Comprehensive Benefit Evaluation of Power Grid Investment Considering Renewable Energy Development from the Perspective of Sustainability

Abstract

To cope with the rapid development of renewable energy, the power grid system needs to invest in and construct transmission and distribution projects. Means of evaluating the economic, social, and environmental benefits generated by power grid investment are of great significance for enterprise cost recovery and government policy formulation. In this paper, an evaluation of the comprehensive benefit of a power grid investment considering renewable energy development from the perspective of sustainability is developed through the use of a hybrid multi-criteria decision-making (MCDM) method. The entropy weight method and fuzzy best worst method (BWM) are jointly employed to weight the comprehensive benefit criteria, which include economic, social, and environmental criteria and eight sub-criteria, and the measurement of alternatives and ranking according to compromise solution (MARCOS) method is utilized to evaluate the comprehensive benefit of a power grid investment. Five power grid investment projects for connecting renewable energy generation to a power grid in Ningxia, China, are selected as a case study, and the results indicate that the power grid investment project PGIP#1 has the largest comprehensive benefit (0.7099), followed by PGIP#3 (0.6800), PGIP#2 (0.6709), PGIP#5 (0.5959), and PGIP#4 (0.5861). The sensitivity analysis shows that the comprehensive benefit of PGIP#1 is always the best, indicating the robustness of the proposed method. By employing the proposed MCDM method to assess the comprehensive benefit of power grid investment projects, this research identifies outstanding projects which can provide guidance for the management of power grid investment and promote the sustainable development of the power industry.

1. Introduction

Against the backdrop of climate change and fossil energy shortages, the world is accelerating the pace of energy transition in order to build up the clean production and consumption of energy and electricity [1,2]. Renewable energy, represented by wind and solar PV energy, has become the development direction and a strategic choice for energy transformation in various countries due to its advantage of zero-emission power generation. Driven by technology, the renewable energy industry is developing rapidly [3,4]. China’s government has proposed the development goal of peaking CO₂ emissions before 2030 and achieving carbon neutrality before 2060. Promoting the installation of renewable energy in the grid is an important means of achieving the above-mentioned goal.

As a basic industry that affects the operation of the country, the power industry needs to focus on the safety and smoothness of power generation, transmission and distribution to ensure economic and social development [5]. Therefore, electric power construction is of great importance and is the focus of the country. The construction of power grid transmission and distribution projects is an important part of the electric power industry. In the context of carbon peaking and carbon neutralization (namely, the dual carbon goal) in China, strengthening the grid construction, especially the ultra-high voltage construction, can effectively solve the problem of grid connection and cross-provincial and cross-regional power transmission for new renewable energy projects [6]. Therefore, to achieve the dual carbon goal, the grid-connected power generation of renewable energy requires the construction of supporting transmission and transformation projects which will drive investment in the power grid. Since the formal launch of the new round of power system reforms in 2015, the relevant national departments have formulated and issued several policy documents [7,8,9], including “Opinions on Further Deepening the Reform of the Power System”, “Measures for the Cost Supervision and Examination of Transmission and Distribution Power Price”, “Pricing Measures of Transmission and Distribution Power for Provincial Power Grid”, “Measures for the Pricing of Transmission Power for Regional Power Grid”, “Pricing Measures of Transmission Power for Trans-provincial and Trans-regional Special Projects”, and so on. The above-mentioned policy documents have established a new, clear, reasonable, scientific, and transparent transmission and distribution power price system which will change the structure of power supply and demand and the regulatory model for the power industry [10]. Moreover, the responsibilities and operating modes of power grid enterprises will also have new positioning.

Under the new transmission and distribution policy, power grid enterprises charge grid fees based on fixed transmission and distribution electricity prices instead of earning the difference between the transmission and sales prices [11]. This functional orientation and operation mode change makes the power grid transmission and distribution investment management particularly important. Power grid enterprises need to strictly control their investment in transmission and distribution projects, pay attention to project benefits, and adapt to the reform of transmission and distribution electricity prices. Therefore, it is of great significance to study the comprehensive benefits of power grid investment in the context of the connection of renewable energy to the grid, which can guide a reasonable power grid investment, improve the efficiency of tge power grid investment, and promote the sustainable development of the electric power industry.

Power grid investment that considers the access of large-scale renewable energy to the electric power grid can provide not only economic benefit but can also impart important benefits to the environment and social development. For example, power grid investment can transmit electricity, including renewable energy power and traditional fossil energy power, which can yield income based on the tariff and power transmission capacity. Meanwhile, power grid investment can be conducive to the connection of renewable energy power to the electric power grid, which can reduce the abandonment of renewable energy power generation, be a substitute for thermal power generation, and reduce CO₂ emissions. Therefore, the comprehensive benefit of power grid investment, which includes multiple benefits such as economic, social, and environmental benefits, needs to be studied. However, considering the development of renewable energy, the different benefits of a power grid investment, which are represented by different criteria, are quite different; this is a multi-attribute decision-making (MCDM) issue, and the attributes must be simultaneously considered.

Recently, scholars have conducted some research on the investment benefits of power grids. Ref. [12] proposes a precision investment method based on the three factors of region, power network, and power supply unit by constructing the precision investment index system of a regional distribution network. Ref. [13] analyzed the key characteristics of grid investments based on the principle of “defining characteristics at the macro level and indicators at the micro level” and established a system of indicators to reflect policy, economic, security, and strategic intentions to optimize capital allocation. Ref. [14] reviewed the global sustainable future initiatives and concluded that the quantification of the costs, benefits, and environment of the global interconnected power grid is in its early stages by studying its advantages and disadvantages. Faced with a mismatch between the power grid enterprises’ investment capacities and investment projects, Ref. [15] proposed a two-tier investment benefit evaluation index system considering the unit investment efficiency and macro investment benefit and established an optimal combination model of maximizing investment benefit and minimizing cost. The model realized the dynamic adjustment of the scheme in the investment cycle. Ref. [16] analyzed the impact of transmission engineering on wholesale price levels, variances, and regional differences and measured the environmental benefits brought by renewable energy generation. Research has found that renewable energy supported by transmission lines significantly reduces electricity prices and emissions. Through a review of the literature, it can be concluded that the research studies relating to the benefits of power grid investment mainly focus on the economic benefit, though several studies also consider the environmental benefit. However, the social benefit of investment in power grid transmission and distribution has been ignored. Meanwhile, the research has mostly focused on optimizing investment allocation strategies in advance, and less research has been performed on verifying the comprehensive benefits after investment. The comprehensive evaluation of the economic, social, and environmental benefits from a sustainable development perspective has not yet been thoroughly studied.

In this paper, a comprehensive benefit evaluation of power grid investment considering renewable energy development from the perspective of sustainability is carried out using a hybrid MCDM method, including the entropy weight method, fuzzy best worst method (BWM), and the measurement of alternatives and ranking according to compromise solution (MARCOS) method. Compared with the current above-mentioned research studies, this paper has two main contributions.

(1) The first contribution of this paper is that a hybrid MCDM method is proposed for the comprehensive benefit evaluation of power grid investment considering renewable energy development from the perspective of sustainability. This hybrid method combines the entropy weight method, fuzzy BWM, and MARCOS method. The objective weighting method (in this paper, the entropy weight method) and the subjective weighting method (in this paper, the fuzzy BWM) are jointly used to determine the criteria weights of the comprehensive benefit of the power grid investment, which can consider the objectivity of the criteria data and the subjectivity of the decision makers. A new MCDM method, namely, MARCOS, which was proposed in 2019, is used to rank the comprehensive benefit of the power grid investment. This is the first time it has been employed in the field of power grid investment.

(2) The second contribution is that a new view for the comprehensive benefit evaluation of a power grid investment that considers renewable energy development is proposed which comprehensively includes multiple benefit criteria, namely, an economic benefit criterion, social benefit criterion, and environmental benefit criterion. Moreover, each criterion also includes several sub-criteria. The economic benefit criterion includes three sub-criteria, namely, the internal rate of return, unit investment income, and the revenue increase for the renewable energy power producers. The social benefit criterion includes three sub-criteria, namely, a reduction in economic losses due to power failure, the promotion of regional economic development benefits, and the promotion of employment benefits. The environmental benefit criterion includes two sub-criteria, namely, a reduction in carbon emissions and a reduction in the abandonment of renewable energy.

By applying the proposed method to an empirical analysis, three main indicators that affect the investment efficiency of the power grid are identified, namely, the “Internal rate of return” (C1) and “Unit investment income” (C2), as well as “Carbon emissions reduction” (C7), with corresponding impact weights of 0.1972, 0.2299, and 0.1451. This article takes “Carbon emissions reduction” (C7) as the main impact indicator for the comprehensive benefit evaluation of the power grid investment, fully considering the important impact of environmental factors on power grid investment.

The structure of this paper is as follows: Section 2 determines the criteria of a comprehensive benefit evaluation of a power grid investment considering renewable energy development from the perspective of sustainability; Section 3 builds a hybrid MDCM method for the comprehensive benefit evaluation of a power grid investment considering renewable energy development from the perspective of sustainability, which includes the entropy weight method, fuzzy BWM, and MARCOS method; Section 4 conducts the empirical analysis, which takes five power grid investment projects in Ningxia, China, as a case study; and the results are discussed in Section 5. Finally, the conclusion is provided in Section 6.

2. Comprehensive Benefit Evaluation Index System of Power Grid Investment Considering Renewable Energy Development

Selecting indicators is crucial in evaluating the comprehensive benefits of power grid investment. The construction of indicators needs to consider both the development of renewable energy and the efficiency of the power grid. In this paper, the comprehensive benefit evaluation index system of power grid investment considering renewable energy development is built from the perspective of sustainability, including the economic benefit, social benefit, and environmental benefit. Moreover, these three benefit criteria include several sub-criteria.

Firstly, a scoring and evaluation team consisting of three business practitioners and three relevant industry professors was established for this paper. According to the relevant literature and the discussion of the scoring evaluation group, a comprehensive benefit evaluation index of power grid transmission and distribution investment considering renewable energy development from the perspective of sustainability was determined, including the economic benefit criterion, social benefit criterion, and environmental benefit criterion. Compared to Ref. [17], this paper takes into account the economic benefits of increasing the profits of renewable energy enterprises and the environmental benefits of reducing wind and solar waste in the criteria system by referring to the evaluation of the power-related side benefits of the ultra-high voltage power grids in references [18,19]. Moreover, the preliminary sub-criteria of the economic benefit criterion, social benefit criterion, and environmental benefit criterion were determined. Then, the expert panel identified the most important benefit sub-criteria based on their expertise and further developed an assessment index system covering the economic, social, and environmental benefits, as shown in Figure 1. The economic benefit criterion includes the internal rate of return (C1), unit investment income (C2), and the revenue increase for the producers of renewable energy power (C3). The social benefit criterion includes the reduction in economic losses due to power failure (C4), the promotion of regional economic development benefits (C5), and the promotion of employment benefits (C6). The environmental benefit criterion includes reductions in carbon emissions (C7) and the abandonment of renewable energy (C8).

3. The Proposed Hybrid Novel MCDM Methodology for the Comprehensive Benefit Evaluation of a Power Grid Investment

The comprehensive benefit of a power grid investment considering the development of renewable energy will be evaluated with the consideration of the eight criteria listed above, as shown in Figure 1. The comprehensive benefit evaluation of a power grid investment project involves multiple aspects, and there may be conflicts between different indicators, and sometimes the differences in the quantitative values of the same indicator cannot fully reflect the comprehensive benefits of the power grid investment. Therefore, subjective and objective joint weighting can be used to determine indicator weights, and the MCDM method can be applied to rank the comprehensive benefits. The following describes the implementation steps of the method.

3.1. The Entropy Weight Method and Fuzzy BWM for the Weight Determination of Criteria

The entropy weight method is an objective evaluation method for determining the weight of criteria according to the difference in the criteria performance data [20]. According to the degree of variation of each criterion, the entropy weight method calculates the index weight by quantifying the difference in the values and obtaining the index information entropy, which can fully mine the information in the original data and objectively display the weight of each criterion [21]. The basic theory of the entropy weight method is illustrated as follows:

Suppose there are n criteria and m alternatives for a targeted issue. The initial matrix X is:

$$\mathrm{X}=\left[\begin{array}{cc}\begin{array}{cc}{x}_{11}& x_{12}\\ x_{21}& x_{22}\end{array}& \begin{array}{cc}\cdots & x_{1n}\\ \cdots & x_{2n}\end{array}\\ \begin{array}{cc}\cdots & \cdots \\ x_{m1}& x_{m2}\end{array}& \begin{array}{cc}\cdots & \cdots \\ \cdots & x_{mn}\end{array}\end{array}\right]$$

(1)

where $x_{ij}$ is the value of the jth criterion of alternative i; i = 1, 2,…, m, and j = 1, 2…, n.

According to the theory of information entropy, the information entropy e_j of a set of data is:

$$e_j=-\frac{1}{\ln m}{{\displaystyle \sum }}_{i=1}^m\left(f_{ij}\ln f_{ij}\right)$$

(2)

$$f_{ij}=\frac{x_{ij}}{{{\displaystyle \sum }}_{i=1}^m{x}_{ij}}$$

(3)

Then, the weight of each criterion can be calculated as:

$$w_j^o=\frac{1-e_j}{{{\displaystyle \sum }}_{j=1}^n\left(1-e_j\right)}$$

(4)

where $w_j^o$ is the weight of the jth criterion.

Then, the objective weights of the criterion system can be obtained through the way shown above.

However, as a type of objective weighting method, the entropy weight method only considers the difference in the criteria value, which may be improper and deviate from the actual in some cases and must be used with subjective weighting method [22]. Therefore, the subjective weighting method, namely, fuzzy BWM, was also employed to determine the weights of the criteria for the comprehensive benefit evaluation of a power grid investment in this paper.

The fuzzy BWM is an extension of the BWM, which represents the qualitative judgment of decision makers through triangular fuzzy numbers to reflect the uncertainty of a qualitative evaluation [23,24]. The fuzzy BWM was developed by Professors Sen Guo and Haoran Zhao in 2017, and Prof. Sen Guo is also the corresponding author of this paper. The detailed theory of the fuzzy BWM for the weighting criteria is provided below.

Step 1. Determine the best and worst criteria.

The panel of experts selected the best sub-criterion C_B and the worst sub-criterion C_W from all sub-criteria based on their expertise.

Step 2. Conduct fuzzy reference comparisons for the best sub-criterion.

The importance of each sub-criterion was evaluated relative to the best and worst sub-criteria via the linguistic terms, which were then transformed into a triangular fuzzy number (TFN) according to the membership function listed in

Table 1. Transformation rules of linguistic terms of expert panel.

Linguistic Terms	Membership Function
Equally Important (El)	(1,1,1)
Weakly Important (WI)	(3/2,2,5/2)
Fairly Important (Fl)	(3/2,2,5/2)
Very Important (VI)	(5/2,3,7/2)
Absolutely Important (Al)	(7/2,4,9/2)

.

Then, the fuzzy comparison matrix can be obtained as:

$$\begin{array}{cc} & \begin{array}{cccc}{C}_1& C_2& \cdots & C_n\end{array}\\ \begin{array}{cc}& C_1\\ \tilde{A}=& C_2\\ & ⋮\\ & C_n\end{array}& \left[\begin{array}{cccc}{\tilde{a}}_{11}& {\tilde{a}}_{12}& \cdots & {\tilde{a}}_{1n}\\ {\tilde{a}}_{21}& {\tilde{a}}_{22}& \cdots & {\tilde{a}}_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ {\tilde{a}}_{n1}& {\tilde{a}}_{n2}& & {\tilde{a}}_{nn}\end{array}\right]\end{array}$$

(5)

where ${\tilde{a}}_{ij}$ is the relative fuzzy preference of sub-criterion i to sub-criterion j.

The expert panel conducts fuzzy reference comparisons for the best sub-criterion; thus, the fuzzy best-to-others vector ${\tilde{A}}_B$ for the comprehensive benefit evaluation of a power grid investment is obtained as:

$${\tilde{A}}_B=\left({\tilde{a}}_{B1}{\tilde{a}}_{B2},\cdots ,{\tilde{a}}_{Bn}\right)$$

(6)

where ${\tilde{a}}_{Bj}$ is the fuzzy preference, represented by TFN of $c_B$ over sub-criterion j.

Step 3. Conduct fuzzy reference comparisons for the worst sub-criterion.

The expert panel conducts fuzzy pairwise comparisons between the worst sub-criterion and other sub-criteria, and the fuzzy others-to-worst vector ${\tilde{A}}_W$ for the comprehensive benefit evaluation of a power grid investment can then be obtained as:

$${\tilde{A}}_W=\left({\tilde{a}}_{1W},{\tilde{a}}_{2W},\cdots ,{\tilde{a}}_{nW}\right)$$

(7)

where ${\tilde{a}}_{iW}$ is the fuzzy preference, represented by TFN of sub-criterion i over $c_W$.

Step 4. Determine the optimal fuzzy weights of the sub-criteria for the power grid investment benefit evaluation.

The optimal fuzzy weights’ determination model for the power grid investment benefit evaluation is constructed as:

$$\begin{array}{l}\min \underset{j}{\max }\left\{\left|\frac{{\tilde{w}}_B}{{\tilde{w}}_j}-{\tilde{a}}_{Bj}\right|,\left|\frac{{\tilde{w}}_j}{{\tilde{w}}_w}-{\tilde{a}}_{jw}\right|\right\}\\ s.t.\left\{\begin{array}{l}{\displaystyle {\displaystyle \sum }_{j=1}^n}R\left({\tilde{w}}_j\right)=1\\ l_j^w\le m_j^w\le u_j^w\\ l_j^w\ge 0\\ j=1,2,\cdots n\end{array}\right.\end{array}$$

(8)

$$R\left({\tilde{w}}_j\right)=\frac{l_j^w+4m_j^w+u_j^w}{6}$$

(9)

where ${\tilde{w}}_B=\left(l_B^w,m_B^w,u_B^w\right)$, ${\tilde{w}}_j=\left(l_j^w,m_j^w,u_j^w\right)$, ${\tilde{w}}_w=\left(l_w^w,m_w^w,u_w^w\right)$, ${\tilde{a}}_{Bj}=\left(l_{Bj},m_{Bj},u_{Bj}\right)$, ${\tilde{a}}_{jw}=\left(l_{jw},m_{jw},u_{jw}\right)$.

Then, Equation (8) is transferred to the following non-linearly constrained optimization problem in the fuzzy BWM.

$$\begin{array}{l}\min \tilde{\xi }\\ s.t.\left\{\begin{array}{l}\left|\frac{{\tilde{w}}_B}{{\tilde{w}}_j}-{\tilde{a}}_{Bj}\right|\le \xi \hfill \\ \left|\frac{{\tilde{w}}_j}{{\tilde{w}}_w}-{\tilde{a}}_{jw}\right|\le \xi \hfill \\ {\displaystyle {\displaystyle \sum }_{j=1}^n}R\left({\tilde{w}}_j\right)=1\hfill \\ \begin{array}{l}{l}_j^w\le m_j^w\le u_j^w\hfill \\ l_j^w\ge 0\hfill \end{array}\hfill \\ j=1,2,\cdots n\hfill \end{array}\right.\end{array}$$

(10)

where $\tilde{\xi }=\left(l^{\xi },m^{\xi },u^{\xi }\right)$.

Considering $l^{\xi }\le m^{\xi }\le u^{\xi }$, it supposes ${\tilde{\xi }}^{*}=\left(k^{*},k^{*},k^{*}\right)$, $k^{*}\le l^{\xi }$; then, Equation (10) can be transferred as:

$$\begin{array}{l}\min {\tilde{\xi }}^{*}\\ s.t.\left\{\begin{array}{l}\left|\frac{\left(l_B^w,m_B^w,u_B^w\right)}{\left(l_j^w,m_j^w,u_j^w\right)}-\left(l_{Bj},m_{Bj},u_{Bj}\right)\right|\le \left(k^{*},k^{*},k^{*}\right)\hfill \\ \left|\frac{\left(l_j^w,m_j^w,u_j^w\right)}{\left(l_w^w,m_w^w,u_w^w\right)}-\left(l_{jw},m_{jw},u_{jw}\right)\right|\le \left(k^{*},k^{*},k^{*}\right)\hfill \\ {\displaystyle {\displaystyle \sum }_{j=1}^n}R\left({\tilde{w}}_j\right)=1\hfill \\ l_j^w\le m_j^w\le u_j^w\hfill \\ l_j^w\ge 0\hfill \\ j=1,2,\cdots n\hfill \end{array}\right.\end{array}$$

(11)

Finally, the optimal fuzzy weights of the sub-criteria for the power grid investment benefit evaluation can be calculated. Moreover, the optimal fuzzy weights of the sub-criteria can be transformed into crisp values, $w_j^s$, according to Equation (9).

Meanwhile, the fuzzy BWM employs the consistency ratio (CR) to test the result validity. The fuzzy weights are acceptable when the CR is less than 0.1.

Based on the objective weight $w_j^o$ obtained from the entropy weight method and the subjective weight $w_j^s$ obtained from the fuzzy BWM, the final weight of the jth sub-criterion for the power grid investment benefit evaluation can be calculated as:

$$w_j=\alpha w_j^o+\left(1-\alpha \right)w_j^s$$

(12)

where $w_j$ is the final weight of the jth sub-criterion for the power grid investment benefit evaluation, and $\alpha$ is the share of objective weight in total weight, which is set as 0.5 in this paper.

3.2. The MARCOS for Ranking the Comprehensive Benefits of Power Grid Investments

The MARCOS is a new MCDM method, proposed in 2019, which conducts a compromise ranking between alternatives and ideal/anti-ideal alternatives [25]. The detailed theory of the MARCOS method is expressed as follows.

Step 1: Build the extended initial matrix.

According to the initial matrix X shown in Equation (1), the extended initial matrix X’ can be built by adding the ideal (AI) and anti-ideal (AAI) solutions, namely:

$$\begin{array}{cc} & \begin{array}{cccc}{C}_1& C_2& \cdots & C_n\end{array}\\ X=\begin{array}{c}AAI\\ A_1\\ A_2\\ \dots \\ A_m\\ AI\end{array}& \left(\begin{array}{cccc}{x}_{aa1}& x_{aa2}& \cdots & x_{aan}\\ x_{11}& x_{12}& a_{13}& x_{1n}\\ x_{21}& x_{22}& a_{23}& x_{2n}\\ \cdots & \cdots & \cdots & \cdots \\ x_{m1}& x_{m2}& \cdots & x_{mn}\\ x_{ai1}& x_{ai2}& \cdots & x_{ain}\end{array}\right)\end{array}$$

(13)

where $x_{aaj}$ and $x_{aij}$ are the jth sub-criterion values of the AAI solution and the jth sub-criterion values of the AI solution.

$$AAI=\left\{\begin{array}{l}\underset{i}{\min }{x}_{ij},ifj\in B\\ \underset{i}{\max }{x}_{ij},ifj\in C\end{array}\right.$$

(14)

$$AI=\left\{\begin{array}{l}\underset{i}{\max }{x}_{ij},ifj\in B\\ \underset{i}{\min }{x}_{ij},ifj\in C\end{array}\right.$$

(15)

where B represents the benefit-type criteria set, and C represents the cost-type criteria set.

Step 2: Normalize the extended initial matrix.

The extended initial matrix can be normalized using Equations (16) and (17), and then the normalized matrix N = [n_ij]_m∗n can be obtained.

$$n_{ij}=\frac{x_{ij}}{\underset{i}{\max }{x}_{ij}},ifj\in B$$

(16)

$$n_{ij}=\frac{\underset{i}{\min }{x}_{ij}}{x_{ij}},ifj\in C$$

(17)

Step 3: Calculate the weighted matrix.

By multiplying the normalized matrix N and the criteria weight w_j, the weighted matrix v_ij can be calculated as:

$$v_{ij}=n_{ij}\times w_j$$

(18)

Step 4: Calculate the utility degrees of the comprehensive benefit of the power grid investment.

In this step, the utility degrees of the comprehensive benefit of the power grid investment can be calculated according to Equations (19) and (20).

$$K_i^{-}=\frac{S_i}{S_{aai}}$$

(19)

$$K_i^{+}=\frac{S_i}{S_{ai}}$$

(20)

where

$$S_i={\displaystyle {\displaystyle \sum }_{i=1}^n}{v}_{ij}$$

(21)

Step 5: Calculate the utility function of the comprehensive benefit of the power grid investment.

In this model, the utility function of the comprehensive benefit of the power grid investment is the compromise of the comprehensive benefit of the power grid investment related to the ideal and anti-ideal solutions, which can be calculated as:

$$f\left(K_i\right)=\frac{K_i^{+}+K_i^{-}}{1+\frac{1-f\left(K_i{}^{+}\right)}{f\left(K_i{}^{+}\right)}+\frac{1-f\left(K_i{}^{-}\right)}{f\left(K_i{}^{-}\right)}}$$

(22)

where $f\left(K_i^{-}\right)$ is the utility function of the comprehensive benefit of a power grid investment related to the anti-ideal solution; $f\left(K_i^{+}\right)$ is the utility function of the comprehensive benefit of a power grid investment related to the ideal solution.

$$f\left(K_i{}^{+}\right)=\frac{K_i^{-}}{K_i^{+}+K_i^{-}}$$

(23)

$$f\left(K_i{}^{-}\right)=\frac{K_i^{+}}{K_i^{+}+K_i^{-}}$$

(24)

Step 6: Rank the comprehensive benefits of the power grid investments.

The combined benefits of the grid investments are ranked according to the utility function. The power grid investment with the largest utility function has the best comprehensive benefit.

3.3. The Framework of the Comprehensive Benefit Evaluation of a Power Grid Investment

In this paper, a hybrid MCDM method was proposed to evaluate the comprehensive benefits of a power grid investment considering renewable energy development by combining the entropy weight method, fuzzy BWM method, and MARCOS method. The entropy weight method and fuzzy BWM method were jointly used to determine the weight of the criteria, and the MARCOS method was used to evaluate the comprehensive benefits of the power grid investment. The detailed procedure for the comprehensive benefit evaluation of a power grid investment considering renewable energy development using the proposed hybrid MCDM method are shown in Figure 2.

4. Empirical Analysis

The Ningxia Hui Autonomous Region (hereafter referred to as Ningxia) is a key region with the highest penetration of renewable energy in China. It is located in northwest China and has rich renewable energy resources. During the 13th Five-Year Plan period, the installed capacity of power generation in Ningxia reached 59.43 million kW. Wind power and photovoltaic power generation continued to develop rapidly, and the installed capacity and power generation of renewable energy accounted for 43.5% and 17.7%, respectively. The proportion of non-hydropower renewable energy power consumption in Ningxia has been among the highest in China for many years. The Ningxia power grid has become the first provincial power grid with renewable energy power generation that exceeds the power load of the whole grid.

The 14th Five-Year Plan for Ningxia energy development, issued by Ningxia government in 2022, has proposed the rapid development of renewable energy, and the renewable energy power generation will be doubled, with an installed capacity of more than 50 million kW. The large-scale penetration of renewable energy requires investment in the power grid, which can guarantee the renewable energy consumption and reduce the abandonment of renewable energy power generation. Therefore, five power grid investment projects for connecting renewable energy generation to the power grid, labelled PGIP#1, PGIP#2, PGIP#3, PGIP#4, and PGIP#5, were selected for the evaluation of their comprehensive benefits from the perspective of sustainability.

To evaluate the comprehensive benefits of these five power grid investment projects by using the proposed MCDM method from the perspective of sustainability, the actual values of eight sub-criteria first need to be obtained. According to feasibility study reports, technical—economic analysis reports, and social impact assessment reports, the eight sub-criteria values of the five power grid investment projects were obtained and are shown in Figure 3.

4.1. Calculating the Weights of the Benefit Criteria

Based on the eight benefit sub-criteria values of the five power grid investment projects, the initial matrix X can be obtained according to the data shown in Figure 3. Then, according to Equations (2) and (4), the objective weights of the eight benefit sub-criteria for the comprehensive benefit evaluation of a power grid investment considering renewable energy development, determined by the entropy weight method, can be calculated as:

$$w^o=\left\{w_j^o\right\}=\left\{0.1573,0.3120,0.1104,0.0571,0.1084,0.0339,0.1104,0.1104\right\}$$

Then, the subjective weights of the eight benefit sub-criteria values will be determined by using the fuzzy BWM method.

Firstly, the panel of experts was asked to select the best and worst benefit sub-criteria, and the results are, respectively “Internal rate of return”, C1, and “Promoting employment benefit”, C6.

Secondly, the importance of the other criteria compared to the “Internal rate of return”, C1, is listed according to Table 1, which is listed in

Table 2. Fuzzy reference comparisons for C1.

Best Criterion	C1	C2	C3	C4	C5	C6	C7	C8
C1	EI	FI	VI	FI	FI	AI	EI	FI

. Then, the ${\tilde{A}}_B$ is:

$${\tilde{A}}_B=\left(\begin{array}{ccc}\left(1,1,1\right)& \left(3/2,2,5/2\right)& \left(5/2,3,7/2\right)\\ \left(3/2,2,5/2\right)& \left(3/2,2,5/2\right)& \left(7/2,4,9/2\right)\\ \left(1,1,1\right)& \left(3/2,2,5/2\right)& \end{array}\right)$$

Thirdly, the fuzzy reference comparisons for “Promoting employment benefit”, C6, were conducted, and

Table 3. Fuzzy reference comparisons for C6.

Worst Criterion	C6
C1	AI
C2	VI
C3	WI
C4	FI
C5	FI
C6	EI
C7	VI
C8	FI

lists the result. Then, the ${\tilde{A}}_W$ is:

$${\tilde{A}}_W=\left(\begin{array}{ccc}\left(7/2,4,9/2\right)& \left(5/2,3,7/2\right)& \left(2/3,1.3/2\right)\\ \left(3/2,2,5/2\right)& \left(3/2,2,5/2\right)& \left(1,1,1\right)\\ \left(5/2,3,7/2\right)& \left(3/2,2,5/2\right)& \end{array}\right)$$

Finally, the optimal fuzzy weights of the eight benefit sub-criteria from the comprehensive benefit evaluation of a power grid investment can be calculated according to Equations (8)–(11), which are shown in Figure 4.

Moreover, the CR is 0.0455, which is less than 0.1. Therefore, the pairwise comparisons of the expert panel for the benefit sub-criteria are consistent, and the subjective criteria weighting results for the comprehensive benefit evaluation of a power grid investment are acceptable. According to Equation (9), the crisp subjective weights of the eight benefit sub-criteria for the comprehensive benefit evaluation of a power grid investment considering renewable energy development, determined by the fuzzy BWM method, can be calculated as:

$$w^s=\left\{w_j^s\right\}=\left\{0.2370,0.1478,0.0735,0.1019,0.1019,0.0560,0.1798,0.1019\right\}$$

Finally, the eight benefit sub-criteria for the comprehensive benefit evaluation of a power grid investment considering renewable energy development can be determined according to Equation (12), which is shown in Figure 5.

4.2. Ranking the Comprehensive Benefits of Five Power Grid Investment Projects

After the eight benefit sub-criteria weights for the comprehensive benefit evaluation of a power grid investment were determined using the entropy weight method and fuzzy BWM, the comprehensive benefits of the five power grid investment projects were comprehensively evaluated using the MARCOS method, and the detailed process is illustrated below.

Firstly, the extended initial matrix X’ can be built according to Equations (13)–(15), and then the normalized matrix N can be calculated according to Equations (16) and (17) and is listed in

Table 4. The normalized matrix N.

	C1	C2	C3	C4	C5	C6	C7	C8
AAI	0.6611	0.5526	0.7013	0.7907	0.7062	0.8393	0.7013	0.7013
PGIP#1	1.0000	1.0000	0.7701	0.7907	1.0000	0.9464	0.7701	0.7701
PGIP#2	0.8954	0.8158	0.8473	0.8140	0.8967	0.8571	0.8473	0.8473
PGIP#3	0.7467	0.6579	1.0000	1.0000	0.9301	1.0000	1.0000	1.0000
PGIP#4	0.6611	0.5526	0.8742	0.8837	0.7062	0.9524	0.8742	0.8742
PGIP#5	0.7955	0.7105	0.7013	0.9302	0.8048	0.8393	0.7013	0.7013
AI	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000

.

Then, the weighted matrix V can be calculated according to Equation (18) and is listed in

Table 5. The weighted matrix V.

	C1	C2	C3	C4	C5	C6	C7	C8
AAI	0.1304	0.1271	0.0645	0.0629	0.0743	0.0378	0.1018	0.0745
PGIP#1	0.1972	0.2299	0.0708	0.0629	0.1052	0.0426	0.1118	0.0818
PGIP#2	0.1765	0.1876	0.0779	0.0647	0.0943	0.0386	0.1230	0.0900
PGIP#3	0.1472	0.1513	0.0919	0.0795	0.0978	0.0450	0.1451	0.1062
PGIP#4	0.1304	0.1271	0.0804	0.0703	0.0743	0.0428	0.1269	0.0928
PGIP#5	0.1568	0.1634	0.0645	0.0740	0.0847	0.0378	0.1018	0.0745
AI	0.1972	0.2299	0.0919	0.0795	0.1052	0.0450	0.1451	0.1062

.

Further, the utility degrees of the comprehensive benefits of the five power grid investment projects can be calculated according to Equations (19)–(21), and the utility functions of the comprehensive benefits of the five power grid investment projects PGIP#1, PGIP #2, PGIP #3, PGIP #4, and PGIP #5 can then be calculated and are listed in

Table 6. The utility degrees and utility functions of comprehensive benefits of five power grid investment projects.

	Ki−	Ki+	f(Ki−)	f(Ki+)	f(Ki)
PGIP#1	1.3403	0.9021	0.4023	0.5977	0.7099
PGIP#2	1.2667	0.8525	0.4023	0.5977	0.6709
PGIP#3	1.2838	0.8641	0.4023	0.5977	0.6800
PGIP#4	1.1067	0.7448	0.4023	0.5977	0.5861
PGIP#5	1.1252	0.7573	0.4023	0.5977	0.5959

.

Finally, according to the utility functions of the comprehensive benefits of the five power grid investment projects, it can be seen that power grid investment project PGIP#1 holds the largest utility function. Therefore, in this paper, power grid investment project PGIP#1 has the largest comprehensive benefit, followed by PGIP#3, PGIP#2, PGIP#5, and PGIP#.

5. Discussion

The comprehensive benefits of five power grid investment projects for connecting renewable energy generation to the power grid, evaluated from the perspective of sustainability, were ranked in consideration of the eight sub-criteria included in the economic, social, and environmental criteria, through the use of the entropy weight method, fuzzy BWM, and MARCOS method. The empirical result indicates that the utility function of the comprehensive benefit of power grid investment project PGIP#1 is the largest, which means that the comprehensive benefit of power grid investment project PGIP#1 is the best.

According to the eight sub-criteria weighting results achieved via the entropy weight method and fuzzy BWM, it can be observed that the objective weights and subjective weights for eight sub-criteria are different. For the objective weights, “Unit investment income” (C2) has the largest weight value, namely, 0.3120, and the second is “Internal rate of return” (C1), while “Promoting employment Benefit” (C6) has the smallest weight value. For the subjective weights, “Internal rate of return” (C1) has the largest weight value, namely, 0.2370, and the second is “Carbon emissions reduction” (C7), while “Promoting employment Benefit” (C6) has the smallest weight value. The objective weights only consider the information embodied in the real value data of the eight sub-criteria, while the subjective weights are determined based on the practical experience of the expert panel. The objective and subjective weights can reflect the different aspects of the eight sub-criteria for the evaluation of the comprehensive benefit of power grid investment.

From Table 4, it can be seen that the “Internal rate of return” (C1), “Unit investment income” (C2), and “Promoting regional economic development benefit” (C5) sub-criteria of power grid investment project PGIP#1 have the best performances among all five power grid investment projects. Meanwhile, these three sub-criteria have large weight values; in particular, the “Unit investment income” (C2) and “Internal rate of return” (C1) hold the first and second positions, respectively, related to the weight. Therefore, from the comprehensive view, the power grid investment project PGIP#1 has the best comprehensive benefit.

To obtain better insight from the application of the proposed method (comprising the entropy weight method, fuzzy BWM, and MARCOS method) in evaluating the comprehensive benefit of a power grid investment for connecting renewable energy generation to the power grid from the perspective of sustainability, a sensitivity analysis was conducted. The cases in which the eight benefit sub-criteria of power grid investment had 10%, 20%, and 30% less and more weight than the base weight are shown in Figure 6.

Taking the “Internal rate of return” (C1) sub-criterion as the example, as the “Internal rate of return” (C1) becomes less important, the utility function values of the power grid investment projects PGIP#1, PGIP#2, and PGIP#5 will be decreased, but the utility functions values of the comprehensive benefits of the power grid investment projects PGIP#3 and PGIP#4 will be increased. Meanwhile, as the “Internal rate of return” (C1) becomes more important, the utility function values of the power grid investment projects PGIP#1, PGIP#2, and PGIP#5 will be increased, but the utility functions values of the power grid investment projects PGIP#3 and PGIP#4 will be decreased. However, the comprehensive benefit of power grid investment project PGIP#1 is always the best. For another seven sub-criteria cases, the comprehensive benefit of power grid investment project PGIP#1 always ranks first. Therefore, it can be concluded that evaluating the comprehensive benefit of a power grid investment project by employing the proposed method, which combines the entropy weight method, fuzzy BWM, and MARCOS method, is effective and robust in this paper.

6. Conclusions

In this paper, the comprehensive benefit of power grid investment is evaluated considering renewable energy development from the perspective of sustainability through the use of the proposed hybrid multi-criteria decision-making (MCDM) method, which combines the entropy weight method and fuzzy best worst method (BWM) for the determination of power grid investment benefit criteria weights and the measurement of alternatives and ranking according to compromise solution (MARCOS) method for ranking the comprehensive benefits of power grid investment projects for connecting renewable energy generation to power grid. An empirical analysis was conducted, focusing on five grid investment projects in Ningxia, China, in which grid investment project PGIP#1 had the best comprehensive benefits, followed by grid investment projects PGIP#3, PGIP#2, and PGIP#5, while grid investment project PGIP#4 had the worst comprehensive benefits.

Moreover, a sensitivity analysis was also conducted, and the result shows that the comprehensive benefit of power grid investment project PGIP#1 is always the best. The method proposed in this paper which combines the entropy weight method, fuzzy BWM, and MARCOS method, is robust and effective for evaluating the comprehensive benefit of a power grid investment considering renewable energy development.

Through subjective and objective evaluations of criteria weights, it is concluded that the grid must focus on the “Internal rate of return” (C1) and “Unit investment income” (C2) as well as “Carbon emissions reduction” (C7) when making project investments in order to obtain better overall benefits.

With the active trading of the power market and the improvements in renewable energy support policies, there is room for continuously updating the grid investment comprehensive benefit evaluation index constructed in this paper. Meanwhile, different evaluation methods can be applied to compare the results of this paper to verify the robustness of the obtained conclusions. It should be mentioned that the proposed MCDM method in this paper can also be employed in other MCDM-related practical issues, such as the comprehensive benefit evaluation of energy storage.

The assessment of grid investment benefits can guide enterprise investment practices, and the method proposed in this paper achieves a comprehensive benefit assessment of grid transmission and distribution projects after investment. However, it is also important to follow up with the pre-investment business case and the operation and maintenance of the investment project. Therefore, the next research direction is to evaluate the costs and expected benefits during the pre-investment and operation and maintenance periods. Therefore, the evaluation of the cost and expected revenue before and during the O&M period is the next direction of our research.