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update irradiance.reindl docs #2193

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update irradiance.reindl docs #2193

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2cf2583
references, variable definition, notes section
RDaxini Aug 30, 2024
83a683a
Update irradiance.py
RDaxini Aug 30, 2024
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55 changes: 34 additions & 21 deletions pvlib/irradiance.py
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Original file line number Diff line number Diff line change
Expand Up @@ -850,15 +850,10 @@ def haydavies(surface_tilt, surface_azimuth, dhi, dni, dni_extra,
def reindl(surface_tilt, surface_azimuth, dhi, dni, ghi, dni_extra,
solar_zenith, solar_azimuth):
r'''
Determine diffuse irradiance from the sky on a tilted surface using
Reindl's 1990 model

.. math::
Determine the diffuse irradiance from the sky on a tilted surface using
the Reindl (1990) model [1, 2]_.

I_{d} = DHI \left(A R_b + (1 - A) \left(\frac{1 + \cos\beta}{2}\right)
\left(1 + \sqrt{\frac{I_{hb}}{I_h}} \sin^3(\beta/2)\right) \right)

Reindl's 1990 model determines the diffuse irradiance from the sky
The Reindl model determines the diffuse irradiance from the sky
(ground reflected irradiance is not included in this algorithm) on a
tilted surface using the surface tilt angle, surface azimuth angle,
diffuse horizontal irradiance, direct normal irradiance, global
Expand All @@ -884,7 +879,7 @@ def reindl(surface_tilt, surface_azimuth, dhi, dni, ghi, dni_extra,
direct normal irradiance in W/m^2.

ghi: numeric
Global irradiance in W/m^2.
Global horizontal irradiance in W/m^2.

dni_extra : numeric
Extraterrestrial normal irradiance in W/m^2.
Expand All @@ -904,23 +899,41 @@ def reindl(surface_tilt, surface_azimuth, dhi, dni, ghi, dni_extra,

Notes
-----
The poa_sky_diffuse calculation is generated from the Loutzenhiser et al.
(2007) paper, equation 8. Note that I have removed the beam and ground
reflectance portion of the equation and this generates ONLY the diffuse
radiation from the sky and circumsolar, so the form of the equation
varies slightly from equation 8.
The Reindl (1990) model for the sky diffuse irradiance, :math:`I_d`, is as
follows:

.. math::

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

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

The ``poa_sky_diffuse`` calculation is generated from 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] Loutzenhiser P.G. et. al. "Empirical validation of models to
compute solar irradiance on inclined surfaces for building energy
simulation" 2007, Solar Energy vol. 81. pp. 254-267

.. [2] Reindl, D.T., Beckmann, W.A., Duffie, J.A., 1990a. Diffuse
.. [1] Reindl, D. T., Beckmann, W. A., Duffie, J. A., 1990a. Diffuse
fraction correlations. Solar Energy 45(1), 1-7.

.. [3] Reindl, D.T., Beckmann, W.A., Duffie, J.A., 1990b. Evaluation of
: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] Loutzenhiser P. G. et. al. "Empirical validation of models to
compute solar irradiance on inclined surfaces for building energy
simulation" 2007, Solar Energy vol. 81. pp. 254-267
:doi:'10.1016/j.solener.2006.03.009'
'''

cos_tt = aoi_projection(surface_tilt, surface_azimuth,
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