Ranking of Sites of Solar Power Plants in Fuzzy Environment

The selection of an appropriate site for solar power plants is crucial for maximizing energy production and ensuring the economic viability of the solar power plant. This literature review aims to explore the key factors that influence the site selection process for solar power plants. By examining relevant scholarly articles and reports, this review identifies and analyzes various factors. The findings of this literature review provide valuable insights for project developers, policymakers, and researchers involved in the planning and development of solar power plants. Relevant literature review is presented in the following paragraphs.

A decision and methodology were presented by Khan and Rathi [1] to locate potential sites for large-scale solar photovoltaic (SPV) plants based on various factors such as “analysis criteria” and “exclusion criteria”.

With the aid of geographic information systems (GIS) and a multi-criterion decision-making (MCDM) technique, Al Garni and Awasthi [2] evaluated and selected the best location for utility-scale solar PV projects. Kereush and Perovych [3] proposed criteria for siting solar PV farms for analyzing available technical information in order to support a decision making process. Akkas et al. [4] considered five cities of Turkey and identified the relative ranking of these cities through ELECTRE, AHP, VIKOR and TOPSIS Methods. Sharma and Singh [5] investigated and understood the optimal site selection and efficiency for photovoltaic systems in solar laboratories and explored the possibilities for their utilization.

A combined approach of Multi Criteria Analysis (MCA) and Geographic Information Systems (GIS) was presented by Khemiri et al. [6], for the optimal placement of solar photovoltaic large farms in Makkah region in western Saudi Arabia. Wang et al. [7] illustrated FAHP, DEA and TOPSIS methods for selection of solar power plant location with a case study of Viet Nam. Authors concluded that the study is useful for location of other industries also. Using a fuzzy logic model, Yousefi et al. [8] selected a spatial site for solar power plants in the Markazi Province of Iran. The results of the research have been visualized and spatially analyzed using Geographic Information Systems (GIS).

Deveci et al. [9] considered 44 factors in selecting the site for a solar power plant. This study examines twenty criteria under four main categories, namely: Economical, Technical, Environmental, and Socio-Political. We conducted this study in response to the lack of literature and in an attempt to determine the importance of the criteria affecting the site selection of solar power plant projects using grey relation methods (GRA and GRP) decision making methods.

Guaita-Pradas et al. [10] combined legal, political, and environmental criteria, including solar radiation intensity, local physical terrain, environment, and climate, as well as location criteria, such as distance from roads and power substations. Furthermore, GIS data (time series of solar radiation, digital elevation models (DEM), land cover, and temperature) are used as additional input parameters to identify areas for solar PV power generation.

Ghasempour et al. [11] reviewed various criteria adopted in various MCDM methods for selection of sites for solar power plants. The authors concluded that the importance of the criteria depends on Economy, region, power network, Operating costs maintenance costs, etc. Asadi and PourHossein [12] adopted VICORE, AHP and TOPSIS for evaluation of location for construction of hybrid renewable energy power plants.

Using Geographical Information Systems (GIS) technology, Colak et al. [13] investigated the possibility of building a solar photovoltaic (PV) power plant in the Malatya Province of Turkey. Suprova et al. [14] conducted a literature review to determine the criteria for selecting these farms based on Geographic Information System (GIS) and Analytical Hierarchy Process (AHP), taking into account factors such as solar radiation potential, site location, transportation, and technological-economic factors.

Shimray and Malemnganbi [15] investigated the degree of importance of factors affecting the selection of solar photovoltaic (PV) sites through a novel logarithmic additive estimation of weight coefficients (LAAW) under a fuzzy environment in their review. They explored the ideal sites for solar power plants through MCDM approaches. The authors concluded that China, Spain, and India are best places for deployment of solar power plants.

In a paper published by Deveci et al. [16] investigated the degree of importance of factors affecting the selection of solar photovoltaic (PV) sites through a novel logarithmic additive estimation of weight coefficients (LAAW) under a fuzzy environment. The study conducted by Soydan [17] sought to determine the most suitable location for solar energy plants and provide the option of building them at the most suitable locations. Using an analytical hierarchy process (AHP) method in GIS, eleven data layers were created (sunshine duration, solar radiation, slope, aspect, road, water sources, residential areas, earthquake fault lines, mine areas, power lines and transformers).

Khajavipour et al. [18] considered Fourteen criteria and prioritized these criteria through integrated Delphi method and FAHP for deployment of solar power plant. Authors concluded that Distance to power lines, distance to main roads and land use were the important criteria for deployment of solar power plant. Alhammad et al. [19] developed a spatial MCDA framework for evaluation of sites for solar power plants with combination of GIS and Analytical Hierarchy Process (AHP) techniques to determine five sub-criteria weights (Slope, Global Horizontal Irradiance (GHI), proximity to roads, proximity to residential areas, and proximity to power lines).

Ayough et al. [20] presented a new method that integrates PROMETHEE and Interactive methods for identification of optimum location of solar power plants. The authors made sensitivity analysis to know the effectiveness of the parameters in the proposed method. Wang et al. [21] proposed Data Envelopment Analysis, Fuzzy Analytic Hierarchy Process and Fuzzy MARCOS methods for selection of solar power plants. The author illustrated the methods with a case study. The study identified three best provinces for deployment of power plant in Indonesia by considering Twenty-Three Criteria.

An Integrated Approach to Grey Relational Analysis, Analytic Hierarchy Process and Data Envelopment Analysis is proposed for in fuzzy environment for multi-attribute analysis for evaluation and selection of alternatives Pakkar [22]. Afshari Pour et al. [23] developed GIS-Fuzzy DEMATEL Model for Site Selection of Solar Power Plant and illustrated with a Case Study of Bam and Jiroft Cities of Kerman Province in Iran.

In summary, the proposed methods are valuable for ranking of solar power plant sites in a fuzzy environment because it enables systematic decision-making that considers uncertainty, multiple criteria, stakeholder preferences, and adaptability to changing conditions.

There has been limited research on fuzzy MCDM models in the energy literature related to the selection of solar power plant sites. This study aims to evaluate the criteria used for selecting solar PV sites and to develop a decision support system based on grey methods (Grey Relation Analysis –GRA and Grey Relation Projection-GRP) and hybrid grey methods (GRA-DEA and GRP-DEA).

3.1 Grey methods

Grey methods dynamically compare each factor quantitatively, based on the level of similarity and variability among factors to establish their relation. GRA method analyzes the relational grade for discrete sequences. GRP method combined the advantages of the grey relation method and projection method.

3.1.1 Grey Relation Analysis (GRA)

The method is explained in the following steps.

Obtain the fuzzy decision matrix. Fuzzy decision matrix contains the pay-off the sub-criteria against the alternative expressed in terms of linguisticvariable. The linguistic variables are assigned with fuzzy numbers.

Obtain Crisp Decision Matrix. Conversion of Fuzzy number into crisp number is made as proposed by Afshari Pour et al. [23].

Normalize the decision matrix. Normalization based on the characteristics of three types of criteria, namely larger-the-better (benefit), smaller-the-better (cost) or nominal-the-best (optimal), is used here to transform the various criteria scales into comparable scales. Normalization formulae are presented below:

$x_{k j}=\frac{x_{k j}-\min x_k(j)}{\max x_k(j)-\min x_k(j)} \ldots$. For benefit attribute        (1)

$x_{k j}=\frac{\max x_k(j)-x_{k j}}{\max x_k(j)-\min x_k(j)} \ldots$. For cost attribute

where, x_kj=normalized value of k^th attribute of j^th alternative.

Determine absolute differences. The absolute difference of the compared series and the referential series should be obtained by the following the equation:

$x_{k j}=\left|x_{0 j}-x_{k j}\right|$     (2)

Find out maximum and minimum absolute differences. The maximum and the minimum difference should be found from the absolute difference of the compared series and the referential series.

$\Delta \min =\min \left(x_{k j}\right) ; \Delta \max =\max \left(x_{k j}\right)$       (3)

Determine grey relation coefficient. In Grey relational analysis, Grey relational coefficient $\xi$ can be expressed as shown in equation:

$\xi_{k j}=\frac{\Delta \min +\rho \Delta \max }{\Delta_{k j}+\rho \Delta \max }$      (4)

where, $\Delta$max: Max difference compared series and the referential series; $\Delta \mathrm{min}$ : Max difference compared series and the referential series; $\rho$ : Distinguishing coefficient lie between 0 and 1. Generally, the distinguishing coefficient $\rho$ is set to 0.5.

Determine ranking of alternatives. From the grey relation coefficient, grey relation grade is determined from the following relation and the alternatives are ranked based on the descending order of grey relation grade:

$G R G(j)=\sum_{k=1}^n w_k * \xi_{k j}$        (5)

3.1.2 Grey Relation Projection (GRP)

The method is explained in the following steps.

Determine Positive and negative ideal Solutions. Calculate grey relation coefficient of each alternative with positive ideal solution and negative ideal solution from the following relation.

$Q_j^{+}=\sum \frac{m_k^{+}+\rho^* \Delta \max }{\Delta_{k j}^{+}+\rho^* \Delta \max } ; \quad \xi_{k j}^{-}=\frac{m_k^{-}+\rho * \Delta \min }{\Delta_{k j}^{+}+\rho * \Delta \min }$                   (6)

where, mi+ and mi+ are minimum and maximum absolute differences.

Determine Grey Relation Projection. Grey Relation Projection of ‘i^th’ alternative on positive (Q_j⁺) and negative (Q_j^-) ideal solutions from the following relation.

$Q_j^{+}=\sum_{k=1}^m \frac{w_k^2 * \xi_{k j}^{+}}{\sqrt{\sum_{k=1}^m w_k^2}} ; Q_j^{-}=\sum_{k=1}^m \frac{w_k^2 * \xi_{k j}^{-}}{\sqrt{\sum_{k=1}^m w_k^2}}$              (7)

Determine Ranking of alternatives. Find relative degree of Grey Relation Projection Grade (GRPD_j) from the following relation. The alternatives are then ranked in decreasing order using gray relation projection grade.

$G R P D_j=\frac{Q_j^{+}}{Q_j^{+}+Q_j^{-}}$              (8)

3.2 Hybrid grey methods

3.2.1 Hybrid Grey Relation Analysis and Data Envelopment Analysis (GRA-DEA)

The Hybrid GRA-DEA method is explained in the following steps:

Determine grey relation coefficient. Grey relational coefficient is determined as presented in Eq. (4).

Determine optimistic grey relation grade. Optimistic grey relation grade is obtained by solving the dual model [22] as discussed below. The model is solved through Lingo 8.0 by developing Code to the model.

Determine pessimistic grey relation grade. Pessimistic grey relation grade is obtained by solving the dual model [22] as discussed below. The model is solved by through Lingo 8.0 by developing Code to the model.

Determine normalized compromised grey relation grade. Normalized grey relation grade is obtained from the following relation.

$\Delta_k(\beta)=\beta \frac{\Gamma_k-\Gamma_{\min }}{\Gamma_{\max }-\Gamma_{\min }}+(1-\beta) \frac{\Gamma_k^{\prime}-\Gamma_{\min }^{\prime}}{\Gamma_{\max }^{\prime}-\Gamma_{\min }^{\prime}}$               (9)

where, $\Gamma_{\mathrm{j}}=$Optimistic grey relation grade; $\Gamma_{\mathrm{j}}^{\prime}=$Pessimistic grey relation grade;$\Gamma_{\max}=\max\left(\Gamma_{\mathrm{k}}\right) ; \Gamma_{\min}=\min\left(\Gamma_{\mathrm{k}}\right); \Gamma^{\prime}{ }_{\max}=\max\left(\Gamma_{\mathrm{k}}^{\prime}\right);$ $\Gamma^{\prime}{ }_{\min}=\min \left(\Gamma^{\prime} \mathrm{k}\right); 0 \leq \beta \leq 1$ is an adjusting parameter, which may reflect the preference of a decision-maker on the best and worst sets of weights. $\Delta_{\mathrm{k}}(\beta)$ is a normalized compromise grade in the range $[0,1]$.

Determine Ranking of alternatives. The alternatives are then ranked in decreasing order using normalized compromised gray relation grade.

3.2.2 Hybrid Grey Relation Projection and Data Envelopment Analysis (GRP-DEA)

Determine Positive and negative ideal solutions. In the Grey Relation Projection method, a normalized decision matrix is considered to find fuzzy positive and fuzzy negative ideal solutions from the following relations.

$V_j^{+}=\max \left(X_{k j}\right) ; V_j^{-}=\min \left(X_{k j}\right)$           (10)

where, X_ij- Elements of normalized decision matrix.

Calculation of grey relation coefficient. The grey relation coefficients of each alternative with respect to positive ideal solution and negative ideal solution are calculated from relation shown in Eq. (6).

Determine optimistic grey relation grade from positive ideal solution and negative ideal solution. Optimistic grey relation grade is obtained by solving the dual model proposed by Pakkar [22] using grey relation coefficients from positive ideal solutions and negative ideal solutions respectively. The models are solved through Lingo 8.0 by developing Code to the model.

Determine Pessimistic grey relation grade from positive ideal solution and negative ideal solution. Pessimistic grey relation grade is obtained by solving the dual model proposed by Pakkar [22] using grey relation coefficients from positive and negative ideal solutions respectively. The models are solved through Lingo 8.0 by developing Code to the model.

Determine normalized grey relation grade from positive ideal solutions. Normalized compromised grey relation grade is determined as presented in Eq. (9).

Ranking of the alternatives. The alternatives are then ranked in decreasing order using the closeness coefficients.

In sum, these methods offer a rigorous, data-driven framework for site selection, allowing for a more holistic, accurate, and future-proof decision-making process. Therefore, their use can be justified in the complex, multi-faceted task of selecting optimal sites for solar power plants.

The objective of this paper was to perform a performance analysis of sites for the location of solar power plants based on four major criteria and twenty sub-criteria, using GRA, GRP, GRA-DEA and GRP-DEA methods in a fuzzy environment. It is also observed that there existed high significant positive correlation in the proposed ranking methods.

The results so obtained are aggregated to arrive the final ranking. From the aggregate ranking, Top-ranked alternatives are Alternative 32 (Rank 1), Alternative 34 (Rank 2), Alternative 49 (Rank 3), Alternative 7 (Rank 4) and Alternative 43 (Rank 5). The alternatives with the highest aggregate rank values are the worst or least preferred. Alternative 19(Rank 50), Alternative 29 (Rank 49), Alternative 27 (Rank 48), Alternative 17 (Rank 47) and Alternative 24 (Rank 46).

To derive more specific reasons for the top ranking of particular alternatives, one would need to closely examine the payoff values associated with each of the 20 criteria for those alternatives, and consider the weight or importance assigned to each criterion. By doing so, you can pinpoint exactly where these alternatives are outperforming their counterparts.

This study is one of the few attempts to evaluate the performance of sites through ensemble ranking for locating solar power plants to the best of our knowledge. It should also be noted there is significant correlation between the proposed rankings. The results of this study have provided useful information about competitive locations for solar power plants and are helpful to decision makers.

The proposed methods in fuzzy environments provide a practical, rational, and robust tool for evaluating and ranking potential solar power plant locations. The proposed methodology also has the advantage of being flexible. The proposed methods may lead to an over-reliance on quantitative data might overlook qualitative aspects that could be crucial for site selection, such as community sentiment or cultural significance.

It is essential that future research be directed towards extending the proposed methodology by incorporating other uncertainty theories, such as intuitionistic and hesitant fuzzy sets. Future research should be directed towards the development of hybrid models using traditional MCDM ratio based methods to maximize their effectiveness and rationality. This study also can be extended to cluster analysis which is a potent statistical tool in categorizing the performance of potential sites for location of solar power plants in specific but to any organization in analyzing their performance.