Unknown correlations in spectral quantities and a method for taking them into account in uncertainty of spectral mismatch in solar cell calibration

Efficacies of solar cells are routinely characterized using solar simulators and a reference cell in accordance with standard testing conditions. Deviation of the spectrum of the light source from the standardized spectrum AM1.5 together with the difference in the spectral responsivities of the reference cell and the solar cell being measured result in measurement errors that are taken into account using the so-called spectral mismatch correction factor (SMCF). This is calculated by integrations using measured spectral data.
Calculation of the uncertainty of the SMCF is far from trivial. Simple uncertainty estimation routines assume that the values of spectral quantities are uncorrelated between wavelengths. This is to a large extent not true. Spectral measurements contain systematic errors due to correlations which cause resulting measurement errors to extend beyond the measurement uncertainties calculated assuming uncorrelated data. The systematic structures are often unknown, which prevents taking them into account.
We have developed a method for estimating limits of uncertainties in the presence of unknown correlations. The method goes through all possible scenarios of deviations using Monte Carlo analysis. Varying spectral error functions are produced by combining spectral base functions, and the distorted spectra are used to calculate the desired quantities. Standard deviations of the different scenarios give uncertainties assuming no correlations, uncertainties assuming full correlation, and uncertainties for an unfavorable case of unknown correlations. We have earlier demonstrated use of the method in analyzing uncertainties of colorimetric properties of lamps [1] and in determining atmospheric ozone content [2].
We now extend our methodology for SMCF of solar cell calibrations. Uncertainty limits of SMCF are calculated considering possible spectral correlations in the spectral irradiance, spectral responsivity of the reference cell, and the detector under test. To validate our estimates, we have compared the resulting uncertainties with uncertainties calculated by six other laboratories making their own assumptions. The worst-case and best-case uncertainties we calculate lie at the maximum and minimum extremes of the comparison. Making assumptions on most probable correlations, we obtain a value close to the median.
This work has received funding from the European Metrology Programme for Innovation and Research (EMPIR) co-financed by the Participating States and from the European Union’s Horizon 2020 research and innovation programme within the joint research project 19ENG01 Metro-PV “Metrology for emerging PV applications.”
[1] Petri Kärhä, Anna Vaskuri, Henrik Mäntynen, Nikke Mikkonen, and Erkki Ikonen, “Method for estimating effects of unknown correlations in spectral irradiance data on uncertainties of spectrally integrated colorimetric quantities,” Metrologia 54, 524 – 534 (2017). https://doi.org/10.1088/1681-7575/aa7b39
[2] Anna Vaskuri, Petri Kärhä, Luca Egli, Julian Gröbner, and Erkki Ikonen, “Uncertainty analysis of total ozone derived from direct solar irradiance spectra in the presence of unknown spectral deviations,” Atmos. Meas. Tech. 11, 3595 – 3610 (2018). https://doi.org/10.5194/amt-11-1-2018