external economies evaluation of wind power engineering project based on analytic hierarchy process and matter element extension model

Research Article External Economies Evaluation of Wind Power Engineering Project Based on Analytic Hierarchy Process and Matter-Element Extension Model Hong-ze Li and Sen Guo School of E

Research Article

External Economies Evaluation of Wind Power

Engineering Project Based on Analytic Hierarchy Process and Matter-Element Extension Model

Hong-ze Li and Sen Guo

School of Economics and Management, North China Electric Power University, Changping District, Beijing 102206, China

Correspondence should be addressed to Sen Guo; guosen324@163.com

Received 20 October 2013; Accepted 24 November 2013

Academic Editor: Hao-Chun Lu

Copyright © 2013 H.-z Li and S Guo This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited 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

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

envi-ronmental 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 inFigure 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 down-ward 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%

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

0 10 20 30 40 50 60

0

10000

20000

30000

40000

50000

60000

70000

80000

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

Year Annual installed capacity

Cumulative installed capacity

The ratio of annual installed capacity in cumulative installed capacity

Figure 1: Wind power installed capacity in China: 2000–2012 Data

source: Chinese Wind Energy Association (CWEA)

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

limita-tions, 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 impor-tance 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: Section 2 intro-duces 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 inSection 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 quan-titative analysis, which is also a compact and efficient tool

Subcriteria

(index)

Criteria · · · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

Figure 2: The hierarchical structure model of AHP for determining

the index weight

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 inFigure 2

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):

𝐵 =[[

[

𝑏11 𝑏12 ⋅ ⋅ ⋅ 𝑏1𝑛

𝑏21 𝑏22 ⋅ ⋅ ⋅ 𝑏2𝑛

⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅

𝑏𝑛1 𝑏𝑛2 ⋅ ⋅ ⋅ 𝑏𝑛𝑛

] ] ]

𝑏𝑖𝑗> 0, 𝑏𝑖𝑖 = 1, 𝑏𝑖𝑗= 𝑏1

𝑗𝑖 (1)

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 of b ijcan

be obtained by pairwise comparison using a standardized

comparison scale of nine levels (seeTable 1)

Step 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

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, if𝑏𝑖𝑗represents the importance of index𝑖 over index 𝑗

and𝑏𝑗𝑘represents the importance of index𝑗 over index 𝑘, 𝑏𝑖𝑗×

𝑏𝑗𝑘must be equal to𝑏𝑖𝑘, where𝑏𝑖𝑘represents the importance

of index𝑖 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):

CR= CI

The CI is

CI=(𝜆max− 𝑛)

The value of RI is listed inTable 2 The 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

𝑛

∑

𝑖=1

2.2 Basic Theory of 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, character-istics, and values based on certain characteristics Things in the name of𝑃, characteristics c, and value v are called the three elements of matter-element R The basic element uses

an ordered triple𝑅 = (𝑃, 𝑐, V) composed of 𝑃, 𝑐, V to describe things, which is also called matter-element

Suppose object 𝑃 can be described by 𝑛 characteris-tics𝑐1, 𝑐2, , 𝑐𝑛 and the corresponding valuesV1, V2, , V𝑛 Then, the matter-element 𝑅 can be called 𝑛-dimensional matter-element, denoted as

𝑅 = (𝑃, 𝐶, 𝑉) =[[

[

𝑅1

𝑅2

⋅ ⋅ ⋅

𝑅𝑛

] ] ]

=[[ [

𝑃 𝑐1 V1

𝑐2 V2

⋅ ⋅ ⋅ ⋅ ⋅ ⋅

𝑐𝑛 V𝑛

] ] ]

where 𝐶 = [𝑐1, 𝑐2, , 𝑐𝑛]𝑇 is the eigenvector, 𝑉 = [V1, V2, , V𝑛]𝑇is the corresponding value of the eigenvector

The basic steps of matter-element extension model are as follows

Table 1: Nine-point comparison scale.

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 scales

Table 2: Random index (RI)

Matrix

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 1.58

Step 1 (determine the classical field matter-element and the

controlled field matter-element) Suppose the classical field

matter-element as

𝑅0𝑗= (𝑃0𝑗, 𝐶𝑖, 𝑉0𝑗)

=[[

[

𝑃0𝑗 𝑐1 V01𝑗

𝑐2 V02𝑗

⋅ ⋅ ⋅ ⋅ ⋅ ⋅

𝑐𝑛 V0𝑛𝑗

] ] ]

=[[ [

𝑃0𝑗 𝑐1 ⟨𝑎01𝑗, 𝑏01𝑗⟩

𝑐2 ⟨𝑎02𝑗, 𝑏02𝑗⟩

⋅ ⋅ ⋅ ⋅ ⋅ ⋅

𝑐𝑛 ⟨𝑎0𝑛𝑗, 𝑏0𝑛𝑗⟩

] ] ] , (7)

where𝑃0𝑗represents the𝑗th grade, 𝐶𝑖is n different

charac-teristics of𝑃0𝑗,𝑉01𝑗is the corresponding value range of𝑃0𝑗

and about𝐶𝑖, respectively;V0𝑖𝑗 = ⟨𝑎0𝑖𝑗, 𝑏0𝑖𝑗⟩(𝑖 = 1, 2, , 𝑛,

𝑗 = 1, 2, , 𝑚), namely, the classical field

Suppose the controlled field matter-element as

𝑅𝑝= (𝑃, 𝐶, 𝑉𝑝) =[[

[

𝑃 𝑐1 V𝑝1

𝑐2 V𝑝2

⋅ ⋅ ⋅ ⋅ ⋅ ⋅

𝑐𝑛 V𝑝𝑛

] ] ]

=[[ [

𝑃 𝑐1 ⟨𝑎𝑝1, 𝑏𝑝1⟩

𝑐2 ⟨𝑎𝑝2, 𝑏𝑝2⟩

⋅ ⋅ ⋅ ⋅ ⋅ ⋅

𝑐𝑛 ⟨𝑎𝑝𝑛, 𝑏𝑝𝑛⟩

] ] ] , (8)

where P represents all the grades of objects to be evaluated

and𝑉𝑝 is the value range of𝑃 about 𝐶; V𝑝𝑖 = ⟨𝑎𝑝𝑖, 𝑏𝑝𝑖⟩(𝑖 =

1, 2, , 𝑛), namely, the controlled field

Step 2 (determine the matter-element to be evaluated)

Sup-pose the matter-element to be evaluated as

𝑅0= (𝑃0, 𝐶, 𝑉) =[[

[

𝑃 𝑐1 V1

𝑐2 V2

⋅ ⋅ ⋅ ⋅ ⋅ ⋅

𝑐𝑛 V𝑛

] ] ]

where 𝑃0 is the matter-element to be evaluated andV𝑖 is the detected concrete data of𝑃0 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 transfor-mation 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

𝐾𝑗(V𝑖) =

{ { { { {

−𝜌 (V𝑖, V0𝑖𝑗)

󵄨󵄨󵄨󵄨

󵄨V0𝑖𝑗󵄨󵄨󵄨󵄨󵄨 , V𝑖∈ V0𝑖𝑗

𝜌 (V𝑖, V0𝑖𝑗)

𝜌 (V𝑖, V𝑝𝑗) − 𝜌 (V𝑖, V0𝑖𝑗), V𝑖∉ V0𝑖𝑗,

(10)

where𝐾𝑗(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 the𝑖th index related to the corresponding classical field,

𝜌 (V𝑖, V0𝑖𝑗) =󵄨󵄨󵄨󵄨󵄨󵄨󵄨V𝑖−1

2(𝑎0𝑖𝑗+ 𝑏0𝑖𝑗)󵄨󵄨󵄨󵄨󵄨󵄨󵄨 − 1

2(𝑏0𝑖𝑗− 𝑎0𝑖𝑗) (11)

|V0𝑖𝑗| represents the value range of classical field of the 𝑖th index related to the𝑗th level; 𝜌(V𝑖, V𝑝𝑗) represents the distance

of the matter-element to be evaluated of the𝑖th index related

to the controlled field,

𝜌 (V𝑖, V𝑝𝑗) =󵄨󵄨󵄨󵄨󵄨󵄨󵄨V𝑖−1

2(𝑎𝑝𝑖+ 𝑏𝑝𝑖)󵄨󵄨󵄨󵄨󵄨󵄨󵄨 − 1

2(𝑏𝑝𝑖− 𝑎𝑝𝑖) (12)

V𝑖 ∈ V0𝑖𝑗 indicates that the value of the𝑖th index is in the classical field of the𝑗th level

Step 4 (determine the index weight) Selecting the

appro-priate 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

Divide the evaluation index system to

Establish the classical field and controlled field

Establish the matter-element to be

evaluated

Establish the correlation function and calculate its value

Determine the index weight by using

AHP

Calculate the correlation degree and

rating

Build the hierarchical structure model

Construct the judgment matrix

Calculate the local weight and consistency test

Calculate the global weight

Conclude the grade level

Build the evaluation index system

be evaluated into j grades

Figure 3: Evaluation procedure of the proposed hybrid evaluation model

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

𝐾𝑗(𝑃0) =∑𝑛

𝑖=1

𝑤𝑖𝐾𝑗(V𝑖) , (13) where𝐾𝑗(𝑃0) is the correlation degree of the 𝑗th level, 𝑤𝑖is the

weight of the𝑖th 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 evaluated𝑃0 belonged to the𝑗∗th

level

Suppose

𝐾𝑗(𝑝0) = 𝐾𝑗(𝑝0) − min 𝐾𝑗(𝑝0)

max𝐾𝑗(𝑝0) − min 𝐾𝑗(𝑝0), (14)

where𝐾𝑗(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

𝑗∗= ∑

𝑚 𝑗=1𝑗𝐾𝑗(𝑝0)

∑𝑚𝑗=1𝐾𝑗(𝑝0), (15)

where𝑗∗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 from𝑗∗

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

Figure 3

3 Case Study

In this paper, a wind power engineering project in Inner

Mongolia city is taken as an example Firstly, the

evalu-ation 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

engineer-ing 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

bene-fit, social benebene-fit, and environmental benefit The external

economies evaluation index system is shown inFigure 4 Of

which, C1, C3, and C5 are qualitative indices, and the others

are quantitative indices All of the indices are the greatest-type

index

3.2 Divide the Index System to Be Evaluated into j 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 and𝑅05, controlled field𝑅𝑝, and the matter-element to be evaluated

𝑅0are as follows:

𝑅01=

[ [ [ [ [ [ [ [

𝑃01 𝑐1 (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=

[ [ [ [ [ [ [ [

𝑃02 𝑐1 (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=

[ [ [ [ [ [ [ [

𝑃03 𝑐1 (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=

[ [ [ [ [ [ [ [

𝑃04 𝑐1 (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=

[ [ [ [ [ [ [ [

𝑃05 𝑐1 (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%)

] ] ] ] ] ] ] ] ,

[ [ [ [ [ [ [ [

𝑃 𝑐1 (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=

[ [ [ [ [ [ [ [

𝑃0 𝑐1 6.91

𝑐2 87%

𝑐3 6.56

𝑐4 82%

𝑐5 6.2

𝑐6 89%

𝑐7 88%

𝑐8 91%

𝑐9 83%

𝑐10 74%

] ] ] ] ] ] ] ] ,

(16)

where𝑅01,𝑅02,𝑅03,𝑅04, and𝑅05represent the classical field;

𝑅𝑝represents the controlled field;𝑅0represents the

matter-element to be evaluated;𝑃01represents the extremely weak

external economies grade,𝑃02 represents weaker grade,𝑃03

represents general grade,𝑃04represents stronger grade, and

𝑃05represents 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 inTable 3

3.5 Determine the Index Weight

3.5.1 Build the Hierarchical Structure Model The AHP

hier-archical structure model for external economies evaluation

of wind power engineering project is shown inFigure 5 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

identi-fied 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

3.5.2 Construct the Judgment Matrix The pairwise

compar-ison 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 inTable 4

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 eigen-value 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 inTable 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 inTable 5

3.6 Calculate the Correlation Degree and Rating The

corre-lation degree value of each grade is as follows:

𝐾1(𝑃0) =∑10

𝑖=1

𝑤𝑖𝐾1(V𝑖) = −0.766,

𝐾2(𝑃0) =∑10

𝑖=1

𝑤𝑖𝐾2(V𝑖) = −0.688,

𝐾3(𝑃0) =∑10

𝑖=1

𝑤𝑖𝐾3(V𝑖) = −0.533,

𝐾4(𝑃0) =∑10

𝑖=1

𝑤𝑖𝐾4(V𝑖) = −0.146,

𝐾5(𝑃0) =∑10

𝑖=1

𝑤𝑖𝐾5(V𝑖) = 0.190

(17)

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 value 𝑗∗ 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, if𝑗∗ = 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 inFigure 6when the weights of external economies indices are changed by±0.1, ±0.2, ±0.3,

±0.4, ±0.5

External economies evaluation

of wind power project (A)

Economic benefit (B1)

Social benefit (B2)

Environmental benefit (B3)

The degree of

promoting the

sustainable

development

of power

industry

(C1)

The degree of

increasing

region GDP

(C2)

The degree of promoting scientific and technological innovation (C3)

The degree of land optimal utilization and value added in project area (C4)

The degree of improving region living standards (C5)

The degree of promoting employment levels (C6)

The degree of reducing pollution gas emissions (C7)

The degree of reducing smoke, industrial wastewater discharge (C8)

The degree of reducing the destruction

of terrestrial vegetation and marine ecosystems (C9)

The degree of energy conservation (C10)

Figure 4: External economies evaluation index system of wind power engineering project

Goal

Sub-criteria (index) Criteria

External economies evaluation of wind power engineering project

Economic benefit Social benefit Environmental benefit

Promoting the sustainable development of power industry

Increasing region GDP

Promoting scientific and technological innovation Land optimal utilization and value added in project area

Improving region living standards

Promoting employment levels

Reducing pollution gas emissions

Reducing smoke, industrial wastewater discharge Reducing the destruction of terrestrial vegetation and marine ecosystems

Energy conservation

Figure 5: Hierarchical structure of external economies evaluation of wind power engineering project

Table 3: The calculation result of correlation function value.

𝐾1(V𝑖) 𝐾2(V𝑖) 𝐾3(V𝑖) 𝐾4(V𝑖) 𝐾5(V𝑖)

Table 4: Pairwise comparison judgment matrices, local weight, and CR

Goal Economic benefit Social benefit Environmental benefit Weight

CR = 0.0012

CR = 0.0827

CR = 0.0000

CR = 0.0541

Table 5: The global weight of each index

Economic benefit (B1) 0.3140

Environmental benefit (B3) 0.5443

As we can see fromFigure 6, 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 inFigure 7when the index scoring

values are changed by±0.1, ±0.2, ±0.3, ±0.4, ±0.5

As we can see fromFigure 7, 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

4.25 4.27 4.29 4.31 4.33 4.35

0 0.1 0.2 0.3 0.4 0.5 Fluctuation value

C1 C2 C3 C4 C5

C6 C7 C8 C9 C10

−0.5 −0.4 −0.3 −0.2 −0.1

Figure 6: Sensitivity analysis result on the index weight

3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6

0 0.1 0.2 Fluctuation value

C1 C2 C3 C4 C5

C6 C7 C8 C9 C10

Figure 7: Sensitivity analysis result on the index scoring

and overcome the shortcomings and inadequacies resulting from the ambiguity and uncertainty inherent The external economies evaluation index system of wind power engi-neering project is constructed considering economic bene-fit, social benebene-fit, and environmental benefit The external economies evaluation method based on the AHP and matter-element extension model is also formulated Taking a wind