Low‐cost outdoor spectral irradiances determination and its application on Concentrator Photovoltaic module power rating and energy yield calculation

In this work, a method to calculate the aerosol content in the atmosphere and the prevailing spectral irradiance of the sunlight is introduced. This method does not aim for low measurement uncertainty but for cost effectiveness and does not require sophisticated equipment. The bases of the method are the clear sky direct normal irradiance (DNI) and a look‐up table calculated with the software tool SMARTS2. The ratio of clear sky DNI to the prevailing DNI in combination with the look‐up table allows the determination of aerosol optical depth (AOD), spectral matching ratios (SMR), and spectral irradiances. Besides the prevailing DNI, the following ambient condition parameters are required: Air pressure, relative humidity, and ambient temperature. This means a weather station and a pyrheliometer are sufficient for the determination of the prevailing spectral irradiance. Obviously, this method cannot guarantee the same accuracy as conventional spectral irradiance measurement methods (e.g., using a spectroradiometer). However, in this work, we demonstrate the potential of this new method as a fall‐back strategy for missing spectral irradiance data. This method is worth using when (C)PV module power output data needs to be evaluated in dependence of the composition of the spectral irradiance, but no regular spectral irradiance data are available. In this paper, the AOD and SMR values determined with the introduced method are compared to measurement data with common measurement devices demonstrating a satisfying agreement. The spectral irradiances calculated with this method are successfully tested for using as the basis for energy yield calculations and for the determination of the CPV module power output at Concentrator Standard Conditions according to IEC 62670‐1.


| INTRODUCTION
The power output of multijunction solar cells typically shows a significant dependence on the composition of the sunlight's spectral irradiance. 1 Therefore, the understanding of the behaviour of the (C)PV module power output and energy yield at prevailing ambient conditions in different seasons and locations demands for spectral irradiance data. However, these data are not available in all cases. The reason is the necessity of expensive equipment as a spectroradiometer or component cell sensors, for instance. For this reason, we have developed a cost-effective method that does not demand for sophisticated equipment. This method only requires the readings of a weather station and of a pyrheliometer, as relative humidity, air pressure, ambient temperature, and direct normal irradiance (DNI) are the input parameters used. From these parameters, aerosol optical depth (AOD 2 ), spectral matching ratios (SMR [3][4][5], and spectral irradiances can be calculated. Obviously, the outcome of this method is not as accurate as obtaining these values from commonly used measurement devices. However, the values calculated with this new method are still an adequate approach if there is no other source of spectral irradiance data available. In this work, we introduce and explain this method in detail. The method is based on the calculation of the clear sky DNI ratio and an AOD look-up table calculated using the software tool SMARTS2. 6 In the look-up table, a single AOD value is retrieved as a function of clear sky DNI ratio, precipitable water (PW), and air mass (AM). Clear sky DNI ratio is the ratio of prevailing DNI to DNI calculated with SMARTS2 with AOD and PW set to zero. The parameters PW and AM can be calculated using commonly available methods. [6][7][8] Once AM, AOD, clear sky DNI ratio, and PW are available, the prevailing spectral irradiance can be calculated using SMARTS2 as in Faine et al. 1 The calculated AOD values are compared to measured data in two different locations: Freiburg, Germany, and New Delhi, India.
Moreover, the spectral irradiances derived from the calculated AOD using SMARTS2 are tested by comparing measured SMR with SMR derived from the calculated spectral irradiance. The correlation between measured and calculated data is assessed by statistical quantities such as the coefficient of determination (R 2 ) and the mean absolute error (MAE).
Furthermore, the spectral irradiances calculated with this method are evaluated for their suitability as basis for energy yield calculations and for determination of the CPV module power output at Concentrator Standard Conditions. 5,9 For this reason, two different types of CPV modules are used as specimen: BSQ D280 and AZUR C3PV CPV modules.

| THE CLEAR SKY DNI METHODOLOGY TO RETRIEVE AOD
The method to calculate the AOD and spectral irradiances from the readings of a pyrheliometer and of a weather station according to this work is described in the following. The main idea behind this method is that the sunlight that hits the Earth's surface is attenuated on its way through the atmosphere by well know processes. 2 The three main processes are Rayleigh scattering by molecules, Mie scattering of the sunlight by microscale particles (aerosols), and the absorption of sunlight by PW. 1,2 These effects are proven to be calculated accurately by software tools like SMARTS2, 6 for instance. However, distinct input parameters need to be available for the correct calculation of spectral irradiances with SMARTS2. The main input parameters are the AM, AOD at 500 nm (AOD 500nm ), and PW. As AM can be calculated from time, latitude, and longitude, PW from relative humidity, air pressure, and ambient temperature, the main aim of the method is to obtain a value representative for AOD 500nm . The method is based on the following steps where the final step is the calculation of spectral 3. Calculation of AM, for every measured DNI and PW value: If PW is not measured it can be calculated from ambient temperature, relative humidity, and air pressure with equation (1) 4. Calculation of DNI ClearSky and DNI prev /DNI ClearSky for specific outdoor measurements.
5. Interpolating AOD 500nm,calc from the look-up table by using the parameters calculated in 3 and 4, which are PW, AM, and DNI prev / DNI ClearSky 6. Calculation of spectral irradiance with SMARTS2 using AOD 500nm,calc , PW calc , and AM as input parameters. Other parameters set as in IEC 60904-3. 10 Step 1 is the calculation of DNI ClearSky as a function of AM as shown in Figure 1 (left). DNI ClearSky is determined as the integral value of the spectral irradiances calculated with SMARTS2. The input parameters for SMARTS2 are set as defined for the AM1.5d reference conditions as listed in IEC 60904-3. 10 However, AOD 500nm and PW are set to a value of zero and AM is varied. The air pressure is set to 1013 mBar as this is sea level standard atmospheric pressure. If the method is used at a location where the air pressure differs strongly from this value, then it is recommended to adjust the air pressure.
Step 2 is the calculation of a look-up table with AOD 500nm as a function of AM, PW and DNI prev /DNI ClearSky using SMARTS2. The DNI-ClearSky value is taken from step 1, which is plotted in Figure 1 Figure 1 (right) shows the calculated DNI prev /DNI ClearSky values versus AOD 500nm . Obviously, DNI prev /DNI-ClearSky versus AOD 500nm is not a unique function. For this reason, additionally PW and AM have to be known to retrieve a distinct AOD 500nm value for a specific DNI prev /DNI ClearSky value. Figure 1 (right) exemplarily shows this for an AM of 1.5 and a PW of 1.2 (red line).
Step 3 is measuring the actual, prevailing DNI prev with a pyrheliometer and calculation of AM. The value for PW could be measured directly if appropriate equipment is available or calculated using Equation (1) as described in Garrison where p 00 is the yearly mean air pressure at sea level (1013.25 mbar), p 0 the yearly mean air pressure at the location, h rel is the relative humidity, and T amb the ambient temperature at the location. The value of AM is calculated using the equations in a previous work. 12 Step 4 is dividing the measured DNI with the value DNI ClearSky corresponding to the prevailing AM as in Figure 1 left. The resulting value of DNI prev /DNI ClearSky is then used together with the values determined for the prevailing PW and the calculated AM to derive a value for the prevailing AOD 500nm in step 5. Finally, in the last step the prevailing spectral irradiance is calculated with the software tool SMARTS2 by using AOD 500nm,calc , PW calc , and AM as input parameters.

| EXPERIMENTAL EVALUATION OF THE METHOD
The method to calculate the AOD from pyrheliometer and weather  Equation (2).
where n is the total number of measured values, y i the measured, and shape would be equivalent to AM1.5d. 12 The wavelength ranges which are typically used are the following: 300-600 nm, 600-900 nm, and 900-1800 nm. 5 The idea of these wavelength ranges

| APPLICATION OF THE METHOD FOR THE EVALUATION OF THE PERFORMANCE OF CPV MODULES USING MULTIJUNCTION SOLAR CELLS
The SMR values derived from the spectral irradiances calculated using the method described in Section 3 can have two exemplarily applications as input parameters for energy yield calculation and for perform- sor. 13 Figure 4 shows the electrical efficiency of the two CPV modules as a function of SMR 12 and SMR 23 . Figure 4 (left) shows the graph for the BSQ and right for the AZUR module as a comparison of SMR value derived from component cell sensor readings (blue) and SMR derived from spectral irradiances calculated using the method described in Section 3 (red). Data recorded at DNI to GNI ratios above 0.8 and ambient temperatures between 15 and 25 C has been used only. It can be seen in Figure 4 that the dependence of efficiency on  Table 1. Similar to Figure 4, data recorded at DNI to GNI ratios above 0. 8

DATA AVAILABILITY STATEMENT
Research data are not shared.