Improving the accuracy of energy yield calculations of tandem solar cell‐based CPV‐modules

Energy yield calculations for CPV modules that use tandem solar cell technology have been performed and analysed in this work. Two BSQ D280 CPV modules were used as specimen: one located in Freiburg, Germany, and one in Greater Noida, India. The current–voltage curves of both modules were measured for several months together with the prevailing ambient conditions. The energy yield in the respective measurement periods were calculated using the software PVsyst. It has been found that the energy yield modelled with PVsyst has a good agreement with the one measured in Freiburg, but deviates by 10% from the one measured in Greater Noida. The reason is most likely the high aerosol content in Greater Noida and thus the non‐appropriate consideration of spectral irradiance impact by PVsyst, which uses air mass and DNI as the only atmospherical parameters. The accuracy of the PVsyst calculation has been strongly improved in this work by using SMR corrected DNI values as input for the PVsyst calculation. In this manner, the impact of spectral irradiance variation on (C)PV module power output can be considered in energy yield calculations by PVsyst. The deviation of the calculated and measured energy yield could be reduced to below 1%.


| INTRODUCTION
Solar cells consisting of several pn-junctions have entered the market of photovoltaic power generation in various manners. Tandem (alias multi-junction) solar cells are used in concentrator photovoltaic (CPV) systems since many years. 1 However, flat plate photovoltaic systems, which are recently dominated by silicon single junction solar cells, are a future market for tandem solar cells. 2 The advantage of tandem solar cells is the higher conversion efficiency compared to single junction solar cells. 3 However, one of the less advantageous characteristics of tandem cells is the dependence of their performance on the solar spectrum. 4 The spectral irradiance itself is strongly varying with daytime, season, and location. On one hand, the reason for this variation is the change of the sunlight's path length (air mass) through the atmosphere and on the other composition of the earth's atmosphere.
Aerosol and water vapour content are the atmospherical parameters with the strongest impact on spectral irradiance and have to be considered when determining the energy output of CPV modules. 5 In this manner, not only the instantaneous power output of CPV power plants that are using tandem solar cells reveals a dependence on the variation of spectral irradiance, but also their yearly energy yield is affected. However, commonly used software tools, for example, PVsyst, 6 which can forecast the energy yield of single junction PV power plants very precisely, only take into account the variation of spectral irradiance by approximation. For instance, PVsyst uses the so-called 'utilisation factors' (UF) that depend on DNI and AM for considering the impact of the variation in spectral irradiance. 7 In this manner, the daily and seasonal variation of the sunlight's path length through the atmosphere is considered. However, the variation of the composition of the earth's atmosphere is neglected. This is an appropriate approach for locations with high yearly DNI and with low aerosol content, as has been shown in Gerstmaier et al. 6 Nevertheless, at locations with significant impact of the aerosol content, this approach fails. As we have shown in this paper, air mass as the only atmospherical parameter is not sufficient to accurately calculate the energy yield of a CPV system in Greater Noida, India. Furthermore, we propose an approach that uses spectral matching ratios to adapt the input parameter DNI in a manner that PVsyst is enabled to accurately calculate the energy yield of this CPV system in Greater Noida, India. A related approach to use spectrally corrected DNI values has been published in Ant on et al. 8 However, in this publication, a spectrally corrected DNI has been proposed for CPV module power ratings rather than as an input value for energy yield calculations.
Furthermore, the spectrally corrected DNI determined in Ant on et al. 8 only uses component cell sensors without considering the measured DNI from Pyrheliometer readings. In our approach, component cell sensor readings are used to determine spectral matching ratios that are then used to correct DNI values measured from a pyrheliometer.

| THE SPECIMEN AND MEASUREMENT SET-UP
The two BSQ-D280 CPV modules used as specimen in this work are shown in Figure 1. The BSQ modules use PMMA dome-shaped lenses to focus the sun light 820-fold onto a triple-junction solar cell. The nominal power output of these CPV modules is 280 W.
One BSQ module (AA-695, Figure 1  For both modules, current-voltage (I-V) characteristics were recorded every few minutes. Together with each I-V curve measurement, the ambient conditions were logged. The ambient conditions recordings include, amongst others, direct normal irradiance (DNI), ambient temperature, and spectral matching ratios (SMR [9][10][11]  where under realistic terrestrial solar spectrum, only the subcells with the two highest band gaps will limit the current. In this manner, these are the two relevant subcells, and thus SMR 12 is the only SMR value considered in this work. Freiburg and at the same time that the module efficiency is close to its peak efficiency. This is however not the case in Greater Noida. The red marking in Figure 2, right, shows that the spectral irradiance at an air mass below 1.5 can correspond to SMR 12 values as low as 0.4 with a module efficiency much lower than the peak efficiency. The reason for this is without much doubt the high and strongly varying aerosol content in Greater Noida. The PVsyst approach is to consider spectral irradiance compositions by using air mass as the only proxy, however, at such high AOD locations, this approach will fail.

| SMR CORRECTED DNI VALUES AS BASIS OF ENERGY YIELD CALCULATION
In the following, a strategy is introduced on how to overcome the approach of PVsyst to consider the influence of spectral irradiance variations by just using air mass as a proxy. This option is to correct the prevailing DNI values with the prevailing SMR 12 value and to use this SMR 12  The main input parameters of PVsyst regarding the electrical  The energy yields that are measured for the specimen modules at their respective locations and measurement periods are shown in Figure 3. The graphs in Figure 3 show the accumulated energy as a function of time. Hourly power output values have been used as basis for the accumulated energy. In addition, the graphs show the comparison with energy yields calculated with PVsyst using the measured DNI as well as the spectrally corrected DNI SMR introduced above.
When using the DNI SMR as input parameter, the UFs for DNI and air mass are kept constant at unity. The left graph in Figure 3 shows   is a measure for the agreement of the instantaneous power outputs of the CPV modules.
where P calc is the calculated hourly power output and P meas the measured one, n is the total number of measurement points, P max is the maximum measured hourly power output, and P min the minimum. DNI values has also led to a low deviation (À0.7%) of calculated to measured energy yield in Freiburg, Germany. However, a low deviation (0.5%) has already been found when using the regular DNI as input parameter for PVsyst at the location of Freiburg. In summary, the new approach of using SMR corrected DNI as input parameter for PVsyst has been found equivalent to the regular approach in Freiburg for one BSQ CPV module. In contrast the energy yield calculation of PVsyst has a much better agreement in Greater Noida when using the SMR corrected DNI for another BSQ CPV module.
The new approach shown in this work is also promising for tandem (alias multi-junction) cell-based flat plate PV modules. Also, this module type has a stronger dependency on spectral irradiance compared to single junction flat plate PV modules. Thus, it will be necessary to consider the spectral variability in the PVsyst energy yield calculations for tandem cell flat pate PV modules, and this can be done in a similar manner as for tandem cell-based CPV modules. However, in this work, we focus on SMR values derived from component cell sensors with their field of view restricted by collimating tubes. 11 In this manner, only the spectral irradiance of the direct sun light is considered, which is appropriate for CPV modules. This approach could be also used for flat plate modules made with tandem solar cells.
In this case, the component cells have to be measured without collimating tubes receiving the full global irradiance.