Suitability of Photovoltaic Power Station Sites Based on Particle Swarm Optimization Model of Fuzzy Hierarchical Analysis—Taking Qujing City of Yunnan Province as Example

Abstract

With the global shift in energy systems and the growing adoption of renewable energy, photovoltaic power generation has become widely implemented worldwide as a clean and efficient energy source. Therefore, scientific and rational locating methods for photovoltaic power stations has become essential. This study employs a particle swarm optimization (PSO) model based on the fuzzy analytic hierarchy process (FAHP) for evaluating the site-suitability of photovoltaic power stations. Taking Qujing City in Yunnan Province as an example, this study comprehensively considered 13 factors in three categories: meteorology, physical geography, and location. In addition, such topographic factors as planar curvature, profile curvature, and LSW were added to the physical geography factors for consideration. In previous studies, less attention has been paid to these factors. Spatial analysis and data integration of influencer factors in the study area were carried out in geographic information system (GIS) technology, with weights assigned for each factor in combination with a fuzzy analytic hierarchy process, but a low consistency effect was delivered. To optimize the consistency effect, the particle swarm optimization algorithm was introduced, and weights with good consistency effects were obtained. Based on such weights, the suitability evaluation was carried out to select photovoltaic power stations. The evaluation results were compared with those obtained from the fuzzy analytic hierarchy process and the genetic algorithm (GA) optimization model based on FAHP and were further verified in the area of the photovoltaic power stations built. It is demonstrated that the accuracy rate of the suitability of Qujing photovoltaic power station site selection based on the particle swarm optimization model of the fuzzy analytic hierarchy process was the highest at 99.3%.

1. Introduction

With increasingly serious outcomes of global climate change, the development and utilization of clean energy has become an important direction in the energy field globally. As a renewable energy source, photovoltaic power generation plays a crucial role in the global shift towards sustainable and environmentally friendly energy. With continuous technological progress and a gradual decline in cost, photovoltaic power generation has become an essential means of attaining the targets of reaching the carbon peak and achieving carbon neutrality. Scientific and rational site selection for photovoltaic power stations is crucial in this process.

The multi-criteria decision-making (MCDM) method is commonly used in the research of photovoltaic power station site selection, among which the analytic hierarchy process (AHP) is widely used. Ahadi et al. used an analytic hierarchy process to evaluate factors such as temperature, air contamination, solar irradiance, sunshine duration, precipitation, dampness, and cloudage to identify optimal locations for solar photovoltaic power stations in Iran [1]. Raza et al. integrated a GIS and AHP to assess various factors, such as solar irradiance, temperature, land use, slope, and proximity to roads, power lines, and urban centers [2]. Elboshy et al. employed an AHP and GIS to evaluate factors such as location, environment, meteorology, and climate to identify the best sites for photovoltaic power stations in Egypt [3]. Zhao et al. applied an AHP and DEMATEL to assess factors such as resources, environment, economy, and society, creating an evaluation system for photovoltaic power station locations with a focus on sites in Inner Mongolia [4]. Zhang et al. employed an AHP and GIS to examine the development of photovoltaic power plants in China, considering the following factors: total solar radiation, the stability of sunshine hours, distance from the road network, distance from cities and towns, and aspect [5]. Due to significant distinction between the consistency of the judgment matrix constructed by the AHP and the consistency of human thinking, Zhang introduced a fuzzy consistency matrix and proposed the FAHP to deliver more accurate consistency judgment standards [6]. Taking into account climate, economy, terrain, environment, and other factors, Noorollahi et al. applied fuzzy logic and GIS-based AHP analysis to identify and evaluate suitable locations for photovoltaic solar power stations [7]. Li et al. evaluated the suitability of photovoltaic power station sites by examining terrain, weather, environment, resources, and other factors and developed a site selection model using the FAHP [8]. However, because the compatibility indicator of the consistency test in the FAHP is a nonlinear programming model, the verification iteration process is complex and prone to error. PSO is a good method for solving nonlinear programming problems. This article adopted the particle swarm optimization algorithm to enhance the compatibility indicator, finally acquiring the weights with good consistency effect.

With the progress of GISs and remote sensing technology, digital terrain analysis (DTA) has been used as an important tool in locating photovoltaic power stations, as well as a digital terrain information processing technology for terrain attribute calculation and feature extraction in digital elevation models (DEMs) [9]. Because terrain factors are an essential parameter for effectively studying and representing geomorphic features, the extraction of terrain factors based on DEMs forms the basis and core content of digital terrain analysis [10]. In selecting photovoltaic power station sites, topographic factors are often considered to include slope, aspect, and altitude [11,12,13]. Therefore, in this study, such terrain factors as planar curvature, profile curvature, and LSW provided a more thorough consideration of how terrain characteristics influenced the site selection of photovoltaic power stations.

By taking Qujing City in Yunnan Province as an example, this study comprehensively explored 13 factors, with other topographic factors added, including planar curvature, profile curvature, and LSW. The spatial analysis and data integration of the influencing factors in the study area were carried out using GIS technology. Based on the FAHP, the weights of the influencing factors were assigned. In addition, the particle swarm optimization algorithm was introduced to optimize the consistency effect, so as to obtain the weights with good consistency effects. Based on the derived weights, the suitability of potential sites for the photovoltaic power station was assessed, and the evaluation results were compared with those obtained from the fuzzy analytic hierarchy process and genetic algorithm optimization model based on the FAHP. The results were further validated by comparing them with findings from areas where photovoltaic power stations have already been established. It is concluded that the particle swarm optimization model, built on the FAHP, provided the most effective site selection for photovoltaic power stations. This research offers a scientific basis for selecting locations where photovoltaic power stations are planned for construction.

2. Materials and Methods

2.1. Research Flowchart and Overview

The research process of this study was divided into several key steps, as illustrated in Figure 1. First, relevant data were collected and preprocessed, including meteorological, physical geography, and location factors. Second, an evaluation indicator system was constructed based on the fuzzy analytic hierarchy process. Third, the PSO algorithm was introduced to optimize the weights of the FAHP model, addressing the low-consistency effect observed in the initial analysis. Finally, the suitability of photovoltaic power station sites was evaluated and verified using geographic information system technology.

2.2. Data Acquisition

This study primarily utilized four types of data: remote sensing data, meteorological data, basic geographic data, and topographic data. Among them, remote sensing data were composed of solar radiation and land use type data; meteorological data were composed of temperature, precipitation, and wind speed data; basic geographic element data were composed of road, water system, residential area, and administrative division data; and terrain data were composed of digital elevation model data. All the above data were treated with projection transformation, range clipping, resampling, and other data processing techniques. WGS 1984 UTM zone 48 N was used as the coordinate reference system, with a spatial resolution of 30 m × 30 m. Detailed data can be found in

Table 1. Study area data.

Data Title	Data Source
DEM data	Geospatial Data Cloud
Solar radiation data	Global Solar Atlas
Meteorological data	Resource Environmental Science and Data Center
Administrative division data	National Platform for Common GeoSpatial Information Services
Residential data	Resource Environmental Science and Data Center
Road data	Open Steet Map
Land use type data	Resource Environmental Science and Data Center

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2.3. General Situation of Study Area

Yunnan Province, located in the southwest of China, is characterized by mountainous plateau terrain, with mountains covering 349,300 square kilometers, or 88.6% of its total land area. Six major rivers flow through the province: the Yangtze, Pearl, Yuanjiang, Lancang, Nujiang, and Daying Rivers. As a result, the region has complex terrain, significant altitude variation, and abundant solar radiation. The average annual sunshine duration in Yunnan is 2200 h, and the total annual solar radiation ranges from 1004.2 to 1852.0 kWh/m² [14].

Qujing, located in eastern Yunnan Province, is at the source of the Pearl River and borders Guizhou and Guangxi. The city’s maximum east-to-west distance is 103 km, while its north-to-south span is 302 km. Qujing covers an area of 28,900 square kilometers, making up 13.63% of Yunnan’s total land area. Located in the middle of the Yunnan Guizhou Plateau, Qujing stands in the Wumeng Mountains, as well as in a transition zone from the eastern Yunnan Plateau to the western Guizhou Plateau. In addition, it is closely connected with the lake basin of the central Yunnan Plateau in the west and gradually transitions to the Guizhou Plateau in the east. Its central part constitutes the watershed between the Yangtze River and the Pearl River. The plateau is well preserved and intact, and its southeast region has a typical karst mound landscape. Under a subtropical plateau monsoon climate, Qujing is affected by the continental monsoon in winter and spring, with sunny weather, sufficient sunlight, and a mild and dry climate; in summer and autumn, it is affected by the marine monsoon, with concentrated precipitation, more rainy days, and a cool and humid climate. The complex plateau topography, coupled with diversified climate types, creates significant vertical differences, with unique three-dimensional climate characteristics. Please refer to Figure 2 for details.

2.4. Indicator Selection and Analysis

In the suitability evaluation of photovoltaic power stations, the influence of many factors was considered. Drawing on insights from the relevant literature and considering the developmental characteristics of Qujing, meteorology, physical geography, and location were selected as three primary indicators, which were further divided into thirteen secondary indicators so as to establish an evaluation indicator system for photovoltaic development suitability and then use the system to evaluate the photovoltaic development suitability of Qujing.

2.4.1. Physical Geography Factors

Physical geography factors include the following: slope, aspect, topographic relief, terrain roughness, planar curvature, profile curvature, LSW, and land use type. According to Islam et al., altitude has a significant impact on the installation of solar photovoltaic panels: the higher the altitude is, the greater the construction challenges are [15]. In northern-hemisphere countries, the best tendency of solar photovoltaic panels is usually south, and their slope direction directly determines the solar radiation acceptance and photovoltaic power generation efficiency [16]. As a basic rule, the site selection of photovoltaic power stations should avoid geological disaster-prone areas, such as those with dangerous rocks, debris flows, karst development, landslides, and seismogenic faults. Topographic factors, including topographic relief, topographic roughness, planar curvature, and profile curvature, have been widely used in evaluation models for the susceptibility of landslides and debris flows [17,18,19] so as to offer a scientific foundation for assessing geological disaster risks in the construction of photovoltaic power stations. LSW, a composite factor proposed by Zhou et al., can balance the contribution of each factor to the expression of the slope body and effectively identify the plant coverage, so it is helpful for identifying the areas suitable for construction [20,21]. In terms of land use, the sites of photovoltaic power stations should give priority to nonarable land, undeveloped land, low-economic-value land, or other similar areas; and, occupying permanent basic farmland or other high-value agricultural land should be strictly avoided so as to realize the rational development and utilization of land resources.

2.4.2. Meteorological Factors

Meteorological factors include solar radiation, air temperature, wind speed, and precipitation. Solar radiation is crucial in determining power generation potential and economic returns. However, under adequate sunlight, air temperature can restrict the optimal functioning of photovoltaic modules [22], and the wetting of rainwater may cause damage to photovoltaic materials, thus compromising the production capacity of photovoltaic modules [23]. In photovoltaic power stations, ideal temperatures enhance panel efficiency, while too much precipitation can lower temperatures and disrupt performance. Thus, it is essential to factor in both temperature and precipitation when planning these plants to ensure stable and efficient operation [24]. Appropriate wind speeds can boost power generation efficiency by reducing the temperature and removing the wind dust particles on photovoltaic cell surfaces; of course, excessive wind speed may damage photovoltaic materials [23,25].

2.4.3. Location Factors

Location factors include distance from residential areas, roads, and water systems. To minimize the impact of photovoltaic power stations on local residents, their locations should be sufficiently distanced from residential areas. Meanwhile, in order to minimize transmission costs and losses, photovoltaic power stations should be close to residential areas but not too close; generally, a distance of 5 km is appropriate [26]. In addition, photovoltaic power stations should be kept within a proper distance from roads, because the transportation and installation of photovoltaic power station equipment need to rely on road traffic. Too long a distance between a power station and a main road may increase transportation costs and cause inconvenience to construction [27]. The land around a water system usually has to face potential flood hazards. If a photovoltaic power station is located near a river or lake, it is necessary to build protective facilities, such as flood embankments, to prevent against possible floods. Therefore, the distance from a water system should be reasonably considered when the site of a photovoltaic power station is selected so as to ensure that the site selection cannot only effectively avoid the flood risk but can also ensure the operational safety of the power station [28]. To sum up, the scientific assessment and rational planning of location factors are an important part of the suitability assessment of photovoltaic power stations’ site selection; this process can provide a basic guarantee for the efficient operation of photovoltaic power stations.

2.4.4. Correlation Analysis and Optimization of Indicators

Physical geography factors are crucial in evaluating the suitability of photovoltaic power stations. Slope and aspect are often considered in the research of photovoltaic power station locations. In this study, topographic factors such as topographic relief, terrain roughness, planar curvature, profile curvature, and the composite factor LSW were comprehensively considered to measure the impact of topographic characteristics on photovoltaic power stations’ locations. However, due to a high correlation between these topographic factors, the direct use of all the factors in an evaluation system may lead to the instability or deviation of the analyzed results. To enhance the model’s accuracy and simplify the indicator system, this study used the Pearson correlation coefficient to analyze the relationships between various terrain factors so as to screen out the most representative terrain factors. The analysis results are shown in

Table 2. Correlation coefficient matrix for terrain factors.

	Slope	Aspect	Terrain Roughness	Planar Curvature	Profile Curvature	Topographic Relief	LSW
Slope	1
Aspect	0.021	1
Terrain roughness	0.895	0.015	1
Planar curvature	−0.002	0.078	0.004	1
Profile curvature	0.403	−0.014	0.322	0.004	1
Topographic relief	0.889	0.028	0.831	0.009	0.422	1
LSW	0.024	0.006	−0.006	0.002	0.006	0.026	1

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As shown in the table above, there is high correlation among terrain roughness, topographic relief, and slope, indicating that these factors have information redundancy to a certain extent. Therefore, this study excluded topographic relief and terrain roughness so as to avoid the interference of repeated indicators on weight distribution. Finally, slope, aspect, planar curvature, profile curvature, and the composite factor LSW were selected as the indicators of physical and geographical factors, which not only have high independence between them but can comprehensively reflect terrain characteristics.

2.5. Construction and Classification of Evaluation Indicator System

Eventually, this study selected 13 influencing factors—solar radiation, air temperature, wind speed, precipitation, slope, aspect, planar curvature, profile curvature, LSW, land use type, distance from residential areas, distance from the road, and distance from the water system—for site selection, establishing an evaluation indicator system for photovoltaic site selection. The primary indicators included physical geography, meteorology, and location, and the secondary indicators were classified by nature, as shown in

Table 3. Evaluation indicator system.

Target	Primary Indicator	Secondary Indicator
Suitability evaluation of photovoltaic power station site selection	Meteorology	Solar radiation
		Air temperature
		Wind speed
		Precipitation
	Physical geography	Slope
		Aspect
		Planar curvature
		Profile curvature
		LSW
		Land use type
	Location	Distance from residential areas
		Distance from the road
		Distance from the water system

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According to the complex landforms of Qujing, the evaluation factors are treated differently. The classification and assignment of each secondary indicator are based on the actual suitability of each factor. A rating of 4 indicates that the indicator is highly suitable, 3 represents that it is moderately suitable, 2 means that it is unsuitable, and 1 signifies that it is very unsuitable. The detailed suitability classification is presented in

Table 4. Suitability grade of photovoltaic station site selection indicators.

Indicator	Suitable (4)	Generally Suitable (3)	Unsuitable (2)	Very Unsuitable (1)
Solar radiation (kWh/m2)	>4.2	4.0–4.2	3.8–4.0	<3.8
Air temperature (°C)	4–13	13–15	15–17	>17
Wind speed (m/s)	3.2–4.4	4.4–5.3	5.3–6.7	>6.7
Precipitation (mm)	717–920	920–971	971–1032	>1032
Slope (°)	0–3	3–20	20–35	>35
Aspect	South, east, southeast Flatland	Southwest, northeast	West, northwest	North
Planar curvature	0–4	4–8	8–15	>15
Profile curvature	<40, 80–200	40–80
LSW	200–240	240–320	>320
Land use type	<0.26	0.26–0.32	0.32–0.38	>0.38
Distance from residential areas (m)	1500–5000	800–1500	500–800	0–500, >5000
Distance from the road (m)	1500–5000	800–1500	500–800	0–500, >5000
Distance from the water system (m)	1500–5000	800–1500	300–800	0–300, >5000

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2.6. Fuzzy Analytical Hierarchy Process

Combining the analytic hierarchy process and fuzzy logic, the method of the fuzzy analytic hierarchy process is used to deal with complex decision problems with uncertainty and fuzziness. By introducing fuzzy set theory, it corrects the limitations of the traditional AHP in dealing with fuzzy information while making the decision-making process more flexible and accurate.

1.

Establishment of fuzzy complementary judgment matrix

This study applies the 0.1–0.9 scale method, as shown in

Table 5. Scale table.

Scale	Definition	Description
0.5	Equally important	The two elements have equal importance when compared
0.6	Slightly important	In comparison, one element is slightly more important than the other
0.7	Obvious importance	In comparison, one element is significantly more important than the other
0.8	More important	In comparison, one element is much more important than the other
0.9	Extremely important	In comparison, one element is extremely more important than the other
0.1, 0.2, 0.3, 0.4	Inverse comparison	If the two factors $r_i$ and $r_j$ are compared to obtain the judgment $r_{ij}$, then the judgment obtained by comparing $r_j$ and $r_i$ is $r_{ji}=1-r_{ij}$

, to express the relative importance between two elements. The 0.1–0.9 scale is a widely used method in the fuzzy analytic hierarchy process to quantify the relative importance of factors. In this scale, a score of 0.5 indicates that two factors are equally important, while scores greater than 0.5 indicate that one factor is more important than the other.

In the fuzzy analytic hierarchy process, pairwise comparisons quantify the relative importance of factors, resulting in the fuzzy complementary judgment matrix R, as shown in Equation (1):

$$R=\left[\begin{array}{cccc}{r}_{11}& r_{12}& \dots & r_{1n}\\ r_{21}& r_{22}& \dots & r_{2n}\\ \dots & \dots & \dots & \dots \\ r_{n1}& r_{n2}& \dots & r_{n\mathrm{n}}\end{array}\right]$$

(1)

where $r_{ij}+r_{ji}=1$ and $r_{ii}=0.5$, indicating equal importance between factors. A value in the range [0.1, 0.5] means that $r_j$ is more important than $r_i$, while a value in (0.5, 0.9] means that $r_i$ is more important than $r_j$.

2.

Weight calculation

For the fuzzy complementary judgment matrix, the expression of the weight W is as follows:

$$w_i={\displaystyle \frac{{\sum }_{j=1}^n{r}_{ij}+\frac{n}{2}-1}{n(n-1)}},i\in N$$

(2)

where n is the number of elements at the same level.

3.

Conformance test

The consistency of the weight value obtained in Equation (2) needs to be tested. This study uses the consistency of the fuzzy judgment matrix to test its consistency principle. Equation (2) is used to obtain the weight vector and construct the characteristic matrix elements, as below:

$$w_{ij}={\displaystyle \frac{w_i}{w_i+w_j}},\forall i,j\in n$$

(3)

The compatibility of the fuzzy matrix is expressed by the compatibility indicator, which meets the following formula:

$$I\left(R, W\right)={\displaystyle \frac{1}{n^2}}\sum _{i=1}^n\sum _{j=1}^n\left|r_{ij}+w_{ij}-1\right|\le 0.1$$

(4)

When the fuzzy matrix R of the primary indicators and the matrix R_i of the secondary indicators satisfy the consistency requirements, the consistency of the overall evaluation matrix is also ensured. The final weight of the secondary indicator factors can be expressed as follows:

$$w_{Ri}={\sum }_{i=1}^n{w}_i{w}_{ip}$$

(5)

where $w_{Ri}$ represents the final weight of each factor in the secondary-indicator layer; $w_i$ is the weight of the primary indicator associated with the factor; and $w_{ip}$ is the subordinate weight of each factor within the secondary-indicator layer.

4.

Determination of weight by FAHP

To evaluate the importance of the 13 factors related to photovoltaic site selection, this study made reference to the scaling method in Table 5, expert opinions, and the relevant literature. The fuzzy judgment matrix at each indicator level was constructed based on the 0.1–0.9 scale method, which quantified the relative importance of factors through pairwise comparisons. Specifically, multiple experts with extensive experience in photovoltaic site selection independently assessed the relative importance of each factor using the 0.1–0.9 scale, where 0.5 indicated equal importance, 0.6 indicated slight importance, and so on, as defined in Table 5. The experts’ scores were then averaged to construct the fuzzy judgment matrices, ensuring that the values accurately reflected the collective judgment of the experts. The fuzzy judgment matrix at each indicator level is constructed below.

$$\mathrm{R}=\left[\begin{array}{ccc}0.5& 0.4& 0.2\\ 0.6& 0.5& 0.3\\ 0.8& 0.7& 0.5\end{array}\right], {\mathrm{R}}_1=\left[\begin{array}{cccc}0.5& 0.6& 0.7& 0.8\\ 0.4& 0.5& 0.4& 0.7\\ 0.3& 0.6& 0.5& 0.7\\ 0.2& 0.3& 0.3& 0.5\end{array}\right]$$

$${\mathrm{R}}_2=\left[\begin{array}{cccccc}0.5& 0.7& 0.7& 0.8& 0.9& 0.6\\ 0.3& 0.5& 0.7& 0.6& 0.7& 0.6\\ 0.3& 0.3& 0.5& 0.6& 0.7& 0.6\\ 0.2& 0.4& 0.4& 0.5& 0.7& 0.4\\ 0.1& 0.3& 0.3& 0.3& 0.5& 0.3\\ 0.4& 0.4& 0.4& 0.6& 0.7& 0.5\end{array}\right], {\mathrm{R}}_3=\left[\begin{array}{ccc}0.5& 0.8& 0.6\\ 0.2& 0.5& 0.2\\ 0.4& 0.8& 0.5\end{array}\right]$$

According to the consistency test theorem for fuzzy matrices, the fuzzy matrices for both the primary and secondary indicators satisfied the experimental consistency requirements. The indicator values at each level were derived by calculating the factor weights using the above formulas, with the results presented in

Table 6. Evaluation indicator system and weights.

Target	Primary Indicator	Primary Indicator Weight	Secondary Indicator	Secondary Indicator Weight	Comprehensive Weight
Suitability evaluation of photovoltaic power station site selection	Meteorology	0.267	Solar radiation	0.300	0.081
			Air temperature	0.250	0.067
			Wind speed	0.258	0.069
			Precipitation	0.192	0.051
	Physical geography	0.316	Slope	0.207	0.065
			Aspect	0.180	0.057
			Planar curvature	0.166	0.052
			Profile curvature	0.153	0.048
			LSW	0.127	0.040
			Land use type	0.167	0.053
	Location	0.417	Distance from residential areas	0.400	0.167
			Distance from the road	0.233	0.097
			Distance from the water system	0.367	0.153

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2.7. Genetic Algorithm Optimization Model

The genetic algorithm, a stochastic global search optimization method inspired by biological systems, simulates natural selection and heredity through processes such as replication, crossover, and mutation. Starting with an initial population, it generates individuals better suited to the environment via random selection, crossover, and mutation, causing the population to evolve toward an optimal area in the search space. This iterative process continues until it converges on a group of individuals best adapted to the environment, providing a high-quality solution to the problem.

The implementation details are described as follows.

• Encoding Scheme and Search Space Representation

The search space is encoded using real-valued vectors, where each individual represents a candidate weight vector, $\tilde{W}=\left(\widetilde{w_1,}\widetilde{w_2,}\cdots ,\widetilde{w_n}\right)$. Each component, $\widetilde{W_i}$, is initialized as a random number within the interval [0, d], where d = 1.5 serves as an empirical upper bound to constrain weight magnitudes. To ensure feasibility, each weight vector is normalized such that ${\sum }_{i=1}^n\widetilde{w_i}=1$. This real-number encoding directly maps the solution space to the genetic representation, avoiding discretization errors associated with binary encoding.

2.

Crossover Operator

A single-point crossover operator is employed. For the two parent vectors $\widetilde{W_p}$ and $\widetilde{W_q}$, a crossover point c is randomly selected $\left(1\le c<n\right)$. The offspring vectors $\widetilde{W_{o1}}$ and $\widetilde{W_{o2}}$ are generated by exchanging segments beyond c. After crossover, offspring vectors are renormalized to maintain $\sum \widetilde{w_i}=1$. The crossover rate is set to $P_c=0.7$, balancing exploration and exploitation.

3.

Mutation Operator

To diversify the population, a mutation operator randomly selects one component $\widetilde{w_k}$ from the weight vector and perturbs it by adding a random value $\delta ~U\left(\mathrm{0,0.1}\right)$. The mutated vector is then clipped to [0, 1] and renormalized. Mutation is applied with a probability $P_m=0.1$, preventing premature convergence while preserving stability.

4.

Reinitialization Strategy

The population is entirely replaced by offspring in each generation (generational replacement). Elite preservation is tested but omitted to avoid local optima stagnation. No explicit reinitialization is performed during iterations, relying on mutation and crossover to maintain diversity.

The specific steps are as follows:

(1)

Initialize population: generate $N=30$ weight vectors, $\widetilde{W_i}$, with components in [0, 1.5], normalized to the unit sum.

(2)

Evaluate fitness: compute the objective function $I_i$ (Equation (4)) and assign the fitness $F_i=-I_i$.

(3)

Tournament selection: select parents by choosing the best among k = 3 randomly sampled individuals.

(4)

Apply crossover: perform single-point crossover with $P_c=0.7$.

(5)

Apply mutation: perturb the weights with $P_m=0.1$.

(6)

Renormalize and update the population.

(7)

Terminate when 100 generations or convergence is reached.

The specific process is shown in Figure 3.

The convergence analysis of the genetic algorithm is shown in the following Figure 4.

2.8. Particle Swarm Optimization Model

In the PSO algorithm, each individual is considered a particle in the search space, without weight or volume, and moves at a specific speed. The speed of each particle is adjusted dynamically based on its own experience and that of the entire swarm. In an n-dimensional space, suppose there are s particles in the swarm, with the position of the i-th particle represented as $X_i=\left(x_{i1},x_{i2},\cdots ,x_{in}\right)$, its flight speed is $V_i=\left(v_{i1},v_{i2},\cdots ,v_{in}\right)$, and its best-known position is $P_i=\left(p_{i1},p_{i2},\cdots ,p_{in}\right)$, known as the individual best position. The best position for the entire swarm is denoted as $P_g$. The speed and position of the i-th particle are updated according to the following formulas:

$$v_{ij}\left(t+1\right)=v_{ij}\left(t\right)+c_1{r}_{1j}\left(t\right)\left(p_{ij}\left(t\right)-x_{ij}\left(t\right)\right)+c_2{r}_{2j}\left(t\right)(p_{gj}\left(t\right)-x_{ij}\left(t\right))$$

(6)

$$x_{ij}\left(t+1\right)=x_{ij}\left(t\right)+v_{ij}\left(t+1\right)$$

(7)

where t denotes the iteration number in the evolutionary process; j and i refer to the j-th and i-th particles, respectively; $c_1$ and $c_2$ are learning factors; and $r_1$ and $r_2$ are independent random numbers within the [0, 1] interval. $c_1$ represents the impact of individual optimal positions on velocity, while $c_2$ represents the impact of community-optimal positions on velocity. $v_{ij}=\left[-v_{max},v_{max}\right]$. The search space for particles is $[-x_{max},x_{max}]$. The velocity of particles in each dimension is constrained to avoid difficulties in convergence due to excessive velocity.

Based on the basic particle swarm optimization algorithm, inertia weights are introduced into the velocity evolution equation to improve its convergence performance. The expression is as follows:

$$v_{ij}\left(t+1\right)=w{v}_{ij}\left(t\right)+c_1{r}_{1j}\left(t\right)\left[p_{ij}\left(t\right)-x_{ij}\left(t\right)\right]+c_2{r}_{2j}\left(t\right)[p_{gj}\left(t\right)-x_{ij}(t)]$$

(8)

where w is the inertia weight, which has a significant impact on search and convergence capabilities.

The particle swarm optimization algorithm is specifically employed to optimize the weight assignment process in the fuzzy analytic hierarchy process. Its objective is to iteratively adjust factor weights to minimize the consistency metric I, which quantifies deviations in the fuzzy judgment matrix R. The convergence mechanism is governed by three key components: the inertia weight ($W=0.7$) preserves historical search directions to avoid abrupt oscillations in weight adjustments, while the balanced learning factors ($c_1=c_2=1.5$) integrate both particle-specific optimizations and swarm-wide collaborations. Velocity clamping ($v_{max}=0.1$) further stabilizes the search by constraining per-iteration weight changes. Although PSO inherently risks local optima due to stochastic dynamics, the interplay between individual and global best positions ($P_i,P_g$) diversifies search trajectories, significantly mitigating—though not eliminating—local trapping risks. The monotonic minimization of I, as an explicit objective function, provides theoretical convergence guarantees.

The specific steps are as follows:

1.

According to the obtained fuzzy judgment matrix $R={(r_{ij})}_{n\times n}$, initialize N vectors, $\widetilde{W_i}=\left(\widetilde{w_1,}\widetilde{w_2,}\cdots ,\widetilde{w_n}\right),i=\mathrm{1,2},\cdots ,N$, where N is the population size and each component of $\widetilde{W_i}$ is a uniform random number in [0, d] (d is a constant used to control the upper limit of each weight). Initialize N corresponding to velocity vectors $\widetilde{V_i}=\left(\widetilde{v_1,}\widetilde{v_2,}\cdots ,\widetilde{v_n}\right),\mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e} i=\mathrm{1,2},\cdots ,N$, and each component of $\widetilde{V_i}$ is a uniform random number in $\left[-v_{max},v_{max}\right]$. In the algorithm, $v_{max}=0.1$, which controls the maximum value of the velocity change in particles in one iteration.

2.

For $\widetilde{W_i}$, calculate $I_i$ as the fitness value of $\widetilde{W_i}$ according to Equation (4).

3.

Compare the fitness values of $W_i$ for each particle in the group, and set the current optimal position $W_i$ as the position corresponding to the best fitness value.

4.

Compare the global best position $W_g$ and the fitness value of $\widetilde{W_i}$ obtained in the previous step, and select $W_i$ with the best fitness value as the current global best position $W_g$.

5.

For each particle in the group, use Equations (7) and (8) to calculate the $\widetilde{W_i}$ for the next iteration.

6.

If the algorithm’s end condition is not reached, go to Step 2; otherwise, go to Step 7.

7.

Output the sorting weight $W_g$ and the compatibility indicator I.

The specific process is shown in Figure 5.

The optimization dynamics of the proposed FAHP-PSO hybrid model were empirically validated through convergence analysis, as shown in the following Figure 6.

Table 7. Comparison of indicator weights.

Indicator	FAHP	FAHP-GA	FAHP-PSO
Solar radiation	0.081	0.074	0.061
Air temperature	0.067	0.088	0.104
Wind speed	0.069	0.07	0.104
Precipitation	0.051	0.157	0.243
Slope	0.065	0.041	0.019
Aspect	0.057	0.049	0.046
Planar curvature	0.052	0.039	0.046
Profile curvature	0.048	0.076	0.069
LSW	0.04	0.187	0.113
Land use type	0.053	0.071	0.048
Distance from residential areas	0.167	0.031	0.017
Distance from the road	0.097	0.072	0.104
Distance from the water system	0.153	0.045	0.026

shows the comparison of the weight results obtained from the fuzzy analytic hierarchy process, the genetic algorithm optimization model, and the particle swarm optimization model.

3. Analysis and Verification of Results

3.1. Analysis of Suitability of Evaluation Indicators

In this study, all the raw data were resampled to a uniform spatial resolution of 30 m so as to generate raster data to meet the analysis requirements. In the ArcGIS 10.8 software environment, spatial analysis was performed on the selected 13 influencing factors according to the classification criteria in Table 4. The results are shown in Figure 7.

3.2. Analysis of Suitability of Photovoltaic Power Plants

Table 7 illustrates the suitability evaluation results of the three methods for photovoltaic power stations, and the results are divided into three levels by using the natural interruption method, as shown in Figure 8.

According to Figure 8, the suitability areas at different grades can be obtained. In the FAHP method, the suitability analysis results show that the suitable area is 7327 square kilometers, accounting for 25.6% of the total area; the generally suitable area is 11,640 square kilometers, accounting for 40.7%; and the unsuitable area is 9628 square kilometers, accounting for 33.7%. In the FAHP-GA method, the suitable area is 10,164 square kilometers, accounting for 35.2%; the generally suitable area is 11,757 square kilometers, accounting for 41.2%; and the unsuitable area is 6673 square kilometers, accounting for 23.3%. In the FAHP-PSO method, the suitable area is 10,052 square kilometers, accounting for 35.2%; the generally suitable area is 11,180 square kilometers, accounting for 39.1%; and the unsuitable area is 7362 square kilometers, accounting for 25.7%. Overall, the FAHP-GA method found the largest suitable area and the smallest unsuitable area; the FAHP method found the largest proportion of suitable area and generally suitable area; and the FAHP-PSO method found the smallest generally suitable area.

3.3. Verification of Site Suitability

According to the comparison of the suitability analysis results between the existing photovoltaic power station areas in Qujing and the three types of photovoltaic power station sites selected above, as shown in Figure 9, Figure 10 and Figure 11, the areas within the purple borders in the figures already have photovoltaic power stations built. The majority of the completed photovoltaic power station H is built in the suitable area of the site selection results, while the majority of parts of E and G are built in the suitable area, with a small portion in the generally suitable area.

This study calculated the suitable, generally suitable, and unsuitable areas for the completed photovoltaic power station in three different site selection results and analyzed the suitability of these three methods for the site selection of Qujing photovoltaic power station. The results are shown in

Table 8. Verification of suitable sites selected for photovoltaic power station.

Method	Suitability	Area (m2)	Proportion (%)
FAHP	Suitable	255,428	6.3
	Generally suitable	140,2674	34.6
	Unsuitable	2,392,004	59.1
FAHP-GA	Suitable	94,163	2.3
	Generally suitable	780,804	19.3
	Unsuitable	3,175,139	78.4
FAHP-PSO	Suitable	26,519	0.7
	Generally suitable	1,010,162	24.9
	Unsuitable	3,013,425	74.4

. It can be concluded that based on the FAHP site selection results, the built-up photovoltaic power plant area accounts for 93.7% of its suitable and generally suitable areas. Based on the FAHP-GA and FAHP-PSO site selection results, the built-up photovoltaic power plant area accounts for 97.7% and 99.3% of its suitable and generally suitable areas, respectively. The FAHP-PSO model achieves a remarkable accuracy rate of 99.3% in identifying suitable areas for photovoltaic power station construction, compared to 93.7% for the FAHP model. From this, it can be concluded that the FAHP-PSO model demonstrated significant advancements over the traditional FAHP method. By introducing the PSO algorithm, the FAHP-PSO model optimized the weight assignment process, addressing the low-consistency issue of the FAHP. Therefore, the particle swarm optimization model combined with the fuzzy analytic hierarchy process achieved the best performance. This model effectively identified suitable areas for photovoltaic power station construction and offers a theoretical basis for governments and businesses in making site selection decisions.

4. Conclusions

Taking Qujing City in Yunnan Province as an example, this study comprehensively explored 13 factors by dividing them into three categories: meteorology, physical geography, and location. And, it further expanded research on terrain factors, especially natural geographical factors, by adding the analysis of terrain factors, such as planar curvature, profile curvature, and LSW, so as to more comprehensively reveal the impact of terrain on the construction of photovoltaic power stations. Building on the fuzzy analytic hierarchy process, this study employed a particle swarm optimization model to assess the suitability of photovoltaic power station sites and compared the results with those from genetic algorithm optimization models. The results indicate that suitable areas in Qujing expand progressively from east to west, with the majority located in the central and western regions. The more contiguous plots are mainly concentrated in Huize County, Malong District, and Luliang County, showcasing an overall spatial distribution characteristic of “less in the east, more in the west, and clustered in the southwest.” The proportions of suitable, generally suitable, and unsuitable areas in the suitability analysis results obtained using the FAHP method were 25.6%, 40.7%, and 33.7%, respectively; the proportions obtained using the FAHP-GA method were 35.2%, 41.2% and 23.3%, respectively; and the proportions obtained using the FAHP-PSO method were 35.2%, 39.1%, and 25.7%. To ensure that the PSO algorithm achieved optimal performance, we systematically calibrated key parameters through iterative experiments. The population size was set to 50 particles, balancing exploration capability and computational efficiency. Convergence analysis revealed that fitness values stabilized gradually, tending towards stability. This suggests that the algorithm effectively escaped local optima while maintaining reasonable computational complexity. Validation with the completed photovoltaic power stations was performed. Based on the FAHP site selection results, the built-up photovoltaic power plant area accounted for 93.7% of its suitable and generally suitable areas. Based on the FAHP-GA and FAHP-PSO site selection results, the built-up photovoltaic power plant area accounted for 97.7% and 99.3% of its suitable and generally suitable areas, respectively. The FAHP-PSO model demonstrated significant advancements over the traditional FAHP method. By integrating the PSO algorithm, the FAHP-PSO model optimized the weight assignment process and achieved a remarkable accuracy rate of 99.3% in identifying suitable areas for photovoltaic power station construction. This improvement highlights the effectiveness of the FAHP-PSO model in providing a more reliable and scientific approach for site selection. Thus, the particle swarm optimization model, built on the fuzzy analytic hierarchy process, yielded the most optimal results for selecting suitable locations for photovoltaic power stations in Qujing. This research offers valuable insights for future studies on photovoltaic power station site selection.

There are many factors that affect the site selection of photovoltaic power stations, and there are differences in the selection of evaluation indicators. However, due to limitations in data acquisition, this study has certain deficiencies in the selection of evaluation indicators, and the evaluation indicator system may not be perfect. In the future, further improvements will be made to the evaluation indicator system. This method should consider the influence of specific terrain in different regions for weight determination, and its application in different regions will be further explored in the future. In addition, future research could extend this work by integrating photovoltaic power generation models to quantify the impact of site selection on energy production, providing a more comprehensive evaluation of the economic and technical viability of photovoltaic power stations in different locations.