Investigation of the Temperature Sensitivity of 20-Years Old Field-Aged Photovoltaic Panels Affected by Potential Induced Degradation

: One effect of moisture ingress on solar panels is potential induced degradation (PID). Solar panels affected by PID experience large leakage currents between the solar cells and the module’s frame, which leads to substantial power degradation. In the present work, the temperature coefﬁcients of 3 old PV panels affected by PID were investigated. In the electroluminescence images, solar cells nearer to the edge of the modules appear darker due to ohmic shunting. IR thermal images acquired under clear sky outdoor conditions show that the majority of the warmer cells (hotspots) were located closer to the edge of the modules. The difference in cell temperature ( ∆ T ) due to PID effect ranges from 7 ◦ C to 15 ◦ C for the 3 ﬁeld-aged modules. The average temperature coefﬁcient of efﬁciency ( β η m ) was found to be − 0.5%/ ◦ C. Also, it was observed that the temperature coefﬁcients of open circuit voltage ( β Voc = − 0.4%/ ◦ C), maximum power point voltage ( β Vmpp = − 0.5%/ ◦ C), and ﬁll factor ( β FF = − 0.2%/ ◦ C), were the underlying factors for the degradation in the P max of the old solar panels affected by PID. This accounted for an average 1.2%/year overall degradation in the efﬁciency of these modules. Most notably, it was discovered that the PV modules affected by PID show negative temperature coefﬁcients of maximum power point current ( β Jmpp ) due to large leakage currents. This observed negative β Jmpp we believe is characteristic of PV panels affected by PID.

According to Naumann et al. [10], high surface defect density on interdigitated back contact (IBC) solar cells results in decreased field effect passivation. Decreased field effect passivation leads to high surface recombination, and hence, causes PID of polarization/passivation (PID-p) type. However, PID-p is temporary and reversible [10,[17][18][19]. Investigations revealed that the transport of mobile ions, especially sodium (Na+) ions, within the PV module bulk is responsible for the PID of shunting (PID-s) type [2,15,20,21]. High conductivity of sodium decorated stacking faults across the solar cell emitter leads to shunting, hence, PID-s [2,20]. PID-s manifests itself in the degradation in the open circuit voltage, short circuit current, and fill factor [2,3]. Hence, PID-s type appears to be the key problem in the field [17].
There have been efforts to prevent PID at the cell and module manufacturing levels, installation, and during operation [2,5,22]. Current-voltage (I-V) characterization, electroluminescence (EL), and infrared (IR) thermography could be used to detect and monitor the onset of PID in PV plants under sunlight or in the dark with external bias conditions [2,21]. PID-s cells are identified as warmer cells in IR thermal images and darker cells in EL images [3,6,15]. According to Carolus et al. [14], Current-voltage (I-V) and external quantum efficiency (EQE) measurements could be used to differentiate PID-s from PID-p. Proposed methods for reversing the PID effect appears to be saddled with other limitations [8,22]. Indeed, the TS IEC 62804-1 standard exists to ensure PID reliability of commercial PV modules. However, the PID effect continues to be a challenge for the PV community [2,6,20,23,24].
In addition to power degradation, PID also induces mismatch losses due to nonuniform degradation [9,20,25,26]. Degraded cells that are affected by PID cause current reverse biasing, which leads to local overheating or joule heating [14,27]. This triggers hotspots, which influence the PV module operating temperature (T m ), hence, the temperature sensitivity [20,25,28]. According to Islam et al. [23], PID in polycrystalline solar panels can accelerate cell crack propagation and can lead to the degradation in the temperature coefficient of efficiency. In addition, Wang et al. [24] observed an increased temperature coefficient of maximum power (P max ) in PV modules affected by PID. Extensive research on the influence of the temperature sensitivity on PV modules main electrical parameters is available in literature [25,26,[28][29][30][31]. However, studies on the influence of PID on the temperature coefficients of PV modules are rare [20,25,26,28]. Moreover, only a few were done on field-aged PV modules [23,24]. Yet, we have not found any report on the influence of PID on the temperature coefficients of the maximum power point voltage (β Vmpp ) and current (β Jmpp ) of PV modules.
A procedure for detecting PID based on temperature coefficient profiling of PID affected field-aged multicrystalline silicon (mc-Si) PV modules is presented in this contribution. I-V characterization, EL, and IR thermal imaging were used for the investigation. It turned out that PV modules affected by PID could be detected by monitoring the temperature coefficient of maximum power point current (β Jmpp ). Section 2 presents the material and methods used for the investigation and the results and the insights from the investigation are presented in Section 3.

Materials and Methods
In the present work, field-aged NESTE NP100G12 multicrystalline silicon (mc-Si) PV modules affected by PID were investigated. The 3 solar panels (namely A, B, and C) were chosen from a batch of solar panels which were installed on a Renewable Energy Park in Dømmesmoen, Grimstad (58.3447 • N, 8.5949 • E), Norway in the year 2000. However, the PV modules on the Energy Park were decommissioned in 2011 and were kept securely for research purposes [32]. In an earlier report on the types of defects and faults modes of these old solar panels by the present authors, EL and IR thermal data of PV panel C was used to show that some of the old PV panels were affected by PID. The manufacture's data sheet and the measured electrical data on the 3 old PV panels (namely A, B, and C) is summarized in Table 1. The PV modules were made using anodized aluminum (Al-) frame, low iron tempered front glass, ethylene vinyl acetate (EVA) encapsulation, white multi-layered Tedlar ® /Polyester/ Tedlar ® (TPT) backsheet, and 2 weatherproof plastic casing junction boxes (accommodating a bypass diode each). Each PV module consists of (12 × 2) series connected solar cells and 3 substrings, refer to Figure 1. The solar cells feature a full area screen-printed Al-grid rear surface with dimensions of 100 × 100 mm 2 and a titania antireflective coating (ARC). tempered front glass, ethylene vinyl acetate (EVA) encapsulation, white multi-layered Tedlar ® /Polyester/Tedlar ® (TPT) backsheet, and 2 weatherproof plastic casing junction boxes (accommodating a bypass diode each). Each PV module consists of (12 × 2) series connected solar cells and 3 substrings, refer to Figure 1. The solar cells feature a full area screen-printed Al-grid rear surface with dimensions of 100 × 100 mm 2 and a titania antireflective coating (ARC).

I-V Measurements
The sampled old solar panels were each taken through electrical performance measurements using an HT ® Instruments I-V 500w I-V Curve Tracer. This was done by following the IEC 60904-1 standard. By these measurements, information on the maximum power (Pmax), open circuit voltage (Voc), maximum power point voltage (Vmpp) short circuit current (Isc), maximum power point current (Impp), fill factor (FF), in-plane irradiance (GI), and module temperature characteristics of each panel at Standard Tes Conditions (STC) was acquired. STC indicates solar cell temperature at 25 °C, GI at 1000 W/m 2 and air mass 1.5 (AM1. 5) spectrum for commercial solar PV panels. The entire experimental procedure was carried out under clear sky in-plane irradiance conditions (960-1060 W/m 2 ). The I-V tracer converted all measurements to STC automatically to minimize errors associated with data acquisition.

Temperature Coefficient Profiling
On a clear sky sunny day in the summer, the PV modules were taken out to the outdoor measuring rack in turns from a storeroom where the modules were kept. The PV module and the reference device were shaded using a cardboard. Measurement was initiated immediately after the shade was removed. The measurements on the 3 field-aged PV modules were done on the same day between 12.30 and 14.30 h and at wind speed less than 2 ms −1 . According to IEC 60891-4 standard, the temperature range of the data values should be at least 30 °C. However, this seems challenging in practical field measurements especially for the investigation site.
A graph of electrical parameters (Pmax, Voc, Isc, FF, ηm, Vmpp, Impp) versus PV module's temperature (Tm) was plotted and a least-squares-fit graph through each data set was acquired to get the relative temperature coefficients. The regression equation for such relation can be represented as y = mx + c, where m and c are the slope (temperature coefficient) and the intercept (the value of the electrical parameter at 0 °C), respectively [33]. The relative temperature coefficient of parameter X (βx) in%/°C was calculated by dividing the slope of parameter X by the intercept of parameter X. That is, βx = m/c.

I-V Measurements
The sampled old solar panels were each taken through electrical performance measurements using an HT ® Instruments I-V 500 w I-V Curve Tracer. This was done by following the IEC 60904-1 standard. By these measurements, information on the maximum power (P max ), open circuit voltage (V oc ), maximum power point voltage (V mpp ), short circuit current (I sc ), maximum power point current (I mpp ), fill factor (FF), in-plane irradiance (G I ), and module temperature characteristics of each panel at Standard Test Conditions (STC) was acquired. STC indicates solar cell temperature at 25 • C, G I at 1000 W/m 2 and air mass 1.5 (AM1. 5) spectrum for commercial solar PV panels. The entire experimental procedure was carried out under clear sky in-plane irradiance conditions (960-1060 W/m 2 ). The I-V tracer converted all measurements to STC automatically to minimize errors associated with data acquisition.

Temperature Coefficient Profiling
On a clear sky sunny day in the summer, the PV modules were taken out to the outdoor measuring rack in turns from a storeroom where the modules were kept. The PV module and the reference device were shaded using a cardboard. Measurement was initiated immediately after the shade was removed. The measurements on the 3 field-aged PV modules were done on the same day between 12.30 and 14.30 h and at wind speed less than 2 ms −1 . According to IEC 60891-4 standard, the temperature range of the data values should be at least 30 • C. However, this seems challenging in practical field measurements, especially for the investigation site.
A graph of electrical parameters (P max , V oc , I sc , FF, η m , V mpp , I mpp ) versus PV module's temperature (T m ) was plotted and a least-squares-fit graph through each data set was acquired to get the relative temperature coefficients. The regression equation for such relation can be represented as y = mx + c, where m and c are the slope (temperature coefficient) and the intercept (the value of the electrical parameter at 0 • C), respectively [33]. The relative temperature coefficient of parameter X (β x ) in%/ • C was calculated by dividing the slope of parameter X by the intercept of parameter X. That is, β x = m/c.

Electroluminescence (EL) Tomography
EL tomography is interesting especially for characterizing old PV panels affected by PID. The 3 sampled PV panels were taken through the EL characterization in a dark room using the BrightSpot EL Test Kit, see Figure 2. The kit comprises of a 24 megapixels modified DSLR (digital single-lens reflex) Nikon D5600 camera, DC power supply set, and computer with data acquisition and image processing software. The image acquisition and processing were done according to the IEC 60904-13 standard and the IEA procedure [3,15]. The EL characterization of the PV modules was done under 0.1I sc and at I sc current density conditions.

Electroluminescence (EL) Tomography
EL tomography is interesting especially for characterizing old PV panels affected by PID. The 3 sampled PV panels were taken through the EL characterization in a dark room using the BrightSpot EL Test Kit, see Figure 2. The kit comprises of a 24 megapixels modified DSLR (digital single-lens reflex) Nikon D5600 camera, DC power supply set, and computer with data acquisition and image processing software. The image acquisition and processing were done according to the IEC 60904-13 standard and the IEA procedure [3,15]. The EL characterization of the PV modules was done under 0.1Isc and at Isc current density conditions.

Figure 2.
Experimental setup of the EL imaging system. The system runs on a DC power supply.

Infrared (IR) Thermal Imaging
The sampled solar panels were also taken through IR thermography using the Fluke Ti400 Infrared Camera (λ ≈ 650 nm) as per the IEA recommended procedure [15] and the IEC 62446-3 standard. Figure 3 shows the outdoor experimental setup. Measurements were done under clear sky field conditions. The IR thermal images were acquired after soaking the PV modules in the sun for at least 15 min, as prescribed by the IEC 62446-3 standard.

Infrared (IR) Thermal Imaging
The sampled solar panels were also taken through IR thermography using the Fluke Ti400 Infrared Camera (λ ≈ 650 nm) as per the IEA recommended procedure [15] and the IEC 62446-3 standard. Figure 3 shows the outdoor experimental setup. Measurements were done under clear sky field conditions. The IR thermal images were acquired after soaking the PV modules in the sun for at least 15 min, as prescribed by the IEC 62446-3 standard.  Figure 4 illustrates the I-V characteristics of the field-aged PV Modules A, B, and C. The I-V curve for the manufacturer's data sheet in 2000 illustrates the I-V characteristics of the panels when they were new, i.e., when they were not affected by PID. However, in 2021, when the solar panels were affected by PID, the 3 panels show similar degradation trend in electrical characteristics. There was ca. 10% degradation in both Isc and Voc and ca. 24% degradation in Pmax over the 20 years. That is, annual degradation of ca. 0.5% in Isc and Voc and ca. 1.2% in Pmax, which agrees with observation elsewhere [34]. This resulted in the decrease in fill factor (F) of ca. 0.3%/year and a drop in efficiency of ca. 1.2%/year, see Table 1. A drop in the Pmax, Isc, Voc, and FF was also observed by other researchers [3,14,15,29].  Figure 4 illustrates the I-V characteristics of the field-aged PV Modules A, B, and C. The I-V curve for the manufacturer's data sheet in 2000 illustrates the I-V characteristics of the panels when they were new, i.e., when they were not affected by PID. However, in 2021, when the solar panels were affected by PID, the 3 panels show similar degradation trend in electrical characteristics. There was ca. 10% degradation in both I sc and V oc and ca. 24% degradation in P max over the 20 years. That is, annual degradation of ca. 0.5% in I sc and V oc and ca. 1.2% in P max , which agrees with observation elsewhere [34]. This resulted in the decrease in fill factor (F) of ca. 0.3%/year and a drop in efficiency of ca. 1.2%/year, see Table 1. A drop in the P max , I sc , V oc , and FF was also observed by other researchers [3,14,15,29].

I-V Characteristics of the PV Panels
It was reported that the effect of PID is more severe under lower irradiation conditions as compared to STC [3,16]. This means that PV modules deployed in the cold regions are more susceptible to the PID effect than those deployed in climates with high regular irradiance conditions. Low irradiance and shading conditions predispose PV modules to mismatch losses, hence, hotspots [33]. These hotspots can induce the onset of PID [16,20,35]. For the 3 field-aged PV modules, the average degradation in the V mpp and I mpp were 0.7% and 0.6% per year, respectively (refer to Table 1). Figure 5 illustrates the relative change (∆) in the electrical parameters of the old solar panels affected by PID over the 20 years. The relative change (∆) in the electrical parameters of the PID affected old solar panels was computed as the difference between the datasheet values (2000) and the values measured in the year 2021, a recommended procedure by Köntges et al. [17].
The position of the box indicates the percentage degradation, and the dots show the outliers. The degree of deviation of the electrical parameter from the mean value is indicated by the length of the box. The degradation in the electrical parameters of the 3 old solar panels follow a similar trend. P max shows more than 20% degradation over the 20 years, refer to Table 1. It appears from Figure 5 that the underlying cause of the P max degradation is the degradation in all electrical parameters, especially degradation in V oc It was reported that the effect of PID is more severe under lower irradiation conditions as compared to STC [3,16]. This means that PV modules deployed in the cold regions are more susceptible to the PID effect than those deployed in climates with high regular irradiance conditions. Low irradiance and shading conditions predispose PV modules to mismatch losses, hence, hotspots [33]. These hotspots can induce the onset of PID [16,20,35]. For the 3 field-aged PV modules, the average degradation in the Vmpp and Impp were 0.7% and 0.6% per year, respectively (refer to Table 1). Figure 5 illustrates the relative change (∆) in the electrical parameters of the old solar panels affected by PID over the 20 years. The relative change (∆) in the electrical parameters of the PID affected old solar panels was computed as the difference between the datasheet values (2000) and the values measured in the year 2021, a recommended procedure by Köntges et al. [17]. It is known that P max is directly related to the maximum power point voltage (V mpp ) and the maximum power point current (I mpp ) by the following relation: However, fill factor (FF) of a PV module could also be written as So, the maximum power output of a PV panel is related to the fill factor as The PV module efficiency (η m ) is related to the P max , module's area (A m ), and the input power (P in ) as That means, any drop or degradation in V oc , I sc , FF, V mpp , and I mpp affects the P max or η m of the PV module directly, refer to Figure 4. Since the P in for η m calculations is assumed as 1 kWm −2 , P max ≈ η m /A m . A m is the product of the solar cell's area and the number of solar cells in the module. From Table 2, the regression plots (which indicates the degree of correlation) for P max versus V oc and V mpp gave R 2 > 97. On the other hand, the R 2 < 0.6 for I sc and I mpp . Resistance losses due to PID is the reason for the higher R 2 values for the fill factor (FF) of the modules, especially for solar panels A and C. The I-V curves of the modules in Figure 4 support this observation. Solar panel C appears to be the least affected by PID, hence, shows the weakest R 2 in both ∆I sc and ∆I mpp , refer to Table 2. This is because PID alters the current flow characteristics of the PV module [5,8,13]. When PID is caused by negative bias, it can induce optical degradation [5]. This is why most of these old solar panels were found to be affected by optical degradation as well.   Degradation in P max , V oc , V mpp , and FF due to PID was also reported by other authors [3,14,16,29]. They believed that the loss in P max due to PID could be up to 100% in severe cases [16]. The I-V characteristics of the old solar panels suggest that they are suffering from PID, as reported in other investigations [2,3,5,8,13,14,16,20,21,24,35]. Figure 6 shows the EL analyses of the solar panels. The EL images were acquired under I sc (Figure 6a-c) and 0.1I sc (Figure 6d-f) forward bias conditions, respectively. The red marked out areas on the images in Figure 6 show some of the areas affected by PID in each PV module. In Figure 6a-c, apart from some darker spots, these images give little or no information on the areas affected by PID. This is because EL under I sc conditions highlights metal contact or shunt issues [3,15]. In fact, contact issues such as cracks and corrosion are highlighted as darker spots in Figure 6a-c. Hence, EL under I sc conditions are less suitable for detecting PID in PV modules, as observed in other studies [3,13,15].  On the other hand, under 0.1Isc conditions, the effect of PID in the field-aged PV modules are well highlighted, see Figure 6d-f. The effect of PID manifests itself in the degradation of the solar cells located closer to the perimeter of the solar panel [8,22]. This accelerated degradation of the cells nearer to the frame of the PV module is due to high leakage currents associated with the PID effect [2,7,24]. Degraded solar cells appear as darker cells in the EL analyses due to strong ohmic shunting of the cell with the panel's  On the other hand, under 0.1I sc conditions, the effect of PID in the field-aged PV modules are well highlighted, see Figure 6d-f. The effect of PID manifests itself in the degradation of the solar cells located closer to the perimeter of the solar panel [8,22]. This accelerated degradation of the cells nearer to the frame of the PV module is due to high leakage currents associated with the PID effect [2,7,24]. Degraded solar cells appear as darker cells in the EL analyses due to strong ohmic shunting of the cell with the panel's Al-frame [24,27].

Electroluminescence Characteristics
The PID affected areas in the solar panels are marked out in red. The trend in Figure 6 is that majority of the darker cells are located close to the edge of the old solar panels. The degradation pattern in Figure 6 suggests that these PV modules are affected by PID, as reported by other authors [3,9,14,15,35].

IR Thermal Image Characteristics
In IR thermal images, solar cells affected by PID appear as warmer cells or hotspots [16,36]. Figure 7 shows the IR thermograms of the 3 old solar panels (A, B, and C). In Figure 7, the areas marked out in white corresponds to the areas marked out in Figure 6. They show some of the areas in the PV modules that have been affected by PID. Figure 7 shows that majority of the warmer cells are located nearer to the perimeter of the old solar panels, as observed elsewhere [3,15,20,35]. It could be seen that the locations of the warmer cells in the IR thermal images ( Figure  7) correspond with the locations of the darker cells in the EL images, refer to Figure 6. Another observation from Figure 7 is that the cells which are closer to the negative terminal (left) of the field-aged PV modules are warmer than the cells which are located nearer to the positive terminal (right), especially those cells that are closer to the Al-frame. This was also reported by other researchers [9,15,35]. This is due to the direction of current flow in a PV module under illumination. Under in-plane radiation, current move by diffusion from the negative to the positive terminal. In PID affected areas, there is high resistance to current flow culminating into high module temperature localized to these areas [20,26,28], as observed in Figure 7. This is opposite to the direction of current flow when the IR thermal imaging is done under forward bias (drift) conditions, as it is done in EL imaging. This also explains why the defective solar cells are clearly seen at the areas closer to the negative terminal in the field-aged PV modules. Also, high negative leakage current accelerates PID degradation [5,9,20,24,35]. Table 3 shows the extracted solar cells' temperatures of the old solar panels from the IR thermograms. The difference in the solar cells' temperature (∆T) extracted from the IR thermograms of each solar panel was calculated according to Equation (4): where TcH is the solar cell with the highest temperature and TcL is the solar cell with the lowest temperature. ∆T due to PID for the 3 modules which have been affected by PID ranges from 7 °C to 15 °C. Our results for these old panels agrees with the ∆T values reported in literature [15]. The reported ∆T values for solar panels affected by PID is in the range of ca. 7.5-30 °C depending on the severity of the PID effect [3,15,16]. Table 3. Difference in temperature (∆T) of the solar cells with the highest temperature (TcH) and It could be seen that the locations of the warmer cells in the IR thermal images (Figure 7) correspond with the locations of the darker cells in the EL images, refer to Figure 6. Another observation from Figure 7 is that the cells which are closer to the negative terminal (left) of the field-aged PV modules are warmer than the cells which are located nearer to the positive terminal (right), especially those cells that are closer to the Al-frame. This was also reported by other researchers [9,15,35]. This is due to the direction of current flow in a PV module under illumination. Under in-plane radiation, current move by diffusion from the negative to the positive terminal. In PID affected areas, there is high resistance to current flow culminating into high module temperature localized to these areas [20,26,28], as observed in Figure 7. This is opposite to the direction of current flow when the IR thermal imaging is done under forward bias (drift) conditions, as it is done in EL imaging. This also explains why the defective solar cells are clearly seen at the areas closer to the negative terminal in the field-aged PV modules. Also, high negative leakage current accelerates PID degradation [5,9,20,24,35]. Table 3 shows the extracted solar cells' temperatures of the old solar panels from the IR thermograms. The difference in the solar cells' temperature (∆T) extracted from the IR thermograms of each solar panel was calculated according to Equation (4): where T cH is the solar cell with the highest temperature and T cL is the solar cell with the lowest temperature. ∆T due to PID for the 3 modules which have been affected by PID ranges from 7 • C to 15 • C. Our results for these old panels agrees with the ∆T values reported in literature [15]. The reported ∆T values for solar panels affected by PID is in the range of ca. 7.5-30 • C depending on the severity of the PID effect [3,15,16]. The severity of the PID effect depends on the module materials-antireflection coating and encapsulation [6,21], module configuration [3,11], climatic conditions such as temperature and humidity [4,24,26], and voltage stress [5,9]. Figure 8 illustrates the characteristics of the relative temperature coefficients of P max (β Pmax ), V oc (β Voc ), I sc (β Jsc ), FF (β FF ), V mpp (β Vmpp ), and I mpp (β Jmpp ) of solar panels A, B, and C. Figure 8 compares the variation of each electrical parameter from the average value measured in the year 2021. Degradation in electrical parameters stems from the degradation in the relative temperature coefficients of PV modules [25,26,29]. That is, PID increases recombination in the emitter region of the solar cell [10,11,[17][18][19], and this leads to a drop in the V oc [25]. A drop in the V oc influence the temperature characteristics of the solar panel [30,37]. A change in the V oc accounts for more than 80% of the temperature sensitivity of the PV modules [25]. From Figure 8, the main root causes for the observed degradation in P max became clearer, unlike in Figure 5. That is, the β Voc and β Vmpp of the PV modules are the main underlying causes of the P max degradation. Figure 8 also suggests that degradation in β FF is significantly responsible for the degradation in P max . This supports the earlier observation in Figure 5 that the solar panels affected by PID experience large resistance losses. Degradation in β Voc and β FF due to PID effects were reported earlier [20,26,28]. Figure 8 also shows clear outliers for β Pmax , β Voc , β Vmpp , and β FF . It could be seen that the majority of these outliers are correlated to higher temperature coefficient values which results from higher T m [38]. This suggests that when T m increases, the reliability of PV modules affected by PID decreases, as observed elsewhere [24,39].

Temperature Coefficient Characteristics
Conceptually, the effect of T m on P max could be derived from Equation (3) because PV module parameters (V oc , I sc , FF) depend strongly on T m [30,32,40]. Hence, could be represented as Interestingly, each of these parameters in Equation (5) depends on different loss mechanisms in the PV module [25,35]. These loss mechanisms mainly depend on the effects of different defects and fault mechanisms on the charge carrier generation-recombination balances at maximum power point (MPP) [35,41]. Therefore, Equations (1) and (5) could be represented in terms of V mpp and I mpp as The V oc is the charge carrier generation-recombination characteristic of a solar panel. So, the temperature sensitivity of a solar panel improves when the V oc increases [40,42]. Moreover, the β Voc of a PV module accounts for 80-90% of the β Pmax of the PV module [25]. For that matter, and inferring from Equation (6), β Vmpp could be assumed to have the greatest impact on the degradation in β Pmax , and hence, on P max degradation. The corre-lation of values of β Voc and β Vmpp to β Pmax degradation is shown in Figure 9. In Figure 9, the regression plots show high correlation of R 2 > 90 and R 2 > 88 for β Voc and β Vmpp , respectively. Indeed, Figures 8 and 9 suggest that the root causes of degradation in the PV modules affected by PID are more accurately profiled using their temperature coefficients. They suggest that the β Voc and β Vmpp are the underlying factors for the degradation in the efficiency of the solar panels.
Energies 2022, 15, 3865 11 of 18 measured in the year 2021. Degradation in electrical parameters stems from the degradation in the relative temperature coefficients of PV modules [25,26,29]. That is, PID increases recombination in the emitter region of the solar cell [10,11,[17][18][19], and this leads to a drop in the Voc [25]. A drop in the Voc influence the temperature characteristics of the solar panel [30,37]. A change in the Voc accounts for more than 80% of the temperature sensitivity of the PV modules [25]. From Figure 8, the main root causes for the observed degradation in Pmax became clearer, unlike in Figure 5. That is, the βVoc and βVmpp of the PV modules are the main underlying causes of the Pmax degradation. In Figure 9a,d, the slopes of the regression plots for PV Module A are 0.14 and 0.19 for βVoc and βVmpp, respectively. However, the average of the slope values of βVoc and βVmpp is ca. 0.17. Interestingly, from Figure 9, the slopes of PV Modules B and C for both βVoc and βVmpp regression plots are ca. 0.17. Also, the slopes of the regression plots for βVmpp are closer to the average 0.17 value. Hence, we can predict the behaviour of βPmax better with the slopes of βVmpp for the PV modules affected by PID. This suggests that a unit change in βPmax is accounted for by 0.17 change in either βVoc or βVmpp for each PV module affected by PID. The values of the slopes from the regression plots of βPmax versus βVoc and βVmpp can be used to monitor PID severity in solar panels. On that basis, Figure 9 suggest that the effect of PID on PV Module A is the severest. Another observation from Figure 9d-f is that, when βPmax is zero, then by extrapolation, βVmpp will be ca. 0.4%/°C, 0.6%/°C, and 0.6%/°C for PV Module A, B, and C, respectively. These values are very close to the βVmpp values for the 3 field-aged PV modules in Table 4. In Figure 9a,d, the slopes of the regression plots for PV Module A are 0.14 and 0.19 for β Voc and β Vmpp , respectively. However, the average of the slope values of β Voc and β Vmpp is ca. 0.17. Interestingly, from Figure 9, the slopes of PV Modules B and C for both β Voc and β Vmpp regression plots are ca. 0.17. Also, the slopes of the regression plots for β Vmpp are closer to the average 0.17 value. Hence, we can predict the behaviour of β Pmax better with the slopes of β Vmpp for the PV modules affected by PID. This suggests that a unit change in β Pmax is accounted for by 0.17 change in either β Voc or β Vmpp for each PV module affected by PID. The values of the slopes from the regression plots of β Pmax versus β Voc and β Vmpp can be used to monitor PID severity in solar panels. On that basis, Figure 9 suggest that the effect of PID on PV Module A is the severest. Another observation from Figure 9d-f is that, when β Pmax is zero, then by extrapolation, β Vmpp will be ca. 0.4%/ • C, 0.6%/ • C, and 0.6%/ • C for PV Module A, B, and C, respectively. These values are very close to the β Vmpp values for the 3 field-aged PV modules in Table 4.  Figure 10 shows the profiles of the temperature coefficients of efficiency, η m (β ηm ) of the 3 solar panels. The average of β ηm has been found to be ca. −0.5%/ • C for the 3 fieldaged PV modules. In literature, the β ηm for mc-Si PV modules is 0.4%/ • C [25,26,[28][29][30]. PV modules in good conditions are expected to be more efficient when PV module operating temperature (T m ) drops below 25 • C [30,32]. However, by extrapolation when T m is equal to zero, η m < 13%, refer to Figure 10. This is characteristic of degraded PV modules which are suffering from resistive losses [20,26,40].
Energies 2022, 15,3865 14 of 18 Figure 10 shows the profiles of the temperature coefficients of efficiency, ηm (βηm) of the 3 solar panels. The average of βηm has been found to be ca. −0.5%/°C for the 3 fieldaged PV modules. In literature, the βηm for mc-Si PV modules is 0.4%/°C [25,26,[28][29][30]. PV modules in good conditions are expected to be more efficient when PV module operating temperature (Tm) drops below 25 °C [30,32]. However, by extrapolation when Tm is equal to zero, ηm < 13%, refer to Figure 10. This is characteristic of degraded PV modules which are suffering from resistive losses [20,26,40].   The average temperature coefficients of the 3 solar panels are shown in Table 4. The observed values for β Voc and β Vmpp agree with the values reported by King et al. [30] for conventional mc-Si PV modules. However, the β Voc values are far less than the −1.2%/ • C reported by Cheng et al. [38] and the −0.7%/ • C reported by Wang et al. [24] for PV modules affected by PID. On the other hand, the β Jsc values are relatively lower for these PV modules that have been affected by PID than observed elsewhere [24,38]. This suggests that in solar panels affected by PID, the contribution from thermally generated electrons towards the overall current density is less.
In addition, the β FF values for the 3 field-aged PV modules are lower than the −0.4%/ • C reported for β FF by Cheng et al. [38] for solar panels affected by PID. The fact that the modules studied by Cheng et al. [38] were aged artificially whiles our modules were field aged should not be ignored. Comparison of lab and field results are to be done with caution due to factors of uncertainty [43,44]. Our values are also in a good agreement with the −0.2%/ • C reported for β FF by Wang et al. [24] for solar panels affected by PID.
Interestingly, the β Jmpp of all the 3 solar panels show negative values. It is believed that the negative β Jmpp values observed for the 3 old solar panels is due to the large leakage current experienced by PV modules affected by PID. Indeed, earlier investigation on the temperature profiles of solar panels affected by optical degradation indicated that negative β Jmpp values are likely when the electrical circuit of the module is affected. However, in such cases, the β Jmpp values are relatively higher and the β Jsc values are by far higher as well. In that investigation, one of the modules affected by optical degradation showed a β Jmpp of −0.01%/ • C and an average β Jsc for the 3 modules was 0.05%/ • C. Moreover, a majority of the darker cells in the EL and warmer cells in IR thermal images were closer to the edge of the PV module affected by optical degradation. This suggests that the module in question is affected by at least optical degradation and PID. It is known that PID can lead to optical degradation and vice versa [5].
Furthermore, an earlier investigation on some of the solar panels under partial shading conditions, negative β Jmpp values were observed for the modules investigated. However, under partial shading conditions, beside the peculiar I-V characteristics, the degradation in the P max strongly depends mainly on the degradation in the β Jmpp and β FF . Moreover, under partial shading conditions, the effect on β ηm becomes far higher, with β ηm ≥ −0.6%/ • C [33]. It therefore suggests that an effective, quick, and reliable method of detecting PID in solar panels is to monitor the temperature coefficients, and specifically, the β Jmpp of PV panels.

Conclusions
The temperature coefficients of 20 years old field-aged mc-Si PV modules which were affected by PID were investigated. Characterization utilized I-V characterization, EL imaging, IR thermal imaging, and temperature coefficient profiling. The results showed that the field-aged PV modules were indeed affected by PID. EL images acquired under 0.1I sc indoor conditions show degraded darker cells located closer to the perimeter of the PV modules. The weak signal of the cells closer to the edge of the modules is due to strong ohmic shunting of the solar cells with the PV module's Al-frame. In the IR thermal images acquired under clear sky conditions, majority of the warmer cells (hotspots) were seen closer to the perimeter of the modules. In addition, areas closer to the negative terminals were also observed to be warmer than areas closer to the positive terminals. Our results show that the module ∆T due to PID ranges from 7 • C to 15 • C for the 3 old solar panels.
The modules show an average degradation of 0.5%/year in both I sc and V oc , 1.2%/year in P max , and 0.3%/year in fill factor. For the 3 field-aged PV panels, the average degradation in the V mpp and I mpp were 0.7% and 0.6% per year, respectively. It turns out that the key underlying causes for PID in the field-aged PV modules and the subsequent degradation is degradation in V oc , V mpp , and FF. The average temperature coefficients of β ηm , β Voc , β Jsc , β FF , β Jmpp , and β Vmpp were found to be −0.5%/ • C, −0.4%/ • C, 0.02%/ • C, −0.2%/ • C, −0.06%/ • C, and −0.5%/ • C, respectively. This shows that all the temperature coefficients of the field-aged modules have undergone some form of degradation. However, it was observed that the β Voc , β Vmpp , and β FF were the primary factors for the degradation in the P max for the old solar PV panels affected by PID. This translated into an average 1.2%/year overall degradation in the efficiency of these modules.
Most interestingly, it was observed that solar panels affected by PID show negative β Jmpp due to large leakage currents. Hence, PID could be detected decisively by monitoring the β Jmpp of solar PV panels. These findings have the potential of enhancing the existing knowledge on defects and faults diagnostics in PV arrays.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author. The data are not publicly available at this time as the data also forms part of an ongoing study.