Most Searched Topics in the Scientiﬁc Literature on Failures in Photovoltaic Installations

: Photovoltaic installations (PVs) are currently one of the fastest-growing sources of renewable energy. Expanded forms of ﬁnancial support and higher electricity prices have resulted in a large increase in its installed capacity. PV installations are increasingly being ordered by industry and privates, often for installations capacity of several hundred kilowatts. In addition to the advantages, photovoltaic installations also have drawbacks. One of these is that the increase in the voltage in the power grid leads to the exclusion of individual installations from the grid. An important issue in the operation of photovoltaic installations is also their reliability during their lifetime. The reliability of photovoltaic installations depends on the random nature of the cloud cover as well as the material’s mechanical degradations. This paper presents a literature analysis using Citespace software in terms of reliability. A detailed bibliometric analysis has been performed to outline the main drawbacks of the PV installations cited by researchers. This literature review forms the basis for further analysis. The paper also presents a new approach to implementing the Multiple-Criteria Decision Analysis (MCDA) method for assessing the risk of failure of PV panels. The obtained results showed the main interests of scientists in the ﬁeld of failure analysis of photovoltaic installations and countries having the largest share in research on this issue. The applied Analytic Hierarchy Process (AHP) analysis enables supporting the process of managing photovoltaic installations by analyzing installation operations in terms of reliability as reliability impacts the proﬁtability of investments and operating costs. The proposed method can be used by the operators of photovoltaic installations or farms.


Introduction
The increase in demand for electricity and the world's dependence on this form of energy, the tense geopolitical situation, and the rising prices of natural resources [1,2], imported very often from countries with unstable political and economic situations [3], is causing an increase in the installed capacity of renewable energy sources [4]. Backyard photovoltaic or wind power plants can significantly increase the security of the energy demand [5]. Expanded forms of financial support [6], in the form of subsidies for installations such as photovoltaic systems or heat pumps [7], are causing a significant increase in installed systems [8]. Investment in sources of electricity, such as photovoltaic panels, can help companies and households during rising energy prices [9].
Since 2004 there has been a gradual increase in the installed capacity of renewable sources. In 2020, the target set by the European Union to achieve a 20% share of renewable energy in total electricity was achieved. According to Eurostat data, in 2020, the share of RES was 21.3%, an increase in 11.7% compared to 2004.
Taking into account the share of renewable energy in the gross final energy consumption, i.e., the extent to which renewable energy is used and the extent to which renewable fuels have replaced fossil fuels in the case of transportation. The European Union's aim was to achieve a 10% share of renewable energy in transportation by 2020. This aim was met, achieving a RES share of 10.2% in 2020. Figure 1 shows the percentage share of renewable sources in electricity generation. In 2020, a renewable share of 37.5% was achieved, an increase in 23.14% compared to 2004.
Energies 2022, 15, x FOR PEER REVIEW 2 of 16 energy in total electricity was achieved. According to Eurostat data, in 2020, the share of RES was 21.3%, an increase in 11.7% compared to 2004. Taking into account the share of renewable energy in the gross final energy consumption, i.e., the extent to which renewable energy is used and the extent to which renewable fuels have replaced fossil fuels in the case of transportation. The European Union's aim was to achieve a 10% share of renewable energy in transportation by 2020. This aim was met, achieving a RES share of 10.2% in 2020. Figure 1 shows the percentage share of renewable sources in electricity generation. In 2020, a renewable share of 37.5% was achieved, an increase in 23.14% compared to 2004. Figure 1. Share of renewable sources in electricity generation, on the basis of [10].
One of the factors through which a high share of renewable energy generation has been achieved is the increase in installed photovoltaic capacity. Figure 2 shows the installed capacity of photovoltaic installations between 2005 and 2020. In 2005, the installed capacity of photovoltaic installations was only 2.17 GW. By 2020, it had already reached 153 GW. One of the factors through which a high share of renewable energy generation has been achieved is the increase in installed photovoltaic capacity. Figure 2 shows the installed capacity of photovoltaic installations between 2005 and 2020. In 2005, the installed capacity of photovoltaic installations was only 2.17 GW. By 2020, it had already reached 153 GW. The increasing contribution of photovoltaic systems to electricity generation creates the need to and analyze such systems in terms of their operational reliability.  The increasing contribution of photovoltaic systems to electricity generation creates the need to and analyze such systems in terms of their operational reliability.

Operation and Failures of Photovoltaic Installations
The operation of photovoltaic power plants and the amount of energy produced depend on the availability and the amount of local solar irradiance, which vary according to cloud cover. Therefore, in the failure and availability analysis of photovoltaic systems, it is necessary to take into account the random nature of cloud cover that directly affects the level of the power output of the photovoltaic panels [11].
A failure is a state in which a system fails to realize its expected function. The failure analysis of a PV installation requires the creation of a model of the installation [12]. A photovoltaic power plant usually consists of photovoltaic panels, an inverter, and the electronics and power electronics that control the plant [13]. Since the output of a photovoltaic power plant depends on the random nature of the cloud cover [14], the plant cannot be represented by a two-state or multi-state model, as these models assume a constant value for the power generated [15].
In countries where the power grid is not geared for distributed energy sources, there may also be a problem with too high a voltage on the grid to which many photovoltaic installations are connected. If the voltage on a phase rises above the limit value, the inverter will disconnect the installation from the grid. If the installation is frequently disconnected, this can have a significant impact on the profitability of the investment [33].

Scientometric Analysis of the Literature
Scientometrics has been defined as the "quantitative study of science, communication in science, and science policy" [34]. The main field of interest in this field is the measurement of the impact of scientific articles and journals and the analysis of citations. Current bibliometric mapping software includes, among others: VOSviewer, CitNetExplorer, SCI2, Sci2Tool, Pajek, and Gephi [35]. One of the programs used for the literature analysis is also CiteSpace [36][37][38][39], which we decided to use as a research tool due to its universality compared to other software. The CiteSpace 6.1.R3 software was created by Dr. Chen of Drexel University, and it can visualize bibliometric results, show knowledge maps of science development and structural interaction, and identify future research status, research focuses, and recent developments of disciplines via statistical analysis [40]. Its design and functionalities are based on Kuhn's theory of scientific development model, Price's frontier theory of science, social network analysis theory, structural holes network theory, etc. [41]. The program allows the analysis of the literature from databases such as Web Science or Scopus. In this article, the Scopus database was analyzed. The Scopus database was considered due to its major academic informational content for bibliometric analysis, simplicity of exporting extensive data in groups, and record collection for past citations.
The keywords "photovoltaic failure" was selected as the search criterion. A total of 1363 articles from 1977 to 2022 were selected for analysis. Figure 3 shows the number of publications per year that contain the selected keywords.   Figure 4 shows the countries from which the analyzed publications originated and the cooperation between them. Table 1 shows the number of publications from the 20 countries with the highest number of publications and centrality. Centrality is defined for each node in the network. This factor measures the probability that any shortest path in the network will pass through that node. A node with a high centrality value is likely to be in the middle of two large communities or subnetworks [42].   Figure 4 shows the countries from which the analyzed publications originated and the cooperation between them. Table 1 shows the number of publications from the 20 countries with the highest number of publications and centrality. Centrality is defined for each node in the network. This factor measures the probability that any shortest path in the network will pass through that node. A node with a high centrality value is likely to be in the middle of two large communities or subnetworks [42].
Based on the results, it can be concluded that countries such as the USA, China, Germany, United Kingdom, Spain, and France have a centrality of more than 0.1, which means that they are important centers for PV failure research and are the most important nodes in the structure of cooperation between countries.     Table 1 shows the number of publications from the 20 countries with the highest number of publications and centrality. Centrality is defined for each node in the network. This factor measures the probability that any shortest path in the network will pass through that node. A node with a high centrality value is likely to be in the middle of two large communities or subnetworks [42].  1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 Figure 5 shows the analysis of the literature by citation. Citespace analyzed the literature into 11 clusters. Each node in the clusters represents the publications analyzed, while the connections between them define the collaboration between authors and mutual citations. Table 2 shows the main areas of research interest in the different clusters shown in Figure 5.  Table 2 shows the main areas of research interest in the different clusters shown in Figure 5. Cell, disconnection, interconnections failure, #94 Faults diagnosing, monitoring of photovoltaic systems   topic at a particular time or is related, for example, to an influx of citations from publications by Nobel Prize-winning authors. Citation bursts can also signal interest in science over a given period. The higher the strength coefficient, the greater the impact a publication has had on the number of citations by other authors. For example, the publication with the highest strength factor concerns the fault diagnosis technique for photovoltaic systems based on artificial neural networks [43]. The largest increase in interest in this topic, and consequently an increase in citations, began in 2018 and continues today. The second publication deals with the comprehensive review of catastrophic faults in PV arrays, while the third publication deals with real-time fault detection in photovoltaic systems [44,45].
Energies 2022, 15, x FOR PEER REVIEW 8 of 16 Figure 6 shows the citation burst for the top 15 publications. The citation burst indicates an increase in the frequency with which an article is cited. It suggests interest in a particular topic at a particular time or is related, for example, to an influx of citations from publications by Nobel Prize-winning authors. Citation bursts can also signal interest in science over a given period. The higher the strength coefficient, the greater the impact a publication has had on the number of citations by other authors. For example, the publication with the highest strength factor concerns the fault diagnosis technique for photovoltaic systems based on artificial neural networks [43]. The largest increase in interest in this topic, and consequently an increase in citations, began in 2018 and continues today. The second publication deals with the comprehensive review of catastrophic faults in PV arrays, while the third publication deals with real-time fault detection in photovoltaic systems [44,45]. On the basis of the citation burst, it can be concluded that the greatest attention of researchers in the field of PV plant failure is focused on fault diagnosis by different methods and real-time monitoring of photovoltaic systems.

Multi-Criteria Decision Analysis with Implementation of Analytic Hierarchy Process of Photovoltaic Panels Failure Risk Assessment
The method is based on a grouping of risk criteria for photovoltaic panels. The assessment is carried out with reference to the designated score values using the Analytic Hierarchy Process (AHP) method [46,47]. In the method under consideration, risk refers to a measure by which one can assess the risks arising from plausible events beyond one's control or from the possible consequences of a decision.
The risk measure is calculated using Equation (1) [48]: where r is the additive value of risk, pj is the point weight for each subcategory criterion j related to design, performance, operational, financial environment or social or On the basis of the citation burst, it can be concluded that the greatest attention of researchers in the field of PV plant failure is focused on fault diagnosis by different methods and real-time monitoring of photovoltaic systems.

Multi-Criteria Decision Analysis with Implementation of Analytic Hierarchy Process of Photovoltaic Panels Failure Risk Assessment
The method is based on a grouping of risk criteria for photovoltaic panels. The assessment is carried out with reference to the designated score values using the Analytic Hierarchy Process (AHP) method [46,47]. In the method under consideration, risk refers to a measure by which one can assess the risks arising from plausible events beyond one's control or from the possible consequences of a decision.
The risk measure is calculated using Equation (1) [48]: where r is the additive value of risk, p j is the point weight for each subcategory criterion j related to design, performance, operational, financial environment or social or surroundings, where j = 1, 2, . . . , m, C j means the method's consideration of the categories for potential alternatives. According to the Analytic Hierarchy Process (AHP) introduced by Thomas L. Saaty, each category was given a percentage weight based on how it would affect the risk in- dex [46]. The procedure for using the AHP involves defining and analyzing the decision problem and setting objectives. A set of criteria is then established, which must be comparable. The next step is to select the appropriate alternatives and determine the consequences of changes in the defined criteria. The outputs are subjected to pairwise comparisons of the selected elements, with a designated advantage of one element over the other, according to a nine-point comparison scale. Finally, the decision is based on the synthesis of the sub-assessments and the selection of the best alternative through the creation of overall rating scales. According to the Saaty scale, individual preferences and specific degrees of advantage are shown in Table 3 [46,47]. Table 3. Scale of relative importance (after Saaty [46,47]).

Interpretation
Value of a ij Definition 1/9 i is absolutely more important than j extreme importance Assigning a relative preference means that the selection and evaluation of each parameter are more accurate. The expert's judgment is used to increase the substantive representativity of the results. First, the pairwise comparison of criteria allows them to be ordered qualitatively and as a matrix is being constructed quantitatively using values from 1/9 to 9, with seventeen possible evaluations thus provided for.
In pairwise comparisons by reference to an n by n matrix (A), so-called reversible pairwise comparisons are made and can be written as [46,47]: where and The matrix is consistent, if: The matrix takes the following form [46,47] As a result of the comparison matrix's pairwise calculations, vectors of the priorities w = (w 1 , . . . , w n ) concerning the importance of elements are obtained. The priority vectors can be presented in the form of a normalized grade using the Saaty fundamental comparison scale [46,47]: hence equality occurs [46,47] In order to verify the consistency of the matrix, the principal eigenvalue λ max corresponding to the highest value of the eigenvector should be determined in line using Equation (9) [46,47]: The pairwise comparisons matrix A = (a ij ) is consistent when its principal eigenvalue is close to n. In order to assess the accordance of deviations, a Consistency Index (CI) is determined using Equation (10) [46,47]: Next, a Consistency Ratio (CR) is calculated, reflecting the extent to which the comparison of the validity of attributes is marked by incompatibility. This is given by [46,47]: where RI is a Random Index that depends on the number of comparable items according to the matrix dimensions listed in Figure 7. . RI values corresponding to matrix dimensions (after Saaty [46,47]).
To calculate consistency indexes and weighting factors, in order to ensure that calculations performed were checked for their accuracy, methods using geometric and arithmetic means as well as matrix multiplication were used. Depending on the designated consistency ratio, preferential information can be accepted or rejected. If the value of CR is greater than the allowed 0.1, an inconsistent matrix is present and preferential information should be verified. In such a case, actions will need to be taken to reduce the low-quality observations and the resultant inconsistencies. Table 4 shows the categories and subcategories to assess the risk of failure of photovoltaic panels. The values for the criteria assessment subcategories are taken according to the severity of the failure, using a scale where low risk is 1, moderate risk is 2, and severe risk is 3. Figure 7. RI values corresponding to matrix dimensions (after Saaty [46,47]).
To calculate consistency indexes and weighting factors, in order to ensure that calculations performed were checked for their accuracy, methods using geometric and arithmetic means as well as matrix multiplication were used. Depending on the designated consistency ratio, preferential information can be accepted or rejected. If the value of CR is greater than the allowed 0.1, an inconsistent matrix is present and preferential information should be verified. In such a case, actions will need to be taken to reduce the low-quality observations and the resultant inconsistencies. Table 4 shows the categories and subcategories to assess the risk of failure of photovoltaic panels. The values for the criteria assessment subcategories are taken according to the severity of the failure, using a scale where low risk is 1, moderate risk is 2, and severe risk is 3. Table 4. Evaluation criteria weights. The analysis was carried out for the six main criteria, which were compared in pairs according to the developed scale shown in Table 5. As the determined CR is less than 0.1, the results obtained are acceptable. The preference vectors determined on this basis are shown in Table 6. The methodology used, due to its universality, can be applied to many photovoltaic installation configurations. The AHP method can be helpful, particularly for large photovoltaic farms. Thanks to this method, it is possible to support farm management processes by analyzing failures and weak points that are the reason for the reduced production of electricity and, consequently, the low profitability of the investment.
In fact, analysts working closer to designers, constructors, and operators of the PV installation were necessary to specify the categories and subcategories as listed in Table 4. The pertinent literature provided in the text served as the basis for the specification of the categories as well. Considering experts' opinions allows for taking into account all the key variables influencing the failure risk of PV installation.
All the key variables are influencing the risk values associated with PV installation failures.
The AHP method provides a scale comprising tolerable risk (6.89-8.27>, controlled risk (8.27-16.21> and unacceptable risk (16.21-20.67). The risk value r(P) was calculated from Equation (1) is 12.79 and corresponds to the controlled risk category. This is due to the high probability of failures such as mechanical degradations. Mechanical degradations are mostly caused by hail and the difficulty in predicting the weather. The industrial can reduce the risk by selecting high-quality components designed and installed by highly qualified people and supported by the proper servicing of the installation.

Conclusions
The analysis shows that the largest number of publications on photovoltaic installation failures have been published by researchers from the USA. US researchers published 331 articles containing the analyzed keyword included in the Scopus database with a centrality index of 0.15. On the other hand, the publications written by scientists from Germany have the highest centrality index (0.20), which means that these studies on PV plant failure in Germany have the highest innovation and are the most frequently cited among scientists working on this topic. Furthermore, based on an analysis of the main interests of researchers, an increased interest in failure analysis using neural networks can be seen. With the use of citation burst, it can be assumed that further research into the use of neural networks will be carried out in the years to come.
The use of software such as CiteSpace makes it possible to analyze past and current trends in science. Software It is obvious that a detailed analysis of several thousand publications in a given field is practically impossible. Even the analysis capacity is rapidly increasing thanks to the extensive use of AI techniques and tools, which is the target of the Big Data Analysis field CiteSpace greatly facilitates the analysis of the literature and identifies the key issues facing scientists in a given field.
An analysis of the literature on the failure of photovoltaic installations has shown that failure monitoring and detection in real time are currently of greatest interest to researchers.
The main purpose of this manuscript is to present new approaches to the failure risk assessment of PV installations, as the obtained results support the management of PV, mainly in terms of strategic modernization plans and rehabilitation techniques. On the basis of the previously performed analysis through research on the failure rate (through performed bibliometric analysis), we propose a modified Multi-Criteria Decision Analysis with the implementation of the Analytic Hierarchy Process to perform a failure risk assessment.
The issue of assessing failure risk by combining different criteria of PV operation criteria remains to be developed. The authors want to emphasize the importance of the presented methodology for PV operators, which expect quick tools in the management process.
The development of photovoltaics represents an opportunity for enhancing national energy independence, which in the current geopolitical situation, is a strong argument for investing in renewable energy sources. The expected rapid demand for energy worldwide would give rise to serious consequences: energy shortage and unaffordable energy price. However, the development of distributed sources such as photovoltaic installations poses a serious problem for countries where the energy comes overwhelmingly from large coalfired power plants and other hydraulic and fossil power plants. One example of such a problem is the disconnection of inverters after an excessive voltage increase at the main grid. Consequently, the development of distributed sources requires the modernization of electricity grids. Therefore, it is important to analyze all aspects of photovoltaic installations, such as potential failures, using MCDA methods to better optimize the operational performance of such installations.