CALCULATION OF THE SHORT-CIRCUIT CURRENT OF COLORED …

CALCULATION OF THE SHORT-CIRCUIT CURRENT OF COLORED BIPV MODULES UNDER FIELD CONDITIONS BY APPLICATION OF SPECTRALLY AND ANGLE RESOLVED MEASUREMENT DATA

Lionel Clasing1, Simon Schaaf1, Ulf Blieske1, Nicholas Riedel-Lyngskær2, Adrián A. Santamaría Lancia2, Nils Reiners3

1Cologne University of Applied Sciences, Faculty for Process Engineering, Energy and Mechanical Systems, Cologne Institute for Renewable Energy, Betzdorfer Str. 2, 50679 Cologne, Germany

2Technical University of Denmark, Department of Photonics Engineering, Roskilde, Denmark 3Fraunhofer Institute for Solar Energy Systems ISE, Electrical Energy Storage Department, Freiburg, Germany

ABSTRACT: The aim of this work is to determine the short-circuit current of colored solar glasses under field conditions, which includes varying solar spectral irradiance, oblique irradiation angles and fractions of diffuse light. Therefore, the field performance of colored building-integrated photovoltaic modules is calculated with spectral solar resource data and angular-dependent spectral responsivity measurements from laboratory testing. This method allows to examine the behavior of modules under test by application of physical laboratory measurements and spectral solar resource data. In order to validate the short-circuit current calculations, monitoring data from field tests are used. In order to assess the results, the short-circuit current is compared with a model using the incidence angle modifier. The results show that the application of angular-dependent spectral responsivity measurements allows to reduce relative mean bias error from 2.26% to 0.25% and relative root mean square error from 2.72% to 1.57% for the blue colored building-integrated photovoltaic module compared to the incidence angle modifier model, respectively. Keywords: BIPV, colored solar glass, short-circuit current, angular-dependent spectral responsivity, IAM

1 INTRODUCTION Colored glasses are of high interest for building-integrated PV (BIPV) applications such as the integration of modules in façades. Using colored glass allows a wide variety of designs for architects and planners. However, to introduce modules with colored glasses to the market, it is crucial to give realistic yield predictions to the investors. As for BIPV modules, the orientation is generally not ideal and thus the share of suboptimal angles of incidence (AOI) on the module surfaces is much higher than at standard photovoltaic (PV) systems. Therefore, it is important to have accurate models for the non-perpendicular incidence cases. The incidence angle modifier (IAM) is normally used to account for reflection losses at the glass-air interface. According to the IEC standard 61853-2:2016, the IAM is derived from the measured change in short-circuit current ISC with changing AOI [1]. A few PV system simulation tools use additional spectral correction factors for specific cell and module types. Such spectral corrections are generally given as simple correlations with air mass [2, 3]. These standard procedures do typically not include spectral measurements and do not consider that the IAM is not only a function of the AOI, but is also varying with different spectra [4]. Therefore, the angular-dependent spectral responsivity (ASR) is applied for the first time to calculate the ISC in a physical measurement setup under field conditions. Prior works about ASR data have focused on laboratory measurements [5, 6] or theory [7, 8]. 2 CALCULATION AND MEASUREMENT OF THE SHORT-CIRCUIT CURRENT 2.1 PV field measurements and data pre-processing In order to investigate the spectral and angular-dependent influence of colored glass for application in BIPV modules in detail, single-cell laminates (200 mm x 200 mm) with blue and grey colored 3.2 mm glass samples, monocrystalline silicon solar cells (156 mm x 156 mm) equipped with two busbars, black back sheet and transparent ethylene-vinyl acetate encapsulant were

examined in this study. The color of the glass is obtained by a thin film multi-layer deposition on the inner glass surface. The outer glass surface is treated, which results in diffuse reflection to achieve improvements in aesthetics and avoid glare effects. In a measurement campaign the data of BIPV modules with different colored glasses and a control reference sample with standard ultra-white solar glass have been recorded under field conditions at the DTU campus in Risø, Denmark. Short-circuit current ISC and back sheet temperature TM of the test samples were measured in 10-second intervals each for horizontal orientation in July and August 2018. The samples are shown in Figure 1. It can be expected that the backsheet temperature TM under field conditions differs from the temperatures in the laboratory measurements, therefore the measured ISC values are temperature corrected. Furthermore, a high-resolved climate dataset with spectral and broadband irradiation, ambient temperature, relative humidity, precipitation and windspeed data for the period under consideration has been recorded at the same location.

Figure 1: BIPV test samples with different colored glasses used for measurements and calculations

The irradiation data includes broadband global horizontal irradiance GHI and diffuse horizontal irradiance DHI measured with two class A pyranometers in 10-second intervals. Direct normal irradiance DNI is measured with a class A pyrheliometer in 10-second intervals, as well. Additionally, spectrally resolved DHI and DNI are measured by two diffraction grating spectroradiometers. The spectrometers are specified for a wavelength range between 300 nm and 1100 nm with a full width half

38th European Photovoltaic Solar Energy Conference and Exhibition

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maximum (FWHM) spectral resolution of 7 nm in 1 nm steps. The spectral measurement data is recorded in 5-minute intervals [9]. Since crystalline silicon solar cells can convert wavelengths up to 1.2 µm, it is necessary to extend the missing wavelength range between 1.1 µm up to 1.2 µm of the measured spectral irradiance dataset for calculation of the ISC. This is done by means of the "Simple Model of the Atmospheric Radiative Transfer of Sunshine" (SMARTS) by Gueymard [10, 11]. The SMARTS model provides spectral GHI, DNI and DHI, but is limited to clear-sky conditions. For that reason, clouds are taken into account in the extended data by application of a cloud scaling factor according to Ernst et al. [12]. However, the spectrally resolved irradiance data is measured by two spectrometers in series, which results in a time offset of about 15 seconds between the start of the first measurement and end of the second measurement. In case of high cloud variability, the irradiance can change significantly during this period. To counteract the resulting uncertainties, the dataset is filtered using a variability index VI according to Stein et al. [13]. For this purpose, the broadband GHI values are used in a 2-minute interval around the respective measured value. If the VI is greater than 1.1, the corresponding measured value is removed. This filters only those values where the irradiance remains approximately identical between the measurements of the two spectrometers in the dataset. 2.2 Laboratory measurements and data pre-processing The ASR measurements in this work were performed by using a modified experimental setup in a laboratory at the TH Köln campus Deutz, Germany [14]. The setup is based on a solar simulator with filter wheel monochromator for PV solar cells (FiMo SR EQE, Aescusoft). It consists of a solar simulator, an upstream optical chopper, two filter-monochromators, an automated rotational sample stage for PV single cell laminates and a data acquisition system. The setup is divided into two rooms, which are only connected by an aperture for the light beam. The illumination source of the solar simulator is a xenon short-arc lamp (1000 W Osram XBO) connected to a stabilized DC power supply. The double filter wheel monochromator contains 40 different bandpass filters and can hence provide a wavelength range from 300 to 1188 nm with a FWHM spectral resolution of 25 nm. The wavelength steps of the measurement are specified by the bandpass filters and are equally distributed. The optical chopper is coupled with a lock-in amplifier to achieve high-precision measurements of the short-circuit current ISC at a specific wavelength. According to the IEC 60904-8 standard, the short-circuit current conditions must be ensured during spectral responsivity (SR) measurements, which is achieved by a 4-quadrant chopper. Furthermore, an appropriate bias illumination is used, as specified in the standard. However, the standard stated that it is sufficient to perform the SR measurements only for one irradiance intensity and one module temperature [15]. Subsequently, the SR measurement results are linearly interpolated and thus allow calculations with 1 nm spectral resolution. The ASR measurements were performed using a fully automated rotational sample stage. A second aperture is used to reduce the size of the monochromatic light spot to a small homogenous area. This light spot is projected completely onto the solar cell, even at high irradiation angles. The angular-dependent measurements were

performed based on the IEC 61853-2 standard, i.e. from -60° up to +60° AOI in 10° steps and down to -80° respectively up to +80° AOI in 5° steps [1]. As significantly increasing uncertainties were observed in an interlaboratory round robin test by Riedel-Lyngskær et al. [16] for AOI > 80°, the ISC calculations in this study are performed only up to AOI < |±80°|. The ASR measurements are linearly interpolated to 1° AOI resolution to obtain an appropriate level of detail in ISC calculations. In the AOI range between the defined 10° and 5° AOI steps, measurements with 1° AOI steps have been performed to determine the deviations between measured and linearly interpolated values. The measured and interpolated values show a good agreement, hence the AOI measurement steps recommended by the IEC 61853-2 standard are used in this study. The ASR plot shows the spectral and angular-dependent effects of the blue glass on the BIPV modules characteristics. However, increasing losses at higher AOI and wavelengths > 500 nm can be observed.

Figure 2: Measured and pre-processed SR of the blue colored PV test sample for different angle of incidence AOI

2.3 IAM measurement and simulation for direct and diffuse beam irradiance According to the IEC 61853-2 standard the IAM for direct beam irradiance can be measured and determined per equation (1) [1].

IAM = 𝐼𝐼𝑆𝑆𝑆𝑆(𝜃𝜃)

𝐼𝐼𝑆𝑆𝑆𝑆(0°) ∗ cos(𝜃𝜃) (1)

Another particular interest is given on modelling the influence of the IAM in diffuse beam irradiance in order to calculate losses by oblique light in a high-level of detail. For that reason, the IAM is applied to the diffuse beam irradiance for calculation of the short-circuit current ISC. In case of horizontal module orientation, only the diffuse sky irradiance must be considered. Hence, the direct and diffuse beam irradiance of the ground reflection can be neglected and a diffuse IAM for ground reflection is not required. However, Martín and Ruiz [17] presented an analytical model to simulate the IAM for standard solar glass based on only one shape parameter, the ar-value. Furthermore, they presented a method to apply the IAM to the sky diffuse beam irradiance, which is used in this work to calculate the ISC by application of ASR laboratory measurements. The experimental setup described in section 2.2 is used with broadband illumination to measure the IAM of each sample. The shape parameter ar is calculated by using the conducted IAM laboratory measurements and iterative fitting to the simulated IAM calculated by equation (2) [17]:


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IAM = 1 − exp (− cos(𝜃𝜃)

𝑎𝑎𝑟𝑟� )

1 − exp (−1 𝑎𝑎𝑟𝑟� ) (2)

In Figure 3 IAM measurements and simulations with Martín and Ruiz model [17] are shown. It can be observed that the simulation is not exactly fitting the measurements. In order to find the best fit, a comparison between different IAM simulation models has been done. The results show that the best agreement is shown by the model of Martín and Ruiz, followed by the ASHREA model [18]. Based on these findings, the model of Martín and Ruiz [17] is used for the simulation of the IAM for ISC calculations with ASR model.

Figure 3: Resulting shape parameters ar for Martín and Ruiz simulation model [17] determined by iterative fitting to IAM laboratory measurements for different colored BIPV modules

Additionally, the IAM model is used for direct beam irradiance in order to calculate the ISC with perpendicular SR0 to compare the results. 2.4 Mathematical expression of short-circuit current Generally, the short-circuit current ISC of a solar PV module can be calculated by the simplified equation (3).

Isc = A*�E (λ)* SR(λ, θ) dλ (3)

The surface area of the module A is multiplied by the integral over the global in-plane spectral irradiance on the PV solar module at a specific wavelength λ and ASR at a specific wavelength λ and AOI θ. The global in-plane spectral irradiance must be specified more in detail to calculate the ISC with an appropriate accuracy. Therefore, the measured DNI is converted to direct in-plane irradiance by multiplying it to the cosine of the AOI. Reflection losses caused by varying AOI are taken into account in the angular-dependent SR(λ,θ). Consequently, an IAM model is not applied for direct beam irradiance in the ASR approach. A diffuse IAM model, as described in section 2.3, is applied to the measured DHI. IAMdiff,sky accounts for the reflection losses of the diffuse sky irradiance, caused by the AOI. The direction of light rays of the diffuse irradiation is assumed isotropic. As a result, the ISC,ASR of a BIPV module is calculated for horizontal orientation by application of ASR by the following equation (4).

I𝑆𝑆𝑆𝑆 ,𝐴𝐴𝑆𝑆𝐴𝐴=A*(�DNI(λ)* cos(θ) *SR(λ, θ) dλ (4) +�DHI(λ)*IAMdiff,sky*SR0(λ) dλ )

Nevertheless, the IAMdir model proposed by Martín and Ruiz [17] is used by multiplying with SR0 for direct beam irradiance to determine the ISC,IAM. The ISC,IAM is utilized to compare the ASR model with the model proposed by Martín and Ruiz for standard solar glass and is calculated by equation (5).

I𝑆𝑆𝑆𝑆 ,𝐼𝐼𝐴𝐴𝐼𝐼=A*(�DNI(λ)* cos(θ)* 𝐼𝐼𝐼𝐼𝐼𝐼𝑑𝑑𝑑𝑑𝑟𝑟 *SR0(λ) dλ (5)

+�DHI(λ)*IAMdiff,sky*SR0(λ) dλ ) 2.5 Model analysis and comparison In order to analyze and compare the calculated short-circuit current ISC for the respective colored module under test, a residual error RE is calculated per equation (6).

RE=𝐼𝐼𝑆𝑆𝑆𝑆,𝐼𝐼𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑟𝑟𝑀𝑀𝑑𝑑 − 𝐼𝐼𝑆𝑆𝑆𝑆,𝑆𝑆𝑀𝑀𝐶𝐶𝐶𝐶𝑀𝑀𝐶𝐶𝑀𝑀𝐶𝐶𝑀𝑀𝑑𝑑 (6) In this equation the residual error is calculated by the difference of the measured and calculated ISC. Thus, the residual error can be used to analyze and validate the calculations by application of the ASR in comparison with IAMdir model for DNI. A mean bias error MBE is calculated to summarize the error for the dataset under consideration according to equation(7).

𝐼𝐼𝑀𝑀𝑀𝑀 =

1𝑛𝑛�𝐼𝐼𝑆𝑆𝑆𝑆,𝐼𝐼𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑟𝑟𝑀𝑀𝑑𝑑 − 𝐼𝐼𝑆𝑆𝑆𝑆,𝑆𝑆𝑀𝑀𝐶𝐶𝐶𝐶𝑀𝑀𝐶𝐶𝑀𝑀𝐶𝐶𝑀𝑀𝑑𝑑

𝑛𝑛

𝑑𝑑=1

(7)

Furthermore, a root mean square error RMSE is calculated by equation (8).

𝑅𝑅𝐼𝐼𝑅𝑅𝑀𝑀 = �1𝑛𝑛��𝐼𝐼𝑆𝑆𝑆𝑆,𝐼𝐼𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑟𝑟𝑀𝑀𝑑𝑑 − 𝐼𝐼𝑆𝑆𝑆𝑆,𝑆𝑆𝑀𝑀𝐶𝐶𝐶𝐶𝑀𝑀𝐶𝐶𝑀𝑀𝐶𝐶𝑀𝑀𝑑𝑑�

2𝑛𝑛

𝑑𝑑=1

(8)

3 RESULTS Figure 4 shows the results of the measured and calculated short-circuit current ISC of the blue colored BIPV module on 3rd of August 2018. The ISC is calculated according to equation (4) by the ASR model with horizontal module orientation. In addition, the residual error for each timestamp calculated by equation (6) is shown.

Figure 4: Measured and calculated short-circuit current ISC (ASR model) for a blue colored PV module with horizontal orientation on 3rd August 2018

The 3rd of August has mostly clear-sky conditions, especially in the morning. In the afternoon its partly


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cloudy and cloud variability increases. The application of a VI model by Stein et al. [13], as described in Section 2.1, filters a few timestamps at which the cloud variability is above the specified threshold. A good agreement between measurement and calculation can be observed for clear-sky conditions. Between 7 am and approximately 2.30 pm the residual error shows a maximum absolute error of 100.85 mA and a MBE of 19.94 mA. From 2.30 pm on, the cloud variability is partly increased and a few filtered timestamps can be observed. The error increases up to a maximum of 245.31 mA at 4.40 pm. The largest errors are either before or after VI filtered timestamps. 3.1 Model validation and comparison A model validation is done to assess the short-circuit current ISC calculations for two different colored BIPV modules and a control reference with standard solar glass. Furthermore, a comparison is done with the IAM model proposed by Martín and Ruiz [17]. Figure 5 shows the residual error of ISC,ASR model in terms of direct beam irradiance as a function of the AOI. Additionally, the residual error of the ISC,IAM is shown. ISC,IAM is calculated by applying the IAM model to account for angular optical losses. Therefore, the SR0 with perpendicular AOI is used. Finally, a linear regression model is calculated, which shows a slightly increasing trend with increasing AOI.

Figure 5: Residual error of calculated and measured short-circuit current ISC of a blue colored BIPV module as a function of angle of incidence AOI. ISC is calculated by two different models accounting for optical losses on 3rd August 2018.

Table I summarizes the results of the absolute and relative MBE and RMSE of the calculated ISC of three different colored BIPV modules on 3rd of August 2018. First, a good agreement for the control reference with a relative MBE of -0.29% and -0.41% can be observed for both models. Second, the results of the ASR model show a decrease of the relative MBE from 2.26% to 0.05% for the blue colored test sample compared to the IAM model. Third, the comparison for the grey colored test samples shows that both models show nearly identical results. Table I: Summarized residual error results of short-circuit circuit ISC calculation of three different BIPV modules with ASR and IAM model on 3rd August 2018

ASR model Control Blue Grey MBE [mA] -14.69 2.41 -27.11 MBErel [%] -0.29 0.05 -0.55 RMSE [mA] 54.22 50.29 60.1 RMSErel [%] 1.06 1.1 1.21

IAMdir model MBE [mA] -20.86 103.8 -33.28 MBErel [%] -0.41 2.26 -0.67 RMSE [mA] 52.22 116.31 63.69 RMSErel [%] 1.02 2.53 1.28 A residual error analysis is done for a time period of 11 days in July and August. The dataset contains 519 timestamps and is filtered by a VI > 1.1, as described in section 2.1. The results for the blue colored BIPV module are presented in Figure 6.

Figure 6: Residual error of calculated and measured short-circuit ISC current of a blue colored BIPV as a function of angle of incidence AOI. ISC is calculated by two different models accounting for optical losses with from 31st July until 10th August 2018.

Table II summarizes the MBE and RMSE of the performed ISC calculations for 11 days in July and August. In comparison with the analysis of one day, the ASR model shows slightly larger MBE and RMSE of 0.25% and 1.57% for the blue colored BIPV module. The residual error for the control reference and grey BIPV module is nearly equal for both calculation models, although the ASR model consistently shows slightly lower errors. Table II: Summarized statistical metrics for residual error of short-circuit current ISC calculation of three different BIPV modules with ASR and IAM model from 31rd July until 10th August 2018

ASR model Control Blue Grey MBE [mA] -9.1 9.74 -21.85 MBErel [%] -0.21 0.25 -0.54 RMSE [mA] 56.47 59.85 71.5 RMSErel [%] 1.32 1.57 1.76 IAMdir model MBE [mA] -16.13 86.29 -23.89 MBErel [%] -0.37 2.26 -0.59 RMSE [mA] 58.72 103.56 75.82 RMSErel [%] 1.37 2.72 1.87 5 SUMMARY The calculated short-circuit ISC of BIPV modules with different colored glasses is presented in this work. Therefore, the ASR is applied for the first time in a calculation model for direct beam irradiance in order to calculate the ISC of colored BIPV modules under field conditions. The calculations are validated with field measurement data of 11 days in July and August for horizontal module orientation. The results of the calculations show a good agreement with the conducted


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field measurements with a MBE of 9.74 mA and -21.85 mA for the blue and grey colored module, respectively. Thus, the ASR model allows to reduce relative MBE from 2.26% to 0.25% and relative RMSE from 2.72% to 1.57% for the blue colored BIPV module compared to the IAMdir model, respectively. In future works the ISC is calculated and validated for BIPV modules with a tilt angle by application of a transposition model for diffuse sky and ground reflected irradiance. Furthermore, the ASR should be additionally applied for diffuse sky irradiance instead of a diffuse IAM model. 6 ACKNOWLEGDEMENTS This project has been financed by the European Fonds for Regional Development North Rhine-Westphalia (EFRE.NRW) 7 REFERENCES [1] IEC 61853-2:2016 Photovoltaic module

performance testing and energy rating - part 2: spectral responsivity, incidence angle and module operating temperature measurements, International Electrotechnical Commission, 2016.

[2] M. Lee and A. Panchula, "Spectral correction for photovoltaic module performance based on air mass and precipitable water," in 43rd Photovoltaic Specialists Conference (PVSC), Portland, OR, USA, 2016.

[3] B. H. King, C. W. Hansen, D. Riley, C. D. Robinson and L. Pratt, Procedure to Determine Coefficients for the Sandia Array Performance Model (SAPM), Sandia National Laboratories, 2016.

[4] F. Plag, I. Kröger, T. Fey, F. Witt and S. Winter, "Angular‐dependent spectral responsivity—Traceable measurements on optical losses in PV devices," Progress in Photovoltaics: Research and Applications, Vol. 26, pp. 565-578, 2017.

[5] I. Geisemeyer, N. Tucher, B. Müller, H. Steinkemper, J. Hohl-Ebinger, M. C. Schubert and W. Warta, "Angle Dependence of Solar Cells and Modules: The Role of Cell Texturization," IEEE Journal of Photovoltaics Vol. 7, pp. 19-24, Jan. 2017.

[6] N. Reiners, U. Blieske and S. Siebentritt, "Investigation on the Angle and Spectral Dependence of the Internal and the External Quantum Efficiency of Crystalline Silicon Solar Cells and Modules," IEEE Journal of Photovoltaics Vol. 8, pp. 1738-1747, Nov. 2018.

[7] M. R. Lewis, E. M. Tonita, C. E. Valdivia, R.-J. K. L. J. Obhi, M. I. Bertoni and K. Hinzer, "Angular Dependence of Textured Bifacial Silicon Heterojunction Solar Cells for High Latitudes," in IEEE 46th Photovoltaic Specialists Conference (PVSC), Chicago, IL, USA, 2019.

[8] S. Pal, A. Reinders and R. Saive, "Simulation of Bifacial and Monofacial Silicon Solar Cell Short-Circuit Current Density Under Measured Spectro-Angular Solar Irradiance," IEEE Journal of Photovoltaics, Vol. 10, No. 6, pp. 1803-1815, 2020.

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Davidsen and G. Benatto, "Direct Beam and Diffuse Spectral Irradiance Measurements in a Nordic Country Analyzed With the Average Photon Energy Parameter," in IEEE 7th World Conference on Photovoltaic Energy Conversion (WCPEC) (A Joint Conference of 45th IEEE PVSC, 28th PVSEC & 34th EU PVSEC), 2018.

[10] C. Gueymard, SMARTS, A Simple Model of the Atmospheric Radiative Transfer of Sunshine: Algorithms and Performance Assessment, 1679 Clearlake Rd., Cocoa, FL 32922: Professional Paper FSEC-PF-270-95, Florida Solar Energy Center, 1995.

[11] C. Gueymard, "Parameterized Transmittance Model for Direct Beam and Circumsolar Spectral Irradiance," Solar Energy (71:5), pp. 325-346, 2001.

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[13] J. Stein, C. Hansen and M. Reno, "The Variability Index: A New and Novel Metric for Quantifying Irradiance and PV Output Variability," in World Renewable Energy Forum, USA, 2012.

[14] K. Meisenzahl, N. Schneble, M. Volk, U. Blieske, L. Clasing, J. Müller-Ost, J. Münzberg and P. Hakenberg, "Measuring the Incidence Angle Modifier of Optically Uncoupled Glass for PV Application," in 36th European Photovoltaic Solar Energy Conference and Exhibition, Marseille, France, 2019.

[15] IEC 60904-8:2014 Photovoltaic devices - Part 8: Measurement of spectral responsivity of a photovoltaic (PV) device, International Electrotechnical Commission, 2014.

[16] N. Riedel-Lyngskær, A. A. P. F. Santamaría Lancia, I. Kröger, M. R. Vogt, C. Schinke, R. S. Davidsen, M. Amdemeskel, M. J. Jansen and P. S. L. H. Manshanden, "Interlaboratory comparison of angular-dependent photovoltaic device measurements: Results and impact on energy rating," Progress in Photovoltaics: Research and Applications, December 2020.

[17] N. Martín and J. M. Ruiz, "A New Model for PV Modules Angular Losses under Field Conditions," International Journal of Solar Energy, pp. 19-31, Vol. 22, No. 1 2002.

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CALCULATION OF THE SHORT-CIRCUIT CURRENT OF COLORED …