The long term performance of PV systems in outdoor environments is usually quantified performance loss rate (PLR) (Jordan et al., 2016). The units of this metric are % per annum (%/a) or loss in power output per year of operation. The sign of this metric aligns with the direction of power change. A typical PLR calculation requires data filtering, model selection, outlier analysis, etc.

PVplr (Curran et al., 2020a; Curran et al., 2020b) is an R package (R Core Team, 2020) that allowed for the calculation of PLR with several different methods and parameters, as opposed to one universal method. This package makes it easy to test different filtering criteria and models to view the impact on a final PLR calculation. Comparisons between PLR methods showed that universal temperature corrections (the XbX + UTC model in PVplr) showed the most consistency and least uncertainty between results because it did not extrapolate temperature between seasonal periods, so this is the method that is used for all PLR calculations in this study.

Another benefit of the PVplr package is the unique ability to calculate non-linear PLR results using piecewise linear models. The piecewise linear model splits a model into linear components with different slopes which are bound by changepoints. While the number of changepoints must be supplied to the model, their values are determined automatically by the fitting algorithm and define where the slope changes occur within the model. This can be used to capture non-linear trends in PV data while still providing the interpretability of linear PLR results, which are the most common. Non-linear PLR is becoming more commonplace with the transition to PERC, given the greater susceptibility to LID and LeTID, which generally create a higher value of loss in a short period at the beginning of operation. Some module warranties have two rated PLR values; one for the first year and a different one for the following years.

The R package name ddiv (Huang et al., 2018a) stands for data driven I-V. The raw data of an I-V curve are the current and voltage values measured during the sweep. The number of measurements, or data points collected per I-V curve, depends on the device and setting used to take the curve, but higher resolution is generally better as it makes it easier to define the I-V trend. Typical numbers of data points include several hundreds to thousands, but can be as low as 40. The raw I-V curves themselves provide little quantitative information, but the parameters that can be extracted from them are desired for characterization. While some values, like the open-circuit voltage (V _OC ), short-circuit current (I _SC ), and maximum power can be pulled directly from the data given a high enough resolution, others require more complex analysis to extract. Series resistances (R _s ) and shunt resistances (R _sh ) require slope calculations at the start and end of the curves extrapolated down to, or near, the end points of the curve. Also, in cases with low resolution I-V curves, it becomes more likely that the actual maximum power will fall further between two measurements, leading to a lower than actual max power.

With indoor methods of I-V, tracing the machine software will typically provide feature results from measured curves, but this can be inconsistent between devices with different software. Additionally, outdoor I-V measurements are unlikely to have their features auto-reported at all. To account for problems like this, the ddiv package was developed to automatically extract I-V feature results from curves. The ddiv package uses spline fitting and moving regression to interpolate higher resolution curves and extract slopes from key points. It provides a consistent and automated way to extract results from curves from any source. It is particularly useful in outdoor I-V timeseries, having been demonstrated on datasets consisting of millions of I-V curves. The Suns-V _OC package uses this package as a dependency in its extraction of I-V features as well.

The Suns-V _OC R package (Wang et al., 2020a) takes the concept of indoor Suns-V _OC measurements (Sinton and Cuevas, 2000) and applies it to outdoor I-V datastreams. Similar to power timeseries measurements, I-V timeseries collect I-V curves at set intervals, usually on the order of every 10 min, of modules under outdoor exposure. Being outdoors, there is much less control over the environment, with I-V curves being taken with significant variation in irradiance and temperature. Despite this variance in weather conditions, they can be corrected with enough data. I-V curves taken in a controlled indoor setting will typically have well controlled irradiance and temperature to ensure consistency between subsequent measurements, making comparisons easier and requiring less data overall.

V _OC measurements are taken with every I-V curve and can be corrected for temperature, leaving a series of V _OC measurements dependent on the outdoor irradiance when the curve was measured. The pseudo I-V curves can be built from these temperature corrected V _OC measurements taken over a range of outdoor irradiance. Once the ideal pseudo I-V curve has been built, the other I-V curves can be corrected to ideal conditions based on temperature and irradiance and compared to the ideal. The differences between the measured and ideal I-V curves provide information about mechanistic loss factors, just as with indoor Suns-V _OC characterization. By comparing the idealized and real curves, one can quantify specific loss parameters and directly observe the wattage lost for each one. The standard loss parameters quantified by this procedure are the uniform current, current mismatch, series resistance, and recombination losses. A visual of these loss parameters is given in Figure 2.

The individual mechanisms are described as follows:

• Uniform current loss—power change due to the I _SC difference from the ideal curve

The R package “netSEM v0.5.0” (Huang et al., 2018b) conducts a network statistical analysis (network structural equation modeling) on a dataframe of coincident observations of multiple continuous variables (Bruckman et al., 2013; French et al., 2015). This analysis uses Markvonian Principal and builds a pathway model by exploring a pool of domain knowledge guided by candidate statistical causal relationships between each of the variable pairs, and selecting the “best fit” on the basis of the goodness-of-fit statistic, such as the adjusted R-squared value, which measures how successful the fit is in explaining the variation of the data. The netSEM methodology is motivated by the analysis of systems that are experiencing degradation of some performance characteristic (or response) under exposure to particular stressors that are considered exogenous variables (or predictors). In addition to the direct relationship between the exogenous variables and the endogenous variable, netSEM investigates potential connections between them through other covariates. The resulting relationship diagram can be used to generate insight into the pathways of the system under observation. These pathways can be good candidates for improving the performance characteristics by identifying sequences of strong relationships that match prior domain knowledge well.

In this study, the endogenous variable is year dy, while the exogenous variables are uniform current loss uni_I, current mismatch loss I_mis, series resistance loss rs, recombination loss rec, and maximum power loss P _mp . Starting with the main endogenous variable to the last exogenous variable through the intermediate variables which are considered as exogenous variables, the nonrecursive relationships usually occur. The package outputs a flow chart style diagram, detailing the relevant characteristics of the uncovered relationships between variables. The pathway threshold cut-offs are defined by the Adj-R ² values of 0.1, 0.4, and 0.7. Pathways with Adj-R ² values below 0.1 are considered to have no correlation and are not connected by a line, while pathways with Adj-R ² values above 0.7 are considered to have strong correlation and are connected by a thick line.

The variables used in the < S t r e s s o r | R e s p o n s e > ( < S | R > ) are time and max power. For outdoor systems, this is best quantified as a performance loss rate (PLR), which gives the percent power loss per year of operation. It is analogous to degradation rates used to quantify PV performance, giving a directly comparable metric of performance between module types. PLR values are determined from the relationship between power and time of a system by using the PVplr R package. We are able to capture piecewise linear PLR values as well, making them an ideal use case for < S | R > modeling. For clarity, PLR values that are referred to as “high” are further from zero than PLR values described as “low” in relation to the amount of power loss observed between them. For example, a PLR of −0.7%/a is referred to as higher than a PLR value of −0.3%/a, as the first value is indicative of higher power loss.

The linear and piecewise linear < S | R > models are shown below in Figure 3 for each module type. The measurements have been normalized to their initial values to prevent bias from different power ratings. There is a clear changepoint trend in the Al-BSF and half-cell PERC modules, with a high initial loss followed by a more stable period. The full-cell PERC modules display a more linear trend, with the linear and piecewise linear models being more similar to each other. There are a number of highly influential outliers in some of the modules, however, which will bias the models and the location of the changepoint.

One of the steps (step 4 for the half-cell PERC and Al-BSF modules, and step 5 for the full-cell PERC modules) showed abnormally low data. After consulting with the operators, it was found that the modules were not properly cleaned before these exposures, resulting in a large decrease in I _SC during measurement. As this change was not due to degradation within the modules and they recovered by the next step, these data were removed.

For both the half-cell PERC and Al-BSF modules, there is a sharp drop in power between the first and second measurements. This drop is captured by the piecewise linear models, which shows an initial loss of −1.70% for the Al-BSF modules and −3.45% for the half-cell PERC modules. After the initial loss period, the modules stabilize and power loss decreases.

It can be observed in Figure 3 that a number of outliers appear at a lower power than the others with the Al-BSF full-cell and particularly the full-cell PERC modules. At the final step, the PERC full-cell modules vary between 99% and 94% of initial power. Comparing the I-V curves of an example outlier (Figure 4) shows that the loss in power is primarily due to a decrease in the fill factor of the module, which suggests that this is a legitimate change in the performance of the module and not a measurement error. As the outliers appear to be legitimate losses, we do not want to remove them from analysis, and instead incorporate them into the uncertainty of our results.

This data trend can be directly used to evaluate the PLR for each of the module groups. For the first calculation, the data are grouped together for each module type and a single model is built for each group. These are the models shown in Figure 3. As some of the data show non-linear trends, non-linear PLR is evaluated using a single changepoint model through the PVplr package (Curran A. et al., 2020). PLR results for each segment are listed in Table 2, along with the Adj-R ², changepoint, and confidence interval for each model.

The Al-BSF modules showed a fitted PLR value of −3.40%/a for the first segment and −0.57%/a for the second, matching the result observed in the piecewise model fit with a trend of a high initial loss then followed by a stable period. The other module with a similar trend, PERC half-cell, showed a similar trend with higher initial PLR of −6.09%/a followed by −0.27%/a after the changepoint. The PERC full-cell modules did not show as strong a changepoint trend as the other modules, seen in both the lower adj-R ² and the similar PLR values for each segment. The PLR values do follow a trend of the first being higher than the second, however, the confidence intervals overlap, so a statistically significant difference between the two PLR values is not established.

The models of the grouped modules are potentially biased by the outliers observed after 3 years of exposure. To address the outliers’ influence on the models, we fit our < S | R > models again to the individual models and compared the results, instead of modeling them all together. Figure 5 shows the distribution of the piecewise linear PLR values for both the first and second segment. There are only two segments, as these are single changepoint models. The original calculations from modeling all the modules together are also shown by the diamonds to the right of each boxplot, with their 83.4% confidence intervals. Some of the confidence intervals could not be shown for the first segment, as there was only one data point available in that range if the changepoint occurs early on in the timeseries. It is observed that the values calculated by modeling the modules together trend very closely with the distributions of the individual module calculations. The half-cell PERC and Al-BSF modules show a much stronger changepoint trend given the clear difference between the first and second PLR values for each segment. Each of these modules shows a high initial loss followed by a longer period of stability. The full-cell PERC modules on the other hand show similar distributions for both segments, again due to the more linear trend. When modeling individually, the outliers are separate and more visible compared to the more regular modules.

Information about the fitting and changepoint magnitudes of the models are given in Figure 6. When modeling by individual module, the Pred-R ² could not be calculated as there were only 5–6 data points, so the Adj-R ² of each model is shown instead. Though there is a range of fitting by individual module, all modules show a median Adj-R ² above 0.9. Again, it is made clear that the full-cell PERC modules show a very inconsistent piecewise linear trend. The changepoints are very consistently located for the Al-BSF and half-cell PERC modules, however, the full-cell PERC piecewise models fit changepoints across the time range of the system, indicating an inconsistent changepoint trend between modules.

The Current-Voltage (I-V) features of these modules are shown below in Figure 7, colored by each of the module groups. Corresponding with an initial loss in max power, there is a drop between the first and second steps in I _SC for the half-cell PERC and Al-BSF modules, and a drop in V _OC as well for the half-cell PERC modules. The series resistance and fill factor are more stable for all module types. The changes in these features are most significant for the half-cell PERC modules, which also show the highest power drop. Given the stability of the measurements of the other modules, this is likely a feature of light induced degradation (LID) with a mixture of boron-oxygen related light induced degradation (BO-LID) and light and elevated temperature induced degradation (LeTID) occurring during the initial 6 months of exposure and saturating afterwards. The exact time frame of the LID cannot be assessed, as it occurred between the first two measurements.

PLR values for the individual minimodules were calculated using the maximum output power (P _MP ) tracking and the PVplr package. The first 30 weeks of data were excluded due to a breakdown of the load units capturing the measurements, and they had to be sent out for shipment. This led to sparse data in the beginning of the time series, which strongly influenced the modeling. As there was enough data to satisfy 2 years of exposure without this initial gap period, it was removed. Linear and piecewise linear < S | R > models are represented by the linear and piecewise linear PLR values. Examples of two of the minimodules are given in Figures 8, 9 for the lowest and highest observed loss in the piecewise linear models, respectively. It is observed that in modules with high loss, such as in Figure 9, there is a strong segmented behavior with high initial losses followed by a period of stability.

The disparities in piecewise calculated loss make more sense when we observe all of the PLR values together in Figure 10. Even among modules of the same type there can be large disparities. The PERC modules show some of the lowest values of PLR, however, this is inconsistent, with significantly different PLR being observed between modules with the same cell or packaging combinations. This would suggest that performance is highly susceptible to factors outside of packaging degradation. It is possible that soiling or differences in wiring are creating different performances between minimodules.

Suns-V _OC loss mechanisms are extracted from the I-V curve timeseries for each of the minimodules. Two examples of the resulting trend are given, from the same modules shown with the highest and lowest PLR results. Figure 11 shows the low PLR module and Figure 12 is the highest PLR module. In both cases, the recombination losses and current mismatch losses cluster strongly around zero, showing no observable trend over time. The other two mechanisms, uniform current and series resistance, show significant deviations from zero, with uniform current being positive and series resistance being negative. The series resistance loss refers to power losses due to the existence of any series resistance, so this should always be less than zero for any real module. Comparing the two modules, however, shows that the series resistance loss is much larger overall for the high PLR module (Figure 12), decreasing from near zero initially. This suggests that series resistance increases are the cause of the difference in PLR between the modules.

The uniform current loss for the minimodules is unexpected, being positive. The uniform current relates to differences between the I _SC of the determined ideal curve and the actual curve, so a positive result indicates that the observed I _SC values of the I-V curves are higher than the curves at the start of the timeseries which are used to define the ‘ideal’ curve for the module. This is consistent across all of the minimodules. In outdoor timeseries the modules are assumed to be in their most ‘ideal’ operating conditions in the initial weeks of exposure, and will then go on to accumulate losses due to various degradation mechanisms over time. The initial month of data is what is used to calculate the ‘ideal’ module I _SC value that all future curves will be compared to. As such, I _SC losses in the initial operation of the modules will create an observed positive uniform current loss in the rest of the measured operation. In this specific instance, the modules needed to be re-wired with shorter and lower gauge wire shortly after installation due measurement problems caused by their lower V _OC values. This post-installation change increased the I _SC of the modules. While this is not an ideal test condition, results can still be evaluated for these modules. First, the uniform current loss is the only component that is influenced by the initial I _SC deviations; all other components are evaluated independently. Second, any I _SC trend in the performance of the modules would still be observable and quantifiable, as an initial I _SC deviation only creates a magnitude offset in the trend. This can be observed in Figures 11, 12 where sharp drops in uniform current loss can be attributed to shading instances on the minimodules.

netSEM modeling was applied next to build and identify the relationships between the P _MP and Suns-V _OC loss mechanisms. Again, examples are given for the two minimodules with high and low PLR values. For the models shown, the Adj-R ² thresholds for the pathways were 0.1, 0.4, and 0.7. These levels control the thickness of the pathways between the variables with thicker lines indicating a better fit and no lines shown for any relationship below an Adj-R ² of 0.1. The stressor and response variables are decimal years (dy) and predicted power (P _mp ), respectively. The P _mp results are the same as those used in the PLR calculations, so the models show the relationships between the Suns-V _OC loss variables and the PLR of the modules.

The low PLR module (Figure 13) only shows a single pathway between measured power and time. None of the other pathways appear in the plot as they all have Adj-R ² values less than 0.1. The interpretation of this is that there are no observed relationships between any of the Suns-V _OC loss mechanisms with each other, time, or power. The only trend that is observed is dy to P _mp , which is analogous to the PLR of the module. While unusual, this does match with the PLR result, which overlapped with zero. A module that is undergoing no observable degradation would not be likely to show trends between degradation features.

Unlike the low PLR module, the high PLR module netSEM model (Figure 14) shows much stronger paths between its variables. The strongest pathway by far is the dy to P _mp path (the PLR pathway), which shows a changepoint model with an Adj-R ² of 0.921. The strong changepoint trend was also observed in the PLR analysis of the modules (Figure 9). The changepoint model is observed numerous times within the netSEM model, suggesting this trend is present in many of the mechanisms of the operation of this module. All of the other trends show fairly low Adj-R ² values with the exception of a stronger trend observed between the series resistance and uniform current loss.

The performance losses of full-sized modules were quite low and consistent, as shown in Figure 3. There were distributions of performance within each module group, however, the results from the combined models were similar to the mean and median of the individual modules. This shows that the observed trends in the modules, namely, the changepoint behavior in the half-cell PERC and Al-BSF, occurred consistently across all of the 10–12 modules in each group.

Unlike the exposure of full-sized modules, the minimodules showed both higher PLR values than expected for fielded modules and did not cluster by module type. There are only a few instances of modules with the same cell and packaging combinations showing overlapping PLR results. It is observed that PERC cells tended to have higher PLR values with the three highest results being PERC cells, however, the extreme nature of the results suggest influences beyond degradation. PLR values of −5%/a over 2 years would be nearly an order of magnitude greater than expected for commercial modules and it is unlikely that outdoor degradation alone would create such power loss results.

For full-sized modules, there is a clear initial power loss for the half-cell PERC and Al-BSF modules, more significantly for the half-cell PERC module. This was observed both in the power (Figure 3) and in the I _SC (Figure 7) of the modules, with the half-cell PERC showing an additional loss in V _OC initially (Figure 7). This is typical behavior of boron-oxygen related light induced degradation (BO-LID), which is expected to be observed more in PERC modules. The BO-LID effects were not observed in the full-cell PERC modules, however, these full-sized modules were from a separate exposure and it is possible they were preconditioned or any BO-LID effects had already saturated by the time the first measurements were taken.

In comparison to full-sized modules, we observed significant variation in the degradation mechanism of minimodules, both between different cell/packaging variants and even within the same module variant. While the PLR results themselves are not very diagnostic, the Suns-V _OC results in Figures 11, 12, and similarly all the remaining results in the Supplementary Material, give additional insight into the performance of the minimodules. In all cases, the current mismatch and recombination values are stable at zero and show little to no relationship to time of power in the netSEM models. Recombination loss is evaluated from decreases in the open-circuit voltage and is certainly something that would appear under cases of LID, as was observed in the half-cell PERC full-sized modules. Comparing the extremes of the PLR results shows a significant difference in the amount of loss due to series resistance, which suggests that the modules experiencing high PLR have much higher series resistance than the lower PLR modules. While degradation mechanisms such as metallization corrosion (Iqbal et al., 2022) can induce series resistance increases, the high degree of power loss suggests that the problems are external of the modules. As minimodules have much lower voltage than full-sized modules, they are more susceptible to the PV connectors and wiring between them and the I-V tracer. It is possible that the observed losses in series resistance are due to changes in the resistance between the load unit and the modules, which would explain why there do not appear to be strong trends between the types of modules. Despite the potential influence from the connections, there are still conclusions that can be made from the modules. The Suns-V _OC results show clearly that the V _OC of the modules are highly stable, and it is unlikely that any recombination increase has occurred during the outdoor period.

The example netSEM models, such as Figures 13, 14, and similarly all the remaining results in the Supplementary Material, show a clear pattern of signal or lack of signal in the performance of the modules. Degradation or performance change can be thought of as a signal over time in the measurements of a module. In a perfect module, one would not expect any internal changes and as such there would be no available signal to model and quantify. Such is the case in the low PLR module. The PLR value for this module is less than zero, but its confidence interval overlaps with zero, so it cannot be stated that any loss at all has occurred in its power production. As such, the netSEM model between the power, time, and Suns-V _OC features shows little signal, with only the trend between time and power having an Adj-R ² above the low threshold of 0.1. Conversely, the high PLR module shows much stronger pathways, particularly between power and time. That the improved pathway fits is an indication that there is observable degradation over time occurring within the high PLR module. There is a consistent trend in the netSEM models where the uniform current and the series resistance show strong paths with each other. The other Suns-V _OC loss mechanisms, recombination and current mismatch, show weaker trends between the other variables, which is expected because they are stable over time. This implies that there is a correlation between the series resistance and the offset between ideal and measured I _SC (Asadpour et al., 2019). Since we observed inconsistency between the modules and there is an extreme R _S loss in some module variants, we believe that the issue should mainly be related to the connectors and wiring between the load unit and minimodules.