# Performance evaluation for sustainability of wind energy project using improved multi-criteria decision-making method

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## Abstract

Wind power can be an efficient way to alleviate energy shortage and environmental pollution, and to realize sustainable development in terms of energy generation. The sustainability assessment of a wind project among its alternatives is a complex task that cannot be solely simplified to environmental or economic feasibility. It requires the consideration of its technological and social aspects as well as other circumstances. This paper proposes a new method for selecting the most sustainable wind projects. The method is based on multi-criteria decision-making techniques. The analytic hierarchy process and entropy weight method are combined to determine the weights of evaluation indexes, and an innovative index-weight optimization method based on the Lagrange conditional extremum algorithm. The fuzzy technique for order preference by similarity to the ideal solution is applied to rank wind project alternatives considering functionality and proportionality of the system. Moreover, the sensitive analysis is applied to verify the robustness of the proposed method. The applicability of the method is demonstrated on a case study from China, where three main wind projects are analytically compared and ranked. The results indicated that the sustainable level of calculated wind power can provide a reference point for the planning and operation of the wind project. The results show that the proposed method is of both theoretical significance and practical application in engineering.

## Keywords

Analytic hierarchy process Comprehensive evaluation index Entropy method Fuzzy technique Order preference Wind power sustainability level## 1 Introduction

The rapid development of the world economy brings potential problems of energy and environment such as global environmental deterioration, shortage of traditional energy resources, and climate change. The growing demand and use of coal, oil, natural gas, and other traditional energy sources, which are unsustainable energies, have generated concerns regarding serious environmental pollution. Given the negative externalities of traditional energy generation activities, the construction and operation of wind energy represent a strategic method to realize sustainable development. Furthermore, wind power would be an important platform for energy supply and plays a leading role in de-carbonization in the near future. However, generating power on a mainstream basis assumes new responsibilities such as the insurance of a reliable and cost-effective functioning of the overall energy system and its contribution to energy security. This becomes problematic because wind power, by nature, is characterized by stochastic fluctuation, which affects the stability of the original power grid and restricts the sustainable development of the renewable energy [1]. Other challenges have been linked to the feed-in tariff (FIT), which is an increasing burden on Chinese government [2] due to the rapid development of wind power. As a result, the development of funding solutions to finance the FIT has increased, thereby resulting in pressure on the renewable industry to lower its costs. A combination of all these challenges may result in a waste of wind resources, an economic deficit on wind projects, and may hinder the sustainable development of wind energy.

“Sustainability” can be described as the endurance of systems and processes. The organizing principle for sustainability is sustainable development, which includes four pillars: technological development, economic growth, social development and environmental protection. Identifying the most sustainable wind project can minimize the use of traditional coal resources, alleviate environmental burdens, and simultaneously contribute to the local economy and increase employment. Currently, studies related to the sustainability of renewable energy resources (RES) to evaluate the power grid have been conducted. Reference [3] evaluated clean energy options for Algerian by applying 13 sub-criteria, of which solar photovoltaic was ranked as the first, followed by wind, biomass, geothermal, and lastly hydropower. Reference [4] provided an empirical evaluation of FIT and the renewable portfolio standard policies that were applied to onshore wind power, of which only FIT policies were suggested to exhibit significant impacts on the installed capacity. The aforementioned studies examined the sustainability of different kinds of renewables, or the partial sustainable characters of wind energy such as wind energy policies. The comprehensive evaluation of sustainable wind energy levels has not been reported. Many wind projects face related difficulties such as ecological harm, construction delays, and economic unprofitability. To better manage these issues, wind projects must be evaluated with sustainability dimensions and structured approaches. The present study performed well-rounded research to measure the sustainability of wind projects in consideration of multiple aspects to serve as an important topic for the sustainable development of wind projects and to fulfill the current research gap.

This paper examines the sustainable performance of wind generation projects as a multi-criteria decision-making (MCDM) problem. The primary MCDM analysis step is the calculation of weights for the various indicators, which includes subjective weighting methods and objective weighting methods. Objective weighting methods emphasize the differences between indices, whereas subjective weighting methods can provide an absolute measure of importance. However, most studies only employ either subjective or objective methods to determine the weights. For example, a comprehensive assessment method that considers voltage and power losses was presented, wherein the weights were determined only by objective judgment [5]. In another case [6], only a subjective methodology combining the analytic hierarchy process (AHP) method and expert feedback was employed to evaluate different renewable energy options. In response to the limitations of subjective and objective weighting methods, both methods were ideally employed in proportion to their designated importance.

Under these circumstances, this paper aims to propose a sustainable level evaluation model for wind generation projects as a decision support tool for scholars and investors with the intention of integrating different sustainable wind project indexes in a multi-index system using the MCDM method. To address the limitations of subjective and objective weighting methods, this paper presents an index weighting optimization method that combines both subjective and objective weighting methods in proportion to their designated importance by using the Lagrange conditional extremum algorithm (LCEA). Lastly, the fuzzy technique for order preference by similarity to the ideal solution (TOPSIS) method is employed to provide a reasonable ranking of the results. This method fully employs existing information to enhance the objectivity of the ranking results.

## 2 Establish index systems

### 2.1 Identification of evaluation indexes and hierarchy

As shown in Fig. 1, the overall target is situated at the first level of the proposed hierarchy *A*. In the second level, the sub-target criteria are denoted as **P**_{1}, **P**_{2}, **P**_{3}, **P**_{4}, and **P**_{5}. The indexes in the 3rd level are listed as *X*_{1}, *X*_{2}, …, *X*_{16}, where **P**_{1} = {*X*_{1}, *X*_{2}, *X*_{3}, *X*_{4}}, **P**_{2} = {*X*_{5}, *X*_{6}, *X*_{7}, *X*_{8}}, **P**_{3} = {*X*_{9}, *X*_{10}}, **P**_{4} = {*X*_{11}, *X*_{12}, *X*_{13}}, and **P**_{5} = {*X*_{14}, *X*_{15}, *X*_{16}}.

### 2.2 Wind technological competitiveness

- 1)
*X*_{1}refers to the total installed capacity of wind farms. - 2)
*X*_{2}refers to the wind power generated over a year, which can be calculated by:where$$W = P_{\rm m} \times 8760$$(1)*P*_{m}is the total active power of wind farms. - 3)
*X*_{3}measures the capacity hours of wind equipment under full load operating conditions for a certain period of time, which is defined as (2), and*P*_{gen}represents the generating capacity and*P*_{ins}is the installed capacity:$$X_{3} = \frac{{P_{gen} }}{{P_{ins} }}$$(2) - 4)
*X*_{4}refers to the outage hours which may be caused by turbine faults, unnecessary repairs and maintenance, etc.

### 2.3 Wind resource profits

- 1)
*X*_{5}refers to the average instantaneous wind speed over a year. - 2)
*X*_{6}refers to the hours of speed higher than 3 m/s over a year. - 3)
*X*_{7}refers to the available resource of raw wind power, which can be calculated according to the following equation:where$$X_{7} = \frac{1}{2}\rho v^{3}$$(3)*v*is the wind speed and*ρ*is the air density. - 4)
*X*_{8}is crucial for wind turbine structure design and aerodynamic loads calculation. Besides the impact on power output, turbulence intensity imposes significant aerodynamic loads on wind turbines. Turbulence intensity is defined as the ratio of the standard deviation of wind speed*V*_{δ}to the mean wind speed of 10 minutes \(\bar{V}_{10}\):$$X_{8} = {{V_{\delta } } \mathord{\left/ {\vphantom {{V_{\delta } } {\bar{V}_{10} }}} \right. \kern-0pt} {\bar{V}_{10} }}$$(4)where$$V_{\delta } = \sqrt {\frac{1}{N}\sum\limits_{i = 1}^{N} {\left( {v_{i} - \overline{v} } \right)^{2} } }$$(5)*v*_{i}is*i*^{th}criteria group of wind speed sample; \(\bar{v}\) is the mean wind speed; and*N*is the total number of wind speed samples. The grading standard of the above indexes can be seen in Table 1.Table 1Grading standard of wind resource index

Wind environment index

Annual mean wind speed (m/s)

Effective wind speed time (hour)

Wind power density (W/m

^{2})Turbulence intensity

Abundant region

6.91

> 5000

> 200

< 0.1

Less abundant region

6.91–6.28

4000–5000

150–200

0.1–0.2

Available region

< 6.28–4.36

2000–4000

< 50–150

0.2–0.3

Not abundant region

< 4.36

< 2000

< 50

> 0.3

### 2.4 Environmental profits for wind project

_{2}, SO

_{2}; ➁ NO

_{x}and unit per environmental profits [9].

- 1)
*X*_{9}refers to the amount of waste such as CO_{2}, SO_{2}, and NO_{x}in tons produced by the thermal plant divided by the energy produced in lifetime. - 2)
*X*_{10}depends on the decrease of pollution from thermal power plants. The degree of pollution of thermal power is related to coal quality, boiler combustion and power generation technology. Taking the environmental profits of a wind project with a capacity of 100000 kW and an annual power generation of 2.3 billion kWh as an example, this project could save 87400 tons of standard coal, which is equal to 180000 tons raw coal. It could also reduce the emission of soot, ash residua, SO_{2}, oxynitride and CO_{2}by 1150 tons, 27600 tons, 1403 tons, 1035 tons, 265000 tons, respectively. If 1 kWh wind energy can avoid 0.18 RMB pollution cost, the environmental profit for 1000 MW wind energy would be 40 million RMB yearly.

### 2.5 Economic benefits for wind project

- 1)
*X*_{11}includes the maintenance cost, installation cost, capital cost, operation cost, replacement cost, and the interest rate over the project lifetime. - 2)
*X*_{12}presents the value of the expected cash inflows of the wind project minus the costs of acquiring the project. This is one of the most commonly used financial techniques in performing an economic evaluation of a project. - 3)
*X*_{13}is also one of the most important financial techniques, which is defined as (6), and*N*_{profit}is net profit,*N*_{worth}is net worth:$$X_{13} = \frac{{N_{profit} }}{{N_{worth} }}$$(6)

### 2.6 Social benefits for wind project

- 1)
*X*_{14}refers to the increase in direct and indirect employment opportunities as a result of wind energy production and use in lifetime. - 2)
*X*_{15}includes the paid hours per kWh produced in lifetime. - 3)
*X*_{16}includes the total capital fund of wind power project per kWh produced in lifetime.

## 3 Comprehensive weight calculation

MCDM provides a comprehensive and reasonable evaluation of the wind power system based on multiple parameters that have a variety of attributes or have overall characteristics that are influenced by many factors [12]. As discussed, the core step of the MCDM analysis is appropriate calculation of weights for the selected indicators.

Firstly, the entropy weight (EW) method was applied to render an objective weighting value for each index. Secondly, AHP was employed to revise the objective weighting and fulfill a comprehensive weighting evaluation. The application of AHP can mitigate the interference caused by the objective factors in the assessment process. An index weight optimization method based on LCEA was then proposed to calculate the reasonable proportions of the weighting provided by AHP and EW, which then provides a comprehensive weighting value for each index.

### 3.1 Objective weight calculation based on EW

*Step 1*: Calculate the probability of the indices for the preparation of the EW method.

*:*

**X***x*

_{ij}is the observed value of the

*j*

^{th}alternative for the

*i*

^{th}index,

*x*

_{ij}> 0. The probability of

*x*

_{ij}is defined as:

*Step 2*: Calculate the entropy value.

*x*

_{ij}is defined as:

*Step 3*: Calculate discrimination factor.

*x*

_{ij}is defined as:

*Step 4*: Calculate the objective weight based on EW method.

**q**_{objective}is defined as:

*q*

_{ij}is the objective weight value of

*q*

_{objective}matrix.

Note that the amount of information that can be provided by an index increases with decreasing entropy. Thus, the index has greater importance and a correspondingly greater objective weight.

### 3.2 Calculation of subjective weights based on AHP

*Step 1*: Structure a decision problem and articulate preferences over indices for the preparation of AHP.

AHP is based on three principles: first, the structure of a model is established; a comparative judgment of the alternatives and indices is then generated; and third, syntheses of the priorities are calculated. For the subjective weighting operation, the power grid experts selected options from the fundamental ranking criteria established according to [13], which is employed to simplify the representation of the degree of expert-chosen preferences to rank the indices.

*Step 2*: Construct an evaluation matrix.

*:*

**A***a*

_{ij}represents the individual preference of the experts according to the relative importance of the two indices based on [13]. Here,

*a*

_{ij}> 0,

*a*

_{ii}= 1, and

*a*

_{ji}= 1/

*a*

_{ij}.

*Step 3*: Derive subjective weights.

*into a vector of subjective weights that can be attached to multiple outcomes. The vector of the subjective weights*

**A***p*

_{ij}belonging to

*x*

_{ij}can be obtained from

*by the eigenvector method.*

**A**

**p**_{subjective}is the eigenvector corresponding to the maximal eigenvalue

*λ*

_{max}of

*.*

**A***Step 4*: Check the consistency.

*C*

_{R}is defined as:

The consistency is defined by the relation among the entries of * A*: \(a_{ij} a_{jk} = a_{ik}\); and

*γ*is the random consistency index. The values of

*γ*are based on [13] for different values of

*k*. If

*C*

_{R}< 0.1,

*is deemed acceptable. Otherwise,*

**A***is considered inconsistent, and matrix*

**A***must be reviewed and improved until*

**A***C*

_{R}< 0.1.

### 3.3 Comprehensive weight calculation based on LCEA

*p*

_{ij}and

*q*

_{ij}are the subjective and objective weights values of

**p**_{subjective}and

**q**_{objective}matrixes, respectively, thereby defining the comprehensive weight as:

*ω*

_{ij}is the value of comprehensive weight matrix, \(k_{i}^{\left( 1 \right)}\) and \(k_{i}^{\left( 2 \right)}\) are constants that satisfy the conditions \(k_{i}^{\left( 1 \right)} > 0,k_{i}^{\left( 2 \right)} > 0\), and \(\left( {k_{i}^{\left( 1 \right)} } \right)^{2} + \left( {k_{i}^{\left( 2 \right)} } \right)^{2} = 1\). The comprehensive values

*y*

_{i}in (16) are defined by applying additive method:

*y*

_{i}. Meanwhile, the weights of indexes actually belong to random variable, which can be described as the sum of the mean value and the random error. The deviation

*ε*

_{i}of

*y*

_{i}based on minimum deviation is defined as:

*λ*is the balance coefficient. The function of

*λ*is to balance the sum of the comprehensive values

*y*

_{i}and deviation values

*ε*

_{i}. These two parts are making identical contribution to (19). Thus, the value of

*λ*is usually defined as 0.5 [14]. According to the above stated conditions for \(k_{i}^{\left( 1 \right)}\) and \(k_{i}^{\left( 2 \right)}\), the LCEA is defined as:

*μ*is the undetermined coefficient of constraints which can be calculated by partial derivatives of the LCEA, when

*μ*is set to zero. Then, the partial derivatives of the LCEA with respect to \(k_{i}^{\left( 1 \right)} ,k_{i}^{\left( 2 \right)}\), and

*μ*are set to zero, as in (21).

*n*+ 1 sub-equations with a total number of 3

*n*+ 1 variables which can be solved by MATLAB, then we can obtain the values of \(k_{i}^{\left( 1 \right)}\) and \(k_{i}^{\left( 2 \right)}\). Substitute \(k_{i}^{\left( 1 \right)}\) and \(k_{i}^{\left( 2 \right)}\) into (15), then we can obtain comprehensive weights \(\varvec{\omega}_{com}\).

### 3.4 Comprehensive evaluation of fuzzy TOPSIS algorithm

Once the index weights are calculated, the wind project assessment can be used to compare wind projects and identify the most sustainable wind project with the help of fuzzy TOPSIS. The fuzzy set theory solves the problems like uncertain and imprecise evaluation data, thereby upgrading the conventional TOPSIS method. The fuzzy TOPSIS algorithm is proposed by combining the fuzzy set theory and the TOPSIS method to evaluate alternatives by calculating the geometric distances from the benefit and cost ideal solutions. The specific steps of fuzzy TOPSIS are presented as follows:

*Step 1*: Normalize the initial index system.

*X*

_{1}is kW while the unit of

*X*

_{2}is kWh. And the magnitude order of

*X*

_{1}and

*X*

_{2}also differs. It is thus not fair to compare different kinds of magnitude order of indexes, because those with the largest values would determine the final results. Therefore, the vector norm method was employed to make the indexes dimensionless and to assign each index a comprehensive weight, ultimately allowing them to determine the final results. The dimensionless value of

*x*

_{ij}is defined as:

*i*= 1, 2, …,

*n*;

*j*= 1, 2, …,

*m*;

*x*

_{ij}≥ 0,

*x*

_{ij}∈(0, 1); and \(\sum\limits_{i = 1}^{n} {\left( {x_{{_{ij} }}^{ * } } \right)^{2} } = 1\). For the benefit-type index, \(x_{ij}^{*} = {{x_{ij} } \mathord{\left/ {\vphantom {{x_{ij} } {\sqrt {\sum\limits_{i = 1}^{n} {x_{ij}^{2} } } }}} \right. \kern-0pt} {\sqrt {\sum\limits_{i = 1}^{n} {x_{ij}^{2} } } }}\) was employed to normalize the initial index, whereas \(x_{ij}^{*} = {{\sqrt {\sum\limits_{i = 1}^{n} {x_{ij}^{2} } } } \mathord{\left/ {\vphantom {{\sqrt {\sum\limits_{i = 1}^{n} {x_{ij}^{2} } } } {x_{ij} }}} \right. \kern-0pt} {x_{ij} }}\) was employed to normalize the cost-type index.

*Step 2*: Aggregate the fuzzy sets for indexes of all alternatives.

*V*= {

*V*

^{L},

*V*

^{M},

*V*

^{H}}. The membership function \(r_{ij} \left( {\tilde{x}_{ij} } \right)\) of a TFN is expressed as:

*V*

^{L},

*V*

^{M}, and

*V*

^{H}are precise numbers, where

*V*

^{L}<

*V*

^{M}<

*V*

^{H}, and

*V*

^{L}and

*V*

^{H}are the available bounds for the evaluation of the criteria uncertainty. The criteria performance is determined with the linguistic terms obtained from the decision makers. The fuzzy decision matrix

*for \(r_{ij} = \{ r_{ij}^{L} ,r_{ij}^{M} ,r_{ij}^{H} \}\) is defined as follows, where \(r_{ij}^{L} ,r_{ij}^{M},\,{\text{and}}\,r_{ij}^{H}\) are the values of matrix*

**R***, and \(r_{ij}^{L} < r_{ij}^{M} < r_{ij}^{H}\).*

**R***Step 3*: Structure the weighted normalized fuzzy decision matrix.

*was constructed by multiplying the fuzzy decision matrix*

**Y***with the weights of criteria as:*

**R***Step 4*: Determine the two types of ideal solutions.

*Y*

^{+}and the cost ideal solution

*Y*

^{−}, which can be computed by (26) and (27), respectively, where

*J*is a benefit criterion while \(\varvec{{J}^{'}}\) is a cost criterion.

*Step 5*: Calculate the distances of each alternative from the two types of ideal solutions.

*Y*

^{+}and

*Y*

^{−}can be obtained based on (28) and (29):

*Step 6*: Calculate the closeness coefficients of all alternatives.

*C*

_{i}can be employed to reflect the distance closest to \(D_{i}^{ + }\) as well as \(D_{i}^{ - }\), which can be computed by:

*C*

_{i}≤ 1 and higher values of

*C*

_{i}result in a better design performance. The values of

*C*

_{i}can be ranked to obtain the final results.

## 4 Experimental applications and analysis

### 4.1 Experimental setup

The proposed method is designed and tested in line with the actual operation of a power grid in Hami City, China. Hami, which is a mainland city, not only has an abundance of wind energy resources but also exhibits multi-level voltage and high penetration of wind power, thereby rendering it ideal for demonstrating the proposed method. To promote the sustainable development and management of the wind power projects and make the utmost use of the wind resource, the sustainability of different regional wind projects of the Hami grid must be assessed and ranked. The tested power system structure exhibits a total wind capacity of 4885.2 MW, and uses 220 kV lines to connect to 750 kV transformer substations.

Parameters of test system

Index | A | B | C |
---|---|---|---|

| 2641.1 | 440.9 | 1803.2 |

| 127235.2 | 74511.6 | 176430.4 |

| 6230 | 6486 | 5763 |

| 197 | 172 | 185 |

| 5.2 | 6.1 | 4.7 |

| 6250 | 7556 | 4021 |

| 918.54 | 923.6 | 873.22 |

| 0.1 | 0.07 | 0.09 |

| 24000 | 19000 | 35000 |

| 98.4 | 17.6 | 72.1 |

| 0.25 | 0.21 | 0.23 |

| 0.77 | 0.71 | 0.69 |

| 0.98 | 0.93 | 0.91 |

| 59 | 34 | 41 |

| 0.22 | 0.18 | 0.2 |

| 110 | 70 | 160 |

### 4.2 Data preprocessing and calculation

*, as presented in (31). Equation (31) demonstrates the differences of some indexes’ values, such as in*

**X***X*

_{1},

*X*

_{2},

*X*

_{10}, and

*X*

_{14}of the three wind projects. On the contrary, other indexes’ values, such as

*X*

_{3},

*X*

_{4},

*X*

_{7},

*X*

_{13}, and

*X*

_{15}, are similar. The sustainability of each region cannot be defined by a single index only. That is to say, the sustainability of a wind power system cannot be accurately determined using only parts of its indexes. Therefore, a comprehensive evaluation of the sustainability of the wind power project must be performed using a comprehensive index system, as is the case here:

### 4.3 Calculation of comprehensive weight based on AHP-EW

The EW method emphasizes the difference between the indexes. Therefore, the present study also applies the AHP method as directed by the experts to revise the calculated results of the objective weights calculation and generate comprehensive evaluation results.

*) is:*

**AP**

**P**_{1}

*) is:*

**X**

**P**_{2}

*,*

**X**

**P**_{3}

*,*

**X**

**P**_{4}

*, and*

**X**

**P**_{5}

*) are defined as follows:*

**X**

**p**_{subjective}= [0.0188, 0.0334, 0.0579, 0.1029, 0.0073, 0.0137, 0.0192, 0.0250, 0.0237, 0.0710, 0.0352, 0.0839, 0.1331, 0.0733, 0.1164, 0.1848]

^{T}. Moreover, the proportions of the objective and subjective weights can be calculated by (17)–(21), and the comprehensive weight index matrixes \(\varvec{\omega}_{com}\) are defined by (16) and are calculated in (39).

### 4.4 Calculation of final results by fuzzy TOPSIS

*is constructed, as shown in (40) using (22)–(24). Further, the positive ideal solution*

**Y***Y*

^{+}and the negative ideal solution

*Y*

^{−}are determined from the weighted normalized decision matrix using (26), (27). Following this, the Euclidean distances (

*D*

^{+}and

*D*

^{−}) between each alternative from Y

^{+}and

*Y*

^{−}are calculated using (28), (29). In the next step, the closeness coefficient

*C*

_{i}of the alternatives is calculated using (30). The results for

*Y*

^{+},

*Y*

^{−},

*D*

^{+}and

*D*

^{−}are summarized in Table 3. Finally, the closeness coefficient

*C*

_{i}is presented in Table 4. The alternatives are arranged in descending order as C > A > B. The following conclusions are generated according to the obtained values of

*C*

_{i}in Table 4. Firstly, the wind project C is the most sustainable aspect of the established power grid. Secondly, and conversely, the minimal value of wind project B characterizes the latter as the least sustainable wind project.

Calculation results of TOPSIS

TOPSIS | A | B | C |
---|---|---|---|

| 0.326160 | 0.235290 | 0.446200 |

| 0.036400 | 0.009250 | 0.026380 |

| 0.859770 | 0.583420 | 1.350070 |

| 0.503060 | 0.482740 | 0.575913 |

Final ranks of three wind projects by fuzzy TOPSIS

Wind project | CE index | Rank |
---|---|---|

A | 0.630872210 | 2 |

B | 0.547217201 | 3 |

C | 0.700978119 | 1 |

Final ranks of three wind projects by OWA

Wind project | OWA | Rank |
---|---|---|

A | 0.633242233 | 2 |

B | 0.611914944 | 3 |

C | 0.665330432 | 1 |

According to Table 5, wind project C remains in the first place, followed by wind project A, and wind project B as the least preferred option. In general, the range of values for the fuzzy TOPSIS method provides a larger difference between wind projects A, B, and C, thereby suggesting the applicability of the fuzzy TOPSIS method in addressing the greater discrimination between the alternatives. The ranking index formed by the fuzzy TOPSIS method considers both the benefit of the ideal solution and cost ideal solution of each index, thereby enabling researchers to approach the selection problem of the sustainable level of the wind projects from multiple perspectives rather than simply selecting the highest OWA score. Therefore, the fuzzy TOPSIS method incorporates the concept of contradiction into the ranking of the compromise solutions, which can improve the quality of ranking results.

## 5 Sensitivity analysis

In Section 3, the values of the weights were determined according to the proposed comprehensive weight calculation method. However, the weight values could be changed following the application of other kinds of methods. Thus, we conducted a sensitivity analysis on these weight values. According to Fig. 1, the 16 sub-criteria were divided into 5 analysis levels, namely technology, wind resource, environment, economy, and society groups. All the initial sub-criteria of each levels were assumed to exhibit rate changes of 0.3, 0.2, 0.1, − 0.1, − 0.2, and − 0.3, respectively, and all the base weights are shown in (39). The sustainable level values and ranks of the wind projects were then recalculated as shown in Fig. 2. *X*-axis represents the rate of base weights of *X*_{i} index, and *Y*-axis is the current values of weights of wind projects A, B, and C.

*X*

_{3}became less important. Thus, they are most sensitive to the weight of

*X*

_{3}. However, wind project C maintained its first ranking as the base case throughout

*X*

_{3}weight changes. The weight decreases in

*X*

_{1},

*X*

_{2}, and

*X*

_{4}generated a more or less decline in the scores of wind projects A, B, and C. However, the weight changes in the technology group did not affect wind project C as it maintained its highest scores in the sustainable evaluation of the wind projects.

*X*

_{5},

*X*

_{6},

*X*

_{7}, and

*X*

_{8}weights are shown in Fig. 3. The sub-criteria weight changes in the wind resource group resulted in small score variations in wind projects A, B, and C following

*X*

_{5},

*X*

_{6},

*X*

_{7}, and

*X*

_{8}sub-criteria changes. Likewise, wind projects C and B were deemed the optimal and worst regional wind projects, respectively, for all sub-criteria weight changes in the wind resource group.

*X*

_{10}than to sub-index

*X*

_{9}, as shown in Fig. 4. The score of wind project C in all three projects was maintained the highest.

*X*

_{11},

*X*

_{12}, and

*X*

_{13}are shown in Fig. 5. According to Fig. 5, the final score of the three alternatives exhibited a slight decrease following a decrease in the weight of sub-criteria of economy group. The weight of

*X*

_{13}exhibited the most sensitivity. However, wind project C maintained the highest scores in the economy group for all economy group weights changes.

*X*

_{15}and

*X*

_{16}. However, the scores of the three wind projects maintained the same decreasing trend as the weight of

*X*

_{14}became less important. Moreover, just as that in the other four sub-indexes groups, wind projects C and B were still deemed the best and worst wind projects, respectively, for all society group sub-criteria weight change.

Above all, three wind projects always keep their ranks, no matter how the sub-criteria weights change. It can be verified that the performance evaluation of wind projects using the proposed comprehensive weights calculation method and fuzzy TOPSIS is robust.

## 6 Conclusion

The present study proposes a combined MCDM framework for the sustainable level of the selection model of wind projects. A hierarchical wind project evaluation criteria framework is proposed and validated. Two MCDM weights decision methods, specifically EW and AHP, are combined by the LCEA method to calculate this set of multilevel criteria, which consists of five main dimensions and 16 sub-criteria. An empirical case study containing three Hami City wind projects in China is used to exemplify the approach and rank the sustainable level of each wind project by the fuzzy TOPSIS method. The results of the case study are robust with regards to the OWA method. In addition, a sensitive analysis is also applied to verify the robustness and effectiveness of the proposed weight calculation approach. The model can thus not only be compatible with different index systems but also identify the greater or weaker level of sustainability for a wind project.

The present study aims to guide researchers and other investors to easily forecast the sustainable performance of wind projects and decide accordingly. This study presents its originality in its comprehensive criteria structure, which is balanced on the five dimensions of sustainability of the wind project. In addition, the combination of its proposed comprehensive weights calculation method (AHP and EW, optimized by LCEA) with the fuzzy TPOSIS method in the selection problem of the sustainable level of the wind project has not been previously published in literature. Distinguishing wind projects from general wind technologies can reduce the over-simplification of decision problems and aid in the evaluation of alternatives in the light of more specific data. The next stage of this research will focus on the design of an application software based on the proposed method to quickly calculate and analyze the sustainability level of wind projects.

## Notes

### Acknowledgements

This work was supported by National Natural Science Foundation of China (No. 51667020), University research projects of Xinjiang Province (No. XJEDU2017I002), Xinjiang Province Key Laboratory Project (No. XJDX1402) and Doctoral Innovation Project (No. XJUBSCX-2015015).

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