Translation of outdoor tandem PV module I–V measurements to a STC power rating

The procedures for the power rating of tandem‐cell‐based concentrator photovoltaic (CPV) modules defined in the international standard IEC 62670‐3 are adapted to the requirements of tandem‐cell‐based flat plate PV modules. The adjusted procedure describes how to translate outdoor measured PV current–voltage characteristics to standard test conditions (STC): 1000 W/m, 25°C cell temperature, AM1.5g spectral conditions. In this work, we describe how to obtain all required input parameters: thermal transient measurements to determine the module temperature coefficients, categorizing and filtering the prevailing spectral irradiance conditions using spectral matching ratios, and determining the 25°C module open‐circuit voltage from dark current–voltage curves. Three specimen PV modules (triple‐junction, III‐V on Silicon and III‐V on Germanium) have been measured for several months outdoors on a dual axis tracking unit at Fraunhofer ISE in Freiburg. In this work, we demonstrate that the CPV module power rating procedures in IEC 62670‐3 are also—in a modified form—to be recommended for the outdoor rating of tandem‐cell‐based flat plate PV modules.

procedure before we demonstrate it using three specimen modules.
One of these modules is built with III-V on Silicon and two with III-V on Germanium tandem cells. The three most important steps of the rating procedure are presented in detail: temperature coefficient determination from thermal transient measurement, deriving the open-circuit voltage at 25 C cell temperature from light and/or dark current-voltage measurements, and how to consider the impact of the composition of the spectral irradiance on tandem cell PV modules using spectral matching ratios (SMRs). 7 In Muller et al., 7 measurement uncertainty of the IEC 62670-3 procedure applied to CPV modules are reported in the range of 5 to 9% rel. , whereas Whitfield and Osterwald, 8 Dirnberger and Kraling, 9 and Dirnberger et al. 10 report uncertainty for the flat plat PV modules measured at STC in the range of 2% to 5% rel. . The reason for the higher measurement uncertainty of IEC 62670-3 is the consideration of the spectral irradiance and its impact on tandem cell's sub cell current matching. Figure 1 gives a schematic overview of the rating procedure used in this work. The rating procedure has been adjusted from IEC 62670-3.

| HOW TO CALCULATE STC POWER OUTPUT OF TANDEM CELL BASED PV MODULES
Details of the IEC 62670-3 procedure have been investigated by Muller et al. 7 The main input of this procedure is current-voltage (I-V) characteristics measured outdoors from the specimen PV module together with the ambient condition parameters. In this work, the specimen module has been tracked in dual-axis mode during the whole measurement period; however, this is not mandatory. The ambient condition parameters required for carrying out the procedure are in plane global irradiance (in our case consequently global normal irradiance [GNI]), global SMRs (SMR global ), ambient temperature, and wind speed. The SMR global shall be determined in the same orientation to the sun as the specimen. SMRs are typically derived from component cell readings but can also be determined from spectroradiometer readings. 11 Component cells are defined as cells, which are optically (absorption and transmission) equivalent to the whole multi-junction cell but electrically behaving as one of the multi-junction's sub cells.
Additionally, to the outdoor I-V measurement, two specific measurements are required: thermal transient measurements (TTM) and an indoor (dark/light) I-V measurement. 7 Exemplary measurement data of TTM and indoor (dark/light) I-V can be found in the next sections.
TTMs are used to determine the module's temperature coeffi- is that the specimen is at 25 C. However, when using light I-V measurements, it is not mandatory to measure V OC at IEC 60904-3 AM1.5g 1 spectral conditions. A sun simulator intensity set in a manner that the specimen module generates the same I SC as it would at STC or a dark I-V curve corrected for series resistance are both appropriate. A comparison of both options is presented in the Section 4.1.
F I G U R E 1 Schematic overview of the rating procedure consisting of three main measurement techniques: outdoor current-voltage (I-V) measurement, thermal transient measurement (TTM) and indoor light/dark I-V measurement. The outcome of the rating procedure are power output values translated to standard test conditions (STC). The average of these values is the module power output at STC. The numbers in the boxes resemble the paragraph in which the corresponding steps are described in more detail. Calculation of short-circuit current (I SC ) at STC has to be iterated. α, β, and γ are the temperature coefficients of maximum power point (P MPP ), open-circuit voltage (V OC ), and I SC . Note that 3.2 could be exchanged by module back temperature measurement if specimen module technology allows.
Typically, the I SC at STC is not available at the beginning of the measurement campaign. This is the reason why the I SC at STC is determined in an iterative manner, explained below.

| Outdoor I-V measurement and data filtering criteria
Outdoor I-V measurements used in this rating procedure are restricted to stable ambient conditions close to STC only. The definition of "stable conditions" and "close to STC" is defined in this work as listed in Table 1. These criteria are based on the criteria defined in IEC 62670-3 for CPV. In difference to IEC 62670-3, the criteria for direct normal irradiance (DNI) are here used for GNI as not a CPV but a flat plate PV module is going to be rated. Furthermore, GNI is limited to between 800 and 1200 instead of DNI between 700 to 1100 W/m 2 as in IEC   Note that I SC at STC is not yet known at the beginning of the cell temperature calculation. However, the value for I SC at STC is determined in an iterative manner, by using the following equation Whereas, N is the number of I-curves, I SC,i is the I SC of a single I-V curve as measured, γ is the temperature coefficient of I SC , T cell,i the calculated cell temperature, and T ref the reference cell temperature (here 298 K).
Note that cell temperature calculation could be avoided if module technology allows for module temperature measurement from backside.

| Translation of measured power output to STC
Once the cell temperature is calculated for each I-V curve close to STC conditions, the final step is the translation of the maximum power output to 25 C cell temperature. This translation is to be carried out by translating efficiency using the following equations 7 and then the multiplying translated efficiency with GNI and module area to get maximum power output.
where i is the number of the measured I-V curve, P MPP,i is the maximum power output, GNI i is the measured global normal irradiance, A is the aperture area of the specimen module, δ is the temperature coefficient of the efficiency, T Cell,i is the calculated cell temperature,

| SPECIMEN AND THE OUTDOOR MEASUREMENT SETUP
The three PV modules used in this work are shown in Figure   SMRs are calculated as given in Equation (5) and they are commonly used to quantify the impact of different spectral irradiance composition on the power output of CPV modules. 11,16,17 where J SC,i and J SC,j are the measured current output readings of the  As can be seen in Figure 4, the V OC derived from light I-V are in very good agreement with the ones derived from dark I-V. The maxi-    Figure 5 have been translated to 25 C cell temperature. The temperature corrected efficiencies of the modules peak around a SMR 12,global value of around 0.9. The peak efficiency is typically found where the sub cells are closest to current matching. 18 Furthermore, in Figure 5

| Results
The results of the rating procedure are listed in Table 3 as mean values and standard deviation of efficiency values. All efficiency values in this table are already translated to 25 C cell temperature.
The Table 3 shows efficiency mean values after application of the three sets of filtering criteria (see also Figure 5).
The first set "GNI stable" shall assure that the specimen module has experienced stable GNI conditions in the period before the I-V sweep. A stable module temperature shall be assured in this manner.
For this reason, the filter 1 to 3 listed in Table 1  The third set "SMR filter" additionally assures that the prevailing spectral conditions are close to AM1.5g reference conditions by additionally applying the SMR filter criteria 6 to 8. In this manner, Table 3 shows that the standard deviation of module efficiency is reduced from around 1% abs. (4% rel. ), to below around 0.5% abs. (2% rel. ), and finally to around 0.2 abs. (1% rel. ).As the application of the IEC 62670-3 on tandem PV modules has been shown promising in this work, future work has still to be done. First of all, a detailed calculation of measurement uncertainty of the application of IEC 62670-3 on tandem PV modules will be needed but is beyond the scope of this paper. However, for CPV modules, the method described in 62670-3 leads to measurement uncertainty in the order of 5 to 9% relative 7 and it is expected that the measurement uncertainty is in a similar range for tandem PV modules. However, the measurement uncertainty is mostly driven by TTM and the SMR values; thus, improvement and further evaluation of both in the context of tandem PV modules is recommended as future work.

| CONCLUSION
The power rating of three tandem solar cell-based flat plate PV modules has been presented in this work. The rating procedure was adapted from the IEC standard 62670-3. As IEC 62670-3 has been shown that thermal transient measurement and dark I-V measurement are shown to be applicable for tandem based modules using three specimen modules. Furthermore, the impact of the restriction of the spectral irradiance prevailing during the outdoor I-V measurement to AM1.5g equivalent spectral irradiance conditions using global SMRs has been presented. In this manner, the variation of prevailing efficiency values, which have been translated to 25 C cell temperature, is reduced significantly. It has been shown that the impact of restriction of GNI is minor compared with the impact by spectral filtering for SMR values. Applying the GNI based filter criteria resulted in standard deviation of between 1.5 and 1.9% rel. , whereas additional filtering for SMR global values to be within ±3% of unity reduced the standard deviation to between 0.5 and 0.8% rel . Overall, it could be demonstrated that the proposed procedure is suited for the outdoor based power rating of flat plate tandem cell modules. and supporting in the scientific discussion. This work was partly funded by the German BMWK through the project KATANA (contract no. 03EE1087A). The authors are responsible for the content of this paper. Open Access funding enabled and organized by Projekt DEAL.

DATA AVAILABILITY STATEMENT
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