Analysis of the degradation of amorphous silicon‐based modules after 11 years of exposure by means of IEC60891:2021 procedure 3

The degradation of two amorphous silicon‐based photovoltaic (PV) modules, namely, of single junction amorphous silicon (a‐Si) and of micromorph tandem (a‐Si/ μ ‐Si), after 11 years of exposure in the south of Spain is analyzed. Their I‐V curves were measured outdoors to study the changes of the electrical parameters in the course of three different periods: during the initial days of exposure, during the first year, and in the subsequent 10‐year period. The translation of the curves to an identical set of operating conditions, which enables a meaningful comparison, was done by the different correction procedures described in the standard IEC60891:2021, including the procedure 3, which does not require the knowledge of module parameters, whose values are typically not available. The annual power degradation rates over the entire 11‐year period are 1.12% for the a‐Si module, which is 3.02% for the first year, and 0.98% for the a‐Si/ μ ‐Si, which is 2.29% for the initial year.


| INTRODUCTION
Amorphous silicon thin-film PV modules offer an alternative to wellestablished crystalline silicon PV (c-Si), with potentially lower manufacturing costs, reduced energy pay-back time, lower weight, and optimal suitability to special applications, for example, building integrated PV. 1 This technology offers a good performance under cloudy skies, high operating temperatures, or partial-shading conditions. 2 Although other thin-film technologies, such as CdTe or CIGS, also provide those advantages over c-Si without implying a strong decrement of the performance, amorphous-based technologies are still a profitable option because they use materials very abundant and nontoxic. 3 Degradation processes of amorphous silicon PV modules have been analyzed in many papers available in the literature. [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] The dispersion of the degradation rates documented by different authors is significantly wider than the dispersion observed on crystalline PV modules, even though there are comparatively many more works addressing the degradation of the latter family of technology, as shown in the comprehensive review conducted by Jordan et al, 21 stating a range box for the long-term annual degradation rate of amorphous based modules manufactured in the last decade between 0.8 and 2%/year. 21 A summary of annual degradation rates, in terms of power, reported in recent articles can be found in Table 1. The column titled Climate expresses the climatic conditions under which the PV modules have been exposed in each cited work, using the Köppen-Geiger index. 22 Further research is required to gain a deeper knowledge about the degradation of amorphous silicon-based modules; this will allow to reduce the uncertainty affecting the estimations of the energy delivered by PV plants based on this technology. As it can be argued from Table 1, single junction amorphous silicon commonly shows degradation rates in the range of 2.0±0.3% per year, 6,11,14,17,20 although lower 6,9,12,18 and higher values 7,16 are reported, reaching even more than 6%/year. In general, a similar dispersion is found for the degradation rates estimated for micromorph modules and also similar or slightly lower values, 4,8,10,13,15,17,19 with a maximum rate around 4%/ year.
In this paper, the performance of two modules is analyzed. The first module is a single-junction hydrogenated amorphous silicon (a-Si: H) module manufactured by Kaneka and with a nameplate stabilized efficiency of 6.3%. 23 The second one is a micromorph tandem a-Si/ μ-Si module with a nameplate stabilized efficiency of 8.5%. 24 Both PV modules were exposed to sunlight for the first time in 2010 and have been exposed outdoors for a period over 11 years without any electric load connected to their terminals. It should be noted that degradation is also dependent on the type of the load and degradation analyses at module level are often conducted with no load for practical reasons. 9,[17][18][19] The dependence of the degradation of a-Si modules on the type of load was investigated by Fanni et al, 25 which observed higher degradation rates for modules under open-circuit conditions. 25 The study carried on over these thin-film modules has been divided into three different parts: (1) the initial strong power drop during the first days of exposure is analyzed; (2) the degradation during the first 12 months is studied; (3) finally, a comparison of the module performance before and after the subsequent 10 years of exposure is performed.
These technologies usually show a significant initial degradation due to the Staebler-Wronski effect. 26 Therefore, it is common to expose the modules outdoors for an initial stabilization period prior to the start of the monitoring campaign. The stabilization period for a-Si is typically considered to be of about 6 weeks. [27][28][29] Other studies report longer periods (one year or more) for a complete stabilization. 10,30,31 Hence, the rates obtained for the first and second analyses, which refer to the first days and to the first year, are affected to some extent by stabilization issues, being only the results of the third analysis representative of the long-term degradation.
This paper relies on a previous study of degradation of PV modules from the same authors, 32 and it is based on the same measurement system. In this paper, a novel translation method has been employed to correct the I-V curves to reference conditions for determining the parameter variation. Most of the translation methods available in literature, including procedures 1, 2, and 4 of IEC60891:2021, 33 require, in addition to the temperature coefficients, which are provided by the manufacturers for new nondegraded PV modules, some additional parameters, which are normally not available in the specifications. Table 4 shows a small survey of some of these methods of correction of I-V curves, providing the parameters required by each one and their meanings. Although IEC60891:2021 also describes methods to estimate such parameters, these tasks require many additional I-V curve measurements, which are usually difficult to be performed without a solar simulator. In this paper, the required corrections are performed by using the procedure 3 of the standard IEC60891:2021. It is an algorithm requiring only a minimum of three measured I-V curves, and no internal parameter or temperature coefficients. Moreover, some experiments show that this interpolation procedure provides much better results than the other ones. 34 Finally, instead of assuming the Standard Test Condition (STC) as reference, the measurements are translated to values of irradiance and cell temperature that are closer to the actual ones, so that the errors added by the correction procedure are minimized. As it has been done in few papers up to now, [35][36][37] in this paper it has been considered the following set of operating conditions: G ¼ 800 W/m 2 and T cell ¼ 35 ∘ C. Ad hoc irradiance and cell temperature defined by the user is Tahri et al. 19 36 -BSk 1.7 Note: inv (within an array connected to an inverter); mpp (alone biased to its maximum power point); -(not specified by the authors).
usually referred as Alternate Reporting Condition (ARC). This paper is organized as follows: Section 2 describes the measurement system and procedures, with a special focus on the I-V curve correction procedure 3 of IEC60891:2021. Section 3 shows the results and plots obtained by the application of the proposed methodology. In Section 4, a comparative analysis and a discussion are presented. The main conclusions of the study are summarized in Section 5.
The modules were exposed on the roof of School of Computer and  been used. Table 2 shows the features of the single-junction amorphous silicon module 23 and of the tandem of amorphous silicon/ microcrystalline silicon module. 24 The symbols α, β, and γ stand for the temperature coefficients of I SC , V OC , and P max , respectively, whereas η is the nameplate efficiency and N s is the number of cells.
Careful attention must be paid to the spectrum when characterizing a-Si modules outdoors, because they have a narrow spectral response. King et al 31 assume for this technology a variation of the performance around a 7% due to spectral changes. Therefore, to obtain realistic degradation rates the indicators to be compared should be estimated under similar spectral conditions, for example, by performing the measurement under clear skies in the same week of different years. To ensure a high spectral similarity, it is possible to compare the I-V curves using the average photon energy (APE), 44,45 which can be calculated from the solar spectrum. In this paper, the latter one has been measured by an EKO MS-710 46 on the module plane, by using the range (350-1050) nm to integrate the APE. Therefore, for every I-V curve, a reading of the APE value is available, having this parameter a strong dependency on the solar position, the season of the year, and the level of temperature, humidity and clouding. 45 Each PV module under study has been tested by five sets of measurements taken during different selected days from the exposure period, which are labeled as a, b, c, d, and e, as it can be seen in Table 3.  On the other hand, procedure 3 does not require any temperature coefficient or internal parameter. It is based only on data from three measured I-V curves: • Curve 1: ðV 1 ½i, I 1 ½iÞ, where i ¼ 1, …, n 1 , measured at an irradiance G 1 and a cell temperature T 1 .
The problem consists in determining, from these three curves, a new Curve 0 given by ðV 0 ½i, I 0 ½iÞ which corresponds to the target conditions G 0 and T 0 . An interpolation is conducted using an auxiliary and G 2 , and T 1 and T 2 respectively, as shown in Equations (1) and (2), where ω is a parameter to be determined. The target irradiance G 0 and temperature T 0 are estimated from G 3 and G 4 , and T 3 and T 4 , respectively, using another unknown parameter ϕ, as shown in Equations (3) and (4). This leads to a system of 4 equations and four unknowns (G 4 , T 4 , ω, and ϕ).
The set of equations defined in the standard has been simplified by defining a new translation parameter ψ ¼ ω Á ϕ and by substituting the values of G 4 and T 4 in Equations (3) and (4). This leads to Equations (5) and (6), which are easily solved by Equation (7). In the case of the example of Figure 1, the solution is ϕ=0.5 and ψ=0.25, and then ω ¼ ψ=ϕ= 0.5.
T A B L E 3 History of the modules and different measuring points with accumulated exposure time The operating conditions of curves 1, 2, and 3 (black dots) are interpolated to obtain the operating conditions of Curves 4 and 0 (magenta stars) The next step is aimed at obtaining the I-V curves. It has been assumed that I SC1 and I SC2 are the short-circuit currents of Curve 1 and Curve 2, respectively. For each point of Curve 1ðV 1 ½i, I 1 ½iÞ, its partner ðV 2 ½j,I 2 ½jÞ is sought in Curve 2 so that the following condition is fulfilled:  (10) and (11). Figure 2i,ii sketches this point-by-point process to obtain the auxiliary Curve 4 and the final corrected Curve 0, respectively.

| Alternative correction procedures
Although the study presented in this paper is based on the Procedure 3 of IEC 60891:2021, only for comparative purposes, the degradation rates of both PV modules have also been estimated using other two approaches described in the same standard, in addition to the simplest possible method as described by Smith et al. 47 (only requiring the three temperature coefficients α, β, and γ). Table 4 provides a brief summary of some of these correction methods.
Contrary to Procedure 3, which requires three initial measured curves, all these other approaches use as start point only one measurement under the initial conditions noted as ðG 1 , T 1 Þ. From the initial set of I-V points, these methods can be used to estimate I SC,2 and V OC,2 , and P max,2 at the target conditions ðG 2 , T 2 Þ.
Due to the fact that these formulas require to know the value of several parameters, although some of them could be provided by the manufacturer, in this work all these coefficients have been determined experimentally using the guides given by IEC 60891:2021 33 and other useful recommendations. 32 However, in this paper, this process is not explained, reporting only the final values of these coefficients for a new module (a nondegraded one) of each type (see Table 5). Finally, although in the literature there are approaches to perform a correction by the angle of incident (see the Sandia Performance Model 49 ), we have not applied this type of correction to our measurements.

| RESULTS
Each measured I-V curve is associated to a row in Table 6, whose identifier Mxn ¼ ⟨ðKjPÞðajbjcjdjeÞð1j2j3Þ⟩ refers to the module (K: Kaneka / P: Phoenix Solar), the measurement point (noted in Table 3 as a, b, c, d, and e), and the selected measured curve (with the subfixes F I G U R E 2 Two interpolations to obtain the corrected Curve 0 from 3 measured curves and the auxiliary Curve 4

1, 2, or 3). Each final corrected curve (the auxiliary curves have not
been included) has also its row in Table 6 marked in bold and with the subfix 0 (e.g., Ka0 or Pa0). As it can be seen, instead of using STC as reference, we have defined our own ARC conditions: 800 W/m 2 of irradiance on module plane and 35 C of cell temperature (values selected based on a rough estimation trying to minimize the gap to correct).
In addition to the main electrical parameters of each curve (calculated using the approach given by Emery 50 ), the value of APE, estimated from the measured spectrum, is provided (see Piliougine et al 45 for the details). Table 7 shows the monthly average value of APE obtained from spectral measurements acquired in Málaga from January 2011 to December 2011 for clear-sky days and irradiance values G ≥ 600 W/m 2 . As it can be seen, the measurement points c, d, and e in Table 6 are characterized by APE values approximately ranging between 1.871 and 1.894 eV, which fit well to the mean values for October, November, and December in Table 7. Great care should be taken when comparing measurements taken in different periods of the year because there could be important spectral variations.
By taking into account that the measurement tests a and b have been performed by the curve tracer PVPM and the other ones by the Kepco/Agilent system, it has been decided to avoid comparing these different sets of measurements when estimating degradation rates.
For example, when comparing in Table 6 the corrected curves Kb0 and Kc0, P max and I SC are greater in the last curve, but this is due to the use of two different measurement systems. In other words, to calculate degradation rates, we must compare measurements performed using the same equipment.
To illustrate the IEC60891:2021 procedure 3, for each module and set of measurements a plot in Figure 3 or Figure 4 shows in black the three selected I-V curves of the same day used as input, and in blue the corrected curve. The most relevant electrical points of each curve, measured or corrected, are also pointed out with a star.
All the plots in Figure 3 are related to measurements performed by the PVPM curve tracer. Besides the low accuracy of this system for characterizing single PV modules, the high level of noise around the open-circuit point is very significant, and also the lack of measured points near to the short-circuit condition. Figure 4 shows measurements acquired with the Kepco/Agilent system, with a better distribution of points that allows good estimations of P max , I SC , and V OC . From our experience, procedure 3 of IEC60891:2021 is very sensitive to noise, due to the propagation of the error of the three measured curves to the corrected one.

| DISCUSSION
Having estimations of each electrical parameter at the different measurement points of 2010, 2011, and 2021, it is possible to determine the respective degradation rates: (1) for the initial 9 days of exposure; (2) for the following 12 months; (3) for the next 10 years; (4) and finally an annual degradation rate for the entire period of 11 years.
Several facts should be highlighted from these results. Because they are modules based on amorphous silicon, during the initial exposure they experiment a very strong degradation. Only during the first days the a-Si module experiments a power drop close to 6%, due to the Staebler-Wronski effect. 26,51 However, for the a-Si/μ-Si case, this effect is lower, although it is also very significant (around 4%) taking into account that only 9 days of exposure have been considered. Focusing on the degradation in terms of power for both modules during the entire first year, the single junction amorphous module has degraded a bit more than 3.02% whereas the micromorph module has experienced an annual power drop close to 2.29%. In both cases, these rates are in agreement to those summarized in Table 1, except for those works 7,16 where the period of study is relatively short (30 months or less). This fact suggests that studies on amorphous silicon technologies require long exposure periods of several years in order to overpass stabilization and obtain realistic degradation rates. Therefore, the most interesting analysis of this paper is the estimation of the annual degradation rates by comparing the measurements before and after the 10-year period (or 11-year period if the first year is also included).
By comparing the measurement points d and e, the power degradation rates in both cases are similar to those obtained for crystalline silicon that are installed in the same site and by using the same measurement equipment. 52 However, whereas in that case the long-term degradation was characterized by a strong decrease of I SC , in the case of the a-Si module the annual drop of current can be neglected, and for the a-Si/μ-Si module it is very low as well. In other words, whereas T A B L E 6 List of measured and corrected I-V curves of each PV module The last column of Table 8 shows the degradation rates for the entire period of 11 years, including the first year of exposure. The power degradation rate for the a-Si module is 1.12%/year. By comparing this value with the results reported in Table 1, it emerges that it is in good agreement with several literature achievements. 9,12,18 On the other hand, the a-Si/μ-Si module has experienced a degradation in terms power of 0.98%, that is a bit lower than the rates reported in the literature.
Finally, the alternative methods which could be used to correct I-V curves and listed in Table 4 have been tested, but IEC 60891:2021 procedure 4 has been excluded because a specific value of ε is not available. For the sake of brevity, the comparative has been only performed for the degradation rate of the maximum power P max , as it can be seen in Table 9.
For the single amorphous module, if only the initial period of exposure is analyzed, the procedures 1 and 2 of the IEC In fact, using a test set of 100 measured curves, IEC 60891:2021 proc. 3 is able to correct the curves with a mean error in P max of only 0.6%, whereas proc. 1 and proc. 2 have errors of 1.9% and 1.8%, respectively (the other two methods have error greater than 2% when correcting P max ). However, this issue is out of the scope of this paper and deserves to be analyzed in detail in a future publication.

| CONCLUSIONS
In this paper, the degradation of two amorphous silicon-based PV modules that were exposed in Málaga for 11 years has been analyzed.
The I-V curves have been measured outdoors by using a suitable measuring system and by converting the selected curves to an identical set of operating conditions by using procedure 3 of the standard literature. An initial significant degradation, during the first 9 days of exposure, has been observed: this leads to a power decay of 6% and 4% for the single junction a-Si and the micromorph, respectively. The power decay is due to significant ohmic losses and, to a lesser extent, also to losses related to the voltage, together with a significant decrease in FF for the a-Si module. After this initial drop, the FF degradation reduces, but the power decay continues with annual rates of slightly over 3% for the a-Si module and nearly 2.3% for the micromorph module. Finally, for the whole 10-year period, the degradation is dominated by the FF decay, and the annual power degradation rates stabilized to values of nearly 1.0%/year for both modules.
These results are not much higher than those ones obtained for crystalline silicon PV modules measured at the same location during the same exposure period. If the first year of exposure is included in our calculus (11-