Site Selection for Solar–Wind Hybrid Energy Storage Plants Based on Triangular Fuzzy Numbers: A Case Study of China

Abstract

Against the backdrop of the energy revolution, global energy demands are rising. Solar–wind hybrid energy storage plants (SWHESPs) are undoubtedly a research hotspot in this field for enhancing energy efficiency. However, the primary challenge in constructing SWHESPs is site selection. This paper aims to comprehensively investigate the site selection process for SWHESPs and determine the optimal site scientifically and objectively by considering various aspects, including technology, society, environment, and economy. This study employs a literature review and the Delphi method to establish the site selection index system of SWHESPs. The triangular fuzzy number (TFN) is used in relative similarity as an objective weight, while the Decision-Making Test and Evaluation Laboratory (DEMATEL) is used as a subjective weight. The comprehensive weights are computed using the Lagrange optimization method. Additionally, the options are ranked and evaluated using Geographic Information System (GIS) and the VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) methods based on prospect theory. The study also performs comparative and sensitivity analyses to confirm the effectiveness of the proposed methods. Proper siting can optimize the efficiency of resource use, which not only helps achieve more efficient use of clean energy but also promotes local economic development and job creation.

1. Introduction

Energy is the most basic engine for social progress, an essential support for economic development, and the basis for human survival. Energy demand is steadily increasing in many nations due to the growing population [1]. In the context of dual-carbon goals, many countries are investing in clean energy, especially wind and solar energy, which are developing rapidly [2]. The use of wind and solar energy in Italy has led to total production exceeding projected levels [3]. Meanwhile, research on solar energy resources in Africa has contributed to narrowing the knowledge gap between countries [4]. China, the largest developing country in the world, has long been a major energy consumer. Due to the limitations of traditional energy resources, new energy sources are being developed quickly. According to relevant information, it is clear that the proportion of installed photovoltaic (PV) and wind power generation is gradually increasing, as shown in Figure 1 and Figure 2. China is committed to vigorously developing these two energy sources, enhancing its influence in the global energy transition. Solar and wind energy resources are abundant and have the advantages of universal distribution, being clean and harmless, having huge reserves, and being available for long-term use. However, relying on them as a single energy source for power generation is still affected by weather and time constraints. China proposes combining these two energy sources to overcome bottlenecks in renewable power generation.

National and international experts have reviewed the relevant literature to assess the practical feasibility of effectively utilizing wind and solar resources. The study shows that combining two energy sources can increase energy efficiency [5]. During the day, the sun shines while the wind is weak, and at night, the opposite occurs. The complementarity is favorable for the widespread use of wind–solar hybrid systems. Energy storage technology can regulate grid load fluctuations by storing power during low demand and releasing it during peak demand in response to changes in grid load. Most sustainable energy research in China uses modeling and simulation to study the power generation capacity of renewable energy sources. It mainly focuses on specific technologies, which are not always applicable [6]. Recently, the combination of energy storage with renewable energy sources has grown faster. The variability of renewable energy can be reduced by adding energy conversion and storage devices into hybrid systems [7,8].

In recent years, China has focused on using energy storage technologies to address the shortcomings of hybrid wind and solar systems and to minimize the effects of uncertainty in combined systems [9]. To ensure the quality of electricity and effectively utilize new energy sources, China plans to establish a multi-energy hybrid power generation and storage plant, with a focus on wind and solar energy. Adopting an empirical method for siting studies is essential for renewable energy, especially for SWHESPs, as the location of where to locate a power plant is directly tied to its safety. Site selection studies use GIS to identify and assess different sites [10,11]. Although siting issues have been widely studied for hydrogen, solar, and battery energy storage, environmental, economic, and social aspects are involved in selecting siting criteria. As new energy technology advances and market dynamics evolve, the siting problem increasingly affects the success of constructing a new energy hybrid storage power plant. Therefore, the siting of SWHESPs remains one of the significant issues that contemporary society needs to address.

The following innovations are proposed in this paper.

• A two-stage evaluation indicator system was made, combining qualitative and quantitative analyses. The method innovatively combines GIS and traditional evaluation methods. It uses spatial data and subjective opinions. This makes it more objective and effective than traditional methods.
• A new evaluation index system is made. DEMATEL and the relative similarity methods based on triangular fuzzy numbers (TFNs) are used together for the first time in renewable energy site selection.
• This paper proposes a new decision-making framework to solve the SWHESP site selection problem by combining prospect theory and the VIKOR method. This framework includes risk preferences, uncertainty, and the decision maker’s (DM’s) subjective bias, giving a more complete and practical solution.

2. Literature Review

2.1. SWHESPs

To achieve carbon neutrality by 2060, China will mainly rely on renewable energy, particularly wind and solar PV, as the main power sources in the green power system. Nevertheless, power generation from single onshore wind and solar PV systems in China is intermittent. Therefore, it is expected that the intermittency and instability of clean energy sources will be reduced by combining wind and solar energy, which offers a workable solution. Numerous scholars have analyzed different aspects of SWHESPs. Tong et al. [12] suggested an optimal combination of renewable energy generation by studying the power demand of 42 countries and created a reliable power system. Liu et al. [13] applied genetic algorithms, system modeling, and uncertainty quantification methods to estimate energy system capacity and maximize efficiency. Gao et al. [14] showed the reliability of combining wind and solar energy and highlighted the importance of developing complementary wind and solar power plants in the future. Cappellen et al. [15] investigated the effect of wind turbine movement on solar panel efficiency and proposed using simulations to verify this impact.

Many scholars believe energy storage technologies can balance supply and demand requirements and improve energy use. Mahmoud et al. [16] chose the appropriate energy sources and coupling locations by examining the benefits and drawbacks of the three primary types, considering coupling mechanical energy storage systems with new energy sources. Papadopoulou et al. [17] assessed the combination of energy storage components using two measures. R Nair et al. [18] argued that for new energy sources to be used efficiently, combining a single energy source with other sources and improving energy supply using energy storage technology is necessary. Zhao et al. [19] emphasized the importance of hydrogen storage and showed that green hydrogen plays a great role in renewable energy systems. Kaan et al. [20] developed hybrid systems to find the best storage battery for hybrid wind and solar systems based on the battery cost. Several studies have demonstrated that energy storage technologies can enhance grid stability, flexibility, and reliability while also optimizing the economic performance of the power system. Energy storage technology is becoming more important in modern power systems.

2.2. Site Selection Issues

Site selection is important in the SWHESP process. It affects the economic value and potential power generation. Proper siting helps reduce costs and optimize resource use [21]. The location of solar and wind energy has been studied. Different techniques and indicators can provide different viewpoints and help, but they have drawbacks. Different countries have made specific analyses of their situations.

Various studies have identified wind energy as one of the most promising energy sources, and selecting the right location for wind farms has become a top priority [22]. Gupta et al. [23] focused on how technical factors affect wind farms and evaluated wind energy resources primarily in terms of wind power density to identify the most efficient matching options. Many scholars have employed different methods to select sites for SWHESPs. Wang et al. [24] proposed the data envelopment analysis (DEA) method to initially screen locations through efficiency targets, invoked the gray system theory to resolve ambiguities, and used a combination of TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) and gray techniques to determine rankings. Jani et al. [25] established a new hybrid availability index by analyzing three perspectives: the availability of resources, the capacity factor, and the energy source itself. Doorga et al. [26] determined the investment in wind power plants from five aspects: climatic, political, environmental, technological, and social, and improved the utilization of generators and decarbonized the grid by setting up relevant devices. Asadi et al. [27] introduced mapping into site selection, determined three first-level indicators of technological, economic, social, and environmental, six second-level indicators, and implemented a regression function using the impact criteria. Wang et al. [28] constructed a framework from five dimensions: topography, economy, resources, climate, and society, and utilized the optimal worst and entropy weights to establish the values of the variables. Zhu et al. [29] proposed a wind–solar complementary fast charging station to address the issue of untimely electric vehicle charging and developed an appropriate charging mode to minimize energy loss.

Considering the existing literature, scholars have focused on the issue of SWHESPs and site selection, but some aspects can still be improved.

• In the literature on new energy power plants, most scholars have researched how to improve power delivery efficiency from the energy source and maintain stability through energy storage technology. However, finding the best way to combine the advantages of different energy sources is still a major challenge.
• Regarding site selection, traditional weighting methods rely on exact data, which makes them less suitable for handling fuzzy factors. Most studies use a single method to evaluate the model, leading to incomplete analyses, and cases are primarily foreign, with fewer cases in China.

Therefore, this study selects an indicator system based on multiple aspects and combines the DEMATEL method with the relative similarity method based on the TFNs to calculate the weights. It uses prospect theory and the VIKOR method to evaluate SWHESP siting options, providing reliable results for determining the optimal location.

3. Establishment of an Evaluation Criteria System

The foundation of SWHESP site selection is determining the relevant factors and building the site selection index system. Currently, the methods for constructing this system include the Delphi method, brainstorming, and scenario analysis [30,31,32]. The site selection indicator system in this research is established using the Delphi method and the literature survey approach to ensure its comprehensiveness and sustainability.

This paper reviews relevant literature in various ways, and ten experts are chosen to form a panel when applying the Delphi method, as shown in

Table 1. Expert information.

Sequence	Unit	Title
1	Xinjiang Uygur Autonomous Region (XUAR) Development and Reform Commission (Xuar, China)	Coordinating member
2	China Energy Construction Corporation Limited (Beijing, China)	Technical personnel
3	Xi’an Jiaotong University (Xi’an, China)	Professor
4	North China Electric Power University (Hebei, China)	Professor
5	Mingyang New Energy Investment Holding Group Company Limited (Co., Ltd.) (Zhongshan, China)	Manager
6	Saneng New Energy Group (Nanjing, China)	Manager
7	Energy Research Institute, Peking University (Beijing, China)	Researcher
8	Bank of China Law Firm (Beijing, China)	Lawyer
9	Tbea Electric Co., Ltd. (Xuar, China)	Manager
10	Shanghai University of Electric Power (Shanghai, China)	Professor

. The requirements for selecting experts are: professors with over five years of expertise in renewable energy research, experts in governmental agencies and construction units, and well-known lawyers from consulting units. The main steps of the Delphi method involve sending questionnaires to experts, who return their opinions. These opinions are then summarized and shared back with the experts to form a consistent opinion. In this paper, three rounds of questionnaires are used to get the experts’ consistent opinion. After expert discussions and literature analysis, the site selection index system, comprising economic, social, technical, and environmental factors, was finalized. The construction process and the specific influencing factors are presented in

Table 2. Evaluation criterion system for SWHESP site selection.

First-Level Indicators	Secondary Indicators	Description
Environmental factor T1	Wind speed T11	The air velocity about a given location on Earth [33].
	Solar radiation T12	Electromagnetic waves and particle streams are emitted into cosmic space [34].
	Distance from the road T13	Spatial distance of the construction site from the road [35].
	Agricultural capacity T14	Relatively stable output power of the various agricultural production factors over time [36].
Social factor T2	Population density T21	Measurement of population distribution [37].
	The attitude of the local population T22	It encompasses the views of people living in a particular area about an event [38].
	Distance from agriculture T23	Spatial distance between the construction site and the area of agricultural activity [39].
	Energy efficiency T24	It refers to benefits in terms of energy savings and reductions in environmentally harmful emissions [40].
Technical factor T3	Electrical facility T31	It refers to the equipment and systems for generating, transmitting, distributing, and using electrical energy. This also includes the grid capacity, which affects power efficiency and the ability [41].
	Distance to the transmission line T32	It refers to the spatial distance between the construction site and the power transmission line [42].
	Wind power density T33	Measuring the abundance of wind energy resources in a given location [27].
	Rated power T34	Maximum output power can be achieved by the machinery and equipment [43].
Economic factor T4	Investment cost T41	It refers to all costs incurred in an investment project [44].
	Local government subsidy T42	Local governments provide enterprises and organizations with financial support [45].
	Distance from the city T43	It is the distance between the construction site and the downtown or central business district [46].
	Operating cost T44	Costs incurred to keep operations running smoothly [47].

and Figure 3. The framework is shown in Figure 4.

4. Materials and Methods

4.1. Determining the Weight of Evaluation Indices

4.1.1. Determining Subjective Weight Using the DEMATEL Approach

The DEMATEL method simplifies the problem using graphical and matrix tools to evaluate the combined impact of the indicators [48]. This paper requires a subjective methodology that integrates and analyses the relationship between different factors, and the characteristics of the DEMATEL method meet these requirements.

The following are the procedures for using the DEMATEL method for weighting:

Step 1. First, the experts score the degree of interaction between the indicators to form an initial direct influence matrix $\tilde{F}$ as in Equation (1):

$$\tilde{F}=\left[\begin{array}{cccc}{f}_{11}& f_{12}& \cdots & f_{1n}\\ f_{21}& f_{22}& \cdots & f_{2n}\\ ⋮& ⋮& ⋰& ⋮\\ f_{n1}& f_{n2}& \cdots & f_{nn}\end{array}\right]$$

(1)

where $f_{ij}$ denotes the degree of direct influence of the indicator $v_i$ on $v_j$.

Step 2. Determine the normalization direct impact matrix $\tilde{E}$ as in Equation (2):

$$\tilde{E}={\left(e_{ij}\right)}_{n\times n}=\tilde{F}/\underset{0\le i\le n}{\max }\sum _{j=1}^n{f}_{ij}$$

(2)

where $0\le e_{ij}\le 1,1\le i\le n$, and $\underset{0\le i\le n}{\mathrm{m}\mathrm{a}\mathrm{x}}{\sum }_{j=1}^n{e}_{ij}=1$.

Step 3. Determine the integrated impact matrix $\tilde{R}$ as in Equation (3).

$$\tilde{R}=\tilde{E}{(I-\tilde{E})}^{-1}$$

(3)

Step 4. Determine the indicator weights ${\omega }_k^{\prime }$ as in Equation (4).

$${\omega }_k^{\prime }=\sqrt{{\left(O_i\right)}^2+{\left(P_i\right)}^2}/\sum _{i=1}^n\sqrt{{\left(O_i\right)}^2+{\left(P_i\right)}^2}$$

(4)

where $O_i=A_i+B_i={\sum }_{j=1}^n{r}_{ij}+{\sum }_{i=1}^n{r}_{ij}$ and $P_i=A_i-B_i={\sum }_{j=1}^n{r}_{ij}-{\sum }_{i=1}^n{r}_{ij}$ represent the centrality and causality, respectively.

4.1.2. Knowledge Base of Relative Similarity Based on TFNs

This paper uses the TFN theory, which transforms fuzzy uncertain linguistic variables into specific values based on certain conversion relations. This method overcomes the limitations of subjective judgment and the lack of cognition. It also provides an effective way for experts to describe the preference relations of evaluation indexes subjectively [49].

• Model building

Set $X=\left\{x_a|a=1,2,\cdots ,p,p\ge 2\right\}$ for the finite set of evaluation groups composed of m experts and $Y=\left\{y_b|b=1,2,\cdots ,q,q\ge 3\right\}$ for the finite set of indexes composed of $q$ indexes. Then, the set of evaluations of indexes given by experts is $U=\left\{u_b|b=1,2,\cdots ,p,p\ge 2\right\}$, and the weights of the indicators given by the experts are $K=\left\{k_b|b=1,2,\cdots ,p,p\ge 2\right\}$. According to

Table 3. Correspondence between five evaluation levels of indexes and TFNs.

Semantic Evaluation Levels	Weighted Semantic Evaluation Levels	TFNs
Excellent	Very important	(8,9,9)
Good	More important	(6,7,8)
Fair	Important	(4,5,6)
Poor	General	(2,3,4)
Unqualified	Not important	(1,1,1)

, we can get the fuzzy evaluation matrix $M={\left(u^{ab}\right)}_{p\times q}$ of the semantics of the indicators given by the experts and the fuzzy evaluation matrix $N={\left(k^{ab}\right)}_{p\times q}$. TFNs are selected using the Saaty 1–9 scale, a common method in decision-making to measure the importance of different criteria. The middle value shows the most likely importance of a criterion. The lower and upper limits show the possible range, reflecting uncertainty in the decision process. The (8,9,9) value represents the “excellent” level. The middle value of 9 indicates the most probable value, the upper limit of 9 is the highest value in the best case, and the lower limit of 8 shows the minimum value in the worst case. The upper and lower limits are close to the middle value, which indicates the stability of the evaluation.

Firstly, the matrix $N$ is normalized, that is

$$N^{\prime }={\left(k^{\prime ab}\right)}_{p\times q}$$

(5)

where $k^{\prime ab}=k^{ab}/{\sum }_{b=1}^q{k}^{ab}$.

Then, $M$ is dot−multiplied with $N^{\prime }$ to obtain the weighted evaluation matrix $Z$ given by the expert.

$$Z=M·N^{\prime }={\left(u^{ab}\right)}_{p\times q}·{\left(k^{\prime ab}\right)}_{p\times n}=Z_{p\times q}^{ij}$$

(6)

The expected value of each evaluation level can be calculated based on Equations (5) and (6).

2.

Calculation of the relative similarity of TFNs

Definition 1.

Let $\tilde{A}=\left\{\widetilde{a_1},\widetilde{a_2},\cdots ,\widetilde{a_m}\right\}$ and $\tilde{B}=\left\{\widetilde{b_1},\widetilde{b_2},\cdots ,\widetilde{b_m}\right\}$ be two sequences of canonical TFNs, where $\widetilde{a_m}=\left(a_m^{\alpha },a_m^{\beta },a_m^{\gamma }\right)$ and $\widetilde{b_m}=\left(b_m^{\alpha },b_m^{\beta },b_m^{\gamma }\right)$ represent the individual fuzzy numbers in each sequence.

$$S\left(\tilde{A},\tilde{B}\right)={\displaystyle \frac{{\sum }_{i=1}^m{a}_i^{\alpha }{b}_i^{\alpha }+a_i^{\beta }{b}_i^{\beta }+a_i^{\gamma }{b}_i^{\gamma }}{{\sum }_{i=1}^{m}max\left\{{\left(a_i^{\alpha }\right)}^2+{\left(a_i^{\beta }\right)}^2+{\left(a_i^{\gamma }\right)}^2,{\left(b_i^{\alpha }\right)}^2+{\left(b_i^{\beta }\right)}^2+{\left(b_i^{\gamma }\right)}^2\right\}}}$$

(7)

$$S\left(\tilde{A},\tilde{B}\right)={\displaystyle \frac{{\sum }_{i=1}^{m}min\left\{{\left(a_i^{\alpha }\right)}^2+{\left(a_i^{\beta }\right)}^2+{\left(a_i^{\gamma }\right)}^2,{\left(b_i^{\alpha }\right)}^2+{\left(b_i^{\beta }\right)}^2+{\left(b_i^{\gamma }\right)}^2\right\}}{{\sum }_{i=1}^m{a}_i^{\alpha }{b}_i^{\alpha }+a_i^{\beta }{b}_i^{\beta }+a_i^{\gamma }{b}_i^{\gamma }}}$$

(8)

$S\left(\tilde{A},\tilde{B}\right)$ is the relative similarity between the triangular fuzzy sequences $\tilde{A}$ and $\tilde{B}$. If $S\left(\tilde{A},\tilde{B}\right)>1$ then $S\left(\tilde{A},\tilde{B}\right)=1$.

Definition 2.

Expected value of fuzzy linguistic values

Let the TFN $\tilde{a}=\left(a^{\alpha },a^{\beta },a^{\gamma }\right)$. The expected value can be derived from Equation (9).

$$E\left(\tilde{a}\right)={\displaystyle \frac{\left[a^{\alpha }+{2a}^{\beta }+a^{\gamma }\right]}{4}}$$

(9)

4.1.3. Objective Weight Calculation Based on the Relative Similarity of TFNs

Relative similarity is used to measure the degree of proximity between fuzzy sets, where expert evaluations are approximately similar, the higher the average relative similarity value [50]. Combining the TFN and the relative similarity can be effective in dealing with uncertainty. In the above-weighted evaluation matrix $Q$, experts $k$ and $t$ judge the results of $n$ indicators under a specific criterion as two triangular fuzzy sequences $Q_k$ and $Q_t$, respectively, and then the relative similarity value of the two triangular fuzzy sequences can be obtained from Equation (7) or Equation (8) as $L(Q_k,Q_t)$. Set the relative similarity matrix between the two experts $L$ through Equation (10). The relative similarity between the evaluation results of the experts is 1.

$$L=\left|\begin{array}{cccc}1& L(Q_1,Q_2)& \cdots & L(Q_1,Q_m)\\ L(Q_2,Q_1)& 1& \cdots & L(Q_2,Q_m)\\ \cdots & \cdots & \cdots & \cdots \\ L(Q_m,Q_1)& L(Q_m,Q_2)& \cdots & 1\end{array}\right|$$

(10)

The average relative similarity between expert $i$ and each of the other experts is calculated with Equation (11).

$$L^{\prime }={\displaystyle \frac{1}{m}}\sum _{l=1,l\ne i}^{m}L(Q_i,Q_l)$$

(11)

The weight of each expert is calculated using Equation (12).

$$W_i^{\prime }=L^{\prime }/\sum _{i=1}^m{L}^{\prime }$$

(12)

The expert’s weighted evaluation matrix $z_{ij}$ is calculated with Equation (9). The initial weights are calculated with Equation (13).

$${\omega }_j^{\prime }=\sum _{j=1}^n{W}_i^{\prime }{z}_{ij}$$

(13)

The final objective weights are obtained through Equation (14).

$${\omega }^{″}={\displaystyle \frac{{\omega }_j^{\prime }}{{\sum }_{j=1}^n{\omega }_j^{\prime }}}$$

(14)

4.1.4. Calculating the Combination Weights

In this study, subjective and objective approaches are integrated to calculate the indicator weights using the Lagrange optimization method, which aims to reduce discriminative information. Least squares and linear weighting are two other common techniques for combined weighting. The Lagrange optimization method not only overcomes the limitations of the linear weighting method, which is restricted to linear problems, but also addresses the inefficiency and high computational workload of the least squares method, especially given the complex factors involved in SWHESPs. The Lagrange optimization method enhances both the accuracy and efficiency of the computation, while also improving the reliability of the weight calculation. The conditions of Equations (15) and (16) need to be met.

$$minF=\sum _{j=1}^n\ln {\displaystyle \frac{{\omega }_j}{{\omega }_k^{\prime }}}+\sum _{j=1}^n\ln {\displaystyle \frac{{\omega }_j}{{\omega }^{″}}}$$

(15)

$$s.t.\sum _{j=1}^n{\omega }_j=1,{\omega }_j>0$$

(16)

Then, the combination weight ${\omega }_j=({\omega }_1,{\omega }_2,\cdots ,{\omega }_n)$ is calculated, as shown in Equation (17).

$${\omega }_j={\displaystyle \frac{\sqrt{{\omega }_k^{\prime }\times {\omega }^{″}}}{{\sum }_{j=1}^n\sqrt{{\omega }_k^{\prime }\times {\omega }^{″}}}}$$

(17)

4.2. Prospect Theory-Based VIKOR Approach Decision Model

The SWHESP siting problem is a complex Multiple Criteria Decision-Making (MCDM) problem, and combining multiple methods in the decision-making process is necessary to avoid inaccuracies from using a single method. TOPSIS, TODIM (an acronym in Portuguese for Interactive and Multicriteria Decision-Making), and VIKOR are common methods. TOPSIS ranks alternatives by calculating the distance from the ideal and negative ideal solutions, but it may not always give accurate results. TODIM ranks alternatives based on the strength of preferences. It is useful for comparing pairs of criteria but does not directly handle conflicts between them. Additionally, neither of the methods considers the DMs’ risk preferences or uncertainty. Therefore, this study uses the VIKOR approach based on prospect theory to address this issue. This approach ranks options based on ideal points and considers conflicts between criteria. In addition, prospect theory helps account for the DM’s subjective risk preferences, influencing the final decision. Combining VIKOR with prospect theory makes the decision-making process more accurate and complete by considering both the objective criteria and the DM’s personal preferences.

4.2.1. Prospect Theory

Prospect theory analyzes the behavior of DMs in complex environments. It converts decision expectations into prospect values by introducing value and weight functions instead of utility and probability functions in traditional stochastic decision theory [51].

In prospect theory, the value function $v\left(·\right)$ and the decision weight function $\pi \left(·\right)$ work together to determine the value of the prospect.

$$V_{ij}=\sum v\left({\psi }_{ij}\right)\pi \left({\omega }_j\right)$$

(18)

where $V_{ij}$ is the prospect value of the program $A_i$ under index $C_j$, $v\left({\psi }_{ij}\right)$ is the value function, and $\pi \left({\omega }_j\right)$ is the decision weight function.

Step 1: Calculate the reference point using Equations (19) and (20).

$${\psi }_{ij}^{+}={\displaystyle \frac{\underset{i}{\min }\underset{j}{\min }d\left(r_{ij},r_j^{+}\right)+\vartheta \underset{i}{\max }\underset{j}{\max }d\left(r_{ij},r_j^{+}\right)}{d\left(r_{ij},r_j^{+}\right)+\vartheta \underset{i}{\max }\underset{j}{\max }d\left(r_{ij},r_j^{+}\right)}}$$

(19)

$${\psi }_{ij}^{-}={\displaystyle \frac{\underset{i}{\min }\underset{j}{\min }d\left(r_{ij},r_j^{-}\right)+\vartheta \underset{i}{\max }\underset{j}{\max }d\left(r_{ij},r_j^{-}\right)}{d\left(r_{ij},r_j^{-}\right)+\vartheta \underset{i}{\max }\underset{j}{\max }d\left(r_{ij},r_j^{-}\right)}}$$

(20)

where $d\left(x_{ij},x_{ik}\right)=\left|x_{ij}-x_{ik}\right|$, $0<\alpha$, $\beta <1$, and $\vartheta =0.5$.

Step 2: Calculate the value function through Equation (21).

$$V\left({\psi }_{ij}\right)=\left\{\begin{array}{c}{V}^{+}\left({\psi }_{ij}^{-}\right)={(1-{\psi }_{ij}^{-})}^{\alpha },\alpha <1\\ V^{-}\left({\psi }_{ij}^{+}\right)=-\theta {\left(1-{\psi }_{ij}^{+}\right)}^{\beta },\theta >1,\beta <1\end{array}\right.$$

(21)

The parameters $\alpha$ and $\beta$ show the DM’s sensitivity to gains and losses. $\theta$ shows the DM’s relative sensitivity to losses compared to gains. $\alpha =\beta =0.88$ [52] indicates the DMs respond equally to gains and losses. $\theta =2.25$ [52] shows losses have a greater impact, which fits the idea of loss aversion. This is supported by behavioral decision theory and is relevant to the context of this study. These parameter values have also been widely used in site selection, effectively capturing the DM’s responses and improving the accuracy of the site selection process [53,54].

Step 3: Calculate the weight function using Equation (22).

$$\pi \left({\omega }_j\right)=\left\{\begin{array}{c}{\pi }^{+}\left({\omega }_j\right)={\displaystyle \frac{{{\omega }_j}^{\gamma }}{{\left[{{\omega }_j}^{\gamma }+{(1-{\omega }_j)}^{\gamma }\right]}^{1/\gamma }}}\\ {\pi }^{-}\left({\omega }_j\right)={\displaystyle \frac{{{\omega }_j}^{\mu }}{{\left[{{\omega }_j}^{\mu }+{(1-{\omega }_j)}^{\mu }\right]}^{1/\mu }}}\end{array}\right.$$

(22)

where ${\pi }^{+}\left({\omega }_j\right)$ and ${\pi }^{-}\left({\omega }_j\right)$ denote the decision weight functions of the DMs for gains and losses, respectively. $\gamma$ and $\mu$ show the DM’s risk preferences for gains and losses, affecting how sensitive they are to both decreases. $\gamma =0.61$ and $\mu =0.69$ [52] model the DM’s behavior in this study.

Step 4: Calculate the value of the prospect using Equations (18) and (23).

$$V_i=\sum _{v\left(x_{ij}\right)\ge 0}{\pi }^{+}\left({\omega }_j\right)V^{+}\left({\psi }_{ij}^{-}\right)+\sum _{v\left(x_{ij}\right)<0}{\pi }^{-}\left({\omega }_j\right)V^{-}\left({\psi }_{ij}^{+}\right)$$

(23)

4.2.2. VIKOR Method

VIKOR is a method that takes into account both collective interests and individual preferences and is able to balance group and individual relationships. The site selection problem is a decision-making problem involving multiple options and factors, and the VIKOR method, based on prospect theory, is suitable for use in situations of uncertainty and can help to select a more realistic option. The precise steps are as follows:

Step 1: Determine the positive ideal solution $f^{+}$ and a negative ideal solution $f^{-}$ of the comprehensive prospect value matrix using Equations (24) and (25).

$$f^{+}=\left\{maxv\left(x_{ij}\right)|j=1,2,\cdots ,n\right\}=\left\{f_1^{+},f_2^{+},\cdots ,f_n^{+}\right\}$$

(24)

$$f^{-}=\left\{minv\left(x_{ij}\right)|j=1,2,\cdots ,n\right\}=\left\{f_1^{-},f_2^{-},\cdots ,f_n^{-}\right\}$$

(25)

Step 2: Calculate the group benefit value $S_i^l$ and the individual regret degree $R_i^l$ of the evaluation program, as shown in Equations (26) and (27).

$$S_i^l=\sum _{j=1}^n\left\{{\omega }_j\left({\displaystyle \frac{d(f_j^{+},v\left(x_{ij}\right))}{d(f_j^{+},f_j^{-})}}\right)\right\},i=1,2,\cdots ,m$$

(26)

$$R_i^l=max\left\{{\omega }_j\left({\displaystyle \frac{d(f_j^{+},v\left(x_{ij}\right))}{d(f_j^{+},f_j^{-})}}\right)\right\},i=1,2,\cdots ,m$$

(27)

where $d\left(x_{ij},x_{ik}\right)=\left|x_{ij}-x_{ik}\right|$.

Step 3: Calculate the trade-off ranking value $Q_i^l$ for the evaluation scheme using Equation (28):

$$Q_i^l=\sigma \left({\displaystyle \frac{S_i^l-\widetilde{S^{-}}}{\widetilde{S^{+}}-\widetilde{S^{-}}}}\right)+(1-\sigma ){\displaystyle \frac{R_i^l-\widetilde{R^{-}}}{\widetilde{R^{+}}-\widetilde{R^{-}}}}$$

(28)

where $\sigma$ is the trade-off coefficient, reflecting the preferences of the DMs, and $\sigma =\left[0,1\right]$. $\widetilde{S^{+}}=\underset{i}{\min }{S}_i^l$, $\widetilde{S^{-}}=\underset{i}{\max }{S}_i^l$, $\widetilde{R^{+}}=\underset{i}{\min }{R}_i^l$ and $\widetilde{R^{-}}=\underset{i}{\min }{R}_i^l$. We take $\sigma =0.5$.

Step 4: The assessment scenarios are ranked according to the $S_i^l$, $R_i^l$, and $Q_i^l$. The smaller the value of $Q_i^l$, the better the scenario.

5. Case Study

5.1. Background of the Case

As energy demand grows, countries are developing new energy sources, with solar and wind energy becoming dominant. Site selection is a pressing issue today, as it significantly affects the operation of power plants. The XUAR, located in northwestern China, is one of the five ethnic minority autonomous regions in the country. The XUAR is an integrated energy base in China, which is essential for global mixed renewable energy generation [55]. The region is rich in wind, light, and potential natural conditions, which provide favorable geographic conditions for siting issues. A company intends to invest in building SWHESPs in the Xinjiang region. The geographical map of the XUAR is shown in Figure 5.

5.2. Phase I: Determining the Preliminary Site of a SWHESP Using GIS

The specific criteria and results from the on-site research are shown in

Table 4. Construction standards for SWHESPs.

Criteria	Standards
Elevation (m)	<1500 [56]
Slope (%)	<5 [57]
Wind speed (m/s)	>4 [58]
Sunshine duration (kWh/m2)	>132 [34]
Average temperature (°C)	>5.6 [59]
Land type	It should not be in water bodies or residential areas [60].

and Figure 6. Five potential locations, M1, M2, M3, M4, and M5, were selected for this study. The data about the five locations is shown in Figure 5 and

Table 5. Geographic information for the five options.

	M1	M2	M3	M4	M5
Latitude	44°6′22″ N	39°59′44″ N	40°4′34″ N	38°25′9″ N	37°18′12″ N
Longitude	93°2′4″ E	82°21′48″ E	87°17′55″ E	79°3′35″ E	81°27′32″ E
Wind speed (m/s)	8.84	6.01	6.95	6.12	5.98
Sunshine duration (kWh/m2)	224.6	258.2	250.03	267.6	288.37

.

5.3. Stage II: Further Site Selection

5.3.1. Determination of Weights

Step 1: The subjective weights of the indicators are calculated through Equations (1)–(4). The relative similarity can be determined using Equations (7) and (8), which are further processed to obtain the objective weights. These weights are shown in Figure 7.

Step 2: The combined weights of the indicators are calculated using Equation (17), as shown in Figure 8.

5.3.2. Program Selection

Step 1: Calculate the reference points using Equations (19) and (20) and the weight function using Equation (22). The results are presented in

Table 6. Reference points.

	${\mathit{\psi }}_{\mathit{i}\mathit{j}}^{\mathbf{+}}$	${\mathit{\psi }}_{\mathit{i}\mathit{j}}^{\mathbf{+}}$	${\mathit{\psi }}_{\mathit{i}\mathit{j}}^{\mathbf{+}}$	${\mathit{\psi }}_{\mathit{i}\mathit{j}}^{\mathbf{+}}$	${\mathit{\psi }}_{\mathit{i}\mathit{j}}^{\mathbf{+}}$	${\mathit{\psi }}_{\mathit{i}\mathit{j}}^{\mathbf{-}}$	${\mathit{\psi }}_{\mathit{i}\mathit{j}}^{\mathbf{-}}$	${\mathit{\psi }}_{\mathit{i}\mathit{j}}^{\mathbf{-}}$	${\mathit{\psi }}_{\mathit{i}\mathit{j}}^{\mathbf{-}}$	${\mathit{\psi }}_{\mathit{i}\mathit{j}}^{\mathbf{-}}$
T11	0.714	0.556	0.556	1	0.714	0.714	1	1	0.556	0.714
T12	0.714	1	1	0.556	0.455	0.556	0.455	0.455	0.714	1
T13	1	0.556	1	0.3846	0.3333	0.333	0.455	0.333	0.714	1
T14	1	1	0.556	0.455	1	0.455	0.455	0.714	1	0.455
T21	0.714	0.333	1	0.714	0.714	0.385	1	0.333	0.385	0.385
T22	0.714	0.455	0.455	1	0.455	0.556	1	1	0.455	1
T23	0.714	0.333	1	1	0.455	0.385	1	0.333	0.333	0.556
T24	0.385	1	1	0.455	0.455	1	0.385	0.385	0.714	0.714
T31	0.455	0.714	0.455	1	0.385	0.714	0.455	0.714	0.385	1
T32	0.714	1	0.714	0.455	0.556	0.556	0.455	0.556	1	0.714
T33	0.455	1	0.714	0.385	0.385	0.714	0.385	0.455	1	1
T34	1	1	1	0.556	1	0.556	0.556	0.556	1	0.556
T41	1	1	1	0.556	1	0.556	0.556	0.556	1	0.556
T42	0.556	1	0.714	0.714	0.714	1	0.556	0.714	0.714	0.714
T43	0.714	1	0.556	0.556	0.556	0.714	0.556	1	1	1
T44	0.455	1	0.556	0.455	0.385	0.714	0.385	0.556	0.714	1

and

Table 7. Weighting functions and ideal solutions.

	${\mathit{\pi }}_{\mathit{i}\mathit{j}}^{\mathbf{+}}$	${\mathit{\pi }}_{\mathit{i}\mathit{j}}^{\mathbf{-}}$	${\mathit{f}}^{\mathbf{+}}$	${\mathit{f}}^{\mathbf{-}}$
T11	0.197	0.182	0.097	−0.201
T12	0.175	0.158	0.103	−0.209
T13	0.122	0.102	0.085	−0.16
T14	0.142	0.122	0.083	−0.161
T21	0.134	0.114	0.094	−0.179
T22	0.146	0.126	0.086	−0.166
T23	0.16	0.141	0.112	−0.222
T24	0.156	0.137	0.102	−0.201
T31	0.106	0.086	0.069	−0.127
T32	0.141	0.121	0.082	−0.159
T33	0.122	0.102	0.08	−0.149
T34	0.121	0.101	0.059	−0.111
T41	0.128	0.108	0.063	−0.119
T42	0.158	0.14	0.078	−0.154
T43	0.154	0.134	0.075	−0.148
T44	0.166	0.148	0.108	−0.217

.

Step 2: Calculate $f^{+}$ and $f^{-}$ of the composite prospect matrix using Equations (24) and (25), as shown in Table 7.

Step 3: Calculate $S_i^l$, $R_i^l$, and $Q_i^l$ using Equations (26)–(28).

$S_i^l$ = (0.492, 0.332, 0.433, 0.583, 0.678)

$R_i^l$ = (0.072, 0.112, 0.112, 0.068, 0.088)

$Q_i^l$ = (0.2796, 0.5, 0.6460, 0.3633, 0.7329)

From the above calculations, we derive a compromise ranking value $Q_i^l$ as: M1 < M4 < M2 < M3 < M5. According to the study, M1 is identified as the ideal location for establishing the SWHESPs among the five alternatives.

To check the reliability of the proposed site selection method, we compared the solar radiation and wind speed data from the selected site with those from the existing SWHESP in Hami, a functioning project. The wind speed was above 7 m/s, and the solar radiation was over 167 kWh/m². These values match the characteristics of the proposed site. This shows that our method works well for SWHESP site selection and can be used in similar areas.

5.4. Analysis of Results

Based on the study, M1 was determined to be the best site for the SWHESP’s development. M1 is an undeveloped area with abundant solar and wind energy resources and is conveniently located. Experts believe that developing power plant projects in this area can be developed further and have a high level of service and public approval. Therefore, M1 is the optimal site with the highest practical and scientific value for establishing the SWHESP.

6. Further Analysis and Discussion

6.1. Sensitivity Analysis

6.1.1. Change in Weights

This study conducted a sensitivity analysis to verify the truthfulness of the findings. In practice, expert opinions are strongly influenced by the situation, which can lead to changes in weighting. Therefore, it needs to be performed based on the weights. We altered the weights under the four first-level indicators by ±10% and ±20%, respectively, and examine the effects of these modifications on the outcomes. This step uses equation $w_{ij}^{*}={\displaystyle \frac{w_{ij}}{{\sum }_{i=1}^n{\sum }_{j=1}^m{w}_{ij}}}$ to ensure that the weights sum to 1. Figure 9 displays the findings.

The sensitivity analysis is presented in the following sections:

Change the T11–T14 weights by ±10% and ±20%, keeping the other indicator weights unchanged, and regularize the system to ensure the sum of the total weight to 1. T21–T24, T31–T34, and T41–T44 have the same steps as T11–T14.

The sensitivity analysis of this study showed that M1 was always the best location for this power plant, although each alternative fluctuated with changes in indicator weights. Therefore, the evaluation procedure used in this study is scientifically valid and realistic.

6.1.2. Sensitivity Analysis for Compromise Factor $\mathsf{\sigma }$

In the decision-making phase of the VIKOR method, grounded in prospect theory, $\sigma$ is a compromise coefficient that reflects the preferences of the DMs. Therefore, a sensitivity analysis is needed.

$\sigma$ was varied within the range [0.2, 0.65] in steps of 0.05 to analyze its effect on the results. As shown in Figure 10. It can be seen that the sensitivity of the compromise coefficient $\sigma$ does not change much and has little impact on the final ranking, which shows good scientific quality.

6.1.3. Sensitivity Analysis for Expert Inputs

To improve the credibility of the results, this paper performed a sensitivity analysis on the expert scores in DEMATEL. We changed the values of T1, T2, T3, and T4 by grouping every four indicators together. The initial score range was [0, 4], and we increased or decreased each score by 1. However, scores that were initially 0 could only increase, not decrease.

Table 8. Sensitivity analysis results for expert scores.

	Changes in T11–T14 Scores		Changes in T21–T24 Scores		Changes in T31–T34 Scores		Changes in T41–T44 Scores
	Increase by 1 Point	Down by 1 Point	Increase by 1 Point	Down by 1 Point	Increase by 1 Point	Down by 1 Point	Increase by 1 Point	Down by 1 Point
M1	$Q_i^l=0.25$	$Q_i^l=0.36$	$Q_i^l=0.29$	$Q_i^l=0.28$	$Q_i^l=0.31$	$Q_i^l=0.28$	$Q_i^l=0.29$	$Q_i^l=0.31$
M2	$Q_i^l=0.5$	$Q_i^l=0.5$	$Q_i^l=0.5$	$Q_i^l=0.5$	$Q_i^l=0.5$	$Q_i^l=0.5$	$Q_i^l=0.5$	$Q_i^l=0.5$
M3	$Q_i^l=0.63$	$Q_i^l=0.66$	$Q_i^l=0.6$	$Q_i^l=0.65$	$Q_i^l=0.66$	$Q_i^l=0.64$	$Q_i^l=0.69$	$Q_i^l=0.62$
M4	$Q_i^l=0.38$	$Q_i^l=0.38$	$Q_i^l=0.32$	$Q_i^l=0.39$	$Q_i^l=0.35$	$Q_i^l=0.36$	$Q_i^l=0.42$	$Q_i^l=0.34$
M5	$Q_i^l=0.78$	$Q_i^l=0.57$	$Q_i^l=0.74$	$Q_i^l=0.73$	$Q_i^l=0.72$	$Q_i^l=0.74$	$Q_i^l=0.51$	$Q_i^l=0.76$
Rank	M1 > M4 > M2 > M3 > M5

illustrates the results of changes in expert scores.

The analysis shows that the results are consistent with the original findings, proving that the scoring process is impartial. The optimal option remains stable even with different expert score inputs, confirming the robustness of the results.

6.1.4. Sensitivity Analysis for TFNs

To assess the impact of the TFNs on the model results, we conducted a sensitivity analysis. We changed the lower, peak, and upper parameters of the five data sets by [−30%, +30%] at the same time. The results are shown in Figure 11.

We can see that the overall ranking of the program is in accordance with the initial ranking, despite slight fluctuations when the parameters are modified. This suggests that the TFNs chosen in this work are reasonable, ensuring that the model produces reliable results under different conditions.

6.2. Comparative Analysis

6.2.1. Comparative Analysis of MCDM Methods

To further illustrate the scientific rigor of the methodology, it is now compared with the TOPSIS method [61], the TODIM method [62], and the VIKOR method [63]. The weights are kept consistent in the calculation, and the results are shown in Figure 12 and

Table 9. Calculation results of the four methods.

	TOPSIS	TODIM	VIKOR	Methodology of This Paper
M1	$S_i=0.5988$	$U_i=0.85$	$Q_i^l=0.2288$	$Q_i^l=0.2796$
M2	$S_i=0.5413$	$U_i=0.72$	$Q_i^l=0.5$	$Q_i^l=0.5$
M3	$S_i=0.5205$	$U_i=0.78$	$Q_i^l=0.6310$	$Q_i^l=0.6460$
M4	$S_i=0.5167$	$U_i=0.65$	$Q_i^l=0.3705$	$Q_i^l=0.3633$
M5	$S_i=0.4632$	$U_i=0.60$	$Q_i^l=0.7329$	$Q_i^l=0.7329$
Rank	M1 > M2 > M3 > M4 > M5	M1 > M3 > M2 > M4 > M5	M1 > M3 > M4 > M2 > M5	M1 > M4 > M2 > M3 > M5

.

The efficiency of the approach suggested in the paper is confirmed by the fact that, regardless of the many approaches employed, M1 is consistently the best answer, and M5 is consistently the worst. Although these three approaches are more widely used in evaluating decision problems, they still have drawbacks. TOPSIS calculations are more homogeneous, TODIM steps are complex, and VIKOR ignores psychological traits. However, the VIKOR method based on the prospect theory can fill these gaps. Therefore, this report employs a thorough and rigorous technique to investigate the site selection for SWHESPs.

6.2.2. Comparative Analysis of Entropy Weighting and Linear Weighting Methods

The linear weighting method and the entropy weighting method are common methods. To check the effectiveness of the hybrid weighting method, we compare these three methods.

Table 10. Calculation results of the three methods.

	Linear Weighting Method	Entropy-Based Method	Methodology of This Paper
M1	$S_i=6.2961$	$Q_i^l=0.224$	$Q_i^l=0.2796$
M2	$S_i=6.5471$	$Q_i^l=0.2978$	$Q_i^l=0.5$
M3	$S_i=6.6096$	$Q_i^l=0.4507$	$Q_i^l=0.6460$
M4	$S_i=5.9448$	$Q_i^l=0.8868$	$Q_i^l=0.3633$
M5	$S_i=5.4966$	$Q_i^l=0.9471$	$Q_i^l=0.7329$
Rank	M3 > M2 > M1 > M4 > M5	M1 > M2 > M3 > M4 > M5	M1 > M4 > M2 > M3 > M5

compares the program rankings based on the three methodological calculations.

Although the traditional methods are often used, they do not fit the situation in this paper. These methods ignore the connections between the factors, which causes M4 to rank lower and leads to differences in the results. This paper combines subjective and objective weights to provide a better way to decide weights and handle the challenges in SWHESP site selection.

7. Conclusions

The structure of the SWHESPs suggested in this research is crucial for mitigating energy demand. Integrating SWHESPs with clean energy can reduce the uncertainty in conventional power generation, optimize energy output, speed up wind and solar energy use, and achieve more efficient and sustainable energy use. Furthermore, it helps in related industries to realize the goal of a more flexible and stable system in the future.

The primary contributions of this research include:

• To develop the SWHESP site selection assessment index system, this research innovatively combines the Delphi method with a literature survey, resulting in a more comprehensive evaluation system. Compared to conventional single-method approaches, this combined approach enhances decision-making robustness.
• Considering the inherent ambiguity of the site selection problem, the integration of TFNs with the DEMATEL method improves weight distribution, making it more reasonable and enhancing the reliability of decision-making.
• This paper is the first to address the SWHESP site selection problem using the VIKOR method combined with prospect theory. This method considers the DM’s behavior under risk. It also uses GIS, which helps handle spatial data. The method uses double screening to solve complex, multidimensional decision-making problems more easily.
• The comprehensive consideration of factors in the siting of energy storage power plants improves the site selection process and provides a critical reference for countries transitioning to clean energy.

The findings of the study allow for the following conclusions:

• Wind speed and solar radiation are crucial factors for energy efficiency in SWHESP siting. Optimized levels of these variables lead to higher energy output compared to traditional siting methods.
• In addition to environmental factors, financial, ecological, and social aspects influence SWHESP siting. Government and local community support are essential for achieving sustainable development and balancing benefits across all areas.
• The site selection evaluation method has been optimized. This work extends the weighting approach to the fuzzy domain, utilizes GIS and the VIKOR method based on prospect theory, improving decision-making accuracy compared to traditional methods.
• Using China as an example, along with real cases, makes the research in this paper more convincing.

This paper also discusses its limitations and potential future directions:

• First, the limitations of the survey may result in a selection of one-sided evaluation indicator elements. Future development should focus on refining the method for screening indicator factors to cover all relevant aspects.
• Due to varying conditions, the approach in this paper only applies to some energy storage power stations. Future work should explore methods that fit more types of power stations.
• Most of the data was collected from experts during the data collection phase, and future research should consider more quantitative analysis techniques.

It is crucial to apply the proposed methodology to other practical issues, as this area of research has recently become topical. In the future, countries will pay increasing attention to using clean energy, and China is working to explore how energy storage technology can enhance energy use efficiency.