PV Defects Identification through a Synergistic Set of Non-Destructive Testing (NDT) Techniques

A synergistic set of NDT techniques, including I–V analysis, UVF imaging, IR thermography, and EL imaging, supports a diagnostics methodology developed in this work to qualitatively and quantitatively identify a wide range of PV defects. The methodology is based on (a) the deviation of the module electrical parameters at STC from their nominal values, for which a set of mathematical expressions was developed that provide an insight into potential defects and their quantitative impact on the module electrical parameters, and (b) the variation analysis of EL images captured at a sequence of bias voltages for a qualitative investigation on the spatial distribution and strength of the defects. The synergy of these two pillars, supported by UVF imaging, IR thermography, and I–V analysis cross-correlating their findings, makes the diagnostics methodology effective and reliable. It was applied on c-Si and pc-Si modules operating from 0–24 years, exhibiting a diversity of defects of varying severity, either pre-existing or formed by natural ageing or externally induced degradation. Defects such as EVA degradation, browning, corrosion in the busbar/interconnect ribbons, EVA/cell-interface delamination, pn-junction damage, e−+hole recombination regions, breaks, microcracks, finger interruptions, and passivation issues are detected. Degradation factors triggering a cascade of internal degradation processes through cause and effect are analysed and additional models are proposed for the temperature pattern under current mismatch and corrosion along the busbar, further empowering the cross-correlation of NDT results. Power degradation was determined from 1.2% in 2 years of operation to more than 50% in modules with film deposition.


Introduction
The photovoltaic (PV)-ageing and performance-degradation modes have been extensively studied as far as they concern weathering due to outdoor conditions [1][2][3], early ageing [4] and long-term operational degradation [5,6]. Indoor ageing and thermal-cycling cumulative exposure were previously studied to predict degradation in the series resistance R s [7] and optical degradation [8]. Reports on sensors, non-destructive testing (NDT), and methodologies focus on the diagnosis of ageing factors and their effects [9][10][11][12][13], whereas analysis of faults linked to degradation factors and defects and their implications are provided in [14][15][16][17][18]. External factors, such as solar radiation, shading, wind, and other environmental parameters, as well as internal factors, along with the conditions that trigger degradation processes, have been investigated in depth. Strong PV-cell temperature T c , fluctuations, or cycles may cause thermal shocks that trigger ageing processes and/or structural deformation [1,2,6,7,9,13]. Ambient temperature T a cycles in cold sites or in  In general, PV-cell shading for a prolonged amount of time may become the forerunner of time-evolving EVA degradation or ageing, and T c patterns may appear due to heat dissipation in the affected cells ( Figure 1). When the shading is transient the effect is reversible and the ageing follows a natural low progression.  As disclosed in this project, cells with extensive EVA browning cause permanent current mismatch, leading to high T c , or hot cells, which degrade or age the physicochemical status of the cells at a fast rate. These may trigger a cascade of ageing factors, bringing the cells into an irreversible state and causing, in turn, further permanent physicochemical changes and high permanent T c patterns, as also reported in other studies [7,11,48]. EVA degradation is usually linked to exposure to high SRD, whereas negligible EVA degradation is expected in cells exposed to low SRD. The UVF image (Figure 2f) of a c-Si module exposed to low SRD (0.2 MWh/m 2 ) displayed no signs of EVA degradation; however, early signs of delamination in the EVA/cell interface along the busbar were present (Figure 3a,b). This appeared to be at the EVA/ARC interface. Severe EVA/cell-interface delamination (Figure 3c,d) and corrosion on the busbar and interconnect ribbon along with EVA browning (Figure 3e,f) were present in a c-Si module exposed to SRD = 48 MWh/m 2 . Adhesive degradation at the EVA/silver interface has been shown to be responsible for the delamination around the cell's metallisation [49,50]. EVA degradation linked to the formation of acetic acid and weakening of the adhesion through the high T c developed may also result in corrosion. The current decrease δI in a shaded cell multiplied with the polarisation volta veloped across the cell Voc,c(n − 1) and the voltage across the diode Vd provides the dissipating into heat which contributes to a further increase in temperature of the s cell above the healthy cells' temperature due to operation under certain condition The current decrease δI in a shaded cell multiplied with the polarisation voltage developed across the cell V oc,c (n − 1) and the voltage across the diode V d provides the power dissipating into heat which contributes to a further increase in temperature of the shaded cell above the healthy cells' temperature due to operation under certain conditions. The heat developed in the shaded cell is then transferred to the environment, as described by Equation (1a). V oc , c is the cell open-circuit voltage, n is the number of cells protected by the bypass diode, A c is the area of the solar cell, and η is the module efficiency.
(h c + h r ) f stands for the heat convection and the radiated-heat coefficients for the front side, whereas (h c + h r ) b is for the back side of the cell. T f and T b stand for the temperatures at the front glass and back side of the PV, respectively [51]. Equation (1a) can be simplified to Equation (1b), assuming T f = T b = T pv , even though up to a 3 • C difference may exist between T f and T b .
The EVA browning in one of the cells of the c-Si M55 module created an effect of partial shading, leading to a current drop of 0.25 A in the operating conditions, as shown in the I-V characteristic (Figure 4a), which in turn led to the affected cell operating at a higher temperature by about 34 • C from the neighbouring unaffected cells of the module, as shown in the IR thermography ( Figure 4b).
The module I-V characteristic was measured using I-V curve analyser PV-KLA (Ingenieurbüro Mencke & Tegtmeyer GmbH, Hameln, Germany) and the IR thermography was captured using an IR camera IC085LV (TROTEC GmbH, Heinsberg, Germany). Equation (1b), for n = 18 and V d = 0.6 V and considering (h c + h r ) f +(h c + h r ) b about 20 W/m 2 K at the conditions of the experiment v w = 2.1 m/s, I T = 760 W/m 2 , and T a = 30.9 • C, predicted the temperature of the affected cell T pv = 74 • C, which is in agreement with the IR thermography ( Figure 4b) showing the affected cell reaching temperatures between 74-79 • C. This explains that the PV temperature pattern developed was due to the current mismatch caused by the cell exhibiting EVA browning. Equation (1b), assuming Tf = Tb = Tpv, even though up to a 3 °C difference may exist between Tf and Tb.
The EVA browning in one of the cells of the c-Si M55 module created an effect of partial shading, leading to a current drop of 0.25 A in the operating conditions, as shown in the I-V characteristic (Figure 4a), which in turn led to the affected cell operating at a higher temperature by about 34 °C from the neighbouring unaffected cells of the module, as shown in the IR thermography ( Figure 4b). The module I-V characteristic was measured using I-V curve analyser PV-KLA (Ingenieurbüro Mencke & Tegtmeyer GmbH, Hameln, Germany) and the IR thermography was captured using an IR camera IC085LV (TROTEC GmbH, Heinsberg, Germany). Equation (1b), for n = 18 and Vd = 0.6 V and considering (hc + hr)f +(hc + hr)b about 20 W/m 2 K at the conditions of the experiment vw = 2.1 m/s, IT = 760 W/m 2 , and Ta = 30.9 °C, predicted the temperature of the affected cell Tpv = 74 °C, which is in agreement with the IR thermography (Figure 4b) showing the affected cell reaching temperatures between 74-79 °C. This explains that the PV temperature pattern developed was due to the current mismatch caused by the cell exhibiting EVA browning.
Milder thermal effects linked to current mismatch were also identified in new modules. The IR image of a brand-new c-Si BIO 175 Wp under operation revealed a hot cell with Tc over 15 °C higher than the temperature of the neighbouring cells in the module (Figure 4d). This is attributed to localised imperfections at the production stage and may signal the onset of degradation. Figure 4c shows the module's I-V characteristic, where δI dropped by 0.03 A in the first 6 V due to associated current mismatch. Such defects are pre-existing and trigger mild degradation.
The above confirms that the hot cells detected via IR thermography were linked to current-mismatch effects. The origin of high temperature differences observed between individual cells and their neighbouring cells, are generally due to current mismatch caused by localised EVA browning, whereas smaller temperature differences may indicate localised shading if the phenomenon is transient; otherwise, indicate the existence of cell microdefects caused during the manufacturing stage, which may become the onset of permanent degradation.  Milder thermal effects linked to current mismatch were also identified in new modules. The IR image of a brand-new c-Si BIO 175 W p under operation revealed a hot cell with T c over 15 • C higher than the temperature of the neighbouring cells in the module (Figure 4d). This is attributed to localised imperfections at the production stage and may signal the onset of degradation.  shows the module's I-V characteristic, where δI dropped by 0.03 A in the first 6 V due to associated current mismatch. Such defects are pre-existing and trigger mild degradation.
The above confirms that the hot cells detected via IR thermography were linked to currentmismatch effects. The origin of high temperature differences observed between individual cells and their neighbouring cells, are generally due to current mismatch caused by localised EVA browning, whereas smaller temperature differences may indicate localised shading if the phenomenon is transient; otherwise, indicate the existence of cell microdefects caused during the manufacturing stage, which may become the onset of permanent degradation.

Hotspots Linked to Corrosion
A case where EVA degradation led to corrosion at the busbars is shown in Figure 5a,b. The affected cell appeared upon close visual inspection to have mild EVA and ARC degradation similar to neighbouring cells. The IR image (Figure 5b) revealed hotspots at the busbars, which may have been due to corrosion, with a temperature 20 • C higher than that of neighbouring cells.
A case where EVA degradation led to corrosion at the busbars is shown in Fi 5a,b. The affected cell appeared upon close visual inspection to have mild EVA and degradation similar to neighbouring cells. The IR image (Figure 5b) revealed hotspo the busbars, which may have been due to corrosion, with a temperature 20 °C higher that of neighbouring cells.
Corrosion may cause a significant increase in the Rs. The latter, due to the Joule e increases the Tc. A certain amount of power I 2 δRs(W) is converted into heat and transfe to the environment at a rate of 2(hc + hr)AcorδTc. Therefore, I 2 δR s = 2(h c + h r )A cor δT c where (hc + hr) was estimated equal to 12.5 W/m 2 K, the area affected by corrosion Aco estimated from the area of the hotspots along the busbars to equal 2.45 cm 2 , the curre operating conditions (800 W/m 2 ) was estimated to be I = 2.4 A (I = 3 A at 10 3 W/m 2 ) the measured δT was 20 °C higher than the temperature of the neighbouring cells. T lead to a δR = 0.021 Ω or 21 mΩ higher than the R of neighbouring cells of the m ule. Hotspots identified through IR thermography indicated resistive busbars or inter nects attributed to corrosion often co-existing with EVA degradation or humidity ing

UVF Imaging for the Detection of EVA Degradation
Corrosion in the busbar and the interconnect ribbon developed due to the acetic formed by EVA photodegradation at high Tc (Figure 3e,f). Under natural ageing an SRD of around 8 MWh/m 2 , corrosion formed on the interconnect ribbon in one of th Si modules. Figure 6a,b shows two signs corrosion, associated with humidity ingress, the T connection between the busbar and the interconnecting ribbon at the front and side of the ODT-660P module. The UVF image of the ODT module ( Figure 6c) shows s of corrosion and EVA degradation. The EVA degradation pattern was symmetri shaped and contoured by a non-UV-fluorescing area because O2 diffused through the sheet and suppressed the fluorescence and photo-bleaching along the cells edges, w also appeared along the busbars. Figure 6d shows a complex pattern of EVA degrad revealed through UVF imaging. The bleached area along the busbar was attributed t weakening of the cell metallisation, which eased O2 diffusion from the back side. Ble ing appeared in the diagonal part of the cell, which showed a non-UV-fluorescent pa possibly due to bending caused by high wind loads impacting the large pc-Si ODT face. Hence, back-sheet delamination started and O2 diffused into the affected cells. patterns did not appear in the UVF images of the smaller M55 modules, which supp Corrosion may cause a significant increase in the R s . The latter, due to the Joule effect, increases the T c . A certain amount of power I 2 δR s (W) is converted into heat and transferred to the environment at a rate of 2(h c + h r )A cor δT c . Therefore, where (h c + h r ) was estimated equal to 12.5 W/m 2 K, the area affected by corrosion A cor was estimated from the area of the hotspots along the busbars to equal 2.45 cm 2 , the current at operating conditions (800 W/m 2 ) was estimated to be I = 2.4 A (I = 3 A at 10 3 W/m 2 ), and the measured δT c was 20 • C higher than the temperature of the neighbouring cells. These lead to a δR s = 0.021 Ω or 21 mΩ higher than the R s of neighbouring cells of the module. Hotspots identified through IR thermography indicated resistive busbars or interconnects attributed to corrosion often co-existing with EVA degradation or humidity ingress.

UVF Imaging for the Detection of EVA Degradation
Corrosion in the busbar and the interconnect ribbon developed due to the acetic acid formed by EVA photodegradation at high T c (Figure 3e,f). Under natural ageing and an SRD of around 8 MWh/m 2 , corrosion formed on the interconnect ribbon in one of the pc-Si modules. Figure 6a,b shows two signs corrosion, associated with humidity ingress, near the T connection between the busbar and the interconnecting ribbon at the front and back side of the ODT-660P module. The UVF image of the ODT module ( Figure 6c) shows signs of corrosion and EVA degradation. The EVA degradation pattern was symmetrically shaped and contoured by a non-UV-fluorescing area because O 2 diffused through the back sheet and suppressed the fluorescence and photo-bleaching along the cells edges, which also appeared along the busbars. Figure 6d shows a complex pattern of EVA degradation revealed through UVF imaging. The bleached area along the busbar was attributed to the weakening of the cell metallisation, which eased O 2 diffusion from the back side. Bleaching appeared in the diagonal part of the cell, which showed a non-UV-fluorescent pattern possibly due to bending caused by high wind loads impacting the large pc-Si ODT surface. Hence, back-sheet delamination started and O 2 diffused into the affected cells. Such patterns did not appear in the UVF images of the smaller M55 modules, which supports the above hypothesis. For the smaller c-Si M55 modules, signs of corrosion were evident at SRD > 24 MWh/m 2 . the above hypothesis. For the smaller c-Si M55 modules, signs of corrosion were evid at SRD > 24 MWh/m 2 .
The UVF image reveals the extent of EVA degradation. The intensity of the fluor cence from the EVA degradation pattern was proportional to the number of chrom phores due to the dissociation of EVA molecules by the UV of the SRD, as also suppor by Figure 2b,d-f. Signs of EVA browning appeared in pc-Si ES modules 124 Wp und natural ageing conditions at SRD > 10 MWh/m 2 , as shown in Figure 2b. The EVA deg dation patterns in small c-Si modules follow the cell geometry. In large modules, the p terns may have non-symmetric shapes, as in Figure 6d, where the bleached area was agonal due to the stress loads that bent the module. Figure 6e,f show UVF images of c SW80 cells that suffered from non-visible cracks. Although UVF imaging may detect EVA browning even at the early stages of f mation, often the latter appears to develop alongside other defects, which gives rise to need for combined diagnostics. I-V analysis and IR thermography are required to prov more details on the effect of EVA degradation in its different modes, combined with imaging on the extent of non-visible cracks, e − +hole recombination centres, Rs, and Rsh

Delamination of EVA/Cell Interface at the Metallisation
Delamination of the EVA/cell interface around the busbar was observed in seve cells of the M55 modules operating for 18 and 24 years, such as the ones shown in Fig  3c,d. EL tests using the short-wave infrared (SWIR) camera Goldeye-P008 (Allied Vis Technologies, Germany) were performed on a M55 module with the module forward ased at 19.5 V-19.8 V (Voc = 21.7 V). The resulting EL images (Figure 7a,b) revealed dar contrast in the delaminated spots around the busbar, whereas the surrounding area w EL bright due to e − +hole recombination. Delamination of the EVA/cell interface cause small decrease in the current proportional to the delaminated area, a small increase in Rs, and a decrease in the Rsh. The effect can be quantified through I-V analysis at the c level. As δRs is usually very small, the Tc profile along the delaminated area was v small, too, and the IR thermography did not detect any essential Tc pattern. The delam nation spots formed during the years of operation expanded in the x-y dimensi whereas new spots appeared whose rate depended on the SRD and the level of the The UVF image reveals the extent of EVA degradation. The intensity of the fluorescence from the EVA degradation pattern was proportional to the number of chromophores due to the dissociation of EVA molecules by the UV of the SRD, as also supported by Figure 2b,d-f. Signs of EVA browning appeared in pc-Si ES modules 124 W p under natural ageing conditions at SRD > 10 MWh/m 2 , as shown in Figure 2b. The EVA degradation patterns in small c-Si modules follow the cell geometry. In large modules, the patterns may have non-symmetric shapes, as in Figure 6d, where the bleached area was diagonal due to the stress loads that bent the module. Figure 6e,f show UVF images of c-Si SW80 cells that suffered from non-visible cracks.
Although UVF imaging may detect EVA browning even at the early stages of formation, often the latter appears to develop alongside other defects, which gives rise to the need for combined diagnostics. I-V analysis and IR thermography are required to provide more details on the effect of EVA degradation in its different modes, combined with EL imaging on the extent of non-visible cracks, e − +hole recombination centres, R s , and R sh .

Delamination of EVA/Cell Interface at the Metallisation
Delamination of the EVA/cell interface around the busbar was observed in several cells of the M55 modules operating for 18 and 24 years, such as the ones shown in Figure 3c,d. EL tests using the short-wave infrared (SWIR) camera Goldeye-P008 (Allied Vision Technologies, Germany) were performed on a M55 module with the module forward biased at 19.5 V-19.8 V (V oc = 21.7 V). The resulting EL images (Figure 7a,b) revealed darker contrast in the delaminated spots around the busbar, whereas the surrounding area was EL bright due to e − +hole recombination. Delamination of the EVA/cell interface caused a small decrease in the current proportional to the delaminated area, a small increase in the R s , and a decrease in the R sh . The effect can be quantified through I-V analysis at the cell level. As δR s is usually very small, the T c profile along the delaminated area was very Sensors 2023, 23, 3016 9 of 23 small, too, and the IR thermography did not detect any essential T c pattern. The delamination spots formed during the years of operation expanded in the x-y dimension, whereas new spots appeared whose rate depended on the SRD and the level of the T c developed. High-resolution EL imaging enabled the investigation of the impact of delamination at the EVA/cell interface. Other defects, such as broken fingers and shunts, were also visible. The combination of a wide range of degradation effects that can be detected through EL imaging gives rise to the need for a combination with other techniques for the quantification of the degradation caused by the individual defects. ensors 2023, 23, x FOR PEER REVIEW 9 of 24 developed. High-resolution EL imaging enabled the investigation of the impact of delamination at the EVA/cell interface. Other defects, such as broken fingers and shunts, were also visible. The combination of a wide range of degradation effects that can be detected through EL imaging gives rise to the need for a combination with other techniques for the quantification of the degradation caused by the individual defects.

Corrosion in Cables and Identification by I-V Analysis
I-V analysis can assist with the quantification of degradation from a wide range of factors and defects, even in cases where corrosion has occurred in the cables, which can be missed from module-oriented IR thermography. Corrosion in a cable connected to the junction box was identified through comparative I-V analysis in two identical PV generators, one fixed and one sun-tracking. The I-V characteristics are shown in Figure 8a,b. The Vm in the sun-tracker (Figure 8b) compared to the fixed PV (Figure 8a) was shifted by 3.5 V, whereas the shift due to their Tc difference was estimated at 1.8 V. Therefore, the Vm and Pm decreases in the sun-tracking system could not be interpreted by the Tc effect alone. The additional δRs was attributed to a hidden corrosion in the cable, since cracks, delamination, or visible corrosion contributing to δRs were not detected by IR, EL, or UVF. Although certain defects can be identified by more than one technique, often a single

Corrosion in Cables and Identification by I-V Analysis
I-V analysis can assist with the quantification of degradation from a wide range of factors and defects, even in cases where corrosion has occurred in the cables, which can be missed from module-oriented IR thermography. Corrosion in a cable connected to the junction box was identified through comparative I-V analysis in two identical PV generators, one fixed and one sun-tracking. The I-V characteristics are shown in Figure 8a,b. The V m in the sun-tracker (Figure 8b) compared to the fixed PV (Figure 8a) was shifted by 3.5 V, whereas the shift due to their T c difference was estimated at 1.8 V. Therefore, the V m and P m decreases in the sun-tracking system could not be interpreted by the T c effect alone. The additional δR s was attributed to a hidden corrosion in the cable, since cracks, delamination, or visible corrosion contributing to δR s were not detected by IR, EL, or UVF. ensors 2023, 23, x FOR PEER REVIEW 9 of 24 developed. High-resolution EL imaging enabled the investigation of the impact of delamination at the EVA/cell interface. Other defects, such as broken fingers and shunts, were also visible. The combination of a wide range of degradation effects that can be detected through EL imaging gives rise to the need for a combination with other techniques for the quantification of the degradation caused by the individual defects.

Corrosion in Cables and Identification by I-V Analysis
I-V analysis can assist with the quantification of degradation from a wide range of factors and defects, even in cases where corrosion has occurred in the cables, which can be missed from module-oriented IR thermography. Corrosion in a cable connected to the junction box was identified through comparative I-V analysis in two identical PV generators, one fixed and one sun-tracking. The I-V characteristics are shown in Figure 8a,b. The Vm in the sun-tracker (Figure 8b) compared to the fixed PV (Figure 8a) was shifted by 3.5 V, whereas the shift due to their Tc difference was estimated at 1.8 V. Therefore, the Vm and Pm decreases in the sun-tracking system could not be interpreted by the Tc effect alone. The additional δRs was attributed to a hidden corrosion in the cable, since cracks, delamination, or visible corrosion contributing to δRs were not detected by IR, EL, or UVF. Although certain defects can be identified by more than one technique, often a single technique is not sufficient to diagnose the nature of a degradation effect. The cross-correlation of findings between the different NDT tools promises a more sensitive and accurate defect diagnosis. Although certain defects can be identified by more than one technique, often a single technique is not sufficient to diagnose the nature of a degradation effect. The cross-correlation of findings between the different NDT tools promises a more sensitive and accurate defect diagnosis.

The Defect Diagnostics Using Cross-Correlation of the NDT Findings: Results, Analysis, and Discussion
The methodology developed consists of two main components: (1) analysis of the deviations of the module electrical parameters V oc , V m, I sc , I m , R s , and R sh at STC from their nominal values, and (2) the study of the variations of EL images captured at various bias voltages while measuring the current allowed into the module. A detailed study to identify cell defects and degradation factors and their effect on the power performance was carried out by cross-correlating findings from I-V analysis and EL, IR, and UVF imaging.
The PV-defect-diagnostics methodology was applied to two groups of modules: (1) c-Si M55/SM55 and (2) pc-Si ODT-660P, with three modules in each group. The nominal values are given in Table 1. The aforementioned modules, with different years of operation for each one, were electrically characterised. The I-V characterisation was performed using GTM-AAA Flash Tester (Keyland, Jiangsu, China), including the I-V tracer, combined with a synchronized PV-temperature-monitoring unit. PV modules were exposed to simulated solar light at 1000 W/m 2 at room temperature. Adjustments for any differences in measured PV temperature from T c = 25 • C were carried out through conversion of the I-V characteristic to STC, according to the I-V translation equations in [52]. The electrical parameters of the modules V oc , V m, I sc , I m , R s , and R sh were then easily extracted from the converted I-V characteristic at STC. R s was determined from one I-V characteristic based on [53]. The electrical parameters expressed at STC were then compared to the nominal values to determine the experimental deviations δV oc , δV m, δI sc , δI m , δR s , and δR sh . In the first component of the methodology, the deviations were also predicted by the equations proposed in Section 3.1, and any differences observed between predicted and experimental deviations of the electrical parameters provided important insights into the electrical parameter(s) mainly responsible for the observed degradation and, indirectly, the nature of the defect.
In the second component, a series of EL images was captured in the dark with each module forward biased at a sequence of bias voltages while monitoring the current allowed into the module. The EL image capture was performed using the Module Fault Tester (Keyland, Jiangsu, China). The EL testing unit utilises a cooled near-infrared CCD camera. The EL images at different bias voltages revealed significant qualitative information on the nature of the defects, which were quantified by the I-V analysis and the analysis of deviations of the module electrical parameters (first component of the proposed methodology). The methodology is described analytically in Section 3.2, along with its application in the two groups of modules, with the main findings reported.
Certain degradation effects revealed through either of the two components of the proposed methodology may need to be cross-checked with IR thermography and UVF imaging where necessary for the final sorting. This highlights the synergistic nature of the proposed NDT methodology.

The Proposed Diagnostics Component Based on the Deviation Analysis of the Module Electrical Parameters: Results and Analysis
The methodology for defect identification is based on the following equations, which determine the deviations of the module electrical parameters at STC from their nominal values.
An expression of the V oc deviation δV oc due to a change in I sc . δI sc is given by Equation (3), which is derived from Equation (4) where n s is the number of cells in the series, I ph the photocurrent, I o is the dark saturation current, k is the Boltzmann constant, and q is the electron charge.
In general, T c and I o are not constant, as assumed in Equation (3). Note that in cases of cells with EVA browning or busbar corrosion, a high δT c pattern is developed in those cells identified through IR thermography. Introducing the effect of the deviations of T c and I o into Equation (4) yields Equation (5).
where n i , n j , etc. denote the number n i of cells with T c higher than 25 • C by δT c,i due to any defects. This is similar for the group of cells n j , etc. The I-V characteristic of M55 module no1 captured with the I-V flash tester and converted to STC is shown in Figure 9a. The decrease of δI sc = 0.80 A from its nominal value (Table 1) was attributed to extended EVA browning (Figure 9b,c). A gradual decrease of 0.15 A in I yielded a total δI sc = 0.95 A. Substituting the above values and (kT c /q) = 0.026 V, m = 1.5 (due to the recombination effect on the ideality factor, m), and n s = 36 into Equation (3) yielded δV oc = 0.525 V, which is less than the experimentally determined δV oc = 0.88 V obtained from Tables 1 and 2. The deviation of δV oc between experiment and theory may not have been due to a low R sh, which can be determined by applying Equation (6), [54], because Table 2 does not support such a hypothesis.  Since the I-V characteristic of M55 module no1 was converted to STC, T c was by principle 25 • C and therefore the additional terms in Equation (5) were zeroed. Introducing the above values into Equation (5) and substituting δV oc = 0.88-0.525 yielded δI o /I o = 0.115 or an 11.5% increase due to extended EVA/cell-interface delamination, which is evident in the EL images of module no1 (Section 3.2.1). Therefore, Equation (5) predicts the total δV oc due to any possible set of deviations of the electrical parameters very close to the experimentally determined value.
The aforementioned gradual drop of δI sc = 0.15 A between 5-10 V (Figure 9a) corresponded to R sh and to a shunt diode due to current mismatch attributed to the EVA/cell-interface delamination spots and to the two cells exhibiting different degrees of browning (Figure 9c). This current mismatch caused a low T c pattern when operating in field conditions, which slightly reduced V oc and V m . In addition, the cracks, small breaks, and EVA/cell-interface delamination shown in Figure 9b and disclosed by the EL analysis below contributed to δI m , as well as an increase of δR s = 0.85 (from Table 2 The methodology proposed in the deviation analysis of module electrical parameters is summarized in Figure 11. The synergy with other NDT techniques is also illustrated. Extraction of the electrical parameters from the I-V characteristic can be carried out with any approach, as provided in the review article [55]. The expression of the deviation δV m is given by Equation (7), which is another fundamental expression for the study of the deviation of electrical parameters. δV m = δV oc − (δI m R s + I m δR s ) Equation (7), using the values from Table 2 and the nominal ones, yielded δV m = 1.18 V, and the measured δV m = 17.4 V − 16.15 = 1.25 V, which is a good prediction that also accounts for the degradation in I m and R s . The above deviation analysis of the electrical parameters provides a first view of the impact of the defects. Figure 9d shows the I-V of module no2 with less EVA browning but extended EVA/cell-interface delamination along the busbar. The latter caused an increase in R s and I o and a decrease in R sh , confirmed from both Table 2 and the EL image analysis in Section 3.2.1. The values in Table 2, with reference to those in Table 1, yielded δV oc = 0.7 V, δV m = 2.72 V, δR s = 1.43 (Table 2) − 0.30 (manufacturer) = 1.13 Ω, and δI m = 0.366 A. Similar to the above, Equation (3) predicted δV oc = 0.14 V, far less than the 0.7 V determined experimentally. This deviation, according to Equations (5) and (6), may have been due to an increase in the I o , that is, a shunt-recombination diode, and to a much lower R sh , as it was supported by the higher I m and lower V m compared to module no1. Table 2 confirms this hypothesis. Substituting the above values into Equation (7) yielded δV m = 2.64 V compared to the aforementioned 2.72 V, which demonstrates the very good description of the defects by the above analysis. Modules no1,2 experienced severe external degradation such as deep shading for long periods, which triggered internal defects whose patterns differed, as confirmed by the EL image analysis in Section 3.2.1. Their degradation, as shown in Table 2, was significant, between 25-28%, which is much higher than the 19.2% expected (considering an average degradation of 0.8%/year) for PV modules experiencing only natural ageing and operating for the same number of years. SM55 no3 showed no EVA browning, and its I-V characteristic is presented in Figure 9e. The module was subject to natural ageing. The EVA/cell-interface delamination was present in all cells, as shown in Figure 10a,b, but it was not as extended as in module no2. Indeed, in Table 2, module no3 showed the least increase in R s compared to no1 and no2 and the smallest P m degradation of 16.8%. The deviation of its electrical parameters was estimated as δV oc = 0.62 V, δV m = 1.41 V, δI sc = 0.347 A, δI m = 0.30 A, and δR s = 0.134 Ω. Equation (7) predicted δV m = 0.94 V, which is much lower than the experimentally determined one, although recombination and delamination effects were taken into account. In this case, the cause of the deviation was the numerous cracks and the grid-line interruptions revealed through EL imaging (Section 3.2.1), whose effect may not be included in Equation (7). This remark allows for the prediction of breaks and cracks in the cells when the δV m estimated by Equation (7) deviates significantly from the measured δV m provided that R sh is not significantly degraded. The methodology proposed in the deviation analysis of module electrical param is summarized in Figure 11. The synergy with other NDT techniques is also illustr Extraction of the electrical parameters from the I-V characteristic can be carried out any approach, as provided in the review article [55]. The methodology proposed in the deviation analysis of module electrical parameters is summarized in Figure 11. The synergy with other NDT techniques is also illustrated. Extraction of the electrical parameters from the I-V characteristic can be carried out with any approach, as provided in the review article [55].

The Proposed Diagnostics Component Based on the Variation Analysis of EL Images: Results and Analysis
The second component of the PV-defect diagnostics was based on the analysis of variations of EL images captured in a sequence of bias voltages while measuring the current allowed into the module. The methodology was further supported by IR thermography Figure 11. Functional flow-block diagram illustrating the deviation analysis of module-electricalparameter methodology and synergy with other NDT techniques.

The Proposed Diagnostics Component Based on the Variation Analysis of EL Images: Results and Analysis
The second component of the PV-defect diagnostics was based on the analysis of variations of EL images captured in a sequence of bias voltages while measuring the current allowed into the module. The methodology was further supported by IR thermography and UVF imaging and the analysis of deviations of the electrical parameters described in Section 3.1.

Case 1: c-Si Modules Operating for 18 and 24 Years
The variation in the EL images captured at an increasing sequence of bias V voltages was studied in terms of the strength and pattern of the light/dark contrasts. This could provide significant information about the quality and condition of the module and the type of defects. A number of findings are deployed below that can be considered for a reliable diagnosis of PV defects: 1.
Breaks, cracks, and grid-line interruptions in cells were easily identified in Figure 12a-i, which show EL images of the c-Si modules no1,2,3 at various biases V. These defects contributed to I decrease, I-V distortion, R s increase, and R sh decrease. These may have caused small current mismatch. The quantitative effect requires I-V analysis. Cracks in the cell edges may not be identifiable in the UVF images due to photo-bleaching.

2.
The dark contrasts in the sequence of EL images captured from low bias V to V = V oc faded away with the increase in the bias V, and this implies that those cells or areas of cells had a lower R sh . This is shown in Figure 12a,b,d,e and Figure 12g,h. Such dark contrasts do not appear in healthy cells.

3.
The EL images captured for V at around V oc and a little higher showed bright EL spots or areas along the busbar that were attributed to e − +hole recombination prevailing at these voltages. This defect increased R s , decreased R sh , and added a shunt diode. Such cases were numerous in the EL images, as shown in Figure 12, especially along the busbar where EVA/cell-interface delamination was the main defect finding. This did not appear in the EL images of the ODT modules in Section 3.2.2, where EVA/cell-interface delamination was not observed. However, bright spots in the EL images may also appear as a result of corrosion in the busbar, as in Figure 12b (cell position 4 from the left in the upper row), which corresponds to the cell with EVA browning and busbar corrosion in Figure 2c. In module no2, bright EL spots started appearing at lower V (Figure 12d), interpreted as damage of the p-n junction with a consequent decrease in V m . 4.
EL images captured at bias V > V oc may show that dark cell contrasts reduced or disappeared, which demonstrates the presence of cell regions with δR s . If the dark contrast is sustained for any V >> V oc it implies cracks, breaks, holes, grid-line interruptions, or inactive regions in cells. Those defected cells contributed to an increase in R s and decrease in R sh and I sc and are numerous in Figure 12, but limited in the ODT modules (Section 3.2.2) corresponding to healthier modules. The overall R s and R sh of the module was determined quantitatively by the I-V analysis, whereas the increase in the R s , δR s can be estimated as described in point 7 below. 5.
In Figure 12c,f,i with V > V oc some dark regions in cells were sustained. This implies regions with δR s . Figure 12g-i show a more uniform EL illumination pattern. The dark regions in Figure 12g were due to degraded R sh and were more numerous than in Figure 12a. Hence, R sh of no3 was lower than that of no1. At bias V > V oc in Figure 12i, the dark regions were due to δR s . In no3 there were fewer than in no1 and much fewer than in no2. That is, the R s in no3 was lower than in no1 and no2. The above statements are in agreement with Table 2. 6.
The EL intensity was spatially more uniform in no3 compared to no1 and no2 at bias V > V oc in Figure 12c,f,g. In that V range, the R s governed current I through the cells. Specifically, I vs. V was higher in no3 than no1 and no2, which implies that R s was lower in no3 and higher in no2, which is in agreement to Table 2. The reverse is also true. In high-bias V the effectiveness in defect identification became poorer because the EL luminosity contrast reduced in almost all cells (Figure 12c,f,i).  Table 3 show the I-V analysis results and Figure 14a-f the EL images of three pc-Si ODT modules with nominal values given in Table 1. Figure 13a shows the I-V of the ODT pc-Si no1 operating for 5 years. Its power degradation was determined to be 52% and the results are given in Table 3. The 12 V decrease in Voc signalled that a string of cells was off. The root cause was a semi-transparent thin film 1.0 g/m 2 of volatile organic effluents naturally and unevenly deposited on the PV glass. That caused strong current mismatch and crucial I-V deformation. The high Rs and low Rsh values in Table 3 are the macroscopic results of the I-V analysis and do not reflect the internal conductivity paths in the cells. With the glass cover cleaned, the I-V (Figure 13b) showed power recovery, where the degradation was now 5.9%, still higher than the average anticipated degradation of 4% for a naturally aged module operating for the same number of years (5). The Rs and Rsh of the cleaned module were consistent with the normal values. ODT no2 and no3 in operation for 4 and 2 years, respectively, showed better I-V profiles, which translated to STC (Figure 13c,d) yielding 2.4% and 1% degradation, respectively.
The EL images of ODT no1 (Figure 14a-d) revealed multiple broken cells, at position (x,y): (6,3), (8,5), (10,6), which remained dark at all bias V. In cell (5,2), a tick sign remained The equality in Equation (8) holds when the defects contribute only to increases in R s, e.g., corrosion. The inequality holds when the modules apart from the δR s suffer from increased localised e − +hole recombination, EVA/interface delamination, and/or R sh to be confirmed by the sequence of EL image-variation analysis (Figure 12a-c). In addition, the deviation analysis of V m yields: V m,nom − V m,STC = I·δR s (10) where I is the current allowed in the module. M55 module no 1 data-V oc,nom = 21.7 V, V bias = 26.7 V, allowed I = I sc = 3.3 A (Figure 12c), R s = 0.85 Ω (Table 2), and R s,nom = 0.30 Ω (manufacturer)-were introduced in Equations (8) and (9). Equation (8) predicted δR s = 1.52 Ω, whereas Equation (9) yielded δR s = 0.85 − 0.30 = 0.55 Ω. This large difference is due to the existence of other defects such as R sh and widely increased e − +hole recombination regions (Figure 12c). In addition, introducing module no1 data-V m,nom = 17.4 V and V m,STC = 16.15 V-into Equation (10) yielded δR s = 0.50 Ω, which is very close to the calculation from Equation (9). Similar analysis may be applied to module no2, where Equation (8) predicted δR s = 1.91 Ω, whereas Equation (9) yielded δR s = 1.13 Ω. This large difference is due to the low R sh confirmed by Table 2 and due to increased e − +hole recombination. In this case, Equation (10) predicted δR s = 1.01 Ω, which is very close to the value provided by Equation (9), equal to 1.13 Ω.  Table 3 show the I-V analysis results and Figure 14a-f the EL images of three pc-Si ODT modules with nominal values given in Table 1. Figure 13a shows the I-V of the ODT pc-Si no1 operating for 5 years. Its power degradation was determined to be 52% and the results are given in Table 3. The 12 V decrease in V oc signalled that a string of cells was off. The root cause was a semi-transparent thin film 1.0 g/m 2 of volatile organic effluents naturally and unevenly deposited on the PV glass. That caused strong current mismatch and crucial I-V deformation. The high R s and low R sh values in Table 3 are the macroscopic results of the I-V analysis and do not reflect the internal conductivity paths in the cells. With the glass cover cleaned, the I-V (Figure 13b) showed power recovery, where the degradation was now 5.9%, still higher than the average anticipated degradation of 4% for a naturally aged module operating for the same number of years (5). The R s and R sh of the cleaned module were consistent with the normal values. ODT no2 and no3 in operation for 4 and 2 years, respectively, showed better I-V profiles, which translated to STC (Figure 13c,d)  at all bias V, which demonstrates a crack. In addition, periphery cells whose dark parts remained even at higher bias-V values were revealed. This implies a δRs, and therefore the Rs was expected to be higher and the Rsh lower than in module ODT no2, as confirmed in Table 3, with no broken parts, as shown in the EL image (Figure 14f). The contrast in the dark parts in some periphery cells and in cell (5,2) decreased when the bias V increased. This implies that those dark regions were due to Rsh. Figure 14e-h correspond to ODT no2 and no3 and exhibited similar effects of dark regions, which reflects issues related to the manufacturing process. ODT no3 had lower Rs, as there was only one dark area in the EL image (Figure 14g,h) that remained relatively dark at high bias V. This is confirmed in Table 3. Indeed, Rsh of no3 was lower than of no1 and no2, as expected, because the cells whose dark contrast decreased with V were more numerous than in the other two modules (Figure 14a-f).     The EL images of ODT no1 (Figure 14a-d) revealed multiple broken cells, at position (x,y): (6,3), (8,5), (10,6), which remained dark at all bias V. In cell (5,2), a tick sign remained at all bias V, which demonstrates a crack. In addition, periphery cells whose dark parts remained even at higher bias-V values were revealed. This implies a δR s , and therefore the R s was expected to be higher and the R sh lower than in module ODT no2, as confirmed in Table 3, with no broken parts, as shown in the EL image (Figure 14f). The contrast in the dark parts in some periphery cells and in cell (5,2) decreased when the bias V increased. This implies that those dark regions were due to R sh . Figure 14e-h correspond to ODT no2 and no3 and exhibited similar effects of dark regions, which reflects issues related to the manufacturing process. ODT no3 had lower R s , as there was only one dark area in the EL image (Figure 14g,h) that remained relatively dark at high bias V. This is confirmed in Table 3. Indeed, R sh of no3 was lower than of no1 and no2, as expected, because the cells whose dark contrast decreased with V were more numerous than in the other two modules (Figure 14a-f). The state of EVA degradation for the ODT modules (Figure 6a-d) with only a few years of operation compared to that of (S)M55 modules (Figure 2c,d) appeared to be healthier, as no EVA browning or delamination in the EVA/cell interface or grid-line interruptions were demonstrated. ODT no1 experienced higher EVA degradation compared to ODT no2 and no3 due to back-sheet delamination caused by stress loads on its large The state of EVA degradation for the ODT modules (Figure 6a-d) with only a few years of operation compared to that of (S)M55 modules (Figure 2c,d) appeared to be healthier, as no EVA browning or delamination in the EVA/cell interface or grid-line interruptions were demonstrated. ODT no1 experienced higher EVA degradation compared to ODT no2 and no3 due to back-sheet delamination caused by stress loads on its large surface. When cleaned from the film of organicgas effluents its P m recovered greatly. The R s of ODT module no3 was determined to be 0.41 Ω, whereas for modules no1 and no2 it was 0.54 Ω and 0.465 Ω, respectively, which corresponds to about 7-9 mΩ/cell. On the contrary, the R s in the smaller cells of M55 modules was 20-25 mΩ/cell, compared to 18 mΩ/cell for a brand-new module, whereas in modules suffering from several defects and with extended delamination, e.g., M55 module no2, the R s was determined to be equal to 40 mΩ/cell. This shows the effect of natural and induced degradation of the cell's electric parameters and power performance.

Modules pc-Si Isc (A) Voc (V) Im (A) Vm (V) Rs (Ω) Rsh (Ω) Pm (W) δPm/Pm %
Passivation issues were also disclosed through EL imaging at high bias voltages. the EL image of the ODT pc-Si module no1 at bias V = 42.5 V (Figure 15a) shows that one of the cells in the rightmost column emitted light due to a break in the passivation when the V > V oc by more than 2 V. This defect started at V = 39.5 V (Figure 15b). surface. When cleaned from the film of organic-gas effluents its Pm recovered greatly. The Rs of ODT module no3 was determined to be 0.41 Ω, whereas for modules no1 and no2 it was 0.54 Ω and 0.465 Ω, respectively, which corresponds to about 7-9 mΩ/cell. On the contrary, the Rs in the smaller cells of M55 modules was 20-25 mΩ/cell, compared to 18 mΩ/cell for a brand-new module, whereas in modules suffering from several defects and with extended delamination, e.g., M55 module no2, the Rs was determined to be equal to 40 mΩ/cell. This shows the effect of natural and induced degradation of the cell's electric parameters and power performance. Passivation issues were also disclosed through EL imaging at high bias voltages. the EL image of the ODT pc-Si module no1 at bias V = 42.5 V (Figure 15a) shows that one of the cells in the rightmost column emitted light due to a break in the passivation when the V > Voc by more than 2 V. This defect started at V = 39.5 V (Figure 15b). The proposed methodology on the variation analysis of EL images at various bias voltages is summarised in Figure 16. The synergy with other NDT techniques is also illustrated.  bright EL spot appears at the edge of the cell in the right column due to a problem in the passivation, whereas in (a), the passivation problem is evident in the same cell.
The proposed methodology on the variation analysis of EL images at various bias voltages is summarised in Figure 16. The synergy with other NDT techniques is also illustrated. surface. When cleaned from the film of organic-gas effluents its Pm recovered greatly. The Rs of ODT module no3 was determined to be 0.41 Ω, whereas for modules no1 and no2 it was 0.54 Ω and 0.465 Ω, respectively, which corresponds to about 7-9 mΩ/cell. On the contrary, the Rs in the smaller cells of M55 modules was 20-25 mΩ/cell, compared to 18 mΩ/cell for a brand-new module, whereas in modules suffering from several defects and with extended delamination, e.g., M55 module no2, the Rs was determined to be equal to 40 mΩ/cell. This shows the effect of natural and induced degradation of the cell's electric parameters and power performance. Passivation issues were also disclosed through EL imaging at high bias voltages. the EL image of the ODT pc-Si module no1 at bias V = 42.5 V (Figure 15a) shows that one of the cells in the rightmost column emitted light due to a break in the passivation when the V > Voc by more than 2 V. This defect started at V = 39.5 V (Figure 15b). The proposed methodology on the variation analysis of EL images at various bias voltages is summarised in Figure 16. The synergy with other NDT techniques is also illustrated.

Discussion
Cross-correlation between the findings from the NDT tool revealed the prevailing defects, their strength, and the effect on PV performance. A diversity of defects and degradation factors was disclosed in the groups of PV modules studied.
The intensity and spatial distribution of the UV fluorescence was directly associated with the degree of EVA degradation, which is proportional to SRD. EVA degradation appeared in UVF images at SRD > 4 MWh/m 2 for natural ageing, whereas EVA browning appeared at SRD > 10 MWh/m 2 .
PV cells shaded for a long time exhibited high T c profiles due to current mismatch, which caused permanent defects: (a) EVA browning (directly disclosed by UVF and optical inspection and indirectly by I-V in cross-correlation with IR), (b) delamination of EVA/cell interface (disclosed by optical inspection and high-resolution EL imaging), and (c) corrosion on the busbar or in the cell interconnects (disclosed by IR thermography and indirectly by I-V analysis).
The e − +hole recombination due to impurities may occur even in brand new modules. T c profiles of 10-20 • C higher than the temperature of neighbouring cells appeared in the IR thermography due to current mismatch. This was also confirmed by studying the EL image and indirectly by I-V-profile analysis. EVA browning can spatially affect the light transmission into the cell and cause current mismatch. This implies a shunt diode, a δR sh , and high T c profiles, which trigger second-order generation defects such as wider and/or deeper EVA browning, and may also lead to delamination and corrosion.
There is a time evolution in the defects analysed, as they depend on SRD and any casual external factors, causing high T c profiles and second-order generation defects, which form avalanches. These defects may not be predictable or predetermined. More crucial than the P m degradation is the I m and V m decrease, which causes mismatch between the strings of modules.
Film deposition on the module, breaks, cracks, grid-line interruptions, R s and R sh , e − +hole recombination centres, and cell-edge passivation issues were demonstrated by studying the variation of EL images captured under a series of bias voltages and the deviation analysis of the electrical parameters of the module using I-V data analysis. In addition, UVF and IR supported the identification of those defects. Prediction of the diversity of families of defects was possible based on the diagnostics methodology developed for the defects.

Conclusions
This paper provides an extended analysis on PV-defect identification in cells and modules based on the synergy of NDT tools, UVF imaging, IR thermography, EL imaging, and I-V analysis. A large number of PV modules operating for different years, from 0 to 24 years, was studied, as they exhibit a wide range of defects. The defects diagnosis is based on the cross-correlation of the findings from the above NDT techniques. It determines the defects qualitatively and quantitatively as concerns their spatial pattern, the strength of their effect, and the performance degradation. A methodology based on the synergy of NDT techniques is proposed with the following two main components focusing on the quantitative and qualitative analysis of defects:

1.
Analysis of the deviations of the module electrical parameters at STC from their nominal values of δV oc , δV m , δI sc , δI m , δR s , and δR sh . This provides an insight into the impact of defects on the module electrical parameters, along with an inference on the origin of the defect to be further identified in synergy with the aforementioned NDT tools and the second component of this methodology.

2.
Variation analysis of EL images captured in a sequence of bias voltages, from V < V oc to V > V oc , and measuring the current allowed into the module. The analysis discloses regions in the cells with δR s , δR sh , shunt diodes, passivation issues, e − +hole recombination centres, holes, cracks, breaks, grid-line interruptions, and further defects identified in synergy with other NDT techniques. The quantification of the impact of defects is further supported by I-V analysis and the first component of this methodology.
Additionally, this research contributes further to defect diagnosis through the model proposed for the temperature effect of the current mismatch between cells in a module and hotspot formation due to corrosion, supported by IR thermography. Furthermore, mathematical models for the quantification of the deviations δV oc and δV m are proposed within the methodology developed for the deviation analysis of the module electrical parameters.
The methodology demonstrated that the external and internal degradation factors and defects, depending on their strength and the environmental and operating conditions, create second-order defects, expanding in space and time and advancing on a cause-and-effect process like an avalanche.
Subsequently, the degradation rate is not a linear function of time and increases more quickly when families of defects are developed. This PV-diagnostics methodology using synergistic NDT tools provides reliable detection of defects and quantitative determination of their impact on the module electrical parameters and would be very useful for the development of a future online monitoring and diagnostics system.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.

Acknowledgments:
The authors express their appreciation to I. Kalintiris from the computer-science and network-technologies department at the University of Peloponnese, Patra branch, for his help in data collection and data management.

Conflicts of Interest:
The authors declare no conflict of interest.

Nomenclature
A c PV-cell area (m 2 ) T f : T b PV-module temperature in the front and back side, respectively (K) A cor I area in a cell with corrosion (m 2 ) T pv , T c PV-module and -cell temperature, respectively (K