Power rating procedure of hybrid concentrator/flat‐plate photovoltaic bifacial modules

Hybrid concentrator/flat‐plate photovoltaic (CPV/flat‐plate PV) technology combines III–V multi‐junction and flat‐plate bifacial solar cells to convert direct, diffuse and rear irradiance into electricity. For the first time, this article presents a procedure to rate the power output of such modules at standard test and standard operating conditions. The reference conditions, data filtering criteria, and translation methods are taken, and in some parts adapted, from the CPV, flat‐plate PV, and bifacial PV International Electrotechnical Commission (IEC) standards. The power rating is based on outdoor measurements performed on two hybrid modules (A = 1088 cm2) equipped with III–V triple‐ or four‐junction solar cells mounted on bifacial positively doped passivated emmiter rear contact (p‐PERC) c‐Si cells. The results show that the modules, named triple‐ and four‐junction EyeCon, convert the reference AM1.5g spectrum with an efficiency of 32.6% and 34.2%, respectively. This exceeds by 1.4%abs and 3%abs the highest value reported so far for a terrestrial module that harvests global irradiance. Additionally, the modules generate 11.5 and 10.9 W/m2 for every 100 W/m2 of rear irradiance to surpass an output of 350 W/m2. Finally, the influence of illumination mode, type of irradiance sensor, and filtering criteria were evaluated, and a simplified alternative with an acceptable power output underestimation of 0.5%rel is presented.

For example, the hybrid CPV/flat-plate PV sub-module (A = 144 cm 2 ) reported in Martínez et al. 1

uses silicone on-glass
Fresnel lenses to concentrate the DNI 226× onto 4J CPV cells that are mounted on an interdigitated back contact (IBC) Si cell. In this way, the sub-module converts up to 36.8% of the global normal irradiance (GNI). An example of a sub-module (A = 32.5 cm 2 ) that uses 3J CPV cells in combination with polymethyl methacrylate (PMMA) convex lenses, reflective secondary optics, and a bifacial Si solar cell is reported in Yamada and Hirai. 4 This sub-module reached a GNI conversion efficiency of 32.7% at a concentration of 203× for the CPV part. At the module level, a hybrid device (A = 0.264 m 2 ) using glass convex lenses, refractive secondary optics, 3J micro-CPV cells (A = 0.36 mm 2 ), and IBC Si cells yielded a 30.5% conversion efficiency of GNI at a concentration of 1000× for the CPV part. 2 Another hybrid module (A = 0.1 m 2 ) also using 3J micro-CPV cells (A = 1 mm 2 ) is the one developed by the Swiss company Insolight. This hybrid module additionally applies PMMA biconvex lenses and monofacial Si cells to convert 24.5% of the available GNI at a concentration of 180× for the CPV part. 3 However, this particular hybrid module is designed for fixed-tilt operation because it is equipped with embedded planar tracking. This technology is based on the idea of sliding the baseplate along the tilted plane in order to align the CPV cells with the focal spots. Therefore, the direct sunlight is not perpendicular to the optics.
Nevertheless, all the efficiency values mentioned above are reported at normal incidence during outdoor operation and not at standard conditions.
In general, hybrid CPV/flat-plate PV technology is particularly suitable for locations where the annual average DNI/GNI ratio is between 60% and 85%. 6 Under hazier conditions, the power generated by the high-efficiency CPV cells (η > 40%) is significantly reduced and undercompensated by the power output of the lower performance flat-plate PV cells (η < 20%). On the other hand, the performance of the latter under clearer sky conditions is not expected to justify its added cost. For these reasons, the non-rated efficiencies reported in the literature span between 24.5% 3 and up to 36.8%. 1 Notably, these values remain below those of conventional CPV modules (η < 38.9%) 7 because their calculation is based on GNI instead of DNI. Nevertheless, it has been demonstrated that hybrid devices are able to generate between 3.5% and 30.6% more power, relative to their CPV part, when the DNI/GNI ratio is between 92% and 57%, respectively. 2,8 Despite all the experimental and theoretical 9,10 knowledge available on hybrid CPV/flat-plate PV technology, nowadays the procedure to determine its efficiency and performance remains unstandardized. For the first time, this article presents a procedure to translate their power output measured outdoors to standard test conditions (STCs) and standard operating conditions (SOCs). Therefore, the approach first defines these reference conditions for hybrid CPV/flat-plate PV modules in Section 2. Hybrid STCs are taken from the common STCs of flat-plate PV modules defined in International Electrotechnical Commission (IEC) 61853-1, 11 and hybrid SOCs are based on the concentrator SOCs defined in IEC 62670-1 12 to allow cross-technology comparisons. Figure 1 shows the flow chart of the entire power rating procedure using a color-coding scheme to reference the source from where each method was taken. From top to bottom, the algorithm described in Figure 1 is explained in detail throughout this article. For instance, in Section 3, we describe the measurement of the spectral and meteorological conditions, as well as the independent acquisition of the light I-V (LIV) characteristics of the CPV and PV arrays using a dual-axis solar tracker. Then, Section 4 presents the filtering criteria necessary to restrict the performance of both cell arrays to SOCs, and Section 5 follows the CPV, IEC F I G U R E 1 Flow chart of the power rating procedure for hybrid concentrator/ flat-plate photovoltaic (CPV/PV) bifacial or monofacial modules. The color of each block indicates the source of the methods used in the algorithm and the black feedback arrow denotes iterative calculations. The acronyms LIV, DIV, TC, and BiFi stand for light I-V, dark I-V, temperature coefficient, and bifacial gain. The Greek letters ε and γ represent the front irradiance response of the flat-plate PV array, ρ corresponds to its rear irradiance response, and φ accounts for its bifaciality factor [Colour figure can be viewed at wileyonlinelibrary.com] 62670-3, 13 and flat-plate PV, IEC 60904-5, 14 standards to calculate their temperature during outdoor operation and at SOC. As shown in Figure 1, the CPV (T CPV ) and flat-plate PV (T PV ) temperature calculation requires the use of the temperature coefficients (TCs) of the cells to iteratively obtain the reference I SC and V OC from a dark I-V curve (DIV) measured at 25 C. Section 6 demonstrates the application of IEC 62670-3 13 to perform the power rating of the CPV cell array at the STC and SOC defined for hybrid CPV/flat-plate PV modules in this work.
In Section 7, we present the power rating of the bifacial PV array following the guidelines of the flat-plate PV standards, IEC 60904 14-17 and IEC 60891. 18 Here, we adapted the current translation equation from IEC 60891 Procedure 1 18 to make it compatible with the newly developed methods that characterize the front (ε and γ) and rear (ρ) irradiance response of the flat-plate PV cells.
Additionally, a method to separate the bifacial I SC of the PV array is used to calculate the bifacial gain (BiFi) and the bifaciality factor (φ) as stipulated in the bifacial PV technical specification, IEC TS 60904-1-2. 19 In Section 8, we combine the independently rated power outputs of the CPV and front side of the PV array (P hyb ) and report the STC and SOC hybrid efficiencies (η hyb ) along with the uncertainty of the fully IEC compliant procedure. Also, in the same section, we investigate and quantify the added uncertainty if the method is simplified.
The procedure is demonstrated with the power rating of the two 4T hybrid modules (A = 1088 cm 2 ) shown in Figure 2. The module on top shows its rear side and is equipped with III-V metamorphic 3J (GaInP/GaInAs/Ge) CPV cells from AZUR Space 20 (hereafter named 3J EyeCon), whereas the one below shows its front side and uses III-V wafer-bonded 4J (GaInP/GaAs/GaInAsP/ GaInAs) CPV cells 21  Additionally, the 48 CPV cells are mounted with a dielectric adhesive onto the top surface of a flat-plate PV array of eight bifacial positively doped passivated emmiter rear contact (p-PERC) c-Si solar cells. 8,22 This enables the flat-plate PV cells to act as heat distributors for the CPV cells. Moreover, the Si cells have a custom size of 91 × 141 mm 2 and a metallization layout optimized for absorption of diffuse and rear side irradiance. Further details about the module development and outdoor performance can be found in Martínez et al. 8 As a last remark, it is important to note that the presented power rating procedure only applies to 4T hybrid bifacial or monofacial CPV/flat-plate PV modules, where the CPV and PV I-V curves can be measured independently while the module remains normal to the sun. This is noteworthy because the performance of state-ofthe-art hybrid CPV/flat-plate PV modules has been demonstrated using conventional dual-axis solar tracking 1,2,4 and novel moduleembedded planar tracking. 3 Therefore, we must mention that the optical losses associated with the angle of incidence when using planar-tracking are not addressed by the characterization methods developed in this work. Nevertheless, these methods apply to rate the optimum power output of such a hybrid module if it is mounted on a dual-axis solar tracker with the planar-tracking disabled. Additionally, 2-terminal (2T) hybrid CPV/flat-plate PV modules are also not addressed by this power rating procedure. Although there are no experimental demonstrations of such 2T devices in the literature, their promising performance (i.e., 0.995ÁP 4T < P 2T < P 4T ), as projected using experimental data in Martínez et al., 5 Figure 3 (gray area). This corresponds to illuminating the CPV array with the direct part of the AM1.5g spectrum, that is the reference AM1.5d spectrum, ASTM G-173-03 AM1.5d, 23 depicted as a red line in Figure 3, and the flat-plate PV array with the difference between both, that is, the reference diffuse irradiance shown as a blue line.
In addition to STC, we follow the approach of CPV module rating and define the SOC for hybrid CPV/flat-plate PV modules based on the concentrator SOC (CSOC), 12 in order to establish a realistic scenario representative of outdoor operation. The goal is to reproduce the electrical and thermal behavior of the concentrator cells as in a CPV module because they contribute the largest fraction to the hybrid power output. These are ambient temperature of 20 C, wind speed of 2 m/s, and illumination with the AM1.5g spectrum scaled to 900 W/m 2 . The latter is accomplished by illuminating the CPV array with the AM1.5d spectrum down-scaled 10% to 810 W/m 2 and the flat-plate PV array with the reference diffuse spectrum also down-scaled 10% to 90 W/m 2 . In this manner, the GNI intensity matches that of DNI at CSOC, that is, 900 W/m 2 , whereas the DNI/GNI ratio from STC is maintained, that is, 0.9. Table 1 summarizes the STC and SOC for hybrid CPV/flat-plate PV modules.
In the case of a bifacial hybrid module, the reference conditions defined in Table 1 apply for the rating of the front side, whereas for the rear side of the flat-plate PV cells, the technical specification for bifacial PV devices, IEC TS 60904-1-2, 19 applies. This specification indicates that the rear power generation should be translated to rear intensities of 100 and 200 W/m 2 in order to obtain the bifacial power gain (BiFi) and the bifaciality factor (φ), as is demonstrated in Section 7. The diffuse irradiance on the front-normal plane (DIF) was calculated as DIF pyr = GNI pyr − DNI pyr and alternatively for comparison as DIF rc = GNI rc (1 − DNI pyr /GNI pyr ). We found that in average the DIF rc was 3.3 ± 1.2% lower than the DIF pyr , mainly because the spectral response of the thermopile pyranometer is significantly higher over the absorption range of the reference cell. The back normal irradiance (BNI) was measured with two rear-facing pyranometers and with two Si reference cells identical to the ones used in the modules and encapsulated in the same way, but with their front side shaded. The front and rear current responsivity of the reference cells and its F I G U R E 3 Spectral irradiance as a function of wavelength of the reference AM1.5 global (gray area) and direct (red line) spectra according to IEC 60904-3. 15 Additionally, the difference of both spectra corresponds to the reference diffuse irradiance (blue line). As summarized in the legend, illumination under these conditions at a cell temperature of 25 C constitutes the STC for hybrid CPV/flat-plate PV modules [Colour figure can be viewed at wileyonlinelibrary.com] temperature dependence was calibrated using the differential spectral responsivity method 26 at 25 C. and 50 C. According to IEC 60904-10, 17 both current responses were found linear within the outdoor measurement range (50-300 W/m 2 ), because they deviated by less than 1.2%. Moreover, all BNI sensors were positioned nearly at the same height and as close as possible to the modules to minimize the influence of spatial nonuniformity. The calculation and measurement of the DIF and BNI with thermopile and reference cell sensors is intended to evaluate their impact on the power rating of the flat-plate PV array, as discussed in Section 8. Additionally, a thermometer and an anemometer were used to record T amb and V wind behind the tracker (not shown in Figure 4).

| RESTRICTIVE FILTERING CRITERIA OF FLUCTUATING OUTDOOR CONDITIONS
Given the dependence of multi-junction CPV technology on spectral (due to the series interconnection of sub-cells) and temperature variation (due to its effects on the cell and optics), we applied the filtering criteria defined in IEC 62670-3 13 to constrain the performance of the CPV and flat-plate PV arrays to CSOC. Table 2, the criteria not only restrict the allowed ranges of DNI, DNI/GNI, T amb , and V wind but also screen out sudden DNI fluctuations, thermal transients and sun tracking deviations. At the same time, a restriction of direct SMR values to be within ±3% of unity shall ensure that the impact of the DNI spectral distribution on the CPV cell power output is equivalent to the one under the reference AM1.5d spectrum.

As shown in
In addition to that, we calculated the global SMR 1-2 value from the measurement of the global spectral irradiance using a spectroradiometer and the external quantum efficiency data of the GaInP and GaInAs component cells, as explained in Section 3. This parameter quantifies the spectral equivalency of the GNI with the T A B L E 1 Standard test conditions (STC) and standard operating conditions (SOC) for hybrid concentrator/flat-plate photovoltaic (CPV/flatplate PV) modules reference AM1.5g spectrum in the response range of the flat-plate Si solar cells. Therefore, we also filtered out global SMR 1-2 values beyond ±3% of unity to ensure spectral compliance between the DIF and the reference diffuse irradiance. Figure 5 shows the constraining effect of the filtering criteria in a plot of global versus direct SMR [1][2] values. The amount of unfiltered data (gray) is reduced to 7% by the IEC 62670-3 criteria (red) and to 2% by additionally filtering for global SMR 1-2 values (blue) between 0.97-1.03.
On the other hand, no BNI filtering criteria were applied because it depends on the already filtered GNI and the surroundings' albedo.
Besides, we measured the BNI with a calibrated reference cell sensor of nearly identical rear spectral response as the PV arrays under test.
Thus, the power rating of the rear side can be considered as if it was performed under the AM1.5 g spectrum, but scaled to 10% and 20% as it is stipulated in the bifacial PV technical specification, IEC TS 60904-1-2. 19 Besides filtering the experimental data and constraining the impact of spectral and meteorological conditions, the criteria summarized in Table 2

| TRANSLATION OF CPV AND FLAT-PLATE PV ARRAY TEMPERATURES TO STANDARD CONDITIONS
Depending on the architecture of the hybrid module, the CPV and flat-plate PV arrays are thermally coupled to a greater or a lesser extent. In the EyeCon configuration where the cells are joined with a dielectric thermal adhesive, the flat-plate PV cells exhibit an inhomogeneous temperature profile with hotspots at the concentration foci.
Also, a higher CPV cell temperature is expected compared with conventional concentrators because the thermal resistance of a Si heat spreader is larger than for a standard metal substrate. Such effects are explained in more detail in Martinez et al. 27 An alternative to lower the mean operating temperature of both arrays is called micro-CPV 28 and consists on reducing the concentrator cell (<1 mm 2 ) and lens size (<5 cm 2 ). This allows to decrease the heat input, which makes the CPV cell temperature less sensitive to the thermal conductance of the substrate.
Additionally, we found that the characterization of SOC performance of hybrid bifacial CPV/flat-plate PV modules requires simultaneous front and rear side illumination due to their dynamic thermal behavior. This means avoiding front shading of the module to characterize the rear side because the PV array temperature decreases at least 12 K when the GNI is blocked. The opposite should also be avoided because the CPV and PV array temperatures increase by more than 18 K when the rear convection and radiation are reduced. Even a short covering event (<10 s) can cause a thermal transient of up to ±8 K due to the small thermal mass of the arrays.

| Calculation of mean CPV and flat-plate PV array temperatures
In this sub-section we calculate the mean cell temperature of the CPV array as described in IEC 62607-3 13 where N s is the number of CPV strings in series (i.e., 12), n is the diode ideality factor (set equal to the number of junctions), k is the where the thermal resistance, R th_array , between each cell array and T amb is calculated with Equation A2 in the appendix, as defined in IEC 62670-3. 13 The mean cell temperatures translated to SOC are also shown in Table 4 above. In average the CPV and PV arrays operated at 64 C and 45 C, respectively.

| POWER RATING OF THE CPV ARRAY
The IEC 62670-3 13 standard contains the linear equations, that is, Equations 4 and 5, necessary to translate the P MPP of the CPV array to a fixed DNI level and cell temperature, for example, STC or SOC.
Thus, after filtering the data according to Table 2 where N is the number of valid measurements after applying the filtering criteria from Table 2, η is the measured efficiency value, δ is the absolute TC of efficiency extracted from five TTM (δ 3J = −0.085% abs /K and δ 4J = −0.070% abs /K), T STCjjSOC is the mean cell T A B L E 4 Mean operating temperature ± standard deviation of the concentrator photovoltaic (CPV) and flat-plate PV arrays of the 3J and 4J EyeCon modules calculated at prevailing ambient conditions from filtered I-V data (T CPV and T PV ) and translated to standard operating condition (SOC) (T CPV_SOC and T PV_SOC ) as described in Section 5.2 Module  under test is recommended in IEC 60904-7 16 to avoid the need of spectral mismatch corrections.
In the following subsections, we present the procedures to separate the front and rear current contributions and the irradiance responses of the bifacial PV array. Nevertheless, the explained procedure will also work for hybrid CPV/flat-plate PV modules using monofacial instead of bifacial flat-plate PV cells.
Additionally, we show how to translate the I-V curves to STC and SOC based on the equations given in Procedure 1 of IEC 60891 18 with slight modifications.

| Separation of bifacial I SC into front and rear contributions
When the PV array is bifacially illuminated, the front and rear power contributions need to be independently translated to STC and SOC.
Thus, the first step consists on splitting the bifacial I SC of the PV array into front and rear components, that is, I SC = I front + I rear . Therefore, we correlated I rear to the I SC of a rear reference solar cell with identical spectral response (I SC_ref ) by calculating the mean ratio between the I SC of the PV array with the front side shaded (I SC_rear ) and I SC_ref corrected to the temperature of the flat-plate PV array, that is, I SC_ratio = mean (I SC_rear /I SC_ref ). For the measurements investigated, the temperature correction is less than 2 K because both devices are only absorbing rear side irradiance.

Figure 8 depicts the I SC_rear as a function of solar azimuth angle
for the PV array (black circles) and for the reference cell sensor (gray triangles), which are both positioned in the northeast (NE) corner of the tracker as shown in Figure 4. As denoted by their ratio (hollow blue triangles), the I SC_rear of the 4J EyeCon module has a mean value of (0.907 ± 0.008) Á I SC_ref_NE . Calculated in the same manner but using the northwest (NW) reference cell, the mean I SC_rear of the 3J EyeCon module that is mounted on the NW corner of the tracker has a value of (0.962 ± 0.011) Á I SC_ref_NW (not shown in Figure 8).
Moreover, the I SC ratio between the northwest and the NE reference cell sensors (hollow red squares) oscillates between 0 and 12% with a mean value of (3.5 ± 3)%. This shows the influence of the surroundings' reflectivity on rear irradiance uniformity as the tracker's background changes during the day. As depicted at the bottom of

| Bifacial PV array characterization of rear irradiance response
Once I rear has been separated from the bifacial I SC , it should be translated to 25 C, using the TC α of the PV array and Equation A4. Then, the rear irradiance response (ρ) is calculated as the mean ratio of I rear_25 C over BNI, that is, ρ = mean (I rear_25 C /BNI). In Figure 9, the rear irradiance response of the 4J EyeCon module at 25 C is shown as a function of solar azimuth angle. The unfiltered data (black circles) describes a parabolic trend that peaks around solar zenith (180 ) and slightly drops towards dawn and dusk (<120 and >240 ). The asymmetric trend is due to the different background view factors at the positions of the PV array and reference cell sensor.
Nevertheless, the filtered data (red circles) fall within the plateau where 60% of the unfiltered data concentrates; thus, both data sets yield a mean value of 3.46 mAÁm 2 /W with a low standard deviation (<1.2%). Displaying similar behavior, the mean rear irradiance response of the 3J EyeCon module is 3.67 mAÁm 2 /W (not shown in Figure 8). That is 6% higher than the 4J EyeCon module due to the reflection losses caused by the bubbles in the lamination layer of the . Figure 10 shows the GNI irradiance response (I front /GNI) as a function of DNI/GNI, where the GNI irradiance response at 25 C linearly decreases. According to Equation 6, the intercept of the linear trend described by the data represents ε, whereas γ corresponds to the sum of ε and the slope. Moreover, the NRMSE of the linear fit applied to the unfiltered data (black circles) assuming γ > 0 (black line) decreased from 7% to 1% when the data was filtered (red circles), but increased to 13% when assuming γ = 0 (dashed line) for the unfiltered data.
Note that γ = 0 would mean that lens-scattered DNI does not contribute to I front of the PV array. Thus, it is important to consider the absorption of scattered DNI, particularly at the DNI/GNI where the power rating is performed, that is 0.9, because neglecting γ results in a 24% underestimation of I front_25 C . As shown in the inset, the fits to the filtered (red line) and unfiltered (black line) data agree within 2% despite the narrow DNI/GNI range covered by the former.
where the temperature corrected ε, γ, and ρ determine the reference short-circuit current and I SC is the short-circuit current of the measured I-V curve. Here, it is important to note that the current temperature correction in Equation 7 is performed on ε, γ, and ρ as stated in the previous subsection, thus the αÁ(T 2 − T 1 ) term from the IEC 60891 Procedure 1 18 is dropped. On the other hand, the voltage translation from the same standard applies without modification as given in Equation 8,  Figure 11).
Additionally, the mean P PV_STCjjSOC at BNI = 0 W/m 2 corresponds to the front power output rated at STCjjSOC (P PV_front_STCjjSOC ) of the PV array of the hybrid CPV/flat-plate PV modules. Furthermore, the slopes of the linear fits applied to P PV_STCjjSOC , as shown in Figure 11, that pass through P PV_front_STC (blue line) and P PV_front_SOC (red line) represent the bifacial power gains (BiFi STCjjSOC ) in absolute units. The bifaciality factor, φ, defined as the ratio between the rear over the front power output, is then calculated as φ = 100 W/m 2 ÁBiFi STC / P PV_front_STC , also in absolute units. As a summary, Table 5 compiles the STC and SOC results for P PV_front , BiFi, and φ of the PV arrays of the 3J and 4J EyeCon modules.
F I G U R E 1 0 Filtered (red circles) and unfiltered (black circles) front irradiance response (I front /GNI) of the PV array of the 4J EyeCon module as a function of direct normal irradiance (DNI)/global normal irradiance (GNI). The linear fit to the unfiltered data allowing γ > 0 (black line) has a significantly smaller normalized root-mean-square error (NRMSE) without bias compared with the fit with γ set to 0 (dashed line  It is important to note that the values listed in Table 6 were calculated with the procedure described in the previous sections based on measurements under double-side illumination using reference cell sensors, the filtering criteria from because this simplifies the characterization of the front irradiance response, that is, ε = mean (I front_25 C /DIF).
The comparison of these four alternative approaches with the one using double-side illumination, reference cell sensors, filtering criteria, and γ > 0 is presented in Figure 12, where the CPV (gray), front (red) and rear (blue) PV power contributions to the total hybrid output are shown for every case. Fourth, the front power output of the bifacial PV array is underestimated by up to 2.5% when the absorption of lens-scattered DNI is neglected (γ = 0) and the calculation of the front irradiance response is simplified to, ε = mean (I front_25 C /DIF). However, if γ = 0 is assumed for the unfiltered data set, the power underestimation raises significantly to 11.8% due to characterization under the prevalent spectral conditions in Freiburg (DNI/GNI = 0.84 ± 0.05), because the mean value of the front irradiance response is statistically decreased.
Based on this analysis, we believe that a simplified hybrid bifacial power rating procedure is acceptable when the CPV array is measured without rear shading, the PV array is characterized under single-side illumination (if no reference rear device is available to split the bifacial I SC ) using pyranometers as GNI and BNI sensors while assuming the absorption of lens-scattered DNI (γ > 0) and at least filtering the CPV data according to the CPV standard, IEC 62670-3. 13 In this case, the hybrid bifacial power output is only 0.5% rel lower and within the uncertainty of the fully compliant procedure, but the complexity and hardware requirements are significantly reduced. For the power rating of the PV array, the bifacial I SC is split into front and rear contributions using a rear reference solar cell to subsequently characterize the irradiance response of each side independently. Then, the I-V curves of the PV array are translated to STC and SOC using procedure 1 in IEC 60891 18  Finally, we found that a simplified power rating procedure, using single-side illumination to characterize the bifacial PV array and pyranometers to measure the GNI and BNI, yielded acceptable results (power underestimation <0.5% rel ) as long as the CPV array data were measured without rear shading and filtered according to IEC 62670-3. 13 Future work shall focus on the energy yield calculation of hybrid CPV/flat-plate PV modules to assess their potential worldwide.

| SUMMARY AND CONCLUSION
The thermal resistance (R th_array ) of the CPV and PV cell arrays (T array ) against ambient temperature (T amb ) is calculated with Equation A2. 13 The expression neglects the effect of wind because it is less than ±1 K in the filtered range between 0.5 and 5 m/s.  13,29 where N S is the number of CPV strings in series, n is the diode ideality factor equal to the number of junctions per cell, k is Boltzmann's constant, q is the elementary charge and T CPV is the mean CPV array temperature. The f Voc value of the 3J and 4J CPV arrays varies between 1.001-1.003 for maximum DNI deviations of 80 W/m 2 below the reference irradiance. Thus, its influence is negligible in the presented cases.
Relying on the verified I SC linearity with respect to temperature, Equation A4 18 translates a measured I SC1 from a temperature T 1 and irradiance G, to I SC2 at a temperature T 2 . The calculation uses the absolute TC of short-circuit current of the device, α, which is given in units of μAÁm 2 /(WÁK) and is valid in the investigated range (25 C-50 C).