Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2013, Article ID 848901, 11 pages http://dx.doi.org/10.1155/2013/848901 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 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% 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 Mathematical Problems in Engineering 80000 60 50 60000 40 50000 40000 30 30000 20 The ratio (%) Installed capacity (MW) 70000 20000 10 2012 2011 2009 2010 2008 2007 2005 2006 2004 2003 2001 2002 2000 10000 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 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 matterelement extension model is put forward: AHP is used to determine the weights of the evaluation indices; the matterelement 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 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 concludes this paper The Hybrid Evaluation Model 2.1 Basic Theory of AHP for Determining the Weights of Evaluation Indices AHP is a practical multicriteria decisionmaking (MCDM) method combining qualitative and quantitative analysis, which is also a compact and efficient tool Mathematical Problems in Engineering 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): Goal ··· Criteria ··· Subcriteria (index) ··· ··· ··· 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 (build the hierarchical structure model) According to the overall goal and characteristic of multicriteria decisionmaking 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 Step (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): ⋅⋅⋅ ⋅⋅⋅ ⋅⋅⋅ ⋅⋅⋅ 𝑏1𝑛 𝑏2𝑛 ] ] ⋅ ⋅ ⋅] 𝑏𝑛𝑛 ] 𝑏𝑖𝑗 > 0, 𝑏𝑖𝑖 = 1, 𝑏𝑖𝑗 = 𝑏𝑗𝑖 (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 bij can be obtained by pairwise comparison using a standardized comparison scale of nine levels (see Table 1) Step (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 (𝜆 max ) as 𝐵𝑤 = 𝜆 max 𝑤 (𝜆 max − 𝑛) (𝑛 − 1) (4) The CI is CI = 𝑏12 𝑏22 ⋅⋅⋅ 𝑏𝑛2 (3) ··· Figure 2: The hierarchical structure model of AHP for determining the index weight 𝑏11 [𝑏21 𝐵=[ [⋅ ⋅ ⋅ [𝑏𝑛1 CI RI CR = ··· ··· (2) 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 of 𝐵 : 𝑏𝑖𝑗 ×𝑏𝑗𝑘 = 𝑏𝑖𝑘 That is, if 𝑏𝑖𝑗 represents the importance of index 𝑖 over index 𝑗 The value of RI is listed in Table 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 (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 ∑𝑤𝑖 = (5) 𝑖=1 2.2 Basic Theory of Matter-Element Extension Model Matterelement extension model is a formalized model which studies extension possibility and extension law of things Matterelement extension model is composed of objects, characteristics, and values based on certain characteristics Things in the name of 𝑃, characteristics c, and value v are 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 object 𝑃 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 𝑃 𝑅1 [𝑅2 ] [ ] [ [ 𝑅 = (𝑃, 𝐶, 𝑉) = [ ] = [ ⋅⋅⋅ 𝑅 [ 𝑛] [ 𝑐1 𝑐2 ⋅⋅⋅ 𝑐𝑛 V1 V2 ] ], ⋅ ⋅ ⋅] V𝑛 ] (6) 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 4 Mathematical Problems in Engineering Table 1: Nine-point comparison scale Scale of importance 2, 4, 6, Definition Equally important Moderately more important Strongly more important Very strongly more important Extremely more important Intermediate value Explanation Two elements contribute equally One element is slightly favoured over another One element is strongly favoured over another An element is very strongly favoured over another One element is most favoured over another Adjacent to the two odd number scales Table 2: Random index (RI) Size (n) RI 0.58 0.9 1.12 1.24 1.32 Matrix 1.41 Step (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 [ 𝑐2 =[ [ ⋅⋅⋅ 𝑐𝑛 [ 𝑃0𝑗 V01𝑗 [ V02𝑗 ] [ ]=[ ⋅⋅⋅ ] [ V0𝑛𝑗 ] [ 𝑐1 ⟨𝑎01𝑗 , 𝑏01𝑗 ⟩ ] 𝑐2 ⟨𝑎02𝑗 , 𝑏02𝑗 ⟩] ], ] ⋅⋅⋅ ⋅⋅⋅ 𝑐𝑛 ⟨𝑎0𝑛𝑗 , 𝑏0𝑛𝑗 ⟩ ] (7) 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 𝑃 𝑐1 𝑐2 ⋅⋅⋅ [ 𝑐𝑛 [ 𝑅𝑝 = (𝑃, 𝐶, 𝑉𝑝 ) = [ [ V𝑝1 V𝑝2 ] ] ⋅ ⋅ ⋅] V𝑝𝑛 ] 𝑃 𝑐1 ⟨𝑎𝑝1 , 𝑏𝑝1 ⟩ ] [ [ 𝑐2 ⟨𝑎𝑝2 , 𝑏𝑝2 ⟩] =[ ], [ ⋅⋅⋅ ⋅⋅⋅ ] [ 𝑐𝑛 ⟨𝑎𝑝𝑛 , 𝑏𝑝𝑛 ⟩] (8) Step (determine the matter-element to be evaluated) Suppose the matter-element to be evaluated as V1 V2 ] ], ⋅ ⋅ ⋅] V𝑛 ] 10 1.49 11 1.51 12 1.54 13 1.56 14 1.57 15 1.58 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 (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 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 𝜌 (V𝑖 , V0𝑖𝑗 ) { { { V𝑖 ∈ V0𝑖𝑗 − , { { V0𝑖𝑗 { 𝐾𝑗 (V𝑖 ) = { { 𝜌 (V𝑖 , V0𝑖𝑗 ) { { { , V𝑖 ∉ V0𝑖𝑗 , { 𝜌 (V , V ) − 𝜌 (V , V ) 𝑖 𝑝𝑗 𝑖 0𝑖𝑗 { (10) 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, 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 𝑃 𝑐1 [ 𝑐2 𝑅0 = (𝑃0 , 𝐶, 𝑉) = [ [ ⋅⋅⋅ [ 𝑐𝑛 1.45 (9) 1 𝜌 (V𝑖 , V0𝑖𝑗 ) = V𝑖 − (𝑎0𝑖𝑗 + 𝑏0𝑖𝑗 ) − (𝑏0𝑖𝑗 − 𝑎0𝑖𝑗 ) (11) |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, 1 𝜌 (V𝑖 , V𝑝𝑗 ) = V𝑖 − (𝑎𝑝𝑖 + 𝑏𝑝𝑖 ) − (𝑏𝑝𝑖 − 𝑎𝑝𝑖 ) (12) V𝑖 ∈ V0𝑖𝑗 indicates that the value of the 𝑖th index is in the classical field of the 𝑗th level Step (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 Mathematical Problems in Engineering Build the evaluation index system Divide the evaluation index system to be evaluated into j grades Establish the classical field and controlled field Build the hierarchical structure model Establish the matter-element to be evaluated Construct the judgment matrix Establish the correlation function and calculate its value Calculate the local weight and consistency test Determine the index weight by using AHP Calculate the global weight Calculate the correlation degree and rating Conclude the grade level 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 (calculate the correlation degree and rating) The correlation degree of the matter-element to be evaluated with all grades is calculated by 𝑛 𝐾𝑗 (𝑃0 ) = ∑𝑤𝑖 𝐾𝑗 (V𝑖 ) , (13) where 𝐾𝑗 (𝑃0 ) represents the correlation degree of the jth level; 𝐾𝑗 (𝑝0 ) represents the minimum of correlation degrees in all levels; max 𝐾𝑗 (𝑝0 ) represents the maximum of correlation degrees in all levels; 𝑗 = 1, 2, , 𝑚 Consider 𝑗∗ = ∑𝑚 𝑗=1 𝑗𝐾𝑗 (𝑝0 ) ∑𝑚 𝑗=1 𝐾𝑗 (𝑝0 ) , (15) 𝑖=1 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 Suppose 𝐾𝑗∗ (𝑃0 ) = max{𝐾𝑗 (𝑃 )}(𝑗 = 1, 2, , 𝑚); then the matter-element to be evaluated 𝑃0 belonged to the 𝑗∗ th level Suppose 𝐾𝑗 (𝑝0 ) = 𝐾𝑗 (𝑝0 ) − 𝐾𝑗 (𝑝0 ) max 𝐾𝑗 (𝑝0 ) − 𝐾𝑗 (𝑝0 ) , (14) 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 Figure 6 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 Figure 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 Mathematical Problems in Engineering The values of classical fields 𝑅01 , 𝑅02 , 𝑅03 , 𝑅04 and 𝑅05 , controlled field 𝑅𝑝 , and the matter-element to be evaluated 𝑅0 are as follows: 𝑃02 𝑐1 𝑐2 𝑐3 𝑐4 𝑐5 𝑐6 𝑐7 𝑐8 𝑐9 𝑐10 [ (2, 4) (20%, 40%)] ] (2, 4) ] ] (20%, 40%)] ] (2, 4) ] ], (20%, 40%)] (20%, 40%)] ] (20%, 40%)] ] (20%, 40%)] (20%, 40%)] 𝑃03 𝑐1 𝑐2 𝑐3 𝑐4 𝑐5 𝑐6 𝑐7 𝑐8 𝑐9 𝑐10 [ (4, 6) (40%, 60%)] ] (4, 6) ] ] (40%, 60%)] ] (4, 6) ] ], (40%, 60%)] (40%, 60%)] ] (40%, 60%)] ] (40%, 60%)] (40%, 60%)] 𝑃04 𝑐1 𝑐2 𝑐3 𝑐4 𝑐5 𝑐6 𝑐7 𝑐8 𝑐9 𝑐10 [ (6, 8) (60%, 80%)] ] (6, 8) ] ] (60%, 80%)] ] (6, 8) ] ], (60%, 80%)] (60%, 80%)] ] (60%, 80%)] ] (60%, 80%)] (60%, 80%)] 𝑃05 𝑐1 𝑐2 𝑐3 𝑐4 𝑐5 𝑐6 𝑐7 𝑐8 𝑐9 𝑐10 [ (8, 10) (80%, 100%)] ] (8, 10) ] ] (80%, 100%)] ] (8, 10) ] ], (80%, 100%)] (80%, 100%)] ] (80%, 100%)] ] (80%, 100%)] (80%, 100%)] 𝑅02 [ [ [ [ [ [ [ =[ [ [ [ [ [ [ 𝑅03 [ [ [ [ [ [ [ =[ [ [ [ [ [ [ 𝑅04 [ [ [ [ [ [ [ =[ [ [ [ [ [ [ 𝑅05 [ [ [ [ [ [ [ =[ [ [ [ [ [ [ 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 evaluated 𝑅0 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 (0, 2) (0%, 20%)] ] (0, 2) ] ] (0%, 20%)] ] (0, 2) ] ], (0%, 20%)] (0%, 20%)] ] (0%, 20%)] ] (0%, 20%)] (0%, 20%)] 𝑅01 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% 𝑃01 𝑐1 𝑐2 𝑐3 𝑐4 𝑐5 𝑐6 𝑐7 𝑐8 𝑐9 𝑐10 [ [ [ [ [ [ [ [ =[ [ [ [ [ [ [ Mathematical Problems in Engineering 𝑃 [ [ [ [ [ [ [ 𝑅𝑝 = [ [ [ [ [ [ [ [ 𝑐1 𝑐2 𝑐3 𝑐4 𝑐5 𝑐6 𝑐7 𝑐8 𝑐9 𝑐10 𝑃0 𝑐1 𝑐2 𝑐3 𝑐4 𝑐5 𝑐6 𝑐7 𝑐8 𝑐9 𝑐10 [ [ [ [ [ [ [ [ 𝑅0 = [ [ [ [ [ [ [ (0, 10) (0%, 100%)] ] (0, 10) ] ] (0%, 100%)] ] (0, 10) ] ], (0%, 100%)] (0%, 100%)] ] (0%, 100%)] ] (0%, 100%)] (0%, 100%)] 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 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 6.91 87%] ] 6.56] ] 82%] ] 6.2 ] , 89%] ] ] 88%] 91%] ] 83%] 74%] 3.5.4 Calculating the Global Weight By calculation, the global weight of each index is listed in Table 3.6 Calculate the Correlation Degree and Rating The correlation degree value of each grade is as follows: 10 (16) 𝐾1 (𝑃0 ) = ∑𝑤𝑖 𝐾1 (V𝑖 ) = −0.766, 𝑖=1 10 where 𝑅01 , 𝑅02 , 𝑅03 , 𝑅04 , and 𝑅05 represent the classical field; 𝑅𝑝 represents the controlled field; 𝑅0 represents the matterelement 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 𝐾2 (𝑃0 ) = ∑𝑤𝑖 𝐾2 (V𝑖 ) = −0.688, 𝑖=1 10 𝐾3 (𝑃0 ) = ∑𝑤𝑖 𝐾3 (V𝑖 ) = −0.533, (17) 𝑖=1 10 𝐾4 (𝑃0 ) = ∑𝑤𝑖 𝐾4 (V𝑖 ) = −0.146, 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 𝑖=1 10 𝐾5 (𝑃0 ) = ∑𝑤𝑖 𝐾5 (V𝑖 ) = 0.190 𝑖=1 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 Figure 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 indices, indices, and indices, respectively 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 Table Since 𝐾5 (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, 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 Figure when the weights of external economies indices are changed by ±0.1, ±0.2, ±0.3, ±0.4, ±0.5 8 Mathematical Problems in Engineering External economies evaluation of wind power project (A) Social benefit (B2) Economic benefit (B1) Environmental benefit (B3) The degree of The degree of The degree of The degree of reducing promoting the The degree of promoting land optimal The degree of The degree of The degree of utilization improving promoting smoke, sustainable reducing increasing scientific and and value region living employment pollution gas industrial development region GDP technological added in standards levels wastewater of power innovation project area (C2) emissions (C5) (C6) discharge industry (C3) (C7) (C4) (C8) (C1) The degree of reducing the destruction The degree of energy of terrestrial vegetation conservation and marine (C10) ecosystems (C9) Figure 4: External economies evaluation index system of wind power engineering project External economies evaluation of wind power engineering project Goal Criteria Economic benefit Promoting the sustainable development of power industry Sub-criteria (index) Increasing region GDP Social benefit Improving region living standards Promoting employment levels Environmental benefit Reducing pollution gas emissions Reducing smoke, industrial wastewater discharge Promoting scientific and technological innovation Reducing the destruction of terrestrial vegetation and marine ecosystems Land optimal utilization and value added in project area Energy conservation Figure 5: Hierarchical structure of external economies evaluation of wind power engineering project Mathematical Problems in Engineering Table 3: The calculation result of correlation function value Index C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 Extremely weak 𝐾1 (V𝑖 ) −0.61375 −0.8375 −0.57 −0.775 −0.525 −0.8625 −0.85 −0.8875 −0.7875 −0.675 Weaker 𝐾2 (V𝑖 ) −0.485 −0.78333 −0.42667 −0.7 −0.36667 −0.81667 −0.8 −0.85 −0.71667 −0.56667 General 𝐾3 (V𝑖 ) −0.2275 −0.675 −0.14 −0.55 −0.05 −0.725 −0.7 −0.775 −0.575 −0.35 Stronger 𝐾4 (V𝑖 ) 0.455 −0.35 0.28 −0.1 0.1 −0.45 −0.4 −0.55 −0.15 0.3 Strongest 𝐾5 (V𝑖 ) −0.26077 0.35 −0.29508 0.1 −0.32143 0.45 0.4 0.45 0.15 0.010256 Table 4: Pairwise comparison judgment matrices, local weight, and CR Goal Economic benefit Social benefit Environmental benefit Economic benefit C1 C2 C3 C4 Economic benefit 1.0000 0.4348 1.8000 C1 1.0000 2.4000 0.5263 0.3125 Social benefit C5 C6 Environmental benefit C7 C8 C9 C10 Social benefit 2.3000 1.0000 3.7000 C2 0.4167 1.0000 0.2564 0.1754 C3 1.9000 3.9000 1.0000 0.7143 C5 1.0000 0.7692 C7 1.0000 0.3125 0.2857 0.7143 Environmental benefit 0.5556 0.2703 1.0000 C4 3.2000 5.7000 1.4000 1.0000 C6 1.3000 1.0000 C8 3.2000 1.0000 0.6667 2.3000 C9 3.5000 1.5000 1.0000 2.6000 C10 1.4000 0.4348 0.3846 1.0000 Weight 0.3140 0.1417 0.5443 CR = 0.0012 Local weight 0.2257 0.6232 0.0950 0.0561 CR = 0.0827 Local weight 0.5436 0.4564 CR = 0.0000 Local weight 0.4877 0.1147 0.0815 0.3161 CR = 0.0541 Table 5: The global weight of each index Criteria Weight Economic benefit (B1) 0.3140 Social benefit (B2) 0.1417 Environmental benefit (B3) 0.5443 Index C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 Local weight 0.2257 0.6232 0.0950 0.0561 0.5436 0.4564 0.4877 0.1147 0.0815 0.3161 Global weight 0.071 0.196 0.030 0.018 0.077 0.065 0.265 0.062 0.044 0.172 10 Mathematical Problems in Engineering As we can see from Figure 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 j∗ 4.33 4.31 4.29 4.27 4.25 −0.5 −0.4 −0.3 −0.2 −0.1 0.1 0.2 Fluctuation value C1 C2 C3 C4 C5 0.3 0.4 0.5 C6 C7 C8 C9 C10 Figure 6: Sensitivity analysis result on the index weight 4.6 4.5 4.4 4.3 4.2 j∗ 3.7.2 Sensitivity Analysis on the Index Scoring The sensitivity analysis result is shown in Figure when the index scoring values are changed by ±0.1, ±0.2, ±0.3, ±0.4, ±0.5 As we can see from Figure 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 4.35 4.1 3.9 3.8 3.7 −0.5 −0.4 −0.3 −0.2 −0.1 3.6 0.1 0.2 Fluctuation value 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 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 engineering project is constructed considering economic benefit, social benefit, and environmental benefit The external economies evaluation method based on the AHP and matterelement extension model is also formulated Taking a wind Mathematical Problems in Engineering 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 Acknowledgments This study is supported by the Beijing Philosophy and Social Science Planning Project (Project no.11JGB070) and Coconstruction Project of Beijing Municipal Supporting Central University Located in Beijing The authors are grateful to the editor and anonymous reviewers for their suggestions in improving the quality of the paper References [1] M Tăukenmez and E Demireli, “Renewable energy policy in Turkey with the new legal regulations,” Renewable Energy, vol 39, no 1, pp 1–9, 2012 [2] X J Sun, D G Huang, and 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