pvlib.irradiance.reindl

pvlib.irradiance.reindl(surface_tilt, surface_azimuth, dhi, dni, ghi, dni_extra, solar_zenith, solar_azimuth)

Determine the diffuse irradiance from the sky on a tilted surface using the Reindl (1990) model.

The Reindl (1990) model [1] [2] determines the diffuse irradiance from the sky on a tilted surface using the surface tilt angle, surface azimuth angle, diffuse horizontal irradiance, direct normal irradiance, global horizontal irradiance, extraterrestrial normal irradiance, sun zenith angle, and sun azimuth angle.

Parameters:

• surface_tilt (numeric) – Panel tilt from the horizontal. See surface_tilt. [°]

• surface_azimuth (numeric) – Panel azimuth. See surface_azimuth. [°]

• dhi (numeric) – Diffuse horizontal irradiance, see dhi. [Wm⁻²]

• dni (numeric) – Direct normal irradiance, see dni. [Wm⁻²]

• ghi (numeric) – Global horizontal irradiance, see ghi. [Wm⁻²]

• dni_extra (numeric) – Extraterrestrial normal irradiance, see dni_extra. [Wm⁻²]

• solar_zenith (numeric) – Solar apparent (refraction-corrected) zenith angles See solar_zenith. [°]

• solar_azimuth (numeric) – Solar azimuth angles. See solar_azimuth. [°]

Returns:

poa_sky_diffuse (numeric) – The sky diffuse component of the solar radiation. [Wm⁻²]

Notes

The Reindl (1990) model for the sky diffuse irradiance, \(I_d\), is as follows:

\[I_{d} = DHI \left(A \cdot R_b + (1 - A) \left(\frac{1 + \cos\beta}{2}\right) \left(1 + \sqrt{\frac{BHI}{GHI}} \sin^3(\beta/2)\right) \right).\]

\(DHI\), \(BHI\), and \(GHI\) are the diffuse horizontal, beam (direct) horizontal and global horizontal irradiances, respectively. \(A\) is the anisotropy index, which is the ratio of the direct normal irradiance to the direct extraterrestrial irradiation, \(R_b\) is the projection ratio, which is defined as the ratio of the cosine of the angle of incidence (AOI) to the cosine of the zenith angle, and \(\beta\) is the tilt angle of the array.

Implementation is based on Loutzenhiser et al. (2007) [3], Equation 8. The beam and ground reflectance portion of the equation have been removed, therefore the model described here generates ONLY the diffuse radiation from the sky and circumsolar, so the form of the equation varies slightly from Equation 8 in [3].

References

[1]

Reindl, D. T., Beckmann, W. A., Duffie, J. A., 1990a. Diffuse fraction correlations. Solar Energy 45(1), 1-7. DOI: 10.1016/0038-092X(90)90060-P

[2]

Reindl, D. T., Beckmann, W. A., Duffie, J. A., 1990b. Evaluation of hourly tilted surface radiation models. Solar Energy 45(1), 9-17. DOI: 10.1016/0038-092X(90)90061-G

[3] (1,2)

Loutzenhiser P. G. et. al., 2007. Empirical validation of models to compute solar irradiance on inclined surfaces for building energy simulation. Solar Energy 81(2), 254-267 DOI: 10.1016/j.solener.2006.03.009