pvlib.spectrum.spectral_factor_jrc

pvlib.spectrum.spectral_factor_jrc(airmass, clearsky_index, module_type=None, coefficients=None)

Estimate a technology-specific spectral mismatch modifier from airmass and clear sky index using the JRC model.

The JRC spectral mismatch model includes the effects of cloud cover on the irradiance spectrum. Model coefficients are derived using measurements of irradiance and module performance at the Joint Research Centre (JRC) in Ispra, Italy (45.80N, 8.62E). Coefficients for two module types are available via the module_type parameter. More details on the model can be found in [1].

Parameters:

• airmass (numeric) – relative airmass. [unitless]

• clearsky_index (numeric) – clear sky index. [unitless]

• module_type (str, optional) –

  One of the following PV technology strings from [1]:

  • 'cdte' - anonymous CdTe module.

  • 'multisi' - anonymous multicrystalline Si module.

• coefficients (array-like, optional) – user-defined coefficients, if not using one of the default coefficient sets via the module_type parameter.

Returns:

mismatch (numeric) – spectral mismatch factor (unitless) which is multiplied with broadband irradiance reaching a module’s cells to estimate effective irradiance, i.e., the irradiance that is converted to electrical current.

Notes

The JRC model parameterises the spectral mismatch factor as a function of air mass and the clear sky index as follows:

\[M = 1 + a_1(e^{-k_c}-e^{-1}) + a_2(k_c-1)+a_3(AM-1.5),\]

where \(M\) is the spectral mismatch factor, \(k_c\) is the clear sky index, \(AM\) is the air mass, \(e\) is Euler’s number, and \(a_1, a_2, a_3\) are module-specific coefficients. The \(a_n\) coefficients available via the coefficients parameter differ from the \(k_n\) coefficients documented in [1] in that they are normalised by the specific short-circuit current value, \(I_{sc0}^*\), which is the expected short-circuit current at standard test conditions indoors. The model used to estimate the air mass (denoted as \(AM\)) is not stated in the original publication. The authors of [1] used the ESRA model [2] to estimate the clear sky GHI for the clear sky index, which is the ratio of GHI to clear sky GHI. Also, prior to the calculation of \(k_c\), the irradiance measurements were corrected for angle of incidence using the Martin and Ruiz model [3].

References

[1] (1,2,3,4)

Huld, T., Sample, T., and Dunlop, E., 2009. A simple model for estimating the influence of spectrum variations on PV performance. In Proceedings of the 24th European Photovoltaic Solar Energy Conference, Hamburg, Germany pp. 3385-3389. 2009. Accessed at: https://www.researchgate.net/publication/256080247

[2]

Rigollier, C., Bauer, O., and Wald, L., 2000. On the clear sky model of the ESRA—European Solar Radiation Atlas—with respect to the Heliosat method. Solar energy, 68(1), pp.33-48. DOI: 10.1016/S0038-092X(99)00055-9

[3]

Martin, N. and Ruiz, J. M., 2001. Calculation of the PV modules angular losses under field conditions by means of an analytical model. Solar Energy Materials and Solar Cells, 70(1), 25-38. DOI: 10.1016/S0927-0248(00)00408-6