Assessing the Environmental Impact Caused by Power Grid Projects in High Altitude Areas Based on BWM and Vague Sets Techniques

Abstract

This study constructed a hybrid model for assessing the environmental impact caused by power grid projects (PGP) in high altitude area (HAA). Firstly, this study analyzed the characteristics of the environment in HAA and the possible environmental impacts caused by the PGP in HAA. On this basis, an evaluation indicator system reflecting the particularity of HAA was established, including three perspectives named natural, social and ecological environment. Next, considering the availability of evaluation index data and the scarcity of evaluation samples, the best and worst method (BWM) was employed to obtain the objective and credible indicator weights. Furthermore, the Vague set theory was introduced into the comprehensive evaluation model, overcoming the shortcomings of comprehensive evaluation model based on fuzzy sets. Finally, the practicability and effectiveness of the proposed hybrid model was validated via a practical PGP in Qinghai-Tibet Plateau. Overall, the results of this paper can play an important supporting role in promoting green construction and sustainable development of PGP. Besides, the proposed hybrid evaluation framework requires fewer index values and evaluation samples, having good applicability and promotion value in handling the evaluation issues with uncertain and incomplete information.

1. Introduction

With the continuous development of society and economy, people have deeply realized the importance of the environment and paid more attention to environmental protection. Environmental protection includes protecting the natural environment and preventing and controlling pollution and other public hazards [1]. That is, when making better use of resources, people have to apply modern scientific environmental theories and methods to further understand the causes and harms of the pollution and destruction to environment and protect the environment in a planned way, which helps to promote the sustainable development of mankind and the environment [2].

China’s power industry paid great attention to the environmental protection in power grids construction [3]. Since the 1970s, in the design and construction of extra high voltage (EHV) transmission project, Chinese power technology researchers have conducted systematic and in-depth studies on the electromagnetic environment influence factors such as power frequency electric field, power frequency magnetic field, radio interference, and audible noise generated by power grid construction projects, and have obtained a large amount of research results [4,5,6]. At present, China has included the environmental impact assessment (EIA) of PGP in environmental protection laws and regulations, making the environmental protection of PGP legal [7].

EIA refers to a series of methods and mechanisms used to analyze, predict and evaluate the environmental impacts caused by the implementation of the projects, to put forward measures for preventing or mitigating the adverse environmental impacts, and to track and monitor the environmental impacts of the project [8]. EIA originated in the United States in 1969 [9]. Subsequently, Japan, France and other countries have promulgated relevant laws, enabling the EIA to be formalized and legalized quickly [10,11]. China promulgated the Environmental Protection Law of the People’s Republic of China (for trial implementation) in 1979, which provided the legal basis for EIA [12]. In 2003, the Environmental Impact Assessment Law of the People’s Republic of China was formally implemented and other supporting management measures and regulations have gradually improved, marking that China’s EIA system has entered a new stage of development [13].

Research on EIA of PGP mainly focused on the issue of electromagnetic environment, first proposed by the United States in 1972 [14]. In the 1970s, Japan, the former Soviet Union and other countries examined the electromagnetic environment of EHV transmission lines, and formulated some corresponding standards in electromagnetic compatibility and environmental protection [15,16,17]. In 1982, the working group of Conference International des Grands Reseaux Electriques (CIGRE) summarized the relatively consistent views of various countries on the calculation and testing technologies of electrostatic induction in power system and the impact of power frequency electric field on ecology [18], providing guidance for the development of China’s EIA development.

The EIA of China’s electric power industry was standardized in the early 21st century [19]. At the end of 2007, the State Environmental Protection Administration organized the relevant agencies to integrate the original EIA standards for PGP and formed the Environmental Protection Management Guideline-EIA for Power Transmission and Transformation Project [20]. In early 2008, the guideline was renamed the Technical Guideline for EIA: Transmission and Distribution Project [21]. In 2014, the EIA guideline, which is more suitable for the development of China’s electric power industry and the actual work of power transmission and transformation EIA, was officially promulgated and implemented [22], signifying that the EIA of China’s power transmission and transformation projects is gradually becoming standardized and rationalized.

As for the evaluation tools, with the deepening of the project EIA research, relevant scholars mainly evaluated the environmental impact through two ways. The first one is the qualitative evaluation system mainly based on clauses, constructing qualitative evaluation by comparing various EIA standards [23,24,25]. The second one is the quantitative evaluation system, which is mainly based on life cycle assessment theory [26,27] and some other theoretical methods, such as technical and economic evaluation [28] and comprehensive evaluation [29,30]. In terms of the evaluation objects, most scholars mainly evaluate the environmental impact of general power projects, including power grid planning projects [31,32] and power grid construction projects [33,34]. Besides, some scholars also conduct EIA for specific power projects, such as ultra/extra high voltage power transmission projects [35] and intelligent substation projects [36].

It is worth noting that China has a vast territory and great geographical differences in different regions [37]. As an important part of China’s electric power industry, PGP under special geographical conditions will inevitably cause certain environmental impacts during their planning, designs and constructions [38,39]. Therefore, assessing the environmental impacts of PGP under special geographical conditions can clarify the environmental impacts of such projects and then put forward targeted environmental protection measures. Meanwhile, it can help to improve the research work on EIA of China’s PGP, which can promote the organic coordination of PGP construction and the environment to achieve the green and sustainable development of China’s electric power industry.

Currently, studies on the EIA of PGP under special geographical conditions are still relatively few in China. Among them, Chinese scholars conducted some studies on high-altitude PGP in terms of the post-project evaluation, construction technology evaluation and EIA, and made some progress. For instance, Pang et al. studied the development status of small hydropower in Tibet, finding that the construction of small hydropower projects had a serious impact on the ecological environment in Tibet. Therefore, the development process should pay attention to the protection of the ecological environment, which can help achieve sustainable development [40]. Similarly, Li constructed a post-evaluation model for hydropower construction projects in Tibet. Taking the hydropower construction project in the Niyang River Basin as an example, the impact of hydropower construction projects in Tibet’s high-altitude regions on the ecological environment was analyzed, showing that environmental protection is an important evaluation criterion for the effect of power grid construction [41]. However, for the PGP in HAA, the related studies focused mainly on the technical level, such as the impact of high-altitude DC project on voltage and reactive power control [42], and the influence of load characteristics of high-altitude PGP on short-circuit current [43], and were less concerned with EIA. According to Huang and Wu [44], PGP in HAA have far-reaching and significant impacts on the economic benefits, social environment, natural environment, ecological environment and future development of the area where the projects are located. Thus, with the current deterioration of the ecological environment, it is particularly important to assess the environmental impacts caused by PGP in HAA, which can not only reflect the comprehensive ability of China to build large-scale PGP in HAA, but also provide a reference for environmental protection in the construction of other high-altitude PGP. Based on this, this study analyzed the environmental characteristics of HAA and constructed a hybrid model for assessing the environmental impacts caused by PGP in HAA based on BWM-Vague set techniques. Furthermore, the scientificity and applicability of the proposed model were verified via the empirical analysis based on an actual PGP in Qinghai-Tibet Plateau. Overall, the main contributions of this paper include:

(1)

This paper takes the environmental characteristics of HAA into account and constructs an EIA model for high-altitude PGP, which helps to clarify the environmental impact of such projects and propose targeted environmental protection measures. Meanwhile, the research results of this paper can be introduced into the grid enterprise standard system, which can improve the studies on EIA of China PGP, playing an important supporting role in the green construction and sustainable development of PGP.

(2)

This paper proposes a comprehensive evaluation framework based on BWM-Vague sets approaches. Firstly, the BWM method can simplify the comparison process through targeted pairwise comparisons and reduce the inconsistency of expert judgment. Besides, the BWM method adopts optimization idea to obtain the weight of indicators, ensuring that the results are objective and credible. Secondly, the Vague set theory is introduced into the comprehensive evaluation model, which overcomes the deficiencies of the traditional fuzzy comprehensive evaluation and can deal well with the comprehensive evaluation issues with uncertain and incomplete information. Overall, the evaluation framework proposed in this paper has lower requirements on the evaluation sample size and sample index values, which can provide an effective evaluation tool for similar problems.

The rest of this paper is organized as follows: Section 2 analyzes the environmental impacts caused by PGP in HAA. Section 3 constructs a hybrid model for assessing the environmental impact of PGP in HAA. Section 4 reports the evaluation framework proposed in this paper. Section 5 verifies the validity and practicability of the proposed model through empirical analysis and the last section summarizes the paper.

2. Analysis on the Environmental Impact of PGP in HAA

2.1. Definition of HAA

According to internationally accepted standards of altitude classification, 1500–3500 m are high altitude where most people can adapt if there is enough time, and 3500–5500 m are the extra-high altitude where the adaptability depends on individual differences.

The topography of China is high in the east and low in the east, with a roughly step-like distribution. The first step of the terrain is the Qinghai-Tibet Plateau, with an average elevation of 4000 m above sea level. On the second step of the terrain, there are large basins and plateaus with an average elevation of 1000–2000 m. Therefore, this paper defines the HAA in China as the Qinghai-Tibet Plateau.

The Qinghai-Tibet Plateau is the highest plateau in the world. In terms of the division of administrative regions, the Qinghai-Tibet Plateau in China includes all of Tibet Autonomous Region and Qinghai Province, the western part of Sichuan Province, the southern part of Xinjiang and parts of Gansu and Yunnan Provinces, as shown in Figure 1. The Qinghai-Tibet Plateau in China runs from the Pamirs in the west to the Hengduan Mountains in the east, horizontally crossing 31 longitudes and is about 2945 km long from east to west. Meanwhile, the Qinghai-Tibet Plateau runs from the south of the Himalayas in the south to the north of the Kunlun and Qilian Mountains in the north, vertically crossing about 13 latitudes and is about 1532 km wide from south to north. The total area of Qinghai-Tibet Plateau is 2.5 million km², accounting for 26.8% of China’s land area. The average elevation of the Qinghai-Tibet Plateau is 4000–5000 m, mainly dominated by mountainous landform with stretching mountains, towering terrain and complex topography. Hence, the Qinghai-Tibet Plateau is known as “roof of the world” and “the third pole of the world”.

2.2. Environmental Characteristics in HAA

Through the above definition of the HAA and their distribution scope, it can be concluded that HAA have the following environmental characteristics.

(1)

High-latitude cold and hypoxic. These are the most important natural features of HAA. In HAA, the temperature of the troposphere decreases with height. Generally, the temperature decreases by 0.6 °C for every 100 m of elevation. Therefore, the winter temperature in HAA is 18–20 °C lower than that of the eastern plain at the same latitude, and the summer temperature is 8–18 °C. People there have to adapt to the plateau environment with high-latitude cold and hypoxic.

(2)

Large area of frozen soil. Due to the bitter cold nature in HAA, China has the biggest permafrost area in the world, with a total area of about 2.15 million km², of which 70% are located in the Qinghai-Tibet Plateau. Frozen soil is divided into permafrost and seasonal frozen soil. In Qinghai-Tibet Plateau, the permafrost area is 1.5 million km² and seasonal frozen soil area is 1.22 million km². It can be seen from the above data that the area of frozen soil is very large in HAA, which greatly affects the construction of PGP.

(3)

Large temperature daily range. The daily range of temperature in HAA is generally large, especially in Qinghai-Tibet Plateau, the average temperature daily range can reach above 20 °C. When the air pressure and temperature changes, the air density will change, affecting the construction of PGP. For example, wind turbines have different rated wind speeds at different air densities, indicating that larger temperature daily range can lead to the unstable performance of wind turbine.

(4)

Low atmospheric pressure. With the gradual increase of elevation, atmospheric pressure will be reduced. According to relevant research and analysis, given that the temperature unchanged, the air density is proportional to the air pressure, that is, the lower the air density, the lower the air pressure. For example, the atmospheric pressure at sea level is 101.3 kPa, and it will decrease to be 50.06 kPa when the altitude rises to 5000 m (

Table 1. The impact of altitude on the pressure.

Parameter	Values
Altitude (m)	0	1000	2000	3000	4000	5000
Atmospheric pressure (kPa)	101.5	90	79.5	70	61.5	50.06

). When the altitude rises to 7000 m, the atmospheric pressure is about one-third of that in the sea level [45].

(5)

Strong causticity. In the Qinghai-Tibet Plateau, the soil is highly corrosive. Especially, in salt lakes and salted areas, the causticity is strong and variable. Besides, compared with the plain area, there is a strong degree of salinization and soil salinity in HAA, which greatly affects the buildings and building materials [46], requiring the selection of building materials with high frost resistance, impermeability, and corrosion resistance when carrying out PGP in the Qinghai-Tibet Plateau.

(6)

Many rare plant and animal resources. The area covered by the examined PGP in Qinghai-Tibet Plateau has 17 species of national key protected mammals, including 5 species of national first-level key protected animals and 12 species of second-level key protected animals, and has 27 species of national key protected birds, including 7 species of national first-level key protection birds and 20 species of national second-level key protection birds. There are 199 species of plants along the PGP, of which 80 species are endemic to the plateau and 4 species are national protected plants. These unique and rare species are the common wealth of the people in the world and cannot be damaged by the construction of PGP. Therefore, scientific and rational construction is needed to avoid affecting the cherished species and create a harmonious environment where people and animals and plants live in harmony.

(7)

Original and fragile natural landscape. The natural landscape of Qinghai-Tibet Plateau is mainly composed of the horizontal zone and the vertical zone. The horizontal zone includes the typical desert ecological landscape system and the valley shrub ecological landscape system. The vertical zone includes high-latitude cold grassland, high-latitude cold meadow, ice and snow zone and so on. These landscapes are characterized by diversity, uniqueness, primitiveness and vulnerability, revealing that, if the project construction process causes damage to them, it will cause a series of reactions and result in the destruction of the whole system.

2.3. Environmental Problems Caused by PGP in HAA

(1) Impact on the natural environment and ecology of nature reserve

To protect the water environment, biodiversity and the plateau ecosystem in the Qinghai-Tibet Plateau, China has established natural protection areas such as Qinghai Hoh Xil, Sanjiangyuan and Selincuo black-necked crane. The construction of the Qinghai-Tibet electric power network project will inevitably have a certain impact on the ecological system along the project. Therefore, reasonable layout and comprehensive design are needed to minimize the impact of the project construction on the nature reserve.

(2) Impacts on vegetation and natural landscape

From the northwest to the southeast, the natural landscape of the Qinghai-Tibet Plateau presents various natural landscapes such as high-altitude cold desert, grassland, meadow and shrub. Meanwhile, there are natural landscapes such as Kunlun Mountains along the project, and there are natural magical Karst landforms on the southern slope of Tanggula Mountain. The examined PGP will span the above natural landscape areas, resulting that the construction of access roads, temporary sites, and the construction of the line tower foundation may all affect the balance of the natural landscape of the Qinghai-Tibet Plateau.

(3) Destroying the living environment of wild animals

In the project area, there are 5 different ecological groups named alpine mountain fauna, high-altitude cold steppe and meadow fauna, desert and semi-desert fauna, forest and shrub fauna, and swamp wetland fauna, including 17 national key protected mammals and 27 national key protected birds. The development of PGP may cause damage to the animal migration pathways and affect animal feeding. In more serious cases, the construction workers may kill animals.

(4) Affecting the water environment of the Qinghai-Tibet Plateau

It is an important task of the construction of the project to ensure that water quality along the project is not polluted. During the construction, the surface and groundwater resources may be polluted by domestic garbage, domestic sewage and construction machine washing wastewater.

(5) Affecting the frozen soil environment

The frozen soil environment in the cold plateau area is extremely fragile, and the tower base area of the transmission line is likely to cause thermal disturbance to the permafrost. Once the frozen soil environment is destroyed, it will be extremely difficult to recover and lead to problems such as the degradation of permafrost, surface destruction and thermal subsidence.

(6) Soil erosion and imbalance of ecosystem

The “Sanjiangyuan” area including Tanggulashan, Qumalai and Zhimao counties in Golmud, Qinghai Province, which the examined PGP passes, is a state-level key prevention and protection area for soil erosion. Golmud in Qinghai Province (excluding Tanggulashan township) is a key monitoring area for soil erosion in Qinghai Province. Qumalai and Zhido county in Yushu prefecture, and Tanggulashan township of Golmud city in Haixi prefecture belong to the key prevention and protection areas for soil erosion in Qinghai Province. The construction along the project is likely to cause geological disasters like landslides, mudslides and rock erosion, resulting the loss, reduction or contamination of soil and water resources in the area.

3. EIA Model of PGP in HAA

3.1. Design of Assessment Index System

High-altitude PGP have significant effects on the surrounding areas in terms of technology, economy, society and the natural environment, and will have a major impact on the future development of HAA. The vulnerability of the ecological environment in HAA makes the project’s EIA particularly critical. However, the general EIA index system has limitations on project evaluation in HAA, causing that it is of great significance to design a scientific and reasonable index system for the EIA of PGP in HAA. According to the above analysis of environmental impacts of high-altitude PGP, the ecological environment in HAA is extremely primitive, fragile and sensitive, which is very difficult to recover after destruction, meaning that the responsibility of ecological protection is of great importance. The post-evaluation on the environmental impact of PGP in HAA mainly includes the post-evaluation of natural environment, social environment and ecological environment. Correspondingly, the uniqueness of HAA should be reflected in the evaluation index system. For example, the post-evaluation of the ecological environment should include specific indicators of HAA such as permafrost and high-altitude cold wetlands.

In line with the above analysis, based on relevant literature references [39,43,44], this article constructs an EIA index system for PGP in HAA, which is comprehensive, compatible, and effective, and involves quantitative and qualitative indicators, as shown in

Table 2. The EIA index system of high-altitude PGP.

First-Level Indicator	Secondary Indicators	Third-Level Indicators	Symbol
Natural environment	Atmospheric environment	Dust concentration	C11
		Suspended particle concentration	C12
		Monthly average air quality	C13
	Water environment	Changes in the concentration of heavy metals (e.g., copper, cobalt, chromium, nickel)	C14
		PH value	C15
		Changes in the number of cherish aquatic animals and plants	C16
		Changes in concentrations of major pollutants (phosphorus, nitrogen, petroleum, and sulfide)	C17
	Electromagnetic environment	Power frequency electric field (electric field generated by sine-varying charges at 50 or 60 Hz)	C18
		Power frequency magnetic field (magnetic field generated by AC power transmission facilities)	C19
		The height of various transmission lines	C1,10
Social environment	Noise	Audible noise (noise caused by electromagnetic environment)	C21
		Daytime plant noise (noise caused by mechanical equipment in the daytime)	C22
		Night plant noise (noise caused by mechanical equipment at night)	C23
	Landscape	The distance between the station and the human landscape	C24
		The distance between transmission lines and human landscape	C25
		The distance between transmission lines and environmentally sensitive points	C26
		The distance between the converter station and the environmentally sensitive point	C27
	Pollutants and waste	Waste treatment rate	C28
		Pollutant treatment rate	C29
Ecological environment	High-altitude cold wetland	Wetland area and its changes	C31
		Salinization degree in wetlands	C32
	High-altitude cold frozen soil	Change in frozen ground area	C33
		Thermal stability and thermal erosion sensitivity of frozen soil	C34
		Frozen soil temperature and thickness	C35
		Ice content of frozen soil	C36
	Animals and plants	Number of rare species	C37
		Preservation of rare animals and plants	C38
		Species diversity	C39
		Animal and plant coverage in high-altitude cold grassland, swamp and meadow	C3,10

.

3.2. BWM-Based Indicator Weight Determination Method

In the comprehensive evaluation of the environmental impact of PGP in HAA, it is firstly needed to determine the weights of EIA indicators. The rationality of the weight will directly affect the quality of the comprehensive evaluation and the final result, which is therefore of crucial importance.

As mentioned before, in the index system of EIA of PGP in HAA, there are many qualitative indicators that are difficult to quantify. Furthermore, the number of PGP in HAA is relatively small, making the traditional objective weighting method based on the degree of differentiation of evaluation objects not applicable in this paper. Therefore, this paper employs the BWM technique to determine the weight of EIA indicators of PGP in HAA. BWM is a subjective weighting method based on the idea of pairwise comparisons, which is similar to AHP. However, it is not an arbitrary comparison but constructs a systematic way of comparisons [47]. The specific steps of BWM are as follows:

Step 1:

Choose a best criterion ${\mathrm{C}}_{\mathrm{B}}$ and a worst criterion ${\mathrm{C}}_{\mathrm{W}}$ from the indicator set $\left\{{\mathrm{c}}_1,{\mathrm{c}}_2,\dots ,{\mathrm{c}}_{\mathrm{n}}\right\}$.

Step 2:

Score the indicator using a number from 1 to 9 to determine the preference degree of the indicator compared to the best indicator. If an indicator is as important as the best indicator, the indicator is assigned a value of 1, and if an indicator is very unimportant relative to the best indicator, the indicator is assigned a value of 9. By this way, a best comparison vector $A_B=\left(a_{B1},a_{B2},\dots ,a_{Bn}\right)$ is constructed, where $a_{Bi}$ represents the degree of preference of indicator i compared to the best indicator, and $a_{BB}=1$.

Step 3:

Determine the degree of preference of indicators compared to the worst indicator. Similarly, the numbers from 1 to 9 are used to score the indicator. If an indicator is as important as the worst indicator, the indicator is assigned a value of 1, and if an indicator is very important relative to the worst indicator, the indicator is assigned a value of 9. By this way, a worst comparison vector $A_W={\left(a_{1W},a_{2W},\dots ,a_{nW}\right)}^T$ is constructed, where $a_{iW}$ represents the degree of preference of indicator i compared to the worst indicator, and $a_{WW}=1$.

Step 4:

Solve mathematical model and get index weight. Theoretically, if the actual weight of the indicator i is $w_i$, then the following formula is established [48]:

$$\frac{w_B}{w_i}=a_{Bi}, \frac{w_i}{w_W}=a_{iW},$$

However, the ratio between the actual weights and the corresponding elements in the comparison vector usually has certain errors. Therefore, a mathematical model based on the optimization theory can be constructed and solved to obtain the optimal weight $\left(w_1^{*},w_2^{*},\dots ,w_n^{*}\right)$. Specifically, the objective function and the constraints of the optimization model are [48]:

$$\min k$$

(1)

$$s.t.\{\begin{array}{l}\left|\frac{w_B}{w_i}-a_{Bi}\right|\le k,\forall i\\ \left|\frac{w_i}{w_W}-a_{iW}\right|\le k,\forall i\\ {\displaystyle \sum _i{w}_i}=1\\ w_i\ge 0,\forall i\end{array}$$

(2)

For n indicators, BWM actually needs to compare $2n-3$ times, while AHP needs to compare $n\left(n-1\right)/2$ times [49]. The BWM method does not require the index to be quantified. In addition, by establishing the best and worst criteria, the process of comparison is greatly simplified and the risk of inconsistency is reduced, which ensures the accuracy of the judgment and can obtain a more reliable weight result via the optimization process.

3.3. Comprehensive Evaluation Method Based on the Vague Set

There are many influencing factors for EIA of PGP in HAA, so uncertainty and incompleteness of information exist everywhere in the assessment process, resulting that the relationship between result and affecting factors is usually non-liner. The fuzzy comprehensive evaluation method can well solve the non-linear relationship between affecting factors and final result, making it widely used in assessing the effect of the influencing factors [50]. However, given the fact that the degree of membership cannot perform addition operation, the traditional fuzzy theory easily loses intermediate information when using the operations of fetching maximum or minimum [51]. As a result, the evaluation result may be distorted. Therefore, this paper proposes an improved evaluation method based on Vague set theory [52], which is an extension of fuzzy set.

Normally, the fuzzy set thinks that the membership degree can be mapped to $\left[0,1\right]$ interval, while the Vague sets holds that the membership degree of each element can be divided into two parts: support and opposition [52]. That is, the membership degree should consist of true membership degree t and false membership degree f. Supposing that U is a domain of discussion and x represents any one element in U, a Vague set in U can be represented by a true membership function $t_A$ and a false membership function $f_A$. Furthermore, $t_A\left(x\right)$ is the lower boundary of the supporting membership degree of x derived from the evidence supporting x, $f_A\left(x\right)$ is the lower boundary of the negative membership degree of x derived from the evidence against x, and the uncertainty is $1-t_A\left(x\right)-f_A\left(x\right)$. $t_A\left(x\right)$ and $f_A\left(x\right)$ associate the real numbers in the interval $\left[0,1\right]$ with each element in U, that is, $t_A\left(x\right):U\to \left[0,1\right]$, $f_A\left(x\right):U\to \left[0,1\right]$.

For the convenience of discussion, this article records $t_A\left(x\right)$ as $t_x$ and $f_A\left(x\right)$ as $f_x$. It is obvious that $t_x+f_x\le 1$. If $t_x=1-f_x$, the Vague sets are reduced to fuzzy sets, and if $t_x=1-f_x=0$ or $t_x=1-f_x=1$, the Vague sets are reduced to normal sets. The specific steps of using Vague set to assess the environmental impacts of PGP in HAA are as follows:

Step 1: Set the corresponding evaluation statements with different levels for each EIA indicator. According to the actual situation of environmental protection and the construction of the PGP, this paper gives five levels of the corresponding comment set $V=\left(V_1,V_2,V_3,V_4,V_5\right)$ = (little impact on the environment, less impact on the environment, general impact on the environment, great impact on the environment, very great impact on the environment), and invites some experts to choose appropriate linguistic variables to express their opinions.

Step 2: According to the aforementioned BWM method, determine the weight of all EIA indicators.

Step 3: Construct the evaluation matrix of Vague set. Specifically, invite the experts to judge all the indicators one by one according to the given comment set V. If $C_i$ represents any one of the environmental factors and $V_j$ ($j=1, 2, 3, 4, 5$) is the comment set, the Vague set evaluation matrix between the evaluation index system C and the comment set V can be constructed as:

$$R=\left(\begin{array}{cccc}{r}_{11}& r_{12}& \cdots & r_{15}\\ r_{21}& r_{22}& \cdots & r_{25}\\ ⋮& ⋮& \ddots & ⋮\\ r_{n1}& r_{n2}& \cdots & r_{n5}\end{array}\right)$$

(3)

where $r_{ij}$ represents a Vague value of the factor ${\mathrm{C}}_i$ on the comment level $V_j$, and $r_{ij}=\left[t_A,1-f_A\right]$. By inviting relevant experts to judge each indicator in accordance with the comment set, the Vague values of all indicators can be obtained, and then the Vague set assessment matrix of the entire index system can be constructed. To more truly represent the degree of hesitation of experts, experts are allowed to abstain from voting. For instance, there are 10 experts judging the influence of a factor ${\mathrm{C}}_i$ in the environment. If 6 experts think that the factor has a very great impact on the environment, 2 experts hold that the impact is great, 1 expert thinks it is general and 1 expert gives up the judgment, the Vague values of the factor ${\mathrm{C}}_i$ on all five comment levels can be expressed as:

$$r_{ij}=\left(r_{i1},r_{i2},r_{i3},r_{41},r_{i5}\right)=\left(\left[0,0.1\right],\left[0,0.1\right],\left[0.1,0.2\right],\left[0.2,0.3\right],\left[0.6,0.7\right]\right).$$

Step 4: According to the index system weights W and Vague set evaluation matrix R, the comprehensive evaluation based on Vague set technique can be:

$$F=W\otimes R=\left(F_1,F_2,F_3,F_4,F_5\right)$$

(4)

$$F_j=(w_1\otimes r_{1j})\oplus (w_2\otimes r_{2j})\oplus \cdots \oplus (w_n\otimes r_{nj}),j=1,2,3,4,5$$

(5)

where F is the comprehensive evaluation result based on Vague set, $F_j$ is the Vague value of the object to be evaluated on the comment set $V_j$, $\otimes$ is the operation symbol of matrix multiplication of Vague set, and $\oplus$ is the operation symbol of finite sum of Vague sets. Therefore, the above calculation needs to use two basic formulas on the Vague set: scalar multiplication and finite sum. If k is a real number on [0,1] interval, A and B are elements on Vague set, and $A=\left[t_A,1-f_A\right]$ and $B=\left[t_B,1-f_B\right]$, then [53]:

$$k\otimes A=\left[k{t}_A,k(1-f_A)\right]$$

(6)

$$A\oplus B=[\min \left\{1,t_A+t_B\right\},\min \left\{1,(1-f_A)+(1-f_B)\right\}]$$

(7)

Step 5: Judge the evaluation results according to the principle of maximum membership degree. Since the Vague value is an interval number, the relative scoring function proposed by Liu and Wang [54] can be adopted as a ranking rule for the membership degree of the Vague set. The formula is as follows:

$$J(x)=\frac{t_x}{t_x+f_x}$$

(8)

4. Framework of the Evaluation Model

Figure 2 shows the framework of the EIA model of PGP in HAA based on BWM-Vague set techniques, from which it can be seen that the comprehensive evaluation framework proposed in this paper consists of three phases.

Phase 1: Identify the assessment index system. In this section, this article firstly defines the geographical location of HAA and clarifies the research object of this article. Secondly, this paper analyzes the environmental characteristics of HAA, and further analyzes the potential environmental issues caused by PGP in HAA. On this basis, an index system for the EIA of PGP in HAA is constructed, including 29 evaluation indicators from three perspectives named natural environment, social environment and ecological environment, which fully reflects the environmental characteristics of HAA and the environmental impacts of PGP.

Phase 2: Determine the weight of assessment index system. Considering that it is difficult to obtain the data of some indicators in the constructed assessment index system and there are few samples that can be used in the comprehensive evaluation, the traditional objective weighting methods based on the degree of difference of the evaluated objects are inapplicable. Therefore, this paper employs the subjective weighting method to determine the index weight. To reduce the subjectivity of the weighting results, this paper introduces the optimization idea into the index weighting process, and proposes an index weighting method based on BWM. By setting the best and worst indicators, the process of pairwise comparison is greatly simplified, and the inconsistency of expert judgment is reduced. Meanwhile, by using the optimization model to solve the index weight, the accuracy and reliability of the weight results are guaranteed.

Phase 3: Assess the environmental impacts of PGP in HAA based on Vague set. First, determine the comment level set of each indicator and invite multiple experts in relevant fields to form an expert group. Secondly, in the case of allowing abstention, inviting each expert to give the membership relationship of each evaluation indicator with respect to each comment level independently, and using Vague set operation rules to generate the Vague set assessment matrix of the index system. Thirdly, combining the index weights with the Vague set assessment matrix, the Vague set membership degrees of natural, social, and ecological environmental impact of PGP in HAA are calculated via Vague set scalar multiplication and finite sum operations. Finally, through the Vague set scoring function, the final comprehensive evaluation results are obtained, reflecting the impact degree of the evaluated high-altitude PGP on the environment.

The assessment framework based on BWM-Vague set proposed in this paper has the following three advantages in assessing the environmental impact of PGP in HAA: First, by analyzing the environmental characteristics of HAA and affecting factors, the targeted index system for the EIA of PGP in HAA is determined. Secondly, taking account of the availability of index data and the limitation of assessment sample, BWM method is applied to determine the weight of index, ensuring the reliability of weighting results. Finally, the Vague set theory is introduced into the comprehensive evaluation model, which overcomes the deficiencies of traditional comprehensive evaluation based on fuzzy set and can effectively solve the problems of comprehensive evaluation with information uncertainty and incompleteness.

5. Empirical Results and Interpretation

5.1. Basic Situation of Example

To verify the practicability and effectiveness of the proposed EIA model, this study took the Qaidam-Lhasa ±400 kV direct-current transmission project (referred to the QLDC project) as an example to conduct the empirical analysis. The QLDC project is one of the three components of the Qinghai-Tibet AC-DC interconnection project, consisting of the Golmud converter station, the Lhasa converter station and the HVDC transmission line, with the transmission capacity of 600 MW for the current period and 1200 MW for the long-term. The project starts from the Golmud converter station in the Qaidam basin in the north and ends at the Lhasa converter station in the south. The total length of the project is 1038 km, including 425 km in Tibet and 613 km in Qinghai Province. The project has an average altitude of 4500 m and a maximum altitude of 5300 m. The length located above 4000 m above sea level exceeds 900 m, making it the largest transmission and transformation project with the largest scale and the most difficult construction in the world’s highest altitude and cold regions. Assessing the environmental impact of the QLDC project can reflect the comprehensive capabilities of China in building large-scale PGP in HAA. At the same time, it can provide a reference for environmental protection in the construction of other high-altitude PGP. Normally, the ecological environment in HAA is extremely fragile, and there is a large amount of information uncertainty and incompleteness in the acquisition of indicator data needed in the EIA. To ensure the smooth implementation of the EIA, this study conducted a questionnaire survey of experts from universities, professional design institutes, power grid companies and local governments, and then validated and analyzed the practicability and effectiveness of the proposed EIA model.

5.2. Index Weight Calculation Results

According to the constructed index system of EIA of PGP in HAA, this study employed BWM technique to determine the weights of indicators. Firstly, determine the best and worst indicators based on experts’ advice. To improve the accuracy of experts’ opinions, this study decomposed the whole evaluation index system into three sub-evaluation index systems based on the first-level indicators named the natural environment sub-system including 10 indicators, the social environment sub-system including 9 indicators and ecological environment sub-system involving 10 indicators.

According to experts’ opinions, the best and the worst indicators of the natural environment sub-system are the monthly average air quality and power frequency electric field, those of the social environment sub-system are the pollutant treatment rate and daytime plant noise, and those of the ecological environment sub-system are the animal and plant coverage in high-altitude cold grassland, swamp and meadow and the number of rare species, respectively. Subsequently, through expert questionnaire survey, the preference degree of each indicator in different sub-system comparing to the best and worst indicators named comparison vector is obtained, as shown in

Table 3. The degree of preference of the evaluation index relative to the best and worst indicator in sub-evaluation index system.

Sub-System ${\mathbf{C}}_1$	Comparison Vector		Sub-System ${\mathbf{C}}_2$	Comparison Vector		Sub-System ${\mathbf{C}}_3$	Comparison Vector
	${\mathit{A}}_{\mathit{B}}$	${\mathit{A}}_{\mathit{W}}$		${\mathit{A}}_{\mathit{B}}$	${\mathit{A}}_{\mathit{W}}$		${\mathit{A}}_{\mathit{B}}$	${\mathit{A}}_{\mathit{W}}$
C11	3	5	C21	4	3	C31	4	5
C12	3	5	C22	7	1	C32	6	3
C13	1	7	C23	5	5	C33	5	4
C14	4	4	C24	4	6	C34	3	5
C15	3	5	C25	3	5	C35	3	5
C16	6	3	C26	5	5	C36	4	6
C17	2	5	C27	3	4	C37	7	1
C18	7	1	C28	3	3	C38	2	5
C19	6	2	C29	1	8	C39	2	4
C1,10	4	3				C3,10	1	7

.

According to Table 3 and Equations (1) and (2), the weights of the indicators in each sub-system can be calculated and the results are shown in

Table 4. Weights and rankings of each indicator in different sub-system.

Sub-System ${\mathbf{C}}_1$	Weights		Sub-System ${\mathbf{C}}_2$	Weights		Sub-System ${\mathbf{C}}_3$	Weights
	${\mathit{w}}_{\mathit{i}}$	Ranking		${\mathit{w}}_{\mathit{i}}$	Ranking		${\mathit{w}}_{\mathit{i}}$	Ranking
C11	0.1489	2	C21	0.1134	5	C31	0.1539	2
C12	0.0901	6	C22	0.0256	9	C32	0.1191	6
C13	0.2296	1	C23	0.0763	8	C33	0.1373	4
C14	0.1193	4	C24	0.1174	4	C34	0.1419	3
C15	0.0663	7	C25	0.0784	6	C35	0.0229	9
C16	0.0554	8	C26	0.0775	7	C36	0.0638	7
C17	0.1200	3	C27	0.1533	2	C37	0.0153	10
C18	0.0269	10	C28	0.1272	3	C38	0.0263	8
C19	0.0474	9	C29	0.2309	1	C39	0.1362	5
C1,10	0.0961	5				C3,10	0.1833	1

, from which several findings are discovered:

(1)

Monthly average air quality (${\mathrm{C}}_{13}$) has the greatest impact on natural environment, followed by the dust concentration (${\mathrm{C}}_{11}$) and the changes in concentrations of major pollutants (${\mathrm{C}}_{17}$), accounting for about 50% of the total weight. In contrast, the power frequency electric field (${\mathrm{C}}_{18}$) affects the natural environment most, followed by the power frequency magnetic field (${\mathrm{C}}_{19}$) and the changes in the number of cherish aquatic animals and plants (${\mathrm{C}}_{16}$), accounting for about 13% of the total weight. The above results show that the atmospheric environment has the greatest impact on the natural environment, and the electromagnetic environment has the least impact on the natural environment. This is because the power grid project has a direct impact on the atmospheric environment, while the impact on the electromagnetic environment appears rather obscure. Therefore, it can be concluded that more attention is paid to the control of the atmospheric environment during the construction of power grid projects. At the same time, attention is paid to pollution factors such as heavy metals and induced enrichment in the water environment, while the degree of attention to other factors is relatively small.

(2)

Pollutant treatment rate (${\mathrm{C}}_{29}$) has the greatest impact on social environment, followed by the distance between the converter station and the environmentally sensitive point (${\mathrm{C}}_{27}$) and waste treatment rate (${\mathrm{C}}_8$), accounting for 51.14% of the total weight. In contrast, the daytime plant noise (${\mathrm{C}}_2$) has the least effect in the natural environment, followed by the night plant noise (${\mathrm{C}}_3$) and the distance between transmission lines and environmentally sensitive points (${\mathrm{C}}_6$), accounting for 17.94% of the total weight. The above results show that, to reduce the impact on the social environment, power grid construction pays more attention to the disposal of wastes and pollutants while less attention is paid to noise. In addition, in the landscape environment, the power grid construction pays more attention to the distance between the converter station and the humanities and the environment landscape while the distance between the power transmission lines and the humanities and the environment landscape is less concerned. This is because the power grid project evaluated in this paper is a large-scale HVDC transmission project with a high transmission line, resulting that with the same distance, the impact of transmission lines on humanistic and environmental landscape is far less than that of the converter station.

(3)

The three indicators that have the most significant impacts on the ecological environment are the animal and plant coverage in high-altitude cold grassland, swamp and meadow (${\mathrm{C}}_{3,10}$), the wetland area and its changes (${\mathrm{C}}_{31}$) and the thermal stability and thermal erosion sensitivity of frozen soil (${\mathrm{C}}_{34}$), accounting for 47.91% of the total weight. The three indicators having the least impacts are the number of rare species (${\mathrm{C}}_{37}$), the frozen soil temperature and thickness (${\mathrm{C}}_{35}$) and the preservation of rare animals and plants (${\mathrm{C}}_{38}$), accounting for only 6.45% of the total weight. The above results show that, in the index system of ecological environment assessment, the weight of each index varies greatly, and the wetland, permafrost and the protection of animals and plants have an impact on the ecological environment. However, with respect to permafrost and plant and animal protection, factors such as area change, thermal stability and thermal erosion sensitivity of frozen soils that respond to dominant features of permafrost in HAA have received special attention, while the hidden factors such as the temperature and thickness of frozen soil and the ice content are not taken seriously. For animal and plant protection, the main concern in power grid construction is plant coverage and species diversity that reflect the overall status of the region’s flora and fauna, while less attention is paid to cherished animals and plants.

5.3. Results of Comprehensive Evaluation

5.3.1. Vague Set Evaluation Matrix

To evaluate the environmental impact of the Qaidam-Lhasa ±400 kV HVDC transmission project, this study invited experts, scholars and officials from universities, professional design institutes, project construction units and local government environmental protection departments to collect the Vague set evaluation values of the project’s EIA indicators through a questionnaire survey. In this study, to ensure the representativeness of the expert group, 20 experts from universities, professional design institutes, power grid companies and local governments were invited and each expert gave the degree of influence of the project on the environment under each evaluation indicator. The impacts of the project on the environment are divided into five levels: little impact on the environment ($V_1$), less impact on the environment ($V_2$), general impact on the environment ($V_3$), great impact on the environment ($V_4$) and very great impact on the environment ($V_5$).

On this basis, combined with the evaluation results given by all experts, we can construct the Vague set value of each indicator. For example, for the evaluation indicator ${\mathrm{C}}_{11}$ in the sub-system ${\mathrm{C}}_1$, no expert thinks that this project has little impact on the environment on the indicator, seven people think it has less impact, five experts insist it be general, three experts state that it has great impact, three experts think it has very great impact and two experts abstained from voting. According to the construction rule of Vague set, the Vague set value corresponding to indicator ${\mathrm{C}}_{11}$ should be:

$$r_{11}=\left(r_{111},r_{112},r_{113},r_{114},r_{115}\right)=\left(\left[0,0.1\right],\left[0.35,0.45\right],\left[0.25,0.35\right],\left[0.15,0.25\right],\left[0.15,0.25\right]\right)$$

Similarly, the Vague values of all indicators in each sub-system can be obtained, and a Vague evaluation matrix of each sub-system can be formed, as shown in

Table 5. Expert reviews on the evaluation index system of the Vague value of each indicator.

Sub-System	Indicators	Vague Values of Indicators under Each Comment Level
		V1	V2	V3	V4	V5
${\mathrm{C}}_1$	C11	[0,0.1]	[0.35,0.45]	[0.25,0.35]	[0.15,0.25]	[0.15,0.25]
	C12	[0,0.15]	[0.25,0.4]	[0.3,0.45]	[0.2,0.35]	[0.1,0.25]
	C13	[0.25,0.35]	[0.2,0.3]	[0.1,0.2]	[0.15,0.25]	[0.2,0.3]
	C14	[0.15,0.2]	[0.45,0.5]	[0.25,0.3]	[0.1,0.15]	[0,0.05]
	C15	[0.05,0.15]	[0.2,0.3]	[0.5,0.6]	[0.15,0.25]	[0,0.1]
	C16	[0.1,0.1]	[0.7,0.7]	[0.15,0.15]	[0.05,0.05]	[0,0]
	C17	[0.1,0.2]	[0.5,0.6]	[0.2,0.3]	[0.1,0.2]	[0,0.1]
	C18	[0.15,0.25]	[0.4,0.5]	[0.25,0.35]	[0.1,0.2]	[0,0.1]
	C19	[0.1,0.15]	[0.45,0.5]	[0.25,0.3]	[0.15,0.2]	[0,0.05]
	C1,10	[0.45,0.5]	[0.35,0.4]	[0.15,0.2]	[0,0.05]	[0,0.05]
${\mathrm{C}}_2$	C21	[0.15,0.25]	[0.4,0.5]	[0.2,0.3]	[0.15,0.25]	[0,0.1]
	C22	[0.2,0.25]	[0.45,0.5]	[0.2,0.25]	[0.1,0.15]	[0,0.05]
	C23	[0.1,0.2]	[0.5,0.6]	[0.2,0.3]	[0.05,0.15]	[0.05,0.15]
	C24	[0,0.1]	[0.2,0.3]	[0.55,0.65]	[0.15,0.25]	[0,0.1]
	C25	[0,0.15]	[0.25,0.4]	[0.45,0.6]	[0.15,0.3]	[0,0.15]
	C26	[0.15,0.25]	[0.6,0.7]	[0.1,0.2]	[0.05,0.15]	[0,0.1]
	C27	[0.05,0.2]	[0.15,0.3]	[0.45,0.6]	[0.2,0.35]	[0,0.15]
	C28	[0,0.05]	[0,0.05]	[0.1,0.15]	[0.7,0.75]	[0.15,0.2]
	C29	[0,0.1]	[0.1,0.2]	[0.5,0.6]	[0.25,0.35]	[0.05,0.15]
${\mathrm{C}}_3$	C31	[0.35,0.45]	[0.4,0.5]	[0.15,0.25]	[0,0.1]	[0,0.1]
	C32	[0.25,0.35]	[0.45,0.55]	[0.15,0.25]	[0.05,0.15]	[0,0.1]
	C33	[0.15,0.2]	[0.4,0.45]	[0.3,0.35]	[0.1,0.15]	[0,0.05]
	C34	[0.05,0.25]	[0.3,0.5]	[0.15,0.35]	[0.2,0.4]	[0.1,0.3]
	C35	[0.2,0.35]	[0.35,0.5]	[0.15,0.3]	[0.1,0.25]	[0.05,0.2]
	C36	[0,0.1]	[0.5,0.6]	[0.35,0.45]	[0.05,0.15]	[0,0.1]
	C37	[0.1,0.2]	[0.65,0.75]	[0.15,0.25]	[0,0.1]	[0,0.1]
	C38	[0.35,0.45]	[0.45,0.55]	[0.1,0.2]	[0,0.1]	[0,0.1]
	C39	[0.2,0.3]	[0.5,0.6]	[0.15,0.25]	[0.05,0.15]	[0,0.1]
	C3,10	[0.15,0.3]	[0.25,0.4]	[0.35,0.5]	[0.1,0.25]	[0,0.15]

.

5.3.2. Comprehensive Evaluation Results Based on Vague Set

In this section, for each sub-system, the weighted Vague values of indicators under different comment levels was calculated via the Vague set multiplication operation expressed in Equation (6), combining the index weight vector and the Vague value evaluation matrix. Furthermore, the Vague set finite sum operation expressed in Equation (7) was employed to obtain the comprehensive Vague value of the object to be evaluated on each comment level.

Specifically, for the three sub-EIA index systems constructed in this paper, according to the weight of each index in Table 4 and the Vague value of each index in Table 5, the weighted Vague value of each index can be calculated. Then, through the Vague set finite sum operation, we can get the comprehensive Vague value of the project on the five comment levels. For example, in the sub-system of natural environment (${\mathrm{C}}_1$), the Vague value of evaluation index ${\mathrm{C}}_{11}$ on comment level $V_1$ is $r_{111}=\left[0,0.1\right]$, and the weight of ${\mathrm{C}}_{11}$ is $w_{11}=0.1489$, then the weighted Vague value of this index on $V_1$ is $w{r}_{111}=\left[0,0.0149\right]$. Similarly, the weighted Vague value of all indicators in each sub-system under each comment level can be obtained, and the comprehensive Vague value of the project in each sub-EIA system under each comment level were calculated accordingly, as shown in

Table 6. Results of comprehensive evaluation about environmental impact of grid project Vague value.

Sub-System	Indicators	Weighted and Comprehensive Vague Values of Indicators under Each Comment Level
		V1	V2	V3	V4	V5
${\mathrm{C}}_1$	C11	[0,0.0149]	[0.0521,0.0670]	[0.0372,0.0521]	[0.0223,0.0372]	[0.0223,0.0372]
	C12	[0,0.0135]	[0.0225,0.0270]	[0.0270,0.0405]	[0.0180,0.0315]	[0.0090,0.0225]
	C13	[0.0547,0.0804]	[0.0459,0.0689]	[0.0230,0.0459]	[0.0344,0.0574]	[0.0459,0.0689]
	C14	[0.0179,0.0239]	[0.0537,0.0597]	[0.0298,0.0358]	[0.0119,0.0179]	[0,0.0060]
	C15	[0.0033,0.0099]	[0.0133,0.0199]	[0.0332,0.0398]	[0.0099,0.0166]	[0,0.0066]
	C16	[0.0055,0.0055]	[0.0388,0.0388]	[0.0083,0.0083]	[0.0028,0.0028]	[0,0]
	C17	[0.0120,0.0240]	[0.0600,0.0720]	[0.0240,0.0360]	[0.0120,0.0240]	[0,0.0120]
	C18	[0.0040,0.0067]	[0.0108,0.0135]	[0.0067,0.0094]	[0.0027,0.0054]	[0,0.0027]
	C19	[0.0047,0.0071]	[0.0213,0.0237]	[0.0119,0.0142]	[0.0071,0.0095]	[0,0.0024]
	C1,10	[0.0432,0.0481]	[0.0336,0.0384]	[0.0144,0.0192]	[0,0.0048]	[0,0.0048]
$F_1$		[0.1482,0.2340]	[0.3520,0.4378]	[0.2155,0.3013]	[0.1212,0.2071]	[0.0773,0.1631]
${\mathrm{C}}_2$	C21	[0.0170,0.0284]	[0.0454,0.0567]	[0.0227,0.0340]	[0.0170,0.0284]	[0,0.0113]
	C22	[0.0051,0.0064]	[0.0115,0.0128]	[0.0051,0.0064]	[0.0026,0.0038]	[0,0.0013]
	C23	[0.0076,0.0153]	[0.0382,0.0458]	[0.0153,0.0229]	[0.0038,0.0114]	[0.0038,0.0114]
	C24	[0,0.0117]	[0.0235,0.0352]	[0.0646,0.0763]	[0.0176,0.0294]	[0,0.0117]
	C25	[0,0.0118]	[0.0196,0.0314]	[0.0353,0.0470]	[0.0118,0.0235]	[0,0.0118]
	C26	[0.0116,0.0194]	[0.0465,0.0543]	[0.0078,0.0155]	[0.0039,0.0116]	[0,0.0078]
	C27	[0.0077,0.0307]	[0.0230,0.0460]	[0.0690,0.0920]	[0.0307,0.0537]	[0,0.0230]
	C28	[0,0.0064]	[0,0.0064]	[0.0127,0.0191]	[0.0890,0.0954]	[0.0191,0.0254]
	C29	[0,0.0231]	[0.0231,0.0462]	[0.1155,0.1385]	[0.0577,0.0808]	[0.0115,0.0346]
$F_2$		[0.0491,0.1530]	[0.2307,0.3346]	[0.3478,0.4518]	[0.2341,0.3380]	[0.0344,0.1384]
${\mathrm{C}}_3$	C31	[0.0539,0.0693]	[0.0616,0.0770]	[0.0231,0.0385]	[0,0.0154]	[0,0.0154]
	C32	[0.0298,0.0417]	[0.0536,0.0655]	[0.0179,0.0298]	[0.0060,0.0179]	[0,0.0119]
	C33	[0.0206,0.0275]	[0.0549,0.0618]	[0.0412,0.0481]	[0.0137,0.0206]	[0,0.0069]
	C34	[0.0071,0.0355]	[0.0429,0.0710]	[0.0213,0.0497]	[0.0284,0.0568]	[0.0142,0.0426]
	C35	[0.0046,0.0080]	[0.0080,0.0115]	[0.0034,0.0069]	[0.0023,0.0057]	[0.0011,0.0046]
	C36	[0,0.0064]	[0.0319,0.0383]	[0.0223,0.0287]	[0.0032,0.0096]	[0,0.0064]
	C37	[0.0015,0.0031]	[0.0099,0.0115]	[0.0023,0.0038]	[0,0.0015]	[0,0.0015]
	C38	[0.0092,0.0118]	[0.0118,0.0145]	[0.0026,0.0053]	[0,0.0026]	[0,0.0026]
	C39	[0.0272,0.0409]	[0.0681,0.0817]	[0.0204,0.0341]	[0.0068,0.0204]	[0,0.0136]
	C3,10	[0.0275,0.0550]	[0.0458,0.0733]	[0.0642,0.0917]	[0.0183,0.0458]	[0,0.0275]
$F_3$		[0.1814,0.2990]	[0.3883,0.5059]	[0.2187,0.3363]	[0.0787,0.1963]	[0.0153,0.1330]

.

Table 6 shows the results of EIA of Qaidam-Lhasa ±400 kV HVDC transmission project based on Vague sets, that is, the Vague values of the impacts of the HVDC transmission project on natural environment, social environment and ecological environment under the five comment levels. According to the score function given in Equation (8), the scores of the impacts of the project on the three sub-environments under different comment levels can be obtained, as shown in Figure 3.

According to Figure 3, the following conclusions can be drawn: (1) For the impact on natural environment, the scores of the project on the five comment levels are 0.162, 0.382, 0.236, 0.333 and 0.085, respectively, which are: $V_2\succ V_3\succ V_1\succ V_4\succ V_5$, indicating that the impact of the project on the natural environment belongs to the second level, that is, the project has less impact on the natural environment; (2) For the impact on social environment, the scores on the five comment levels are 0.055, 0.257, 0.388, 0.261 and 0.038, respectively, which are: $V_3\succ V_4\succ V_2\succ V_1\succ V_5$, revealing that the impact of the project on social environment belongs to the third level, that is, the project has a general impact on social environment; (3) For the impact on ecological environment, the scores of the projects on the five comment levels are 0.206, 0.440, 0.248, 0.089 and 0.017, respectively, showing that $V_2\succ V_3\succ V_1\succ V_4\succ V_5$. Therefore, the impact of the project on social environment belongs to the second level, indicating that the project has less impact on ecological environment.

6. Conclusions

The continuous development of social economy puts forward higher requirements on the environmental protection of PGP. Environmental impact assessment is an important part of the environmental protection of PGP and the prerequisite for the subsequent environmental protection work. High-altitude areas are the key and difficult areas for China’s power grid construction, having unique natural, social and ecological environments, making assessing the environmental impact caused by the PGP in these areas be of great theoretical and practical significance. Considering the difficulties in the previous studies of EIA of PGP in HAA, such as the selection of evaluation indicators reflecting the environmental characteristics of HAA and the incompleteness and uncertainty of indicator information, this study proposed a hybrid method for assessing the environmental impact caused by PGP in HAA based on BWM-Vague set techniques. Firstly, based on the analysis of the environmental characteristics of HAA and the impacts that PGP may have on the environment, an index system of EIA considering the environmental characteristics of HAA was constructed from the aspects of nature, society and ecology. Secondly, considering the availability of indicator values and the sample size for evaluation, a BWM-based index weighting method was proposed. By establishing the best and worst criteria, the comparison process was simplified and the result was ensured by the optimization model. Then, considering the characteristics of EIA in HAA and the disadvantages of traditional fuzzy comprehensive evaluation, this study introduced Vague set theory into the comprehensive evaluation framework, and proposed an improved fuzzy comprehensive evaluation method based on Vague set theory. Finally, taking the Qaidam-Lhasa ±400 kV HVDC transmission project in the Qinghai-Tibet Plateau as an example, the empirical analysis was carried out to verify the validity and practicability of the model. The research results of this paper can be used as an integral part of grid enterprise standard system, which can play an important supporting role in grid enterprise standard system construction, promoting the green and sustainable development of power grid enterprises.

According to the weight results obtained by BWM, monthly average air quality and power frequency electric field are the indicators with the largest and the smallest weights in natural sub-EIA system. In the social sub-EIA system, the pollutant treatment rate and the daytime plant noise have the greatest and least influence on social environment. In the ecological sub-EIA system, the animal and plant coverage in high-altitude cold grassland, swamp and meadow and the number of rare species are, respectively, the indicators with the largest and the smallest weights. Therefore, air quality, pollutant disposal and animal and plant coverage are the most important factors that affect the degree of impact of PGP on the environment, which need to be considered in the construction and operation of PGP in HAA. In addition, the comprehensive evaluation results based on Vague set show that the evaluated Qaidam-Lhasa ±400 kV HVDC transmission project has less impact on the natural environment and the ecological environment, and has a general impact on the social environment. Combined with the results of BWM weights and the comprehensive evaluation based on Vague set, the Qaidam-Lhasa ±400 kV HVDC transmission project performs well in animal and plant protection, electromagnetic impact control, noise control and frozen soil and wetland protection. However, there are still deficiencies in the control of PH value about water environment, protection of natural and cultural landscape and disposal of waste and pollutant. Thus, a further job is required in the subsequent project operation stage, aiming to minimize the impacts of PGP in HAA on the natural, social and ecological environment and promote the green construction and sustainable development of PGP in HAA.

Overall, the comprehensive evaluation model based on BWM-Vague set proposed in this paper can fully reflect the environmental characteristics of HAA from three aspects of nature, society and ecology, and can effectively assess the environmental impact of PGP in HAA. Meanwhile, the evaluation framework proposed in this paper has fewer requirements on the number of samples and the sample index data, so it can well deal with the comprehensive evaluation issues with information uncertainty and incompleteness, having good applicability and significance for popularizing, which can provide an effective evaluation tool for similar comprehensive evaluation issues in other fields. Although the model presented in this paper has achieved satisfactory results in empirical terms, there is still room for improvement when extended to other fields. First, the evaluation object in this paper is the environmental impact of PGP in HAA. If the model is extended to other fields, the index system needs to be adjusted accordingly. Secondly, the method of index weighting in this paper is BWM approach, which relies on experts’ judgments. When there are multiple experts and the results of expert judgments are inconsistent, the opinions of all experts need to be comprehensively considered, which requires a BWM-based group decision-making technique. Finally, the comprehensive evaluation method based on Vague set reduces the subjectivity of the evaluation by adding experts’ numbers and allowing experts to abstain from voting. It is worth noting that the method assumes that all experts’ judgments have the same degree of importance, but, in fact, due to difference in knowledge, background, experience and other conditions, the degrees of importance of different experts’ judgments are not the same. For example, an expert who is the authority in the field of water environment protection believes that the project has a great impact on the water environment. However, other experts think the impact is general. According to the Vague set evaluation rules in this paper, the project considers that the project has a general impact on the water environment, but actually the project may have a great impact on the water environment. Therefore, for different experts, it is more objective to give their judgments different weights according to their knowledge, background and experience, so that the final evaluation results not only consider the importance of the indicators, but also consider the authoritative of experts’ judgment, making the results more scientific and reliable. This can be a direction that can be further studied in future research.