Spectral mismatch uncertainty estimation in solar cell calibration using Monte Carlo simulation

This software package can be used to make a Monte Carlo simulation-based analysis of the uncertainty of the spectral mismatch factor in a solar cell calibration. The input parameters of the analysis include uncertainties of the spectral irradiance, spectral responsivity of the reference cell, and the spectral responsivity of the solar cell under test. Spectral irradiance has been further divided into its subcomponents; calibration, signal to noise ratio, bandwidth, wavelength, and stability that all contribute to the uncertainty.

The unique feature of this analysis is that it considers effects of possible correlations that may cause systematic spectrally varying errors in the spectral quantities. The code generates spectrally varying errors functions that go through possible scenarios of errors that the uncertainties permit. Resulting variances can be used to estimate boundaries of the uncertainties; maximum in a case of severe correlations, minimum in the case of full (unity) correlation, and random for the case of no correlations. These can be further used to derive the most likely uncertainty as the average of the three figures obtained.

There are four data files in this package that are required to run the code.

1. E_sun.txt file contains the spectral irradiance AM1.5G that is the standardized spectrum to be used in calibration of solar cells.

2. E_meas.txt contains the spectral irradiance of the solar simulator and the corresponding uncertainties. The contents of the text file are as follows:

Column   Content

1        Wavelength / nm

2        Spectral irradiance of the solar simulator / W/m²nm

3        Uncertainty due to Signal-to-Noise ratio / %

4        Uncertainty due to Radiometric Calibration / %

5        Uncertainty due to Stability / %

6        Uncertainty due to Bandwidth / %

7        Uncertainty due to Wavelength / %

3. S_ref.txt contains the spectral responsivity of the reference cell and the corresponding uncertainty. The contents of the text file are as follows:

Column     Content

1          Wavelength / nm

2          Spectral responsivity of the reference cell / mA m²/W

3          Uncertainty in spectral responsivity of the reference cell / mA m²/W

4          Relative uncertainty in the spectral responsivity of the reference cell / %

4. S_DUT contains the spectral responsivity of the detector under test and the corresponding uncertainty. The contents of the text file are as follows:

Column     Content

1          Wavelength / nm

2          Spectral responsivity of the detector under test / m Am²/W

3          Uncertainty in spectral responsivity of the detector under test / mA m²/W

4          Relative uncertainty in the spectral responsivity of the detector under test / %

All uncertainties in the files are given as expanded uncertainties with coverage factor k = 2. The uncertainties that the code gives are standard uncertainties with coverage factor k = 1.

There are two Matlab code files provided in this package. MC_smm_main.m is the main code file that is to be run. MC_simulation.m is a function file supplementing the main code.

MC_smm_main.m reads the input parameters' data from the four data files and interpolates all data to 290 nm - 1200 nm wavelengths with a step size of 1. The number of runs and the number of base functions is also defined in the main file. The main code generates a plot with number of base functions N on the x-axis and the standard uncertainty / % on the y-axis for the input parameter under study.

MC_simulation.m is a function file. It creates orthogonal base functions and generates normally distributed random numbers that are used to produce weights "delta" for the N base functions. The weights and the base functions are used to produce distorted spectra of the parameter under study. This parameter is then inserted in Equation 1 in the function code file (line 75 - 84). The function file returns the standard uncertainty. The function is called in the main code file in lines 50 – 56.

In addition to the plot, the software generates a .txt file which contains the number of base functions N as column 1 and the Standard uncertainty / % as column 2 for the input parameter under study. As default, the software performs Monte Carlo analysis of the spectral responsivity of the detector under test. To test effect of other parameters, lines 26-32 are to be modified in the main code file (MC_smm_main.m). Also, lines 19 - 21 and lines 75 - 84 in the function file (MC_simulation.m) are to be modified as per the instructions provided in the code.

The code is to be repeated with all input parameters. The resulting data can then be used to estimate uncertainties for varying cases of possible correlations.