matrices are listed in Table4.Table 4
Pairwise comparison judgment matrices, local weight, and CR.
Goal
Economic benefit
Social benefit
Environmental benefit
Weight
Economic benefit
1.0000
2.3000
0.5556
0.3140
Social benefit
0.4348
1.0000
0.2703
0.1417
Environmental benefit
1.8000
3.7000
1.0000
0.5443
CR = 0.0012
Economic benefit
C1
C2
C3
C4
Local weight
C1
1.0000
0.4167
1.9000
3.2000
0.2257
C2
2.4000
1.0000
3.9000
5.7000
0.6232
C3
0.5263
0.2564
1.0000
1.4000
0.0950
C4
0.3125
0.1754
0.7143
1.0000
0.0561
CR = 0.0827
Social benefit
C5
C6
Local weight
C5
1.0000
1.3000
0.5436
C6
0.7692
1.0000
0.4564
CR = 0.0000
Environmental benefit
C7
C8
C9
C10
Local weight
C7
1.0000
3.2000
3.5000
1.4000
0.4877
C8
0.3125
1.0000
1.5000
0.4348
0.1147
C9
0.2857
0.6667
1.0000
0.3846
0.0815
C10
0.7143
2.3000
2.6000
1.0000
0.3161
CR = 0.0541


### 3.5.3. Calculate the Local Weight and Consistency Test

After the pairwise comparison judgment matrices are constructed, they are then translated into the corresponding largest eigenvalue problem and further to find the normalized and unique priority weight for each index. According to (2)–(4), the local weight of each index and the CR of pairwise comparison judgment matrices can be obtained, just as shown in Table 4. It can be seen that the CR of each of the pairwise comparison judgment matrices is well below the rule-of-thumb value of CR equal to 0.1. This clearly implies that the wind experts are consistent in the preference ratings given in the pairwise comparison matrix.


### 3.5.4. Calculating the Global Weight

By calculation, the global weight of each index is listed in Table5.Table 5
The global weight of each index.
Criteria
Weight
Index
Local weight
Global weight
Economic benefit (B1)
0.3140
C1
0.2257
0.071
C2
0.6232
0.196
C3
0.0950
0.030
C4
0.0561
0.018
Social benefit (B2)
0.1417
C5
0.5436
0.077
C6
0.4564
0.065
Environmental benefit (B3)
0.5443
C7
0.4877
0.265
C8
0.1147
0.062
C9
0.0815
0.044
C10
0.3161
0.172


## 3.5.1. Build the Hierarchical Structure Model

The AHP hierarchical structure model for external economies evaluation of wind power engineering project is shown in Figure5. The goal of our problem is to evaluate the external economies of wind power engineering project, which is placed on the first level of the hierarchy. Three factors, namely, economic benefit, social benefit, and environmental benefit, are identified to achieve this goal, which form the second level of the hierarchy, namely, criteria. The third level of the hierarchy consists of 10 indices, and the economic benefit, social benefit, and environmental benefit include 4 indices, 2 indices, and 4 indices, respectively.Figure 5
Hierarchical structure of external economies evaluation of wind power engineering project.


## 3.5.2. Construct the Judgment Matrix

The pairwise comparison judgment matrices obtained from wind experts in the data collection and measurement phase are combined using the geometric mean approach at each hierarchy level to obtain the corresponding consensus pairwise comparison judgment matrices through using a standardized comparison scale of nine levels. The results of pairwise comparison judgment matrices are listed in Table4.Table 4
Pairwise comparison judgment matrices, local weight, and CR.
Goal
Economic benefit
Social benefit
Environmental benefit
Weight
Economic benefit
1.0000
2.3000
0.5556
0.3140
Social benefit
0.4348
1.0000
0.2703
0.1417
Environmental benefit
1.8000
3.7000
1.0000
0.5443
CR = 0.0012
Economic benefit
C1
C2
C3
C4
Local weight
C1
1.0000
0.4167
1.9000
3.2000
0.2257
C2
2.4000
1.0000
3.9000
5.7000
0.6232
C3
0.5263
0.2564
1.0000
1.4000
0.0950
C4
0.3125
0.1754
0.7143
1.0000
0.0561
CR = 0.0827
Social benefit
C5
C6
Local weight
C5
1.0000
1.3000
0.5436
C6
0.7692
1.0000
0.4564
CR = 0.0000
Environmental benefit
C7
C8
C9
C10
Local weight
C7
1.0000
3.2000
3.5000
1.4000
0.4877
C8
0.3125
1.0000
1.5000
0.4348
0.1147
C9
0.2857
0.6667
1.0000
0.3846
0.0815
C10
0.7143
2.3000
2.6000
1.0000
0.3161
CR = 0.0541


## 3.5.3. Calculate the Local Weight and Consistency Test

After the pairwise comparison judgment matrices are constructed, they are then translated into the corresponding largest eigenvalue problem and further to find the normalized and unique priority weight for each index. According to (2)–(4), the local weight of each index and the CR of pairwise comparison judgment matrices can be obtained, just as shown in Table 4. It can be seen that the CR of each of the pairwise comparison judgment matrices is well below the rule-of-thumb value of CR equal to 0.1. This clearly implies that the wind experts are consistent in the preference ratings given in the pairwise comparison matrix.


## 3.5.4. Calculating the Global Weight

By calculation, the global weight of each index is listed in Table5.Table 5
The global weight of each index.
Criteria
Weight
Index
Local weight
Global weight
Economic benefit (B1)
0.3140
C1
0.2257
0.071
C2
0.6232
0.196
C3
0.0950
0.030
C4
0.0561
0.018
Social benefit (B2)
0.1417
C5
0.5436
0.077
C6
0.4564
0.065
Environmental benefit (B3)
0.5443
C7
0.4877
0.265
C8
0.1147
0.062
C9
0.0815
0.044
C10
0.3161
0.172


## 3.6. Calculate the Correlation Degree and Rating

The correlation degree value of each grade is as follows:(17)K1(P0)=∑i=110wiK1(vi)=-0.766,K2(P0)=∑i=110wiK2(vi)=-0.688,K3(P0)=∑i=110wiK3(vi)=-0.533,K4(P0)=∑i=110wiK4(vi)=-0.146,K5(P0)=∑i=110wiK5(vi)=0.190.SinceK5(P0)=max{Kj(P0)}(j=1,2,3,4,5), it is shown that the external economies of this wind power engineering project belongs to “strongest” grade.


## 3.7. Sensitivity Analysis

Sensitivity analysis is performed according to the external economies index system of wind power engineering project. The valuej* represents the external economies level deflection degree to its adjacent levels. We use j*∈(0,1),(1,2),(2,3),(3,4) and (4,5) to represent the external economies level “extremely weak,” “weaker,” “general,” “stronger,” and “strongest,” respectively. For example, if j*=3.2, it shows that the external economies level belongs to “stronger” but closer to the “general” level more; if j*=3.7, it shows that the external economies level belongs to “stronger” but closer to the “strongest” level more. In this paper, by calculation, j*=4.3∈(4,5), the external economies level belongs to “strongest” but closer to the “stronger” level more.


### 3.7.1. Sensitivity Analysis on Index Weight

The result of sensitivity analysis is shown in Figure6 when the weights of external economies indices are changed by ±0.1, ±0.2, ±0.3, ±0.4, ±0.5.Figure 6
Sensitivity analysis result on the index weight.As we can see from Figure6, whatever the weights of all the indices fluctuate, the value of j* remains in the scope of (4.25, 4.35), so they have a really general effect on the evaluation result and it can be said that their sensitivity is general. In detail, with the weights of external economies indices C2, C6, C7, and C8 increasing, the “strongest” level of external economies is enhanced gradually and the weight of C7 is the most sensitive. With the weights of external economies indices C1, C3, C5, and C10 increasing, the external economies level has the trend of deviating from the “strongest” level to “stronger” level gradually and the weight of C10 is the most sensitive factor. The weights changes of external economies indices C4, C9 have little effect on the external economies level, so their sensitivities are weak.


### 3.7.2. Sensitivity Analysis on the Index Scoring

The sensitivity analysis result is shown in Figure7 when the index scoring values are changed by ±0.1, ±0.2, ±0.3, ±0.4, ±0.5.Figure 7
Sensitivity analysis result on the index scoring.As we can see from Figure7, with the scoring values of external economies indices C2, C6, and C7 decreasing, the external economies level deviates from the “strongest” level to “stronger” level gradually, which indicates that these indices have a significant impact and the sensitivity is relatively stronger, and the C7 scoring is the most sensitive. The external economies indices C1, C3, C4, C5, C8, C9, and C10 have very little effect on the evaluation result, which indicates that the sensitivity is not strong. The external economies level in this wind power engineering project lies between “strongest” and “stronger,” and as the index scoring value decreases, the degree of external economies level will change from “strongest” level to “stronger” level gradually.From the above two sensitivity analysis, it can safely draw the conclusion that C2, C7, and C10 are the sensitive indices in the external economies evaluation of wind power engineering project, namely, “the degree of increasing region GDP,” “the degree of reducing pollution gas emissions,” and “the degree of energy conservation.” In the construction and management process of the wind power engineering project, these factors should be focused and analyzed mainly in order to enhance the project external economies and reduce the obstacles of wind power project construction.


## 3.7.1. Sensitivity Analysis on Index Weight

The result of sensitivity analysis is shown in Figure6 when the weights of external economies indices are changed by ±0.1, ±0.2, ±0.3, ±0.4, ±0.5.Figure 6
Sensitivity analysis result on the index weight.As we can see from Figure6, whatever the weights of all the indices fluctuate, the value of j* remains in the scope of (4.25, 4.35), so they have a really general effect on the evaluation result and it can be said that their sensitivity is general. In detail, with the weights of external economies indices C2, C6, C7, and C8 increasing, the “strongest” level of external economies is enhanced gradually and the weight of C7 is the most sensitive. With the weights of external economies indices C1, C3, C5, and C10 increasing, the external economies level has the trend of deviating from the “strongest” level to “stronger” level gradually and the weight of C10 is the most sensitive factor. The weights changes of external economies indices C4, C9 have little effect on the external economies level, so their sensitivities are weak.


## 3.7.2. Sensitivity Analysis on the Index Scoring

The sensitivity analysis result is shown in Figure7 when the index scoring values are changed by ±0.1, ±0.2, ±0.3, ±0.4, ±0.5.Figure 7
Sensitivity analysis result on the index scoring.As we can see from Figure7, with the scoring values of external economies indices C2, C6, and C7 decreasing, the external economies level deviates from the “strongest” level to “stronger” level gradually, which indicates that these indices have a significant impact and the sensitivity is relatively stronger, and the C7 scoring is the most sensitive. The external economies indices C1, C3, C4, C5, C8, C9, and C10 have very little effect on the evaluation result, which indicates that the sensitivity is not strong. The external economies level in this wind power engineering project lies between “strongest” and “stronger,” and as the index scoring value decreases, the degree of external economies level will change from “strongest” level to “stronger” level gradually.From the above two sensitivity analysis, it can safely draw the conclusion that C2, C7, and C10 are the sensitive indices in the external economies evaluation of wind power engineering project, namely, “the degree of increasing region GDP,” “the degree of reducing pollution gas emissions,” and “the degree of energy conservation.” In the construction and management process of the wind power engineering project, these factors should be focused and analyzed mainly in order to enhance the project external economies and reduce the obstacles of wind power project construction.


## 4. Conclusions

Scientific and effective evaluation on the external economies of wind power engineering project is an important part for the scientific exploitation and sustainable development of wind power project. Many factors which are varied and complex affect the external economies of wind power engineering project, such as economic factors, social factors, and environmental factors. Therefore, a reasonable external economies evaluation that considers multiple attributes needs to be performed, which can provide theoretical support for wind power engineering project construction planning. In this paper, a hybrid evaluation model of external economies of wind power engineering project is proposed based on AHP and matter-element extension model, which can solve complex system problems constituted by multilevel factors and overcome the shortcomings and inadequacies resulting from the ambiguity and uncertainty inherent. The external economies evaluation index system of wind power engineering project is constructed considering economic benefit, social benefit, and environmental benefit. The external economies evaluation method based on the AHP and matter-element extension model is also formulated. Taking a wind power engineering project in Inner Mongolia city as an example, the feasibility of this proposed hybrid evaluation model is proven. The analysis result shows that the external economies of wind power engineering project in Inner Mongolia city belong to the “strongest” level, and “the degree of increasing region GDP,” “the degree of reducing pollution gas emissions,” and “the degree of energy conservation” are the sensitive factors which should be focused and analyzed mainly in the construction and management process of wind power engineering project.



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*Source: 848901-2013-12-21.xml*