'''
The “Fresnel Equations” for Diffuse radiation on Inclined photovoltaic Surfaces (FEDIS)
is an analytical solution of diffuse transmission based on the rigorous integration of
an alternate form of the Fresnel equations. The approach leads to a simple yet accurate
relative transmittance model (often referred to as incident angle modifier or angle of
incidence model) that reconciles the solar energy sensed by pyranometers and PV panels.
Parameters
----------
aoi : Angle of incidence in degrees.
rfnt: the refractive index of the pyranometer cover
For a fused silica dome over a CMP22, the rfnt is 1.4585
rfn: the refractive index of the PV cover
The suggested value is 1.5
surface_tilt : numeric
Surface tilt angles in decimal degrees.
The tilt angle is defined as degrees from horizontal
(e.g. surface facing up = 0, surface facing horizon = 90).
Returns
-------
cd : the incidence angle modifier (IAM) for direct radiation
cuk: the IAM for diffuse radiation from the sky
cug: the IAM for diffuse radiation from the ground reflection
Usage
----------
The solar energy received by a PV can be given by
F = cd*Fd + cuk*Fuk + cug*Fug
Fd, Fuk, and Fug are the POA irradiances, observed by the pyranometer,
that are associated with direct radiation, diffuse radiation from the sky, and
diffuse radiation from ground reflection, respectively.
An example can be found in Eq.(1-2) from the reference
rfnt = 1.4585
rfn = np.arange(nPV)
aoi = np.arange(n)
surface_tilt = np.arange(n)
cd, cuk, cug = FEDIS(aoi, surface_tilt, rfn, rfnt )
Will return 2 dimensional arrays (nPV, n)
n represents the number of total scenarios
nPV represents the number of PV cover types
Example
-------
belta = np.arange(100)*0.9
rfn = np.array([1.3, 2.0])
theta0p = belta*np.pi/180.0
aoi = theta0p*180.0/np.pi
surface_tilt = belta
cd, cuk, cug = FEDIS(aoi, surface_tilt, rfn, rfnt )
print( cd[0][:] )
print( cuk[0][:] )
print( cug[0][:] )
This generate the results of Fig.3 in the reference
Reference
----------
Xie, Y., M. Sengupta, A. Habte, A. Andreas, The "Fresnel Equations for Diffuse
radiation on Inclined photovoltaic Surfaces (FEDIS), Rew. Sus. En. Rev., 161, 112362
'''