Solar Panel Cooling System Evaluation: Visual PROMETHEE Multi-Criteria Decision-Making Approach

Abstract

The energy sector is interested in sustainable solar power plants. It is obvious that the working temperature of solar panels, which is significantly higher than the specified working cell temperature in hot climes, has a significant impact on efficiency and longevity. The selection of solar panel cooling systems, on the other hand, is worrisome since the choice process incorporates ergonomic, technical, economic, and environmental issues. The goal of this research is to (1) present a multi-criteria decision-making approach that is both quantitative and qualitative in nature for selecting solar panel cooling systems; (2) outrank nine alternative solar panel cooling systems with eleven performance measures for each alternative to assist decision makers in determining the best viable choice; and (3) visualize the relationship between the different solar panel cooling systems and performance measures under consideration. The proposed approach is to compare and rank solar panel cooling systems, as well as their validation and evaluation through sensitivity analysis. When operating efficiency is prioritized, finned air cooling is shown to be the best solar panel cooling technique, whereas thermosiphon cooling is the best alternative when emission reduction criteria are prioritized. A comparison of the findings shows that phase change material cooling and forced convection cooling performed worst in almost all cases.

1. Introduction and Background Review

In pursuit of green technology innovations, the energy industry demonstrates a focus on long-term sustainability renewable energy generation. The goal is to generate and transfer power to major domestic and industrial customers by 2030. It is concerned with a number of factors, for example, energy generation, public awareness, demand, and the risk at which local and national transmission occurs. The manufacturers of solar panel modules are more interested in improving the efficiency of solar panels; for this, they need meticulous alternative selection and assessment. There are challenges and opportunities in solar modules [1,2] influenced by ambient temperature, solar radiation intensity, the solar panels’ surface temperature, dust, and shading, among other factors that may be overcome by adopting a suitable cooling and cleaning system. Solar panel cooling approaches [3,4] use several physical ways employing various flow media to minimize the solar panels’ surface temperature. These approaches are categorized as either passive (no external energy is needed) or active (additional energy is utilized to circulate the cooling fluid). Passive approaches [5,6] include the use of fins or expanded surfaces to facilitate heat transfer, the use of phase change material to absorb heat produced in the panel, the use of heat pipe cooling, and convection via natural circulation water or air cooling. Active approaches [7,8] involve the circulation of air or water over the panel surfaces, both with and without the assistance of fins. There are several factors to consider when comparing active and passive solar panel cooling systems. However, the comparative ease of operation depends on the specific cooling system being used, as well as factors such as the size and location of the system; the required level of maintenance; the effective performance, particularly in hot and humid environments; and the cost when evaluating different solar panel cooling systems. For example, studies [7,8] have shown that water spraying can reduce the temperature of solar panels by up to 23 °C and significantly increase their electrical efficiency. Temperature impact affects efficiency and panel life span despite greater energy generation [9,10]. Likewise, researchers [5,11,12] have documented the recovery of useful electrical power with considerable changes in the heat dissipation process of solar panels by using various passive or active panel cooling processes. Although cooling clearly increases renewable energy production [5], it necessitates an additional structure that can extract heat from the panel and distribute it elsewhere. Notably, the design and maintenance [13] of a cooling strategy can be expensive, and the cost of system maintenance may outweigh the benefits of increased power generation. When compared to silicon-based panels [14], thin-film solar panels [15] are less influenced by a rise in temperature. Also, the effectiveness of solar panel cooling systems may vary depending on various factors such as the climate, panel design, and the type of cooling approach used. Recently, studies [16] have shown that the use of nano-fluids improves the heat transfer coefficient, solar panel power, and system performance. Past studies [17,18] have also proposed the use of phase change material cooling and microchannel heat sink cooling. However, there is no conclusive evidence to suggest which solar panel cooling strategy is the most effective, as it depends on various factors [4]. It is obvious that selecting the best solar panel cooling system necessitates the use of mathematical tools to analyze the alternatives. As a result, multi-criteria decision analysis is the ideal tool and can be used well in certain scenarios. The PROMETHEE (Preference Ranking Organization METHod for Enrichment Evaluations) decision-making method compares options based on a set of criteria [19]. There are several studies that have applied the PROMETHEE in various ways, such as in the selection of the most appropriate variant of the solar water supply system [20], ranking sites for solar farms [21,22], evaluating the effectiveness of integrated shading devices for office buildings [23], and for decision making in solar plant locations [24], as it allows for the consideration of multiple criteria, and can help decision makers to assess energy technologies [25]. Similarly, it is evident that researchers justified the importance of reliability information to evaluate solar panel selection [26]. On the other hand, strategies are developed to select an efficient solar panel, and a comprehensive comparative analysis is presented [27].

Multiple qualitative and quantitative metrics were used to evaluate, assess, and rate the various solar cooling systems. For example, Mardani et al. [28] reviewed multi-criteria approaches in sustainable and renewable energy system problems. Wang et al. [29] used multi-criteria decision analysis as a key tool to evaluate renewable energy technologies in households. Seker and Kahraman [30] proposed a socio-economic evaluation model for sustainable solar panels by integrating the analytic hierarchy process and multiplicative multi-objective ratio analysis method. Similarly, Krysiak and Kluczek [31] assessed the sustainable development of photovoltaic modules using a multi-criteria decision-making method based on the analytic hierarchy process [32]. Similarly, a multi-attribute decision-making approach based on intuitionistic fuzzy logic is adopted to select and assess solar panels [33].

The motivation to evaluate solar panel cooling systems is to improve solar panel efficiency and output. When solar panels get too hot, their efficiency drops, resulting in less energy output. The temperature of the solar panels may be adjusted by integrating cooling devices, resulting in enhanced efficiency and output. Existing research has mostly focused on the installation of cooling systems in residential buildings and their influence on energy efficiency. However, research evaluating the effectiveness of various cooling technologies and their effects on the long-term durability of solar panels is lacking. Furthermore, research has been performed in certain geographic locations, and further studies that outrank cooling systems are needed.

The goal of this research is to present a multi-criteria decision-making approach that is both quantitative and qualitative in nature for selecting solar panel cooling systems, to assist decision makers in determining the best viable choice, and to visualize the relationship between the different solar panel cooling systems and performance measures under consideration. The proposed approach provides substantial support in comparing and ranking solar panel cooling systems, as well as their validation and evaluation through sensitivity analysis. Six different scenarios, depending on the subjective and objective importance given to each performance measure, are possible choices.

This paper is divided into eight sections. The Section 1 provides an introduction; the Section 2 presents various attributes, performance measures, and alternative solar panel cooling systems; and the Section 3 presents alternative solar panel cooling systems. Section 4 presents the adopted MCDM approach steps. Section 5 and Section 6 then present the implementation of the proposed approach and sensitivity analysis using subjective and objective criterion weights, respectively. Section 7 discusses management benefits, while Section 8 concludes the paper with conclusions and future study directions.

2. Attributes and Performance Measures

There are several benefits of cooling solar panels, which include improving panel overall efficiency, reducing energy consumption, and extending the panel lifespan. By lowering the temperature of the panels, either through passive cooling techniques or more advanced cooling systems [4], the electrical conversion efficiency of the panels can be increased, resulting in higher energy production [34]. Additionally, reducing the temperature of the panels can also help to reduce the wear and tear on the system, leading to a longer lifespan for the panels and a higher return on investment [35]. Furthermore, by reducing energy consumption through more efficient cooling mechanisms, the environmental footprint of the solar system can be minimized, making it a more sustainable option for generating renewable energy [36]. It is decided to make use of a systematic multi-criteria analysis approach to identify the competitiveness of each alternative. The multiple attributes opted to evaluate alternative solar panel cooling systems are as follows: cooling effectiveness, energy efficiency, environmental impact, durability, noise, panel size and weight, and or cost as decision-making attributes (refer to Figure 1). Decision makers opt for multiple combinations of attributes to be evaluated in order to select the most suitable panel cooling system to improve overall efficiency.

As represented in Figure 1, the adopted performance measures to evaluate cooling techniques are briefly described below.

Energy Efficiency (PM01): Energy efficiency is crucial for solar panel cooling since it lowers the amount of energy used for cooling and raises the overall effectiveness of the solar panel system. The surface temperature of the solar panel can be managed by utilizing more energy-efficient cooling techniques, which helps to maximize the electrical conversion efficiency of the solar panel. This can result in considerable drops in energy usage while raising the solar system’s output of energy [37]. In order to increase the effectiveness of solar panels, a number of researchers have used cutting-edge cooling techniques. The electrical efficiency is a function of the cell temperature [23], and it is mathematically estimated by researchers.

Cooling cost (PM02): The cost of cooling solar panels plays an important role in determining the overall cost-effectiveness and return on investment of the solar system [38]. While advanced cooling techniques may improve the electrical conversion efficiency and extend the lifespan of the solar panels, additional supplies and installation charges may also be required, raising the overall cost of the system. Therefore, it is important to consider the costs of cooling technologies and weigh them against the potential benefits in terms of energy production and system longevity [39].

Reliability factor (PM03): Reliability refers to the ability of components of the cooling system to operate without failure or malfunction over time [40]. If the cooling system fails, the temperature of the solar panels can rise, which can have detrimental effects on the energy output and lifespan of the system [41]. Thus, it is crucial for the cooling system to be reliable. Additionally, a reliable cooling system can help to minimize maintenance and repair costs, as well as reduce downtime, ensuring that the solar system operates over its expected lifetime with minimal interruptions [2,30].

Carbon emission (PM04): The carbon footprint of the downstream processing and manufacturing of solar cooling systems is highlighted by researchers [17,42,43], indicating that any cooling system’s environmental impact is an important consideration. Additionally, government policies promote solar energy modules due to their low-carbon emission profile. Therefore, employing more energy-efficient cooling systems in solar modules is an important task. Carbon emissions of the entire system can be reduced, making it a more sustainable option for generating renewable energy [44].

Ergonomic factor (PM05): In the development of solar cooling systems, the primary focus is on technology feasibility, sustainability, and energy efficiency. However, ergonomics could indirectly play a role in selecting solar cooling techniques by ensuring the safety and comfort of individuals involved in the installation, operation, and maintenance of the solar system [45]. By designing these cooling systems to be ergonomically efficient, risks associated with injury, fatigue, and discomfort could be reduced, ultimately improving the overall safety and performance of the system.

Panel temperature dropping (PM06): The operating temperature of a solar panel has a significant impact on its energy output and lifespan, and excessive temperatures can negatively affect overall efficiency and performance [35,36]. Therefore, reducing the operating temperature of the solar module is one of the primary approaches to increasing power generation [46]. Various cooling techniques are being explored to decrease the operating temperature of solar panels and increase their efficiency. The drop in the operating temperature achieved through these cooling approaches can lead to a significant increase in power output, ranging from 20% to 30%, depending on the cooling approach adopted.

Panel size and shape (PM07): The solar cooling system’s effectiveness is often measured in terms of the decrease in operating temperature of the solar panels, and hence, the area of the panel indirectly impacts the cooling requirements [35]. Larger solar modules have more surface area that is exposed to the sun and absorb more energy, resulting in higher operating temperatures. Therefore, larger solar modules may potentially require more powerful cooling systems to maintain their operating temperatures within the desired range. However, the efficiency of solar panels also varies with their size, efficiency, and technology, which may be important factors in selecting a cooling technique [47,48].

Degradation resistance (PM08): It is evident that [49] there are multiple reasons why degradation, i.e., corrosion, coating formation, and scaling, can occur in solar cooling systems. For example, exposure to different environmental factors, including humidity, saltwater, and other pollutants, can lead to corrosion and scaling. Similarly, chemical reactions between the cooling medium and the solar panel materials can also cause corrosion and coating formation. For example, copper in the system can form copper salts that can affect the solar panel’s performance. The materials with lower resistance to corrosion are more likely to corrode and form coatings. Incorrect system design or installation can also contribute to corrosion and coating formation. For example, using dissimilar metals in a cooling system can lead to galvanic corrosion.

Thermal decomposition (PM09): One of the potential challenges [16,50,51,52] that could arise in a solar cooling system is thermal decomposition, which means physical degradation of heat transfer fluids. Heat transfer fluids are used [53] in some cooling systems to improve heat transfer and reduce the operating temperature of solar panels. However, the fluids can suffer physical and thermal decomposition and degradation over time, which reduces their effectiveness. Some of the factors that can cause physical degradation in heat transfer fluids include the fluid’s properties, such as viscosity and thermal stability, the operating temperature range, and the type of solar panels used. Additionally, exposure to ultraviolet radiation, oxygen, and other environmental factors can also contribute to fluid degradation. If the fluid is not replaced or maintained regularly, its ability to transfer heat effectively can decrease, which can negatively affect the solar panel’s performance [39,40,41]. Therefore, it is crucial to ensure that the heat transfer fluid used in a solar cooling system is selected carefully and maintenance and replacement schedules are adhered to in order to maintain the system’s optimal performance.

Leakage issues (PM10): Leakage issues are a significant challenge in solar cooling systems that use heat transfer fluids, as these fluids can leak through damaged piping or seals. The loss of fluid from the system not only reduces its effectiveness in cooling solar panels but can also potentially damage other components in the system. Moreover, the leakage of fluids can create safety concerns, as they may pose a risk to the environment or human health. Therefore, it is crucial to consider potential leakage issues when designing, installing, and maintaining solar cooling systems and take appropriate measures to prevent or mitigate them [1,3,8].

Impact of any equipment failure (PM11): Electric equipment failure/or any power supply failure can impact the overall performance and reliability of the system, which can indirectly affect the cooling system’s ability to maintain the desired operating temperatures of the solar panels [54]. If the electric/non-electric equipment fails, it may lead to a complete shutdown of the system, which can have a domino effect on other components, including the cooling system. Additionally, if the cooling system is not designed or installed correctly [55,56], it may be more susceptible to failures caused by electric equipment failures, such as a power surge or overload, which may impact its ability to cool the solar panels effectively. Thus, the impact of any equipment failure on a solar cooling system depends on various factors, including the type and severity of the failure, the system’s design and installation, and the overall maintenance and operation of the system [3,44].

Thus, various alternatives for solar panel cooling in solar power plant installations have been represented in Figure 1 and briefly described in the following section.

3. Solar Panel Cooling Systems: Alternatives

Solar panel cooling systems use several physical methods, such as sensible and latent heat storage and dissipation or heat convection techniques employing different media, and they are evaluated to examine the reduction in panel operating temperature. These systems are classified as having either a passive approach or an active approach (refer to Figure 1). Active cooling systems [3,4] often perform better in terms of temperature reduction than passive cooling systems. Passive cooling [3,4] does not require much energy to operate and instead relies on natural cooling, which takes longer to cool over time.

Finned air cooling (A1) employs a natural heat transfer process in which heat from the solar panel is transmitted to the fins and then travels through convection by natural wind movement [57]. Heat pipe solar cooling systems (A2) use heat pipes to dissipate heat from solar panels, reducing the temperature and increasing their efficiency. The heat pipes work by transferring excess heat from the panels to the cooler end of the system, where it is dissipated into the air or water [58]. This cooling system has been found to be an attractive option in hot climates [59]. Researchers [60] have conducted studies on the effectiveness of heat pipe solar cooling systems.

Phase change materials (A3) have been used to cool solar panels and increase their efficiency, particularly in hot climates. It works by absorbing the excess heat from the panels and storing it until the temperature drops, providing a buffer against temperature fluctuations [17]. When the panels start to heat up, the phase change material melts and absorbs the heat. As the temperature decreases, the phase change materials then solidify and release the stored heat. Thermosiphon cooling systems (A4) involve a closed-loop system containing a working fluid, such as acetone, that undergoes a phase change to cool a solar panel [61]. On the other hand, a thermosiphon with a clay pot cooling system (A5) uses the clay pot as the medium for evaporative cooling to cool a solar panel [61]. Both systems use the same basic principle of thermosiphon cooling, but they differ in the method of heat dissipation. The clay pot version of the system relies on the process of water evaporation using a simple clay pot placed on top of the solar panel, while the standard thermosiphon cooling system makes use of a working fluid to remove heat by undergoing a phase change in a closed-loop system. Both of these systems are effective in cooling solar panels and improving their performance, but the choice between them depends on factors such as the specific application, location, and cost considerations.

A forced air cooling system (A6) for solar panels is a type of cooling system that uses a fan to circulate air over the solar panels to reduce their temperature. The cool air can be produced in a number of ways, including compressor-cooled refrigerant or chilled water. This type of cooling system is often used in sunny areas where the heat from the sun can cause the solar panels to overheat, which can reduce their efficiency and lifespan [62,63,64]. By cooling the panels with forced air, their temperature can be regulated, which can help to maximize their energy output and improve their overall performance. This type of cooling system is efficient and cost-effective and is often used in residential and commercial solar power systems.

Evaporative cooling systems (A7) [65] and water spray cooling systems (A8) [66] both use water to cool an area, but the methods and efficiencies are different. Evaporative cooling systems rely on the process of evaporation to cool the air, whereas water spray cooling systems function by directing a spray of water into the air to lower air temperature. Evaporative cooling systems are more efficient in low-humidity areas, while water spray cooling systems are more efficient in high-humidity areas. Additionally, evaporative cooling systems are more energy-efficient than water spray systems, while water spray cooling systems are often used in outdoor settings and for cooling large areas. Both systems have unique advantages and limitations, and the choice between the two depends on the specific application. Nano-fluid cooling systems (A9) can be either active or passive. Some of the researchers studied [16,52,62] active cooling systems that use nano-fluids as a coolant in conjunction with traditional cooling methods such as air or water cooling, while other researchers [67] studied passive cooling systems that rely solely on a nano-fluid coolant to dissipate heat.

However, there is no conclusive evidence to suggest which solar panel cooling strategy is the most effective, as it depends on various factors. Different cooling techniques have been used successfully in a number of cases, making choosing difficult [4]. Thus, it is evident [40,44] that choosing the appropriate solar panel cooling system involves the use of a scientific instrument to evaluate the options. So, multi-criteria decision making (MCDM) is the best instrument and has been utilized well in these circumstances. The step-by-step details of the adopted methodologies are presented in the following section, followed by their application.

4. Adopted MCDM Methodology

The most commonly used multi-criteria decision-making approaches [68,69,70] include the analytic hierarchy process (AHP), elimination and choice-translating algorithm (ELECTRE), technique for order of preference by similarity to the ideal solution (TOPSIS), and Preference Ranking Organization METHod for Enrichment of Evaluations (PROMETHEE). Compared to AHP, TOPSIS, and ELECTRE, Visual PROMETHEE has the capability of incorporating decision making via positive and negative preference flow. Visual management of performance using the PROMETHEE technique is appealing in the assessment of alternatives due to concepts like preference flow, weights, geometrical analysis for interactive aid (GAIA) plane, and sensitivity analyses. Partially and completely ranking the options also aids in determining the preferred alternative. However, those who make decisions are frequently interested not just in rating options, but also in determining the superiority of one over another (if such a superiority exists). The adopted methodology for an effective selection of solar panel cooling systems is explained step-by-step below.

Step 1: Decision matrix [70]:

Supposing there are i alternative solar panel cooling systems and j evaluation measures in outranking these cooling panels. PM_ij is the j performance measure’s value for solar panel cooling system i. The decision matrix’s structure is shown in

Table 1. Decision matrix: alternatives, performance measures, and their weights.

Alternative Solar Panel Cooling System i	Performance Measure j
	1	2	…	j
1	PM11	PM12	…	PM1j
2	PM21	PM22	…	PM2j
…	…	…	…	…
i	PMi1	PMi2	…	PMij
Performance measure weightage Wj	W1	W2	…	Wj

below. There are j performance measures and i alternative solar panel cooling systems, and W_j is the amount of significance assigned to each assessment criterion j.

Step 2: Performance measure weightage (W_j) [71,72,73]:

W_j estimates might be subjective or objective. Variations in assessment metrics are employed in the accepted strategy to evaluate the divergence in the ranking of various solar panel cooling systems. The adopted method takes into account both sorts of weights. The objective weights technique employs mathematical models like entropy calculation, such as in [74]; details of this are explained below. The decision matrix values of the j^th performance measure for the i^th solar panel cooling system are standardized using Equation (1) if the objective of the performance measure is maximization. In contrast, Equation (2) is opted for if the performance measure objective is minimization, wherein S_ij is the standardized value for the j^th performance measure of the i^th solar panel cooling system; PM_ij is the j^th evaluation measure’s value for the i^th solar panel cooling system (refer to Table 1). After standardization of all performance measures, the decision matrix is expressed in matrix form in Equation (3), as seen below.

$${\mathrm{S}}_{\mathrm{i}\mathrm{j}}=\left[\frac{{\mathrm{PM}}_{\mathrm{ij}}-\underset{\mathrm{j}}{\min }{\mathrm{P}\mathrm{M}}_{\mathrm{i}\mathrm{j}}}{\underset{\mathrm{j}}{\max }{\mathrm{P}\mathrm{M}}_{\mathrm{i}\mathrm{j}}-\underset{\mathrm{j}}{\min }{\mathrm{P}\mathrm{M}}_{\mathrm{i}\mathrm{j}}}\right]$$

(1)

$${\mathrm{S}}_{\mathrm{i}\mathrm{j}}=\left[\frac{{\underset{\mathrm{j}}{\max }\mathrm{PM}}_{\mathrm{ij}}-{\mathrm{P}\mathrm{M}}_{\mathrm{i}\mathrm{j}}}{\underset{\mathrm{j}}{\max }{\mathrm{P}\mathrm{M}}_{\mathrm{i}\mathrm{j}}-\underset{\mathrm{j}}{\min }{\mathrm{P}\mathrm{M}}_{\mathrm{i}\mathrm{j}}}\right]$$

(2)

$${\mathrm{S}}_{\mathrm{i}\mathrm{j}}^{\prime }=\left[\begin{array}{cccc}{\mathrm{S}}_{11}& {\mathrm{S}}_{12}& \dots & {\mathrm{S}}_{1\mathrm{j}}\\ :& :& :& :\\ :& :& :& :\\ {\mathrm{S}}_{\mathrm{i}1}& {\mathrm{S}}_{\mathrm{i}2}& \dots & {\mathrm{S}}_{\mathrm{i}\mathrm{j}}\end{array}\right]$$

(3)

Entropy E_j, according to its definition, is determined using the following Equation (4), and W_j, the performance measure objective weight, is determined by using Equation (5).

$${\mathrm{E}}_{\mathrm{j}}=-\frac{\sum _{\mathrm{i}=1}^{\mathrm{m}}{[\mathrm{S}}_{\mathrm{i}\mathrm{j}}\ast \mathrm{l}\mathrm{n}\left({\mathrm{S}}_{\mathrm{i}\mathrm{j}}\right)]}{\ln \left(\mathrm{m}\right)}$$

(4)

$${\mathrm{W}}_{\mathrm{j}}=\frac{1-{\mathrm{E}}_{\mathrm{j}}}{[1-\sum _{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{E}}_{\mathrm{j}}]}$$

(5)

In comparison, subjective weights [71] refer to the relative importance of performance measures in a multi-criteria decision making (MCDM) problem and are determined based on the judgment or opinion of the decision maker. In other words, the weights are not calculated mathematically but are assigned based on the subjective perception or expertise of the decision maker. The subjective weights are often obtained through surveys, interviews, expert opinions, or other qualitative methods.

Step 3: Outranking flow estimation [75]:

To start, we initially constructed a generalized preference function ${\mathrm{P}\mathrm{F}}_{\mathrm{i}=\mathrm{a},\mathrm{i}=\mathrm{b}}^{\mathrm{j}}$, where (a, b) is a pair of solar panel cooling systems and j is the performance measure. Each ${\mathrm{P}\mathrm{F}}_{\mathrm{i}=\mathrm{a},\mathrm{i}=\mathrm{b}}^{\mathrm{j}}$ lies between 0 and 1. For given performance measure j, if ‘i = a’ solar panel cooling system is evaluated over ‘i = b’, then any one of the following preferences occurs based on the ${\mathrm{P}\mathrm{F}}_{\mathrm{i}=\mathrm{a},\mathrm{i}=\mathrm{b}}^{\mathrm{j}}$ function value. If the ${\mathrm{P}\mathrm{F}}_{\mathrm{i}=\mathrm{a},\mathrm{i}=\mathrm{b}}^{\mathrm{j}}$ function value is exactly equal to zero, then there is no preference for option a over alternative b. If the ${\mathrm{P}\mathrm{F}}_{\mathrm{i}=\mathrm{a},\mathrm{i}=\mathrm{b}}^{\mathrm{j}}$ function value is close to zero, then the option ‘a’ solar panel cooling system has a weak preference over the ‘b’ solar panel cooling system. If the ${\mathrm{P}\mathrm{F}}_{\mathrm{i}=\mathrm{a},\mathrm{i}=\mathrm{b}}^{\mathrm{j}}$ function value is close to one, there is a substantial preference for the option ‘a’ solar panel cooling system over ‘b’. Lastly, if the ${\mathrm{P}\mathrm{F}}_{\mathrm{i}=\mathrm{a},\mathrm{i}=\mathrm{b}}^{\mathrm{j}}$ function value is exactly equal to one, then there is a stringent preference for the option ‘a’ solar panel cooling system over ‘b’.

Subsequently, using these preference function values, the preference index ${\mathrm{P}\mathrm{I}}_{\mathrm{i}=\mathrm{a},\mathrm{i}=\mathrm{b}}^{}$, which has a value range of 0 to 1, is calculated for each pair of choices using Equation (6), as below.

$${\mathrm{P}\mathrm{I}}_{\mathrm{i}=\mathrm{a},\mathrm{i}=\mathrm{b}}=\left[{\sum }_{\mathrm{j}=1}^{\mathrm{j}}{(\mathrm{W}}^{\mathrm{j}}\times {\mathrm{P}\mathrm{F}}_{\mathrm{i}=\mathrm{a},\mathrm{i}=\mathrm{b}}^{\mathrm{j}}\right)]÷[{\sum }_{\mathrm{j}=1}^{\mathrm{j}}{\mathrm{W}}^{\mathrm{j}}]$$

(6)

In Equation (6), ${\mathrm{W}}^{\mathrm{j}}$ is the weight associated with each solar cooling system evaluation measure j, and the preference index ${\mathrm{P}\mathrm{I}}_{\mathrm{i}=\mathrm{a},\mathrm{i}=\mathrm{b}}$ displays a preference for the option ‘a’ solar panel cooling system over option b, considering all j performance measures (j ϵ 1 to j). If ${\mathrm{P}\mathrm{I}}_{\mathrm{i}=\mathrm{a},\mathrm{i}=\mathrm{b}}$ equals perfectly zero, then there is zero preference for alternative a over b; if ${\mathrm{P}\mathrm{I}}_{\mathrm{i}=\mathrm{a},\mathrm{i}=\mathrm{b}}$ equals approximately zero, then there is a low preference for a over b; if ${\mathrm{P}\mathrm{I}}_{\mathrm{i}=\mathrm{a},\mathrm{i}=\mathrm{b}}$ equals approximately to one, then there is a high preference for alternative a over b, and if ${\mathrm{P}\mathrm{I}}_{\mathrm{i}=\mathrm{a},\mathrm{i}=\mathrm{b}}$ is exactly equal to zero, then there is a perfect preference for alternative a over b. Finally, using the preference index, the outranking flows ${\mathrm{F}}_{\mathrm{a}}^{+}$ and ${\mathrm{F}}_{\mathrm{a}}^{-}$ are quantified using the following Equations (7) and (8), respectively, where i is the number of alternatives (i ϵ 1 to i), excluding alternative i = a.

$${\mathrm{F}}_{\mathrm{a}}^{+}=\frac{1}{\mathrm{i}-1}\sum _{\mathrm{i}=1}^{\mathrm{i}}{\mathrm{P}\mathrm{I}}_{\mathrm{a},\mathrm{i}}$$

(7)

$${\mathrm{F}}_{\mathrm{a}}^{-}=\frac{1}{\mathrm{i}-1}\sum _{\mathrm{i}=1}^{\mathrm{i}}{\mathrm{P}\mathrm{I}}_{\mathrm{i},\mathrm{a}}$$

(8)

Step 4: Calculation of net outranking flow and final ranking [76]:

The aforementioned predicted outranking flows ${\mathrm{F}}_{\mathrm{a}}^{+}$ and ${\mathrm{F}}_{\mathrm{a}}^{-}$ for each option are used to determine each alternative’s dominance over the others. Positive ranking flow quantifies the ‘a’ solar panel cooling system’s dominance over the other alternative solar panel cooling systems, whereas negative ranking flow quantifies alternative a’s dominance over the other alternatives. ${\mathrm{F}}_{\mathrm{a}}^{+},{\mathrm{F}}_{\mathrm{b}}^{+},{\mathrm{F}}_{\mathrm{a}}^{-},$ and ${\mathrm{F}}_{\mathrm{b}}^{-}$ estimated outranking flows for each option a and b and were utilized to determine which option is dominant over the others. By understanding the outranking flow for any two choices, outranking relations can be inferred. Thus, a partial ranking is determined based on the outranking relations between any two choices as follows: if {[(${\mathrm{F}}_{\mathrm{a}}^{+}$ > ${\mathrm{F}}_{\mathrm{b}}^{+}$) and (${\mathrm{F}}_{\mathrm{a}}^{-}$ < ${\mathrm{F}}_{\mathrm{b}}^{-}$)] or (${\mathrm{F}}_{\mathrm{a}}^{+}$ ≥ ${\mathrm{F}}_{\mathrm{b}}^{+}$) or (${\mathrm{F}}_{\mathrm{a}}^{-}$ ≤ ${\mathrm{F}}_{\mathrm{b}}^{-}$)},then solar panel cooling system ‘a’ has preference over ‘b’; if {(${\mathrm{F}}_{\mathrm{a}}^{+}$ = ${\mathrm{F}}_{\mathrm{b}}^{+}$)} and or {(${\mathrm{F}}_{\mathrm{a}}^{-}$ = ${\mathrm{F}}_{\mathrm{b}}^{-}$)}, then alternative ‘a’ has preference over ‘b’; and if the information is otherwise inconsistent, then alternative a is incompatible with b. Net outranking flow for alternative a is obtained using ${\mathrm{F}}_{\mathrm{a}}$= ${\mathrm{F}}_{\mathrm{a}}^{+}$ − ${\mathrm{F}}_{\mathrm{a}}^{-}$; while net outranking flow for alternative b is obtained using ${\mathrm{F}}_{\mathrm{b}}$= ${\mathrm{F}}_{\mathrm{b}}^{+}$ − ${\mathrm{F}}_{\mathrm{b}}^{-}$. A complete ranking is subsequently obtained as follows: if ${\mathrm{F}}_{\mathrm{a}}$ > ${\mathrm{F}}_{\mathrm{b}}$, then alternative a has complete preference over alternative b; if ${\mathrm{F}}_{\mathrm{a}}$ = ${\mathrm{F}}_{\mathrm{b}}$, then alternative a has complete indifference compared to alternative b. The complete ranking is obtained by ordering the alternatives in decreasing order of their net flow scores. The net flow score is a measure of the overall performance of an alternative, which takes into account the positive and negative outranking flows with respect to all other alternatives. The PROMETHEE I method is used to obtain the positive and negative outranking flows, whereas the PROMETHEE II method is used to obtain a complete ranking, and it considers all the alternatives and criteria involved in the decision-making problem. The final ranking obtained using the PROMETHEE provides a global view of the alternatives and facilitates the selection of the best option. The application of the above methodology for an efficient ranking of solar panel cooling systems is presented in the subsequent section.

5. Application of the MCDM Approach

The presented approach extends considerable support to comparing and ranking solar panel cooling systems along with their validation and sensitivity analyses. The step-wise application of the proposed multi-criteria decision-making approach for selecting solar panel cooling systems is presented as follows.

Step 1: This step is used to identify potential alternative solar panel cooling systems for evaluation. Each solar panel cooling system is evaluated using eleven performance measures; to start, equal weights are assigned to these measures. For the decision matrix on hand, refer to

Table 2. Sample data for each alternative obtained via expert/published research.

Units		Performance Measures j
		$ PM01	PM02	PM03	PM04	PM05	PM06	PM07	PM08	PM09	PM10	PM11
		%	5-Point	USD/sq. m	Kg	5-Point	°C	Sq. m	Impact	Impact	5-Point	Impact
Objective		Maximize	Maximize	Minimize	Minimize	Minimize	Maximize	Minimize	Maximize	Minimize	Minimize	Minimize
Weightages Wj		1	1	1	1	1	1	1	1	1	1	1
Alternatives i	# A1: [77,78]	3.5	5	USD 58	High	1	12.50	25	Very high	Low	Low	Very low
	A2: [78,79,80]	7	2	USD 168	Low	5	14.20	670.84	Low	Average	High	Low
	A3: [81,82]	9	4	USD 1125	Low	3	23.00	16.73	Low	High	High	Low
	A4: [83,84,85]	7	2	USD 25	Low	4	23.00	670.84	High	High	High	Very high
	A5: [61]	9	1	USD 25	High	6	28.00	18.49	High	High	High	High
	A6: [86,87,88]	4	3	USD 68	High	2	22.00	77.44	Low	Low	Low	Very high
	A7: [88]	13.5	2	USD 75	High	7	40.00	56.25	Very low	Low	High	Very high
	A8: [89]	13.5	2	USD 75	High	8	40.00	56.25	Low	Low	High	Very high
	A9: [90,91]	17	1	USD 540	Very high	9	10.20	125.0	Low	Very high	High	High

Note: for ^# and ^$, refer to Figure 1.

.

In Table 2, the solar panel finned air-cooling system (A1) has an average of 3.5% energy efficiency at an estimated cooling cost per square meter of a solar panel of USD 58, and this panel cooling system is highly reliable. The effects of carbon emissions on the environment are highly alarming. In the opinion of researchers [92,93], the alternative A1 has an extremely low effect as well as very little usage of electrical equipment in the cooling system network and is very supportive in terms of corrosion resistance. Similarly, Franklin et al. [77] stated that the finned air-cooling system is good and practical for installation and maintenance due to reduced physical deterioration and leakage difficulties. In light of numerous assessment parameters, one can, therefore, obtain comparable readings for any other alternative solar panel cooling system networks. Thus, for a given performance measure, one can see differences in values corresponding to alternative cooling systems. Not a single alternative outperforms others in all eleven measures. For selected performance measures, the selective solar panel cooling system score is better than the others. In other words, no single solar panel cooling system yields the best overall performance measures. Considering the multiple-attribute measure decision situation presented above, the application of the approach adopted to evaluate and rank these solar panel cooling system is presented here below.

Step 2: At this step, six sets of performance measure weights (equal weights, objective weights using the entropy technique, and four subjective weights) are chosen. Set 1 signifies an equal weighting of all performance measures, Set 2 is objective weights using the entropy approach, and Set 3 to Set 6 are subjective weights; refer to

Table 3. Performance measure weights to evaluate solar panel cooling systems.

Performance Measures j	# Set 1	Set 2	Set 3	Set 4	Set 5	Set 6
$ PM01	0.091	0.038	0.035	0.040	0.050	0.600
PM02	0.091	0.110	0.650	0.040	0.050	0.040
PM03	0.091	0.152	0.035	0.600	0.050	0.040
PM04	0.091	0.065	0.035	0.040	0.500	0.040
PM05	0.091	0.043	0.035	0.040	0.050	0.040
PM06	0.091	0.051	0.035	0.040	0.050	0.040
PM07	0.091	0.141	0.035	0.040	0.050	0.040
PM08	0.091	0.076	0.035	0.040	0.050	0.040
PM09	0.091	0.056	0.035	0.040	0.050	0.040
PM10	0.091	0.204	0.035	0.040	0.050	0.040
PM11	0.091	0.064	0.035	0.040	0.050	0.040

Note: ^$ refer to Figure 1. ^# Set 1: equal weightage to all performance measures; Set 2: weightage to all performance measures using entropy approach; Set 3: 65% weightage to reliability, with others having 4% each; Set 4: 60% weight to cost, with others having 4% each; Set 5: 50% weightage to emission and others having 5% each; and Set 6: 60% weightage to efficiency and others having 4% each.

below.

Step 3: In this step, as significantly large mathematical computations are needed, it is preferred to adopt the Visual PROMETHEE soft tool. So, using it, two preference flows (${\mathrm{F}}_{\mathrm{i}}^{+}$ and ${\mathrm{F}}_{\mathrm{i}}^{-}$) and the net outranking flow (${\mathrm{F}}_{\mathrm{i}}$) were obtained for each alternative solar panel cooling system i, as presented in

Table 4. Partial and complete outranking flows for each alternative solar cooling system vs. the sets of weights.

			Alternatives i
			# A1	A2	A3	A4	A5	A6	A7	A8	A9
Set of weightages	$ Set 1	${\mathrm{F}}_{\mathrm{i}}$	0.4098	0.0597	−0.0854	−0.0283	−0.0668	0.2003	−0.2095	−0.1195	−0.1603
		${\mathrm{F}}_{\mathrm{i}}^{+}$	0.5655	0.3053	0.2962	0.2435	0.2242	0.3986	0.1611	0.2170	0.2215
		${\mathrm{F}}_{\mathrm{i}}^{-}$	0.1557	0.2456	0.3815	0.2718	0.2911	0.1983	0.3706	0.3365	0.3818
	Set 2	${\mathrm{F}}_{\mathrm{i}}$	0.4382	0.077	−0.2293	0.0061	−0.1433	0.2852	−0.2007	−0.1375	−0.0958
		${\mathrm{F}}_{\mathrm{i}}^{+}$	0.5948	0.2847	0.2295	0.2391	0.1707	0.466	0.1431	0.1807	0.2231
		${\mathrm{F}}_{\mathrm{i}}^{-}$	0.1566	0.2077	0.4588	0.233	0.3141	0.1808	0.3438	0.3182	0.3189
	Set 3	${\mathrm{F}}_{\mathrm{i}}$	0.6536	−0.0884	0.3437	−0.1223	−0.214	0.1807	−0.2689	−0.2343	−0.2500
		${\mathrm{F}}_{\mathrm{i}}^{+}$	0.7135	0.1175	0.4906	0.0937	0.0863	0.2916	0.062	0.0835	0.0853
		${\mathrm{F}}_{\mathrm{i}}^{-}$	0.0599	0.206	0.1469	0.2161	0.3003	0.1109	0.331	0.3178	0.3353
	Set 4	${\mathrm{F}}_{\mathrm{i}}$	0.2610	0.0963	−0.562	0.0758	0.0588	0.1665	−0.0155	0.0241	−0.1050
		${\mathrm{F}}_{\mathrm{i}}^{+}$	0.3295	0.2043	0.1303	0.1954	0.1869	0.2537	0.1476	0.1722	0.1319
		${\mathrm{F}}_{\mathrm{i}}^{-}$	0.0685	0.1081	0.6923	0.1196	0.1281	0.0872	0.1631	0.1481	0.2369
	Set 5	${\mathrm{F}}_{\mathrm{i}}$	0.3379	−0.1922	−0.4407	−0.4093	0.0757	0.2227	−0.0027	0.0468	0.3618
		${\mathrm{F}}_{\mathrm{i}}^{+}$	0.4798	0.2804	0.1629	0.1339	0.2921	0.388	0.2574	0.2881	0.5718
		${\mathrm{F}}_{\mathrm{i}}^{-}$	0.1419	0.4726	0.6036	0.5432	0.2163	0.1653	0.2601	0.2413	0.2100
	Set 6	${\mathrm{F}}_{\mathrm{i}}$	0.1803	0.0263	−0.0376	−0.0125	−0.0294	0.0882	−0.0922	−0.0526	−0.0705
		${\mathrm{F}}_{\mathrm{i}}^{+}$	0.2488	0.1343	0.1303	0.1071	0.0987	0.1754	0.0709	0.0955	0.0975
		${\mathrm{F}}_{\mathrm{i}}^{-}$	0.0685	0.1081	0.1679	0.1196	0.1281	0.0872	0.1631	0.1481	0.168

Note: for ^$, refer to Table 3, and for ^#, refer to Figure 1. ${\mathrm{F}}_{\mathrm{i}}$: net preference flows; ${\mathrm{F}}_{\mathrm{i}}^{+}$: positive preference flows; and ${\mathrm{F}}_{\mathrm{i}}^{-}$: positive preference flows.

as follows.

In Table 4, there are two preference flows (${\mathrm{F}}_{\mathrm{i}}^{+}$ and ${\mathrm{F}}_{\mathrm{i}}^{-}$), and these values help to draw a partial ranking. It also shows incomparability between solar panel cooling system alternatives when both (${\mathrm{F}}_{\mathrm{i}}^{+}$ and ${\mathrm{F}}_{\mathrm{i}}^{-}$) preference flows have conflicting rankings. Similarly, in Table 4, ${\mathrm{F}}_{\mathrm{i}}$ is the net preference flow, and it is a complete ranking of solar panel cooling system alternatives. For example, in Table 4, for set 1, when the corresponding values for alternatives A1 and A2 are compared using positive outranking flow (${\mathrm{F}}_{\mathrm{i}}^{+}$), it is evident that $({\mathrm{F}}_{\mathrm{A}1}^{+}=0.5655)>({\mathrm{F}}_{\mathrm{A}2}^{+}=0.3053);$ however, when A1 and A2 are compared using negative outranking flow (${\mathrm{F}}_{\mathrm{i}}^{-}$), it is evident that $({\mathrm{F}}_{\mathrm{A}1}^{-}=0.1557)<({\mathrm{F}}_{\mathrm{A}2}^{-}=0.0.2456).$ This demonstrates that option A1 has a stronger preference than alternative A2. Similarly, when all alternatives are compared based on overall outranking flow (${\mathrm{F}}_{\mathrm{i}}$), ${\mathrm{F}}_{\mathrm{A}1}$ = 0.4098 and has the highest value when compared to the remaining eight alternatives, whereas alternative A7 has the lowest net outranking value, ${\mathrm{F}}_{\mathrm{A}7}$ = −0.2095, implying that A1 is the first preference and A7 is the last preference.

Step 4: Using the previously calculated step 3, outranking flows, a ranking network diagram, and a geometrical analysis for the interactive plane are derived. Details are presented below.

Figure 2 shows the positive outranking flow ${\mathrm{F}}_{\mathrm{i}}^{+}$ in the left column and the negative outranking flow ${\mathrm{F}}_{\mathrm{i}}^{-}$ in the right column for each alternative i. Outranking flows are arranged in such a way that the best are projected at the top of the column. The center column represents the net outranking flow ${\mathrm{F}}_{\mathrm{i}}$. For each alternative, a representative line is drawn from its ${\mathrm{F}}_{\mathrm{i}}^{+}$ to the corresponding ${\mathrm{F}}_{\mathrm{i}}^{-}$ score. For any given two alternatives, if the representative lines are parallel, the alternative representing the top line is preferred. On the other hand, if the two lines intersect, the corresponding alternatives are incomparable. By correlating Table 4 and Figure 3, for outranking flow ${\mathrm{F}}_1^{+}$, alternative A1 dominates all other alternatives; for outranking flow ${\mathrm{F}}_7^{+},$ alternative A7, the water-sprayed solar panel cooling system, highly underperforms compared to all other alternatives; for outranking flow ${\mathrm{F}}_1^{-}$, alternative A1, the finned air sink solar panel cooling system, dominates all other alternatives; and for outranking flow ${\mathrm{F}}_3^{-}$, alternative A3 highly underperforms compared to others. Generally, these positive and negative outranking flows induce two different rankings. In order to circumvent this scenario, a complete ranking based on net flow $\mathrm{F}$ was obtained and is presented in Figure 3 as follows.

From Figure 3, it is evident that alternative A1, the ‘finned air-cooling system’, surpasses all alternatives. Alternative A6, the forced air solar panel cooling system, performs as the next best option. Both of these options are best suited for dry, arid environments, while alternative A7, the water-sprayed solar panel cooling system, is least preferred over other alternatives. Subsequently, a network diagram was drawn (refer to Figure 4) in which each alternative is represented by a ‘node’ and its preference over other alternatives by an ‘arrow’.

For example, in Table 4 for set 1, when the corresponding net outranking flow (${\mathrm{F}}_{\mathrm{i}}$) values for all alternatives are compared, it is evident that (${\mathrm{F}}_{\mathrm{A}1}$ = 0.4098) > (${\mathrm{F}}_{\mathrm{A}6}$ = 0.2003) > (${\mathrm{F}}_{\mathrm{A}2}$ = 0.0597) > (${\mathrm{F}}_{\mathrm{A}4}$ = −0.0283) > (${\mathrm{F}}_{\mathrm{A}5}$ = −0.0668) > (${\mathrm{F}}_{\mathrm{A}3}$ = −0.0854) > (${\mathrm{F}}_{\mathrm{A}8}$ = −0.1195) > (${\mathrm{F}}_{\mathrm{A}9}$ = −0.1603) > (${\mathrm{F}}_{\mathrm{A}7}$ = −0.2095). Considering this net outranking relationship, the network diagram is drawn as presented in Figure 4. In Figure 4, it is evident that alternative A1, a passive cooling approach, is preferred over A6, which is an active cooling approach. When comparing all three active cooling approaches, A2, A4, and A3, approach A2 is preferred over both A4 and A3, whereas cooling approaches A4 and A3 are not comparable. Similarly, it is evident that passive cooling systems are outperforming active cooling systems, with the exception of forced air cooling system A6.

The Visual PROMETHEE represents the results in the GAIA (geometrical analysis for interactive assistant) plane (refer to Figure 5).

In the GAIA plane (Figure 5), it is evident that solar panel cooling systems A1 and A3 are scoring opposite to A4 and A9; similarly, it is also apparent that the solar panel cooling systems A2 and A6 are scoring opposite to A5, A8 and A7. Solar panel cooling approach A1 scores better for measures PM02, PM05, and PM11 (refer to Figure 1). It is also observed that, as far as solar panel cooling systems A5, A8, and A7 are concerned, these cooling systems perform best for only one measure, i.e., panel temperature dropping. Similarly, when comparing active cooling approach A6 and passive cooling approach A2, both perform satisfactorily for the PM01, PM08, PM09, and PM10 performance measures. However, from Figure 5, it is evident that A6 scores better than A2. Thus, decision makers not typically having any pre-determined weights in mind warrants the need for sensitivity analysis. Hence, a feature of the Visual PROMETHEE software is adopted for this purpose. The details of the sensitivity analysis and results are presented here in the following section.

6. Sensitivity Analysis

Sensitivity analysis is performed to evaluate the deviation in the ranking of alternative solar panel cooling systems. Six sets of weights (equal weights, objective weights using the entropy approach, and four subjective scalings) of performance measure weights (refer to Table 3) are opted for in the sensitivity analysis. In subjective scaling, four scenarios are considered. Scenario 1 is based on technical experts who have knowledge about the workings of solar panel cooling systems; they prefer highly reliable solar cooling systems and so suggested having the highest importance of 65% to measure the reliability measure (PM02) compared to other measures. On the other hand, as in scenario 2, the management is keen on minimizing cooling system operating costs (PM03) as an economic concern and sets 60% weightages to cooling costs. In comparison, 60% weightages to environmental measures are seen in scenario 3, which is based on green and sustainable energy management; decision makers in this scenario are keen on minimizing carbon emissions by installing, operating, and maintaining environmentally friendly solar cooling systems. The last scenario, scenario 4, is that of an operational manager, whose target is to lower the amount of energy used for cooling and raise the overall effectiveness of the solar panel system, and suggested having 60% weightage to energy efficiency as crucial for the solar panel cooling system. On the contrary, objective weighting eliminates manmade disturbances and makes results accord more with the facts. The objective weights method makes use of mathematical models, such as entropy analysis [94]. Accordingly, the sensitivity analysis was performed relying on assigned entropy weights in the Visual PROMETHEE. The outcomes of the sensitivity analysis are presented below in Figure 6a–d.

Similarly, sensitivity analysis was performed using subjective weightage Set 3. Below, Figure 7a–d represent corresponding outcomes representing partial ranking, complete ranking, the network diagram, and the GAIA plane, respectively.

In Figure 7, the decision maker’s objective is to have a reliable solar cooling system to mitigate any level of operation risk. From Figure 7c, it is evident that A3, i.e., the phase change material cooling approach, is a more reliable solar panel cooling system compared to A2 (heat pipe cooling) and thermosiphon cooling with and without the material fluid pot (A2 and A4) in the category of passive cooling systems. However, A7, A8, and A9, active cooling systems, are the least reliable.

In the same way, Figure 8a–d below represent analysis corresponding to partial ranking, complete ranking, the network diagram, and the GAIA plane, respectively, for subjective weight applications. But, in this case, the highest weightage of 60% is set to cost measure (refer to Set 4 in Table 3). Here, when the management objective is to have a cost-effective solar cooling system, A3 is the least preferred cooling system compared to A2, A4, and A5 in the category of passive cooling systems. This is opposite to the finding from Figure 7. However, when there is management that has economic concerns, alternative A1 dominates all other alternatives on hand.

Likewise, the following Figure 9a–d represent analysis corresponding to partial ranking, complete ranking, the network diagram, and the GAIA plane, respectively, for the highest subjective weightage of 60% to an evaluation measure PM04 (refer to Set 5 in Table 3). As the management objective is to have an environmentally friendly solar cooling system, the passive cooling approaches A2, A3, and A4 are the least preferred solar panel cooling systems compared to A1 and A5 in the same category. However, in this case, the nanomaterial fluid cooling system is still outranked by the finned air cooling system.

Lastly, Figure 10a–d represent analyses corresponding to partial ranking, complete ranking, the network diagram, and the GAIA plane, respectively, for the highest subjective weightage of 60% set to an evaluation measure, PM01 (refer to Set 6 in Table 3). Here, the management objective is to have energy-efficient solar panel cooling systems where passive cooling systems outrank active cooling systems.

Thus, from the analysis, it is evident that for each scenario, the solar panel cooling system performance is sensitive to variation in performance measure weightages. The overall ranking for each alternative solar panel cooling system corresponding with multiple sets of weights assigned to performance measures is presented here in

Table 5. Ranking for each alternative solar panel cooling system corresponding with multiple sets of weights assigned to performance measures.

Set of Weightages		$ Set 1	Set 2	Set 3	Set 4	Set 5	Set 6	Overall Rank
Alternative solar panel cooling systems	# A1	1	1	1	1	2	1	1
	A2	3	3	4	3	7	3	3
	A3	6	9	2	9	9	6	9
	A4	4	4	5	4	8	4	7
	A5	5	7	6	5	4	5	4
	A6	2	2	3	2	3	2	2
	A7	9	8	9	7	6	9	8
	A8	7	6	7	6	5	7	6
	A9	8	5	8	8	1	8	5

Note: For ^$, refer to Table 3, and for ^#, refer to Figure 1.

. Subsequently, the complete outranking flow (refer to Table 4) for each alternative is aggregated to drive overall ranking. Thus, after the sensitivity analysis, it is evident that solar panel cooling system alternatives A1 and A6 are found to be the best choice over other alternatives.

7. The Managerial Perspectives of the Study

To stay competitive, solar panel manufacturing companies must focus on technological developments that are cost-effective and very responsive to market changes. These changes are changes in energy demand, changes in the cooling system parts and components as per customer demand, changes in the existing cooling system, large fluctuations in the energy demand and mix, changes in the government regulations that are related to safety and the environment, etc. It is well known that the performance of any solar panel module is susceptible to multiple factors. Traditional solar panel cooling systems are selected based on climate, type of panel, energy requirements, and cost. There is evidence that changing the cooling system from one configuration to another has an impact on the amount of energy generated by the solar panels; the amount of fluid required for cooling may change, which could impact the stability of the temperature of the solar panels and could, in turn, impact energy generation. However, the impact of changing a cooling system in solar energy modules will depend on the specific cooling system and the specific solar panel installed.

The study that is reported in the present paper clearly revealed that the performance of solar panel cooling systems is very likely to change whenever the environment is changed, either due to changes in the technical or non-technical operating scenarios. But, there is no guarantee that every change will lead to desirable conditions. It is also very risky to make a change without assessing the relative merit of the same from the viewpoint of system performance. The decision maker may find the methodology that is presented in this paper attractive for many reasons, as this method is capable of treating multi-criteria situations. It possesses an ability to incorporate decision making using threshold indifferences and preferences, as was explained in Section 3 and Section 4. Concepts such as partial outranking, complete outranking, the graph and network diagram, and the feasibility of carrying out sensitivity analyses made this approach to the assessment of solar panel cooling system alternatives very attractive. The threshold weightage facilitates the comparison of alternatives using operational, environmental, and economic measures. One may compare alternatives using any sets of performance measures and their weights to decide the points of preference, indifference, and ignorance among choices. The concept of outranking relationships as a network diagram helps in the ordering of the nondominated alternative cooling systems. The presented approach aids in the synthesis of the preference relationship for each alternative solar panel cooling system in order to establish the required outranking relationship across solar panel cooling options in the context of all of the desired performance measures.

Thus, there are many decision situations in which the decision maker must choose among a finite number of alternatives, which are evaluated on a common set of multiple criteria. While evaluating the alternative solar panel cooling systems, it may be of interest to assess how similar and dissimilar the various solar panel cooling systems are and identify which performance measures play a significant role in establishing such relationships. This issue can be taken up with the help of the Visual PROMETHEE MCDM approach. The Visual PROMETHEE assesses the competitiveness of alternative solar panel cooling systems. Here, the adopted approach has the ability to incorporate positive and negative preferences. It synthesizes the preference relationships for each alternative to produce the desired outranking relationship between all of the alternatives. Concepts such as preference flow, weights, geometrical analysis for the interactive aid (GAIA) plane, as well as sensitivity analyses make this approach attractive in the assessment of solar panel cooling systems. Partial and complete ranking also helps identify the most preferred solar panel cooling system. However, decision makers are often interested not only in ranking solar panel cooling systems but also in establishing the superiority of one solar panel cooling system over another (if it exists). The PROMETHEE extends considerable support in this regard.

The practical significance of evaluating solar panel cooling systems within the context of solar power plant operation cannot be underestimated. Solar power plants may boost their energy production and, hence, their profitability by incorporating the proper cooling systems. There are numerous cooling solutions available, including both passive and active ones, and the method chosen will be determined by criteria such as climate, resource availability, and overall cost-effectiveness. This is especially relevant in areas with high ambient temperatures when solar panel efficiency can be severely reduced. Aside from the economic benefits, cooling measures can help to ensure the long-term viability of solar power facilities. The overall energy consumption of the power plant may be lowered by lowering the energy required to cool the panels, resulting in a smaller carbon footprint. This is consistent with global sustainability objectives.

8. Conclusions

This paper presents an approach for the assessment of solar panel cooling systems using the Visual PROMETHEE multi-criteria approach. The approach that was reported in the paper is found to be useful in ranking the choices among different alternative solar panel cooling systems using multiple performance measures. A total of nine possible alternative solar panel cooling systems were analyzed based on variations in cooling effectiveness, energy efficiency, environmental impact, durability, noise pollution, and system size, weight, and cost. Using this approach, outranking flows, partial ranking, complete ranking, the network, and the GAIA plane were obtained, with the objective being to explore the strong and weak points of each of the alternative solar panel cooling systems. The obtained results enabled the identification of groups of performance measures expressing similar preferences. For example, thermosiphon cooling and nanomaterial fluid cooling systems are preferred for their economic, ergonomic, and environmental measures. Meanwhile, thermosiphons with a clay pot cooling system, water spray cooling systems, and evaporative cooling systems are preferred only to drop solar panel temperature, which is also supported by Moharram et al. [94]. These systems are preferred for solar modules installed in very hot and dry climates. On the contrary, two passive cooling approaches, i.e., finned air cooling and phase change material cooling systems, have preference over reliability, ergonomics, and electric equipment failure risk measures. In short, the contributions of this study are as follows:

• It presented a multi-criteria decision-making approach that takes into account both quantitative and qualitative criteria;
• It outranked alternative solar panel cooling systems to determine the best viable choice using the PROMETHEE;
• It visualized the relationship between the different solar panel cooling systems and performance measures under consideration.

As can be seen from Table 5, the outranking of nine solar panel cooling systems is A1 > A6 > A2 > A4 > A5 > A3 > A8 > A9 > A7 when equal weights are assigned to each criterion. However, it is to be noted that equal weights to all the criteria are an exaggeration, and this is just used as a reference. On the other hand, when each criterion is weighted using the entropy approach, the preference of solar panel cooling system is A1 > A6 > A2 > A4 > A9 > A8 > A5 > A7 > A3. Sometimes, certain operating requirements need a maximization of the reliability of the cooling system, and in this case, the ranking is observed to be A1 > A3 > A6 > A2 > A4 > A5 > A8 > A9 > A7. On the other hand, when the need is to focus on minimizing cost, the preference is A1 > A6 > A2 > A4 > A5 > A8 > A7 > A9 > A3. In comparison, to maximize the efficiency of the solar plant, the outrank of nine alternatives is observed to be A1 > A6 > A2 > A4 > A5 > A3 > A8 > A9 > A7, and to minimize environmental impact by minimizing CO₂ emissions, the approach then suggests the preference order as A9 > A1 > A6 > A5 > A8 > A7 > A2 > A4 > A37, which shows that A9 is the best option. The overall outrank for nine alternatives is also derived as A1 > A6 > A2 > A5 > A9 > A8 > A4 > A7 > A3.

Thus, nine different solar panel cooling systems were identified, and the multi-criteria analysis tool Visual PROMETHEE was used. Six possible scenarios are examined based on the priority assigned to each performance metric. Under each situation, the best solar panel cooling strategy to the worst cooling approach has been ranked. When operational efficiency was given the most weight, finned cooling was revealed to be the best solar panel cooling method, whereas thermosiphon cooling was the best cooling solution when the emission reduction criteria were given the most weight. The second-best method was found to be forced air cooling under equal weights, entropy weights, and 60% weightage to economic and component failure risk. The third choice is a heat pipe passive cooling system. Future research directions are set to focus on the assessment of hybrid solar panel cooling systems that are better integrated with energy management systems for improved overall performance. Comparison experiments can be executed by comparing the proposed Visual PROMETHEE approach with other MCDM methods to show its effectiveness as a future scope. One can also include performance metrics such as maintainability, technical implementation challenges, and sustainable solutions. Similarly, one can involve the development of new testing protocols and standards that can be used to assess the reliability and performance of these systems over time.