Improving the Selection of PV Modules and Batteries for Off-Grid PV Installations Using a Decision Support System

Abstract

In the context of isolated photovoltaic (PV) installations, selecting the optimal combination of modules and batteries is crucial for ensuring efficient and reliable energy supply. This paper presents a Decision Support System (DSS) designed to aid in the selection process of the development of new PV isolated installations. Two different multi-criteria decision-making (MCDM) approaches are employed and compared: AHP (Analytic Hierarchy Process) combined with TOPSIS (technique for order of preference by similarity to ideal solution) and Entropy combined with TOPSIS. AHP and Entropy are used to weight the technical and economic criteria considered, and TOPSIS ranks the alternatives. A comparative analysis of the AHP + TOPSIS and Entropy + TOPSIS methods was conducted to determine their effectiveness and applicability in real-world scenarios. The results show that AHP and Entropy produce contrasting criteria weights, yet TOPSIS converges on similar top-ranked alternatives using either set of weights, with the combination of lithium-ion batteries with the copper indium gallium selenide PV module as optimal. AHP allows for the incorporation of expert subjectivity, prioritising costs and an energy yield intuitive to PV projects. Entropy’s objectivity elevates criteria with limited data variability, potentially misrepresenting their true significance. Despite these discrepancies, this study highlights the practical implications of using structured decision support methodologies in optimising renewable energy systems. Even though the proposed methodology is applied to a PV isolated system, it can effectively support decision making for optimising other stand-alone or grid-connected installations, contributing to the advancement of sustainable energy solutions.

1. Introduction

In recent years, there has been a global shift toward the widespread adoption of renewable energy sources (RESs). Many countries are actively encouraging and implementing policies to facilitate the large-scale integration of RESs into their energy mix, with the aim of gradually phasing out conventional power generation methods that rely on nuclear and fossil fuels [1]. In fact, the necessity of RESs in the energy sector is undoubted, not only to address the climate change, the fossil resource scarcity, and the increasing costs of nuclear power, but also to reduce the energy dependence on fuels imported from other countries [2,3,4]. However, when planning a new RES installation project, as in any other project, several criteria can affect the success of such a project. As a consequence, selecting the commercial model of the components involved in the future installation can be considered a problem, where several factors can affect the performance and economic viability of the installation.

1.1. Background and Significance

Among the different non-hydro RESs, wind and photovoltaics (PVs) are the two most promising sources, suffering an exponential growth over recent years [5]. Since 2013, and up to 2022, wind power plants have increased their worldwide capacity by more than 330% (from 266,918 MW to 898,824 MW), and PV installations have had an increase of 1035% (from 101,745 MW to 1,053,115 MW) [6]. In fact, Ram et al. [7] estimated a 100% primary energy supply covered by a mix of RESs in 2050, with PVs as the leader, covering 69%, followed by wind energy (18%); see Figure 1. This massive share of PVs can be supported by the solar power available on the Earth’s surface (≈1700 TW), and by the fact that only utilising a small fraction of this power is sufficient to meet the global energy needs [8]. Consequently, PV installations will play a crucial role in the future energy sector. Moreover, PV installations have the possibility of being installed not only as huge power plants connected to the grid, but also as stand-alone or self-consumption systems [9,10,11]. In these cases, the PV installation can be on the roofs of residential and non-residential buildings [12] or used to power isolated areas far from grid electricity [13,14]. Consequently, PV power can help in the decentralisation of the power system, which is considered one of the main pillars for a future sustainable world [15].

1.2. Literature Review

As in any other industrial project, when developing a PV installation, various criteria influence the project’s success. Studies have identified numerous factors affecting PV systems. Pradhan and Panda [16] identified 10 external criteria, with solar irradiance and temperature being the primary ones, while others depend on these two. Another study reviewed 24 criteria, categorising them into environmental, PV system, system installation, system costs, and miscellaneous factors, noting that each criterion can impact performance positively or negatively [17]. Rediske et al. [18] focused on site selection criteria, identifying 28 factors across socio-environmental, location, economic, political, climate, and orography categories, with solar radiation and proximity to infrastructure being crucial. With regard to the economic feasibility, Oliveira et al. [19] highlighted 29 criteria, emphasising initial investment cost, power generation, operational costs, solar radiation, and system lifespan, and noting that additional criteria can affect energy efficiency and financial costs. Recently, Aslam et al. [20] also found that PV efficiency is influenced by the tilt angle, shading, dust accumulation, irradiance, temperature, and PV module technology.

Considering all the criteria previously detailed, different alternatives can be proposed when planning a PV installation project. Therefore, it is essential to conduct an impartial evaluation of the various alternatives and prioritise them based on the analysed/considered criteria in each case. To overcome this, decision support systems (DSSs) can be efficient decision tools enabling systematic comparisons and the selection of the best alternatives, facilitating the decision-making process [21]. In this regard, multi-criteria decision-making (MCDM) methodologies can be used to weight the criteria and rank the alternatives under consideration, being included as the necessary decision-aid tools in the DSS [22,23,24]. MCDM has been widely used in the energy sector. Several studies have prioritised RESs for electricity generation in various countries, including China [25], Turkey [26], Saudi Arabia [27], Poland [28], and Vietnam [29]. Other research has focused on the optimal location of RES installations, often combining MCDM with geographical information systems for projects such as PV installations [30,31,32,33], wind power plants [34,35,36,37,38], hydropower [39], biomass [40], wave-based power plants [41,42], solar-based green hydrogen [43], and hybrid pumped hydro storage [44]. Additionally, MCDM has been used to prioritise RES projects [45], maintain work orders for hydroelectric power plants [46], find solutions to energy shortages with hybrid RES-hydrogen sources [47], and determine the optimal configuration of a renewable energy community [48].

1.3. Motivation and Contribution

Currently, there are several categories for the main elements of a PV installation that can affect its performance. As a consequence, selecting the commercial model of the such components can also be considered a problem [49], where several factors can affect the performance and economic viability of the installation. Moreover, it should be noted that to evaluate a PV project’s performance, not only one perspective (such as cost or benefit) should be considered [50], but also design parameters, technical restraints, and stakeholders’ interests [51]. In this regard, the combination of a DSS with MCDM is ideal to finding the best alternative under different criteria. Given the multitude of MCDM approaches, some systematic reviews have analysed the most common MCMD approaches used in RES problems. According to Mardani et al. [52], the analytical hierarchy process (AHP)/fuzzy AHP and integrated methods have been the most used, whereas Rigo et al. [53] concluded that AHP has also been the most used (both in the weighting process of the criteria and to evaluate the alternatives), followed by the technique for order of preference by similarity to ideal solution (TOPSIS) and the elimination and choice expressing reality (ELECTRE), having evaluated the alternatives.

This paper proposes a DSS following three phases related to the traditional stages of a DSS [54]: data collection (search for the problem and information related to it), design (the development of alternatives to analyse), and choice (the analysis of the alternatives and selection of one). The choice phase of this DSS is based on MCDM, which is used to determine the main components of an isolated PV installation (PV modules and batteries) considering a comprehensive set of factors and including both technical and economic aspects. Moreover, two different strategies used to weight the criteria considered were analysed and compared (the subjective AHP method and the objective Entropy method), combining them with TOPSIS to rank the alternatives [52,53]. Even though AHP has recently been used in numerous works [55,56,57,58,59,60,61], there are several studies against it, mainly due to its subjective consideration [62,63]. Consequently, this DSS multifaceted evaluation tries to provide an answer for the following questions:

• How do the criteria weights obtained from the AHP method compare with those obtained from the Entropy method?
• Which of the criteria weighting method (AHP or Entropy) provides a more effective foundation for evaluating and ranking PV modules and batteries using the TOPSIS method?
• How do the rankings of PV modules and batteries differ when using TOPSIS with criteria weighted by AHP versus those weighted by the Entropy method?
• Can the proposed three-phase DSS framework effectively support decision making for optimising stand-alone PV installations by selecting the most suitable PV module and battery technologies?

A real case study, located in Albacete (Spain) was considered to address all these questions. The three-phase DSS framework developed in this research can be adopted for decision making in sizing and selecting the main components of both off-grid and grid-connected PV installations. The multi-criteria decision-making approach used in the choice phase, which combines criteria-weighting methods (AHP and Entropy) with the TOPSIS technique, can provide valuable insights for practitioners and researchers investigating the technical and economic viability of different commercial technologies for optimising the designs of various solar energy systems. The rest of the paper is organised as follows: Section 2 describes the proposed methodology, Section 3 presents the case study, Section 4 details the results and discussion, and finally, the conclusions are presented in Section 5.

2. Methodology

Developing a new isolated PV installation involves installing a new PV system in an area to harness solar energy efficiently. To ensure the success and sustainability of the new isolated PV installation project, the proposed DSS includes three stages, (i) data collection, (ii) design, and (iii) choice, as depicted in Figure 2.

2.1. Data Collection

It is important to obtain several data regarding the PV installation that is going to be designed. These data involve not only weather conditions of the specific location but also the daily needs of the client. The following data were collected:

• Solar irradiation and temperature analysis. Both the solar irradiance and the temperature affect the behaviour of the PV modules [64]. On one hand, a PV module transforms the solar irradiance it receives into an electrical current, increasing its output as the irradiance increases. On the other hand, the electrical efficiency of the module decreases as the module temperature increases, due to the transformation of solar energy into heat [65]. These parameters can be assessed by directly measuring them at the specific site, using several online tools (like PVGIS [66]) or through a specific PV software, which usually has databases included (like PVSYST ©). The aim of this step is to determine if the location is suitable for a PV installation.
• Estimation of consumption. As the installation is off-grid, an exhaustive consumption questionnaire should be provided to the users of the installation. This means to know the installed and future electrical equipment, its electrical characteristics, and how the user will use the electrical receivers (hours/day, seasonality, during weekends…), as it is vital for the size of the PV installation and the batteries bank.
• Installation data. Several data regarding the installation system should be defined, highlighting the following:

  –

  The system’s direct current voltage.

  –

  The system’s alternating current voltage.

  –

  The type of installation (rooftop or on-site) and available surface for it.

  –

  The modules’ inclination and orientation.

  –

  The batteries’ autonomy days.

  –

  The possibility of a future expansion of the system.

Based on the information obtained, the criteria, attributes, and objective function defining the distinctive features of each alternative will be established. As this study was focused on optimising a real PV installation in a specific location, some criteria analysed by other authors (refer to Section 1) are not here considered. Specifically, technical criteria, economical criteria, and system installation criteria will be taken into account to optimise the isolated installation.

2.2. Design

This phase is related to the development of the alternatives to analyse. They are proposed depending on different PV modules and batteries technologies. They both must fulfill the design specifications of the IEC 61215 [67] and IEC 61427 [68] standards to guarantee their engineering integrity, respectively.

With regard to PV modules, there are mainly two technologies: crystalline silicon and thin film. Likewise, each main group involves different types of technologies; see Figure 3 [69]. Between them, crystalline silicon technologies represent nearly 95% of the total module production due to their high efficiency, low cost, and a long service time, whereas thin-film technology, mainly cadmium telluride and copper indium gallium selenide (CIGS) represent the remaining 5% [70,71].

As for batteries, lead-acid batteries have traditionally been used in isolated installations [72]. The technological development of electronic load controllers in recent times has made it possible to introduce lithium-ion batteries, widely used in grid-connected self-consumption installations, into isolated installations [73]. The use of lithium-ion batteries makes it possible to simplify the electrical installation by being able to work at higher voltages on the direct current side, take advantage of the greater discharge capacity and useful life of lithium-ion batteries compared to lead-acid batteries, and reduce the physical space of the battery bank [74].

With all these possibilities of PV modules and batteries, several alternatives for the isolated PV installation can be proposed. For each alternative, a specific PV program (i.e., PVSYST ©) should be used to determine the technical performance of the installation as well as the economical costs, depending on the criteria under consideration.

2.3. Choice

This phase is where the MCDM techniques are used to determine the optimum solution. In this particular case, as already determined in Section 1, two weighting criteria methods were analysed and compared (AHP and Entropy), combining them with TOPSIS to rank the alternatives.

2.3.1. Weighting Phase

The weights of the criteria were calculated using two different methods: AHP and Entropy.

AHP

In 1980, Professor Saaty introduced the AHP method [75], a MCDM model structured hierarchically, where the top level represents the overarching objective, the intermediate level encompasses all criteria and subcriteria, and the bottom level contains the alternatives to be evaluated. In this study, AHP’s application was used to weight the criteria, detailed as follows:

• Designing the hierarchical model: The problem is structured into a three-level hierarchy comprising the objective, the criteria, and the alternatives (see Figure 4).
• Assigning and evaluating priorities: This step aims to determine the criteria weights through direct scaling or pairwise comparisons, generating a priority matrix W. Each matrix element represents the relative priority between row and column criteria, following a pre-defined scale (refer to

  Table 1. Fundamental pairwise comparison scale proposed by Saaty. Own elaboration based on [75].

  Scale	Verbal Scale	Explanation
  1	Equal importance	Two criteria contribute equally to the objective
  3	Moderate importance	Experience and judgement favour one criterion over another
  5	Strong importance	One criterion is strongly favoured
  7	Very strong importance	One criterion is very dominant
  9	Extreme importance	One criterion is favoured by at least one order of magnitude of difference

  ). This pairwise comparison was carried out by a group of experts in the field.

The mathematical procedure entails solving Equation (1):

$$\left(\begin{array}{ccc}{\displaystyle \frac{w_1}{w_1}}& \cdots & {\displaystyle \frac{w_1}{w_n}}\\ ⋮& \ddots & ⋮\\ {\displaystyle \frac{w_n}{w_1}}& \cdots & {\displaystyle \frac{w_n}{w_n}}\end{array}\right)\left(\begin{array}{c}{w}_1\\ ⋮\\ w_n\end{array}\right)=\lambda \left(\begin{array}{c}{w}_1\\ ⋮\\ w_n\end{array}\right),$$

(1)

where the matrix W is obtained by assigning weights ($w_j$) associated with the pairwise comparison of criteria $C_j$ ($j=1,2,\dots ,n$), being positive numbers. This expression can also be written as

$$W·\overrightarrow{w}=\lambda ·\overrightarrow{w},$$

(2)

where $w_i·{\sum }_{j=1}^n\frac{1}{w_j}$ and $\frac{1}{w_j}·{\sum }_{i=1}^n{w}_i=\frac{1}{w_j}$. By normalising the matrix, the sum of the columns yields the vector $\overrightarrow{w}$. Equations like Equation (1) (or Equation (2)) are then solved to obtain the priority vector $\overrightarrow{w}=[w_1,w_2,\dots ,w_n]$, which represents the relative importance of each criterion. Normalisation yields vector $\overrightarrow{w}$ by summing the matrix columns.

The method exemplifies mathematical principles of reciprocity, homogeneity, and consistency [76]. Specifically, consistency is gauged using the consistency ratio ($CR$) following Equation (3):

$$CR=\frac{CI}{RI},$$

(3)

where $RI$ represents the random consistency index (average index derived by simulating 100,000 randomly generated reciprocal matrices, adhering to the Saaty scale previously defined [77]), and $CI$ denotes the consistency index:

$$CI=\frac{{\lambda }_{\max }-n}{n-1}.$$

(4)

In Equation (4), ${\lambda }_{max}$ is the principal eigenvalue from Equation (1), and n is the dimension of the matrix. The acceptability of the $CR$ varies depending on the dimension of the matrix n, with different thresholds applied. Specifically, the matrix consistency is considered acceptable if the $CR$ is equal to or lower than the values displayed in

Table 2. $CR$ threshold for n dimensions [78,79].

n	3	4	n ≥ 5
$CR$	$0.05$	$0.08$	$0.10$

.

To carry out the aggregation of the individual priorities of the vectors’ weight, the arithmetic mean is used [80].

Entropy

Entropy is an objective methodology proposed by Zeleny in 1982 [81] to calculate the weight of each criteria ($w_j$), avoiding the use of experts in the weighting phase [82]. The steps of this method are as follows:

• Normalisation of the decision matrix: The normalised value of the $C_j$ in the alternative i is called $p_{ij}$ and is determined from [83]:

  $$p_{ij}=\frac{x_{ij}}{{\displaystyle \sum _{i=1}^n{x}_{ij}}},$$

  (5)

  where $x_{ij}$ is the evaluation of alternative $A_i$ relative to criterion $C_j$.
• Determine the entropy of each criterion: The calculation is performed according to Equation (6):

  $${\displaystyle E_j=-K·\sum _{i=1}^m{p}_{ij}·log\left(p_{ij}\right),}$$

  (6)

  where K is a constant obtained as

  $$K={\displaystyle \frac{1}{log\left(m\right)}},$$

  (7)

  where m is the number of alternatives. In this way, the importance of a criterion is proportional to the amount of information intrinsically provided by the set of alternatives with respect to that criterion [84].
• Weight calculation: Finally, the weight w of each criterion is calculated according to Equation (8):

  $$w_j={\displaystyle \frac{1-E_j}{{\displaystyle \sum _{j=1}^n(1-E_j)}}}$$

  (8)

2.3.2. Ranking of Alternatives: TOPSIS

TOPSIS relies on the concepts of ideal and anti-ideal solutions for alternative selection (the selected alternative minimises the distance to the positive ideal solution and maximises distance to the negative ideal solution), including the following as key components:

A_i

Alternatives, where $i=1,\dots ,m$;

C_j

Criteria, where $j=1,\dots ,n$;

$x_{ij}$

Alternative $A_i$ evaluation relative to criterion $C_j$;

$w_j$

Criterion weight derived from the weighting phase (Section 2.3.1), where $j=1,\dots ,n$.

Figure 5 visually depicts the method with five alternatives ($A_1,\dots ,A_5$), two criteria ($C_1$ and $C_2$), and ideal and anti-ideal points. $A_3$ is the closest alternative to the ideal solution, while $A_2$ and $A_4$ are the farthest ones from the anti-ideal. TOPSIS computes weighted distances to the ideal and anti-ideal, employing multivariate data analysis [85].

The TOPSIS algorithm encompasses the following [86]:

• Decision matrix construction. The method evaluates a decision matrix like the one shown in

  Table 3. Decision matrix.

  	${\mathit{w}}_1$	${\mathit{w}}_2$	…	${\mathit{w}}_{\mathit{n}}$
  	${\mathit{C}}_{\mathbf{1}}$	${\mathit{C}}_{\mathbf{2}}$	…	${\mathit{C}}_{\mathit{n}}$
  $A_1$	$x_{11}$	$x_{12}$	…	$x_{1n}$
  $A_2$	$x_{21}$	$x_{22}$	…	$x_{2n}$
  ⋮	⋮	⋮	⋱	⋮
  $A_m$	$x_{m1}$	$x_{m2}$	…	$x_{mn}$

  , where there are m alternatives ($A_1,A_2,\dots ,A_i,\dots ,A_m$) evaluated according to n criteria ($C_1,C_2,\dots ,C_j,\dots ,C_n$), represented by values $x_{ij}$ (the evaluation of the alternative $A_i$ following criterion $C_j$). The vector $\overrightarrow{w}=[w_1,w_2,\dots ,w_j,\dots ,w_n]$ expresses the weights of the factors of $C_j$, which is obtained following Section 2.3.1, always fulfilling that ${\displaystyle \sum _{j=1}^n{w}_j=1}$.
• Decision matrix normalisation. The matrix from Table 3 is normalised as follows:

  $${\overline{n}}_{ij}={\displaystyle \frac{x_{ij}}{{\displaystyle \sqrt{\sum _{j=1}^n{\left(x_{ij}\right)}^2}}}}.$$

  (9)
• Normalised weighted matrix generation. The previous matrix is weighted (${\overline{v}}_{ij}$) following the weights of the criteria:

  $${\overline{v}}_{ij}=w_j·{\overline{n}}_{ij}$$

  (10)
• Positive and negative ideal solution identification. The positive solution ${\overline{A}}^{+}$ and negative solution ${\overline{A}}^{-}$ are determined as follows:

  $${\overline{A}}^{+}=\{{\overline{v}}_1^{+},\dots ,{\overline{v}}_n^{+}\}=\{(\underset{i}{max}{\overline{v}}_{ij},j\in J)(\underset{i}{min}{\overline{v}}_{ij},j\in J^{\prime })\}$$

  (11)

  $${\overline{A}}^{-}=\{{\overline{v}}_1^{-},\dots ,{\overline{v}}_n^{-}\}=\{(\underset{i}{min}{\overline{v}}_{ij},j\in J)(\underset{i}{max}{\overline{v}}_{ij},j\in J^{\prime })\}$$

  (12)

  where J is related to maximising criteria, and $J^{\prime }$ is related to minimising criteria.
• Distance to the ideal solutions’ calculation. The distance between each alternative and the positive and negative solutions are estimated following a Euclidean m-multidimensional distance:
  • Distance to positive ideal solution ${\overline{d}}_i^{+}$:

    $${\overline{d}}_i^{+}=\sqrt{{\displaystyle \sum _{j=1}^n{({\overline{v}}_{ij}-{\overline{v}}_j^{+})}^2}}$$

    (13)
  • Distance to negative ideal solution ${\overline{d}}_i^{-}$:

    $${\overline{d}}_i^{-}=\sqrt{{\displaystyle \sum _{j=1}^n{({\overline{v}}_{ij}-{\overline{v}}_j^{-})}^2}}$$

    (14)
• Relative proximity to the ideal solutions’ computation. The relative proximity ${\overline{R}}_i$ to the ideal solution is

  $${\overline{R}}_i={\displaystyle \frac{{\overline{d}}_i^{-}}{{\overline{d}}_i^{+}+{\overline{d}}_i^{-}}}$$

  (15)
• Alternatives’ ranking. Following the value of ${\overline{R}}_i$, the closer it is to 1, the better the alternative.

Despite that AHP can also be used to rank the alternatives, TOPSIS relies on Euclidean distance to determine proximity to an ideal solution, which can provide a more objective result, being less susceptible to the subjectivity of the decision-maker.

3. Case Study

To test the proposed DSS, a real isolated PV installation was considered. This installation is located in Chinchilla de Monte Aragón (Albacete, Spain, refer to Figure 6). The specific coordinates of the installation are 38°55′59″ N, 1°43′33″ W. The house is a small one, composed of a living room with a kitchenette, a bathroom, and one bedroom.

The province of Albacete has a markedly continental climate, with very cold winters contrasting with a very hot summer period. The climate, in general, is quite dry [87]. Figure 7 shows the number of sunny, partly cloudy, and cloudy days per month of the location as well as the average temperature of the location. According to Figure 7a, this location could be suitable for a PV installation, showing a high number of sunny days from June through September (which is ideal for maximising solar energy production) and a significant number of partly cloudy days from November through March, being able to capture a reasonable amount of solar energy depending on the technology and orientation of the PV panels. With regard to the temperature (Figure 7b), the location could also be suitable for a PV installation. The winter temperatures, with average minimums around 0–5 °C are favourable for PV module efficiency. While extreme cold can pose challenges, the temperature range shown does not appear to be excessively low, reducing the risk of significant performance degradation due to freezing conditions. Moreover, the moderately high summer temperatures (average maximum around 30–35 °C) are not exceptionally extreme.

4. Results

Following the three-step DSS method proposed in Section 2, the results are organised according to the three stages: (i) data collection, (ii) design, and (iii) choice.

4.1. Data Collection

To know the characteristics and the use of the installation, a questionnaire was provided to the owner. This questionnaire aimed to determine the use of the PV installation as well as the electrical devices planned to be used (including their power, expected hours of use, etc.). Once all these data were collected, the PVSYST © software was used to determine the following PV installation data:

• Average electricity daily consumption: $7.5$ kWh/day.
• Autonomy of the system: 3 days.
• Use of the system: permanent.
• Suggested PV power: 2572 Wp.
• Suggested storage capacity: 559 Ah.

In considering the available space of the rooftop of the house, its orientation, inclination, and the general characteristics of the parcel of land, together with the use of the future PV installation, it was decided to allocate the PV modules on the rooftop. Moreover, due to its geographical location, the orientation of the modules was 0° South, with an inclination of 30° to the horizontal. An inclination of 30° is considered the optimum one for permanent use throughout the year, usually defined as the latitude of the location minus 10° [89].

Figure 8 shows the monthly solar irradiation of the installation’s location according to PVSYST ©, which is based on the Meteonorm meteorological database. Both the irradiation reaching the horizontal surface and the receptor plane are depicted. The red curve representing the solar irradiation hitting the horizontal surface has a pronounced peak around the summer months, which is desirable for maximising solar energy capture. However, the irradiation levels drop off significantly during the winter months. However, the blue dashed “receptor plane” curve (which represents the solar irradiation hitting the tilted PV module surface) shows a flatter profile across the months. While there is still some seasonal variation, the dips in winter irradiation are far less pronounced, suggesting that high levels of solar energy can be captured year-round at this location.

4.2. Design

As already stated in Section 2.2, there are several types of PV module technologies and batteries, which were used to pose the alternatives under analysis. In this particular case, four PV commercial modules were considered (each one with a different technology), as well as two battery types.

The four PV module technologies under consideration, the reason/s why they were considered, and the commercial model can be seen in

Table 4. PV module technologies and commercial models.

Technology	Reasons to Consider It	Commercial Module
Cadmium telluride	Has the potential to compete with crystalline silicon, with an efficiency of 18.6% [90]	First Solar FS-6440-P (440 Wp)
Mono crystalline	Projected to maintain its enduring role as the cornerstone of the industry [91]	Longi Solar LR5-54HPH-420M (430 Wp)
CIGS	CIGS cells minimise material wastage in production, nearly matching the efficiencies of conventional silicon-based PV modules, and yields equivalent output power [92]	Eterbright CIGS-3350A1 (335 Wp)
Bifacial	Increases the power output by 5–30%, by just increasing their initial costs up to 15.6%  [93]	Axitec AXIbiperfect GL WB AC-430TGBL/108WB (430 Wp)

.

Regarding the batteries, both lead-acid and lithium-ion batteries are two extended and commonly used technologies for isolated PV installations, as already stated in Section 2.2. Traditionally, lead-acid technology was the most established one for these installations, but the lithium-ion ones have been taking the preferable position in recent years. Specifically, the commercial models considered were the following:

• Lead-acid battery: Rolls 4 × 2 Sealed-Plates 12-CS-11PS (12 Vcc and 296 Ah).
• Lithium-ion battery: Pylontech Force H2/384 (384 Vcc and 37 Ah).

Combining the four PV modules and two storage technologies yields the eight alternatives used in this study:

A₁

Cadmium telluride module with lead-acid battery;

A₂

Mono crystalline module with lead-acid battery;

A₃

CIGS module with lead-acid battery;

A₄

Bifacial module with lead-acid battery;

A₅

Cadmium telluride module with lithium-ion battery;

A₆

Mono crystalline module with lithium-ion battery;

A₇

CIGS module with lithium-ion battery;

A₈

Bifacial module with lithium-ion battery;

4.3. Choice

Once the alternatives are defined (refer to Section 4.2), the decision-making process should be carried out.

Firstly, the criteria to determine the optimum solution among the different alternatives are established. In total, eight different technical and economic criteria are considered in this case, which are based on previous studies developed by the authors [94]:

C₁

Annual production (electrical generation produced yearly), measured in kWh/year. Obtained through simulations with PVSYST ©. It must be maximised.

C₂

Performance ratio, a dimensional value obtained through simulations with PVSYST ©. It must be maximised.

C₃

Standardised production, measured in kWh/kWp day and obtained through simulations with PVSYST ©. It must be maximised.

C₄

Losses of the system, measured in kWh/kWp day, obtained through simulations with PVSYST ©. These losses are understood as generated energy by the PV installation, but not used by the user. Consequently, the lower its value, the better the installation’s design, and it must be minimised.

C₅

Ease of installation, dimensionless and (ranked as 0–0.5–1) mainly affected by the configuration and type of battery to install. It must be maximised.

C₆

Battery life, understood as the useful life of batteries, measured in years and obtained through simulations with PVSYST ©. It must be maximised.

C₇

Availability to expand the installation (dimensionless, ranked 0–1), understood as the possibility to add new PV panels without needing to modify the two main elements of the installation (load regulator and/or PV inverter). It must be maximised.

C₈

Installation cost, measured in €/Wp, considering the initial elements’ costs and their installation’s costs (which mainly depend on the number of PV panels and the battery type to install in each alternative). Obtained through simulations with PVSYST ©. It must be minimised.

4.3.1. Weighting Phase

The two weighting methods of AHP and Entropy defined in Section 2.3.1 are compared.

To assign weights to the criteria with AHP, a group of three experts was considered. They were asked to compare the different techno-economical criteria through the pairwise scale proposed by Saaty (refer to Table 1). The profiles of the experts consulted are the following:

E₁

Owner of the house and main user of the PV installation under development.

E₂

Installer, person in charge of executing the installation, with a wide experience in the PV sector.

E₃

Technologist, highly qualified professional in the RES sector, specialises in PV installation designs.

Table 5. Expert E₁ pairwise comparison of the different criteria.

	C1	C2	C3	C4	C5	C6	C7	C8	w	$\mathit{CR}$
C1	1.00	3.00	3.00	1.00	5.00	1.00	1.00	1.00	1.683	0.095
C2	0.33	1.00	3.00	1.00	5.00	1.00	3.00	1.00	1.397
C3	0.33	0.33	1.00	1.00	3.00	1.00	1.00	1.00	0.854
C4	1.00	1.00	1.00	1.00	3.00	1.00	1.00	1.00	1.082
C5	0.20	0.20	0.33	0.33	1.00	1.00	0.33	0.20	0.378
C6	1.00	1.00	1.00	1.00	1.00	1.00	3.00	1.00	1.156
C7	1.00	0.33	1.00	1.00	3.00	0.33	1.00	0.14	0.737
C8	1.00	1.00	1.00	1.00	5.00	1.00	7.00	1.00	1.632

,

Table 6. Expert E₂ pairwise comparison of the different criteria.

	C1	C2	C3	C4	C5	C6	C7	C8	w	$\mathit{CR}$
C1	1.00	5.00	1.00	3.00	0.33	5.00	1.00	0.20	0.974	0.099
C2	0.20	1.00	1.00	3.00	0.20	1.00	0.33	0.14	0.397
C3	1.00	1.00	1.00	3.00	0.20	0.33	0.20	0.14	0.437
C4	0.33	0.33	0.33	1.00	0.20	1.00	0.33	0.14	0.285
C5	3.00	5.00	5.00	5.00	1.00	9.00	3.00	0.33	2.101
C6	0.20	1.00	3.00	1.00	0.11	1.00	0.20	0.11	0.371
C7	1.00	3.00	5.00	3.00	0.33	5.00	1.00	1.00	1.335
C8	5.00	7.00	7.00	7.00	3.00	9.00	1.00	1.00	2.973

and

Table 7. Expert E₃ pairwise comparison of the different criteria.

	C1	C2	C3	C4	C5	C6	C7	C8	w	$\mathit{CR}$
C1	1.00	1.00	1.00	1.00	7.00	1.00	3.00	5.00	1.501	0.047
C2	1.00	1.00	1.00	1.00	5.00	3.00	5.00	5.00	1.725
C3	1.00	1.00	1.00	1.00	3.00	3.00	3.00	5.00	1.566
C4	1.00	1.00	1.00	1.00	3.00	3.00	5.00	3.00	1.554
C5	0.14	0.20	0.33	0.33	1.00	0.33	1.00	0.33	0.324
C6	1.00	0.33	0.33	0.33	3.00	1.00	5.00	3.00	0.949
C7	0.33	0.20	0.33	0.20	1.00	0.20	1.00	1.00	0.351
C8	0.20	0.20	0.20	0.33	3.00	0.33	1.00	1.00	0.416

show pairwise comparisons of the different criteria according to the three experts, specifying the $CR$ value. As can be seen, all the experts fulfill the $CR$ requirement, with values lower than $0.10$ (as the matrix is $n=8\to CR\le 0.10$, refer to Table 2), validating their opinions’ consistency.

Following the AHP method, and the opinions given by the experts, the main criteria involved in the decision making were C₈ (installation cost) followed by C₁ (annual production) and C₂ (performance ratio), as highlighted in Figure 9. Moreover, some experts’ opinions were inhomogeneous, not concluding to a clear priority among the other criteria. In fact, the other five criteria have similar weights, ranging between 9 and 11%. This is due to the different profiles of the panel of experts, which provides a clear vision of the diverse opinions of the main stakeholders involved in the PV installation with regard to some criteria.

Following the Entropy method, the quantitative data from the evaluation of each alternative are needed. All these data came from the PVSYST © simulation results but for C₅, which depends on the type of battery (0,5 for lead-acid batteries and 1 for lithium-ion batteries).

Table 8. Evaluation of alternative $A_i$ relative to criterion $C_j$. The arrow denotes if the criterion should be maximised (↑) or minimised (↓).

	C1 (↑)	C2 (↑)	C3 (↑)	C4 (↓)	C5 (↑)	C6 (↑)	C7 (↑)	C8 (↓)
A1	5942.81	38.89	2.12	0.71	0.50	6.70	0.00	1.76
A2	5842.66	39.73	2.16	0.67	0.50	6.70	1.00	1.68
A3	5616.82	40.78	2.22	0.73	0.50	6.70	1.00	1.90
A4	6429.93	35.42	1.93	0.79	0.50	6.60	1.00	1.90
A5	5944.88	38.94	2.12	0.71	1.00	15.00	0.00	1.42
A6	5844.98	39.85	2.17	0.67	1.00	15.00	1.00	1.32
A7	5619.05	40.88	2.22	0.73	1.00	15.00	1.00	1.54
A8	6431.76	35.42	1.93	0.79	1.00	15.00	1.00	1.25

shows the evaluation of each alternative relative to every single criterion. As this method is based on the variability and dispersion of the data for each criterion to determine its degree of uncertainty, the greater the variability in the data for a criterion, the lower its weight, as high variability indicates less useful information. By applying this method, it is observed that the most important criterion is C₇ (availability to expand the installation). This is followed by C₆ (battery life) and C₅ (ease of installation), accounting for more than 95% of the total weights of the criteria. As a consequence, the rest of the criteria obtain really low weights, ranging between 0.2–2.5%; refer to Figure 9.

From previous paragraphs, and derived from Figure 9, a severe difference is observed between the weights of the criteria depending on the used method. On the one hand, the AHP method assigns the highest weights to the installation cost and the annual production criteria (C₈ and C₁, respectively), which aligns with typical priorities for optimising PV installations. In contrast, due to the limited variability in the data for criteria C₇, C₆, and C₅ across the alternatives, the Entropy method assigns the highest weights to those criteria. It should be noted that, with this method, criteria with more consistent and less dispersed data will receive higher weights, reflecting their relative importance in the decision-making process. However, it is evident that considering such a criterion as the most important one is not practical in the context of optimising a PV installation. The binary nature of C₇, together with the little dispersion of the evaluation of the alternatives for criteria C₆ and C₅, result in minimal variability, thereby disproportionately increasing their weights when applying this method. This outcome underscores a limitation of the Entropy method in situations where certain criteria are binary or exhibit limited variability, as it may not accurately reflect their true significance in the decision-making process. Consequently, AHP seems to provide more “realistic” results, in terms of similarity to previous works focused on the optimisation of PV installations.

4.3.2. Ranking of Alternatives: TOPSIS

With the priority vectors of the criteria ($\overrightarrow{w}$), both with AHP and Entropy, the TOPSIS method was used to prioritise the alternatives under study. After normalising the matrix, the weighted, normalised decision matrix was determined, obtaining the positive ideal solution $d_i^{+}$ and the negative ideal solution $d_i^{-}$. From these values, the relative proximity of each alternative $P{R}_i$ to the positive ideal solution was determined; see

Table 9. Positive ($d_i^{+}$) and negative ($d_i^{-}$) ideal solution and relative proximity of each alternative to the positive ideal solution ($P{R}_i$), considering the AHP and Entropy weighting methods.

	AHP				Entropy
	${\mathit{d}}_{\mathit{i}}^{+}$	${\mathit{d}}_{\mathit{i}}^{-}$	${\mathit{PR}}_{\mathit{i}}$	Ranking	${\mathit{d}}_{\mathit{i}}^{+}$	${\mathit{d}}_{\mathit{i}}^{-}$	${\mathit{PR}}_{\mathit{i}}$	Ranking
A1	0.05	0.03	0.35	8	0.27	0.03	0.10	8
A2	0.03	0.04	0.58	4	0.05	0.27	0.86	6
A3	0.04	0.05	0.57	5	0.04	0.27	0.86	4
A4	0.04	0.05	0.57	6	0.04	0.27	0.86	5
A5	0.04	0.03	0.43	7	0.27	0.05	0.14	7
A6	0.03	0.05	0.64	2	0.03	0.27	0.89	2
A7	0.02	0.05	0.69	1	0.02	0.27	0.93	1
A8	0.03	0.05	0.61	3	0.04	0.27	0.88	3

. These results are graphically displayed in Figure 10. The three main alternatives according to the TOPSIS ranking, both with the AHP and Entropy weighting methods, are A₇, A₆, and A₈, respectively (Figure 10A), all of them based on lithium-ion batteries, with an easier installation and longer useful life (related to C₅ and C₆). Specifically, alternative A₇ is based on CIGS modules. This solution offers a new possibility for this kind of project, as in 2021, less than 1% of the PV installations were based on this technology [95].

Following the AHP criteria weights’, the authors want to highlight that, even though an alternative such as A₇ is considered the best one, it is neither the most economical alternative (related to C₈, refer to Figure 10B) nor the alternative with the highest annual production (C₁, refer to Figure 10C), which were the most valued criteria according to AHP. However, due to the CIGS PV modules, it provides the highest performance ratio (C₂) and, therefore, the best standardised production (C₃), and has the possibility to be expanded (C₇); lastly, in relation to the losses of the system (C₄), even it is not the alternative with the minimum ones, it would allow more consumption from the house without needing an expansion of the PV system. Consequently, this alternative A₇ is a compromise solution among the different criteria, as it is expected from applying the MCDM methodology. By considering the Entropy criteria weights, alternative A₇ obtains the optimum value in the three most important criteria (C₇, C₆, and C₅), which is also fulfilled by alternatives A₆ and A₈, following the TOPSIS ranking. In fact, the Entropy-weighted TOPSIS results suggest that when high priority is placed on battery life, installation ease, and future expandability, the CIGS module combined with lithium-ion batteries emerges as the top choice among the alternatives considered, with a proximity of $0.93$ to the ideal solution.

Despite the differences in criteria weighting, Table 9 remarkably shows that the ranking of alternatives using TOPSIS is exactly the same for both the AHP and Entropy weightings. In fact, the Spearman rank correlation coefficient of the alternatives’ ranking is 0.93, highlighting a high positive correlation. This highlights an interesting outcome—while the two weighting methods produced vastly different criteria priorities, they ultimately converged to identify the same set of top-ranked alternatives when combined with TOPSIS. This suggests that for this specific problem, the TOPSIS method is relatively robust in determining the highest-ranked options, even if the underlying criterion levels of importance differ substantially. Moreover, for both weighting methods, alternatives A1 and A5 consistently rank 8th and 7th, respectively, suggesting that cadmium telluride modules may be an inferior choice for isolated PV installations, regardless of the type of battery.

4.4. Discussion

Traditionally, when designing isolated PV installations, most stakeholders are only focused on two aspects: reduce economical costs and increase annual production. This reduces or even neglects the importance of other criteria, such as the useful life of the elements or its ease of installation and expansion. Through using a DSS combined with MCDM, and analysing several techno-economical factors, as well as different technologies of the main elements involved, it is possible to optimise stand-alone PV system designs. This research considered a diverse set of criteria, reflecting the multi-faceted nature of such projects. While the AHP and Entropy methods produced starkly different criterion weightings, TOPSIS converged on an identical set of top 3 alternative rankings using either set of weights. This suggests TOPSIS’s robustness in determining top options despite divergent criteria priorities.

Remarkably, the lithium-ion battery alternatives (A₆, A₇, A₈) dominated the top ranks across both weighting scenarios. This aligns with the growing industry shift toward lithium-ion over traditional lead-acid batteries for off-grid PV installations due to benefits like higher discharge capacity, longer lifetimes, and simplified installation requirements. The top-ranked A₇ alternative’s use of CIGS PV modules offers an innovative solution, as this technology still has a limited current market share (<1%) but seems to provide a new technical and economic beneficial possibility to overcome these installations, which can increase their electrical generation without having an extortionate price.

The contrasting criterion weights from the AHP and Entropy methods provide insights into their respective strengths and limitations. AHP’s subjectivity allows the incorporation of expert judgment, yielding weights that prioritise installation costs and energy production, which are common priorities for PV projects. Specifically, when deciding the panel of experts for AHP, it is recommended that they have different backgrounds, subsequently providing a wider and counter-weighted view and evaluation of the criteria and resulting in more robust and informed decisions. Conversely, Entropy’s objectivity based on data dispersion elevates criteria exhibiting limited variability, which may misrepresent their true significance for the problem context. To leverage the advantages of both approaches, the compromised weighting method that combines AHP and Entropy could be explored. This integrated technique may provide a balanced perspective by fusing subjective expert inputs with objective data-driven insights. Additionally, incorporating fuzzy logic can further enhance this method, especially in situations characterised by high uncertainty and low-quality information. Fuzzy logic allows for more flexible and nuanced decision making by modelling uncertainty and imprecision inherent in complex problems. By integrating fuzzy logic with AHP and Entropy, the method can better handle ambiguous data and provide more robust and reliable weighting criteria, thereby improving the overall decision-making process.

5. Conclusions

This study proposes a DSS of three phases based on MCDM for optimising stand-alone PV system designs. A combination of AHP/Entropy criterion weighting with TOPSIS for alternative ranking is used. Despite disparities in criterion weights from the two weighting approaches, TOPSIS consistently identified lithium-ion battery solutions among the top-ranked alternatives, with the CIGS module and lithium-ion pairing emerging as the optimal choice. This work highlights several key conclusions:

• The proposed DSS provides a rigorous framework for evaluating complex PV system alternatives based on multiple technical and economic criteria.
• While criterion weights differed substantially between the AHP and Entropy methods, TOPSIS proved robust in converging on similar alternative rankings.
• Lithium-ion batteries outperformed traditional lead-acid for this off-grid application due to factors like a higher discharge capacity and longer lifetimes.
• The CIGS module technology, though currently niche, showed promise by being the top-ranked solution when paired with lithium-ion batteries.
• AHP’s subjectivity allows prioritising intuitive criteria like costs and energy yield, while Entropy’s objectivity may disproportionately weight criteria with limited data variability. Therefore, it is recommended to consider both weighting approaches, or explore combining them through techniques like the compromised method, to leverage their respective strengths.

Ultimately, this DSS approach provides a valuable decision support tool for stakeholders planning stand-alone PV projects, facilitating the rigorous evaluation of design alternatives to identify optimal systems that balance technical performance and economic viability. Moreover, the DSS proposed can be used for other installations (in terms of location, size, type, etc.) if adapted accordingly (criteria and alternatives), and authors encourage stakeholders to carry out similar analyses when designing a new RES installation.