def pvl_clearsky_haurwitz(ApparentZenith):
'''
Determine clear sky GHI from Haurwitz model
Implements the Haurwitz clear sky model for global horizontal
irradiance (GHI) as presented in [1, 2]. A report on clear
sky models found the Haurwitz model to have the best performance of
models which require only zenith angle [3].
Parameters
----------
ApparentZenith : DataFrame
The apparent (refraction corrected) sun zenith angle in degrees.
Returns
-------
ClearSkyGHI : DataFrame
the modeled global horizonal irradiance in W/m^2 provided
by the Haurwitz clear-sky model.
Initial implementation of this algorithm by Matthew Reno.
References
----------
[1] B. Haurwitz, "Insolation in Relation to Cloudiness and Cloud
Density," Journal of Meteorology, vol. 2, pp. 154-166, 1945.
[2] B. Haurwitz, "Insolation in Relation to Cloud Type," Journal of
Meteorology, vol. 3, pp. 123-124, 1946.
[3] M. Reno, C. Hansen, and J. Stein, "Global Horizontal Irradiance Clear
Sky Models: Implementation and Analysis", Sandia National
Laboratories, SAND2012-2389, 2012.
See Also
---------
pvl_maketimestruct
pvl_makelocationstruct
pvl_ephemeris
pvl_spa
pvl_ineichen
'''
Vars = locals()
Expect = {'ApparentZenith': ('x<=180', 'x>=0')}
var = pvl_tools.Parse(Vars, Expect)
ClearSkyGHI = 1098.0 * pvl_tools.cosd(ApparentZenith) * (np.exp(
-0.059 / pvl_tools.cosd(ApparentZenith)))
ClearSkyGHI[ClearSkyGHI < 0] = 0
return ClearSkyGHI
def pvl_clearsky_haurwitz(ApparentZenith):
'''
Determine clear sky GHI from Haurwitz model
Implements the Haurwitz clear sky model for global horizontal
irradiance (GHI) as presented in [1, 2]. A report on clear
sky models found the Haurwitz model to have the best performance of
models which require only zenith angle [3].
Parameters
----------
ApparentZenith : DataFrame
The apparent (refraction corrected) sun zenith angle in degrees.
Returns
-------
ClearSkyGHI : DataFrame
the modeled global horizonal irradiance in W/m^2 provided
by the Haurwitz clear-sky model.
Initial implementation of this algorithm by Matthew Reno.
References
----------
[1] B. Haurwitz, "Insolation in Relation to Cloudiness and Cloud
Density," Journal of Meteorology, vol. 2, pp. 154-166, 1945.
[2] B. Haurwitz, "Insolation in Relation to Cloud Type," Journal of
Meteorology, vol. 3, pp. 123-124, 1946.
[3] M. Reno, C. Hansen, and J. Stein, "Global Horizontal Irradiance Clear
Sky Models: Implementation and Analysis", Sandia National
Laboratories, SAND2012-2389, 2012.
See Also
---------
pvl_maketimestruct
pvl_makelocationstruct
pvl_ephemeris
pvl_spa
pvl_ineichen
'''
Vars=locals()
Expect={'ApparentZenith':('x<=180','x>=0')}
var=pvl_tools.Parse(Vars,Expect)
ClearSkyGHI=1098.0 * pvl_tools.cosd(ApparentZenith)*(np.exp(- 0.059 / pvl_tools.cosd(ApparentZenith)))
ClearSkyGHI[ClearSkyGHI < 0]=0
return ClearSkyGHI
def pvl_kingdiffuse(SurfTilt, DHI, GHI, SunZen):
'''
Determine diffuse irradiance from the sky on a tilted surface using the King model
King's 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, diffuse horizontal
irradiance, global horizontal irradiance, and sun zenith angle. Note
that this model is not well documented and has not been published in
any fashion (as of January 2012).
Parameters
----------
SurfTilt : float or DataFrame
Surface tilt angles in decimal degrees.
SurfTilt must be >=0 and <=180. The tilt angle is defined as
degrees from horizontal (e.g. surface facing up = 0, surface facing
horizon = 90)
DHI : float or DataFrame
diffuse horizontal irradiance in W/m^2.
DHI must be >=0.
GHI : float or DataFrame
global horizontal irradiance in W/m^2.
DHI must be >=0.
SunZen : float or DataFrame
apparent (refraction-corrected) zenith
angles in decimal degrees.
SunZen must be >=0 and <=180.
Returns
--------
SkyDiffuse : float or DataFrame
the diffuse component of the solar radiation on an
arbitrarily tilted surface as given by a model developed by David L.
King at Sandia National Laboratories.
See Also
--------
pvl_ephemeris
pvl_extraradiation
pvl_isotropicsky
pvl_haydavies1980
pvl_perez
pvl_klucher1979
pvl_reindl1990
'''
Vars = locals()
Expect = {
'SurfTilt': ('num', 'x>=0'),
'SunZen': ('x>=-180'),
'DHI': ('x>=0'),
'GHI': ('x>=0')
}
var = pvl_tools.Parse(Vars, Expect)
SkyDiffuse = DHI * ((1 + pvl_tools.cosd(SurfTilt))) / 2 + GHI * (
(0.012 * SunZen - 0.04)) * ((1 - pvl_tools.cosd(SurfTilt))) / 2
return SkyDiffuse
def pvl_isotropicsky(SurfTilt, DHI):
'''
Determine diffuse irradiance from the sky on a tilted surface using isotropic sky model
Hottel and Woertz's model treats the sky as a uniform source of diffuse
irradiance. Thus the diffuse irradiance from the sky (ground reflected
irradiance is not included in this algorithm) on a tilted surface can
be found from the diffuse horizontal irradiance and the tilt angle of
the surface.
Parameters
----------
SurfTilt : float or DataFrame
Surface tilt angles in decimal degrees.
SurfTilt must be >=0 and <=180. The tilt angle is defined as
degrees from horizontal (e.g. surface facing up = 0, surface facing
horizon = 90)
DHI : float or DataFrame
Diffuse horizontal irradiance in W/m^2.
DHI must be >=0.
Returns
-------
SkyDiffuse : float of DataFrame
The diffuse component of the solar radiation on an
arbitrarily tilted surface defined by the isotropic sky model as
given in Loutzenhiser et. al (2007) equation 3.
SkyDiffuse is the diffuse component ONLY and does not include the ground
reflected irradiance or the irradiance due to the beam.
SkyDiffuse is a column vector vector with a number of elements equal to
the input vector(s).
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] Hottel, H.C., Woertz, B.B., 1942. Evaluation of flat-plate solar heat
collector. Trans. ASME 64, 91.
See also
--------
pvl_reindl1990
pvl_haydavies1980
pvl_perez
pvl_klucher1979
pvl_kingdiffuse
'''
Vars = locals()
Expect = {'SurfTilt': 'x <= 180 & x >= 0 ', 'DHI': 'x>=0'}
var = pvl_tools.Parse(Vars, Expect)
SkyDiffuse = DHI * (1 + pvl_tools.cosd(SurfTilt)) * 0.5
return SkyDiffuse
def pvl_isotropicsky(SurfTilt,DHI):
'''
Determine diffuse irradiance from the sky on a tilted surface using isotropic sky model
Hottel and Woertz's model treats the sky as a uniform source of diffuse
irradiance. Thus the diffuse irradiance from the sky (ground reflected
irradiance is not included in this algorithm) on a tilted surface can
be found from the diffuse horizontal irradiance and the tilt angle of
the surface.
Parameters
----------
SurfTilt : float or DataFrame
Surface tilt angles in decimal degrees.
SurfTilt must be >=0 and <=180. The tilt angle is defined as
degrees from horizontal (e.g. surface facing up = 0, surface facing
horizon = 90)
DHI : float or DataFrame
Diffuse horizontal irradiance in W/m^2.
DHI must be >=0.
Returns
-------
SkyDiffuse : float of DataFrame
The diffuse component of the solar radiation on an
arbitrarily tilted surface defined by the isotropic sky model as
given in Loutzenhiser et. al (2007) equation 3.
SkyDiffuse is the diffuse component ONLY and does not include the ground
reflected irradiance or the irradiance due to the beam.
SkyDiffuse is a column vector vector with a number of elements equal to
the input vector(s).
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] Hottel, H.C., Woertz, B.B., 1942. Evaluation of flat-plate solar heat
collector. Trans. ASME 64, 91.
See also
--------
pvl_reindl1990
pvl_haydavies1980
pvl_perez
pvl_klucher1979
pvl_kingdiffuse
'''
Vars=locals()
Expect={'SurfTilt':'x <= 180 & x >= 0 ',
'DHI':'x>=0'
}
var=pvl_tools.Parse(Vars,Expect)
SkyDiffuse=DHI * (1 + pvl_tools.cosd(SurfTilt)) * 0.5
return SkyDiffuse
def pvl_clearsky_ineichen(Time, Location, LinkeTurbidity=-999):
'''
Determine clear sky GHI, DNI, and DHI from Ineichen/Perez model
Implements the Ineichen and Perez clear sky model for global horizontal
irradiance (GHI), direct normal irradiance (DNI), and calculates
the clear-sky diffuse horizontal (DHI) component as the difference
between GHI and DNI*cos(zenith) as presented in [1, 2]. A report on clear
sky models found the Ineichen/Perez model to have excellent performance
with a minimal input data set [3]. Default values for Linke turbidity
provided by SoDa [4, 5].
Parameters
----------
Time : Dataframe.index
A timezone aware pandas dataframe index.
Location : dict
latitude
vector or scalar latitude in decimal degrees (positive is
northern hemisphere)
longitude
vector or scalar longitude in decimal degrees (positive is
east of prime meridian)
altitude
an optional component of the Location struct, not
used in the ephemeris code directly, but it may be used to calculate
standard site pressure (see pvl_alt2pres function)
TZ
Time Zone offset from UTC
Other Parameters
----------------
LinkeTurbidityInput : Optional, float or DataFrame
An optional input to provide your own Linke
turbidity. If this input is omitted, the default Linke turbidity
maps will be used. LinkeTurbidityInput may be a float or
dataframe of Linke turbidities. If dataframe is provided, the same
turbidity will be used for all time/location sets. If a dataframe is
provided, it must be of the same size as any time/location dataframes
and each element of the dataframe corresponds to any time and location
elements.
Returns
-------
ClearSkyGHI : Dataframe
the modeled global horizonal irradiance in W/m^2 provided
by the Ineichen clear-sky model.
ClearSkyDNI : Dataframe
the modeled direct normal irradiance in W/m^2 provided
by the Ineichen clear-sky model.
ClearSkyDHI : Dataframe
the calculated diffuse horizonal irradiance in W/m^2
provided by the Ineichen clear-sky model.
Notes
-----
This implementation of the Ineichen model requires a number of other
PV_LIB functions including pvl_ephemeris, pvl_date2doy,
pvl_extraradiation, pvl_absoluteairmass, pvl_relativeairmass, and
pvl_alt2pres. It also requires the file "LinkeTurbidities.mat" to be
in the working directory. If you are using pvl_ineichen
in a loop, it may be faster to load LinkeTurbidities.mat outside of
the loop and feed it into pvl_ineichen as a variable, rather than
having pvl_ineichen open the file each time it is called (or utilize
column vectors of time/location instead of a loop).
Initial implementation of this algorithm by Matthew Reno.
References
----------
[1] P. Ineichen and R. Perez, "A New airmass independent formulation for
the Linke turbidity coefficient", Solar Energy, vol 73, pp. 151-157, 2002.
[2] R. Perez et. al., "A New Operational Model for Satellite-Derived
Irradiances: Description and Validation", Solar Energy, vol 73, pp.
307-317, 2002.
[3] M. Reno, C. Hansen, and J. Stein, "Global Horizontal Irradiance Clear
Sky Models: Implementation and Analysis", Sandia National
Laboratories, SAND2012-2389, 2012.
[4] http://www.soda-is.com/eng/services/climat_free_eng.php#c5 (obtained
July 17, 2012).
[5] J. Remund, et. al., "Worldwide Linke Turbidity Information", Proc.
ISES Solar World Congress, June 2003. Goteborg, Sweden.
See Also
--------
pvl_maketimestruct
pvl_makelocationstruct
pvl_ephemeris
pvl_haurwitz
'''
Vars = locals()
Expect = {'Time': (''), 'Location': (''), 'LinkeTurbidity': ('optional')}
var = pvl_tools.Parse(Vars, Expect)
I0 = pvl_extraradiation.pvl_extraradiation(var.Time.dayofyear)
__, __, ApparentSunElevation, __, __ = pvl_ephemeris.pvl_ephemeris(
var.Time, var.Location,
pvl_alt2pres.pvl_alt2pres(var.Location['altitude'])) # nargout=4
ApparentZenith = 90 - ApparentSunElevation
ApparentZenith[ApparentZenith >= 90] = 90
if LinkeTurbidity == -999:
# The .mat file 'LinkeTurbidities.mat' contains a single 2160 x 4320 x 12
# matrix of type uint8 called 'LinkeTurbidity'. The rows represent global
# latitudes from 90 to -90 degrees; the columns represent global longitudes
# from -180 to 180; and the depth (third dimension) represents months of
# the year from January (1) to December (12). To determine the Linke
# turbidity for a position on the Earth's surface for a given month do the
# following: LT = LinkeTurbidity(LatitudeIndex, LongitudeIndex, month). Note that the numbers within the matrix are 20 * Linke
# Turbidity, so divide the number from the file by 20 to get the
# turbidity.
mat = scipy.io.loadmat('LinkeTurbidities.mat')
LinkeTurbidity = mat['LinkeTurbidity']
LatitudeIndex = np.round_(
LinearlyScale(Location['latitude'], 90, -90, 1, 2160))
LongitudeIndex = np.round_(
LinearlyScale(Location['longitude'], -180, 180, 1, 4320))
g = LinkeTurbidity[LatitudeIndex][LongitudeIndex]
ApplyMonth = lambda x: g[x[0] - 1]
LT = pd.DataFrame(Time.month)
LT.index = Time
LT = LT.apply(ApplyMonth, axis=1)
TL = LT / float(20)
else:
TL = var.LinkeTurbidity
# Get the absolute airmass assuming standard local pressure (per
# pvl_alt2pres) using Kasten and Young's 1989 formula for airmass.
AMabsolute = pvl_absoluteairmass.pvl_absoluteairmass(
AMrelative=pvl_relativeairmass.pvl_relativeairmass(
ApparentZenith, model='kastenyoung1989'),
Pressure=pvl_alt2pres.pvl_alt2pres(var.Location['altitude']))
fh1 = np.exp(var.Location['altitude'] * ((-1 / 8000)))
fh2 = np.exp(var.Location['altitude'] * ((-1 / 1250)))
cg1 = (5.09e-05 * (var.Location['altitude']) + 0.868)
cg2 = 3.92e-05 * (var.Location['altitude']) + 0.0387
# Dan's note on the TL correction: By my reading of the publication on
# pages 151-157, Ineichen and Perez introduce (among other things) three
# things. 1) Beam model in eqn. 8, 2) new turbidity factor in eqn 9 and
# appendix A, and 3) Global horizontal model in eqn. 11. They do NOT appear
# to use the new turbidity factor (item 2 above) in either the beam or GHI
# models. The phrasing of appendix A seems as if there are two separate
# corrections, the first correction is used to correct the beam/GHI models,
# and the second correction is used to correct the revised turibidity
# factor. In my estimation, there is no need to correct the turbidity
# factor used in the beam/GHI models.
# Create the corrected TL for TL < 2
# TLcorr = TL;
# TLcorr(TL < 2) = TLcorr(TL < 2) - 0.25 .* (2-TLcorr(TL < 2)) .^ (0.5);
# This equation is found in Solar Energy 73, pg 311. It is slightly
# different than the equation given in Solar Energy 73, pg 156. We used the
# equation from pg 311 because of the existence of known typos in the pg 156
# publication (notably the fh2-(TL-1) should be fh2 * (TL-1)).
ClearSkyGHI = cg1 * (I0) * (pvl_tools.cosd(ApparentZenith)) * (np.exp(
-cg2 * (AMabsolute) *
((fh1 + fh2 * ((TL - 1)))))) * (np.exp(0.01 * ((AMabsolute)**(1.8))))
ClearSkyGHI[ClearSkyGHI < 0] = 0
b = 0.664 + 0.163 / fh1
BncI = b * (I0) * (np.exp(-0.09 * (AMabsolute) * ((TL - 1))))
ClearSkyDNI = np.min(
BncI,
ClearSkyGHI * ((1 - (0.1 - 0.2 * (np.exp(-TL))) /
(0.1 + 0.882 / fh1))) / pvl_tools.cosd(ApparentZenith))
#ClearSkyDNI=ClearSkyGHI*((1 - (0.1 - 0.2*(np.exp(- TL))) / (0.1 + 0.882 / fh1))) / pvl_tools.cosd(ApparentZenith)
ClearSkyDHI = ClearSkyGHI - ClearSkyDNI * (pvl_tools.cosd(ApparentZenith))
return ClearSkyGHI, ClearSkyDNI, ClearSkyDHI, BncI
def pvl_kingdiffuse(SurfTilt,DHI,GHI,SunZen):
'''
Determine diffuse irradiance from the sky on a tilted surface using the King model
King's 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, diffuse horizontal
irradiance, global horizontal irradiance, and sun zenith angle. Note
that this model is not well documented and has not been published in
any fashion (as of January 2012).
Parameters
----------
SurfTilt : float or DataFrame
Surface tilt angles in decimal degrees.
SurfTilt must be >=0 and <=180. The tilt angle is defined as
degrees from horizontal (e.g. surface facing up = 0, surface facing
horizon = 90)
DHI : float or DataFrame
diffuse horizontal irradiance in W/m^2.
DHI must be >=0.
GHI : float or DataFrame
global horizontal irradiance in W/m^2.
DHI must be >=0.
SunZen : float or DataFrame
apparent (refraction-corrected) zenith
angles in decimal degrees.
SunZen must be >=0 and <=180.
Returns
--------
SkyDiffuse : float or DataFrame
the diffuse component of the solar radiation on an
arbitrarily tilted surface as given by a model developed by David L.
King at Sandia National Laboratories.
See Also
--------
pvl_ephemeris
pvl_extraradiation
pvl_isotropicsky
pvl_haydavies1980
pvl_perez
pvl_klucher1979
pvl_reindl1990
'''
Vars=locals()
Expect={'SurfTilt':('num','x>=0'),
'SunZen':('x>=-180'),
'DHI':('x>=0'),
'GHI':('x>=0')
}
var=pvl_tools.Parse(Vars,Expect)
SkyDiffuse=DHI*((1 + pvl_tools.cosd(SurfTilt))) / 2 + GHI*((0.012 * SunZen - 0.04))*((1 - pvl_tools.cosd(SurfTilt))) / 2
return SkyDiffuse
def pvl_klucher1979(SurfTilt, SurfAz, DHI, GHI, SunZen, SunAz):
'''
Determine diffuse irradiance from the sky on a tilted surface using Klucher's 1979 model
Klucher's 1979 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
horizontal irradiance, extraterrestrial irradiance, sun zenith angle,
and sun azimuth angle.
Parameters
----------
SurfTilt : float or DataFrame
Surface tilt angles in decimal degrees.
SurfTilt must be >=0 and <=180. The tilt angle is defined as
degrees from horizontal (e.g. surface facing up = 0, surface facing
horizon = 90)
SurfAz : float or DataFrame
Surface azimuth angles in decimal degrees.
SurfAz must be >=0 and <=360. The Azimuth convention is defined
as degrees east of north (e.g. North = 0, South=180 East = 90, West = 270).
DHI : float or DataFrame
diffuse horizontal irradiance in W/m^2.
DHI must be >=0.
GHI : float or DataFrame
Global irradiance in W/m^2.
DNI must be >=0.
SunZen : float or DataFrame
apparent (refraction-corrected) zenith
angles in decimal degrees.
SunZen must be >=0 and <=180.
SunAz : float or DataFrame
Sun azimuth angles in decimal degrees.
SunAz must be >=0 and <=360. The Azimuth convention is defined
as degrees east of north (e.g. North = 0, East = 90, West = 270).
Returns
-------
SkyDiffuse : float or DataFrame
the diffuse component of the solar radiation on an
arbitrarily tilted surface defined by the Klucher model as given in
Loutzenhiser et. al (2007) equation 4.
SkyDiffuse is the diffuse component ONLY and does not include the ground
reflected irradiance or the irradiance due to the beam.
SkyDiffuse is a column vector vector with a number of elements equal to
the input vector(s).
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] Klucher, T.M., 1979. Evaluation of models to predict insolation on tilted
surfaces. Solar Energy 23 (2), 111-114.
See also
--------
pvl_ephemeris
pvl_extraradiation
pvl_isotropicsky
pvl_haydavies1980
pvl_perez
pvl_reindl1990
pvl_kingdiffuse
'''
Vars = locals()
Expect = {
'SurfTilt': ('num', 'x>=0'),
'SurfAz': ('x>=-180'),
'DHI': ('x>=0'),
'GHI': ('x>=0'),
'SunZen': ('x>=0'),
'SunAz': ('x>=-180')
}
var = pvl_tools.Parse(Vars, Expect)
GHI[GHI < DHI] = DHI
GHI[GHI < 1e-06] = 1e-06
COSTT = pvl_tools.cosd(SurfTilt) * pvl_tools.cosd(SunZen) + pvl_tools.sind(
SurfTilt) * pvl_tools.sind(SunZen) * pvl_tools.cosd(SunAz - SurfAz)
F = 1 - ((DHI / GHI)**2)
SkyDiffuse = DHI * ((0.5 * ((1 + pvl_tools.cosd(SurfTilt))))) * ((1 + F * (
((pvl_tools.sind(SurfTilt / 2))**3)))) * ((1 + F * (((COSTT)**2)) * ((
(pvl_tools.sind(SunZen))**3))))
return SkyDiffuse
def pvl_haydavies1980(SurfTilt,SurfAz,DHI,DNI,HExtra,SunZen,SunAz):
'''
Determine diffuse irradiance from the sky on a tilted surface using Hay & Davies' 1980 model
Hay and Davies' 1980 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,
extraterrestrial irradiance, sun zenith angle, and sun azimuth angle.
Parameters
----------
SurfTilt : float or DataFrame
Surface tilt angles in decimal degrees.
SurfTilt must be >=0 and <=180. The tilt angle is defined as
degrees from horizontal (e.g. surface facing up = 0, surface facing
horizon = 90)
SurfAz : float or DataFrame
Surface azimuth angles in decimal degrees.
SurfAz must be >=0 and <=360. The Azimuth convention is defined
as degrees east of north (e.g. North = 0, South=180 East = 90, West = 270).
DHI : float or DataFrame
diffuse horizontal irradiance in W/m^2.
DHI must be >=0.
DNI : float or DataFrame
direct normal irradiance in W/m^2.
DNI must be >=0.
HExtra : float or DataFrame
extraterrestrial normal irradiance in W/m^2.
HExtra must be >=0.
SunZen : float or DataFrame
apparent (refraction-corrected) zenith
angles in decimal degrees.
SunZen must be >=0 and <=180.
SunAz : float or DataFrame
Sun azimuth angles in decimal degrees.
SunAz must be >=0 and <=360. The Azimuth convention is defined
as degrees east of north (e.g. North = 0, East = 90, West = 270).
Returns
--------
SkyDiffuse : float or DataFrame
the diffuse component of the solar radiation on an
arbitrarily tilted surface defined by the Perez model as given in
reference [3].
SkyDiffuse is the diffuse component ONLY and does not include the ground
reflected irradiance or the irradiance due to the beam.
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] Hay, J.E., Davies, J.A., 1980. Calculations of the solar radiation incident
on an inclined surface. In: Hay, J.E., Won, T.K. (Eds.), Proc. of First
Canadian Solar Radiation Data Workshop, 59. Ministry of Supply
and Services, Canada.
See Also
--------
pvl_ephemeris
pvl_extraradiation
pvl_isotropicsky
pvl_reindl1990
pvl_perez
pvl_klucher1979
pvl_kingdiffuse
pvl_spa
'''
Vars=locals()
Expect={'SurfTilt':('num','x>=0'),
'SurfAz':('x>=-180'),
'DHI':('x>=0'),
'DNI':('x>=0'),
'HExtra':('x>=0'),
'SunZen':('x>=0'),
'SunAz':('x>=-180'),
}
var=pvl_tools.Parse(Vars,Expect)
COSTT=pvl_tools.cosd(SurfTilt)*pvl_tools.cosd(SunZen) + pvl_tools.sind(SurfTilt)*pvl_tools.sind(SunZen)*pvl_tools.cosd(SunAz - SurfAz)
RB=np.max(COSTT,0) / np.max(pvl_tools.cosd(SunZen),0.01745)
AI=DNI / HExtra
SkyDiffuse=DHI*((AI*(RB) + (1 - AI)*(0.5)*((1 + pvl_tools.cosd(SurfTilt)))))
return SkyDiffuse
def pvl_klucher1979(SurfTilt,SurfAz,DHI,GHI,SunZen,SunAz):
'''
Determine diffuse irradiance from the sky on a tilted surface using Klucher's 1979 model
Klucher's 1979 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
horizontal irradiance, extraterrestrial irradiance, sun zenith angle,
and sun azimuth angle.
Parameters
----------
SurfTilt : float or DataFrame
Surface tilt angles in decimal degrees.
SurfTilt must be >=0 and <=180. The tilt angle is defined as
degrees from horizontal (e.g. surface facing up = 0, surface facing
horizon = 90)
SurfAz : float or DataFrame
Surface azimuth angles in decimal degrees.
SurfAz must be >=0 and <=360. The Azimuth convention is defined
as degrees east of north (e.g. North = 0, South=180 East = 90, West = 270).
DHI : float or DataFrame
diffuse horizontal irradiance in W/m^2.
DHI must be >=0.
GHI : float or DataFrame
Global irradiance in W/m^2.
DNI must be >=0.
SunZen : float or DataFrame
apparent (refraction-corrected) zenith
angles in decimal degrees.
SunZen must be >=0 and <=180.
SunAz : float or DataFrame
Sun azimuth angles in decimal degrees.
SunAz must be >=0 and <=360. The Azimuth convention is defined
as degrees east of north (e.g. North = 0, East = 90, West = 270).
Returns
-------
SkyDiffuse : float or DataFrame
the diffuse component of the solar radiation on an
arbitrarily tilted surface defined by the Klucher model as given in
Loutzenhiser et. al (2007) equation 4.
SkyDiffuse is the diffuse component ONLY and does not include the ground
reflected irradiance or the irradiance due to the beam.
SkyDiffuse is a column vector vector with a number of elements equal to
the input vector(s).
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] Klucher, T.M., 1979. Evaluation of models to predict insolation on tilted
surfaces. Solar Energy 23 (2), 111-114.
See also
--------
pvl_ephemeris
pvl_extraradiation
pvl_isotropicsky
pvl_haydavies1980
pvl_perez
pvl_reindl1990
pvl_kingdiffuse
'''
Vars=locals()
Expect={'SurfTilt':('num','x>=0'),
'SurfAz':('x>=-180'),
'DHI':('x>=0'),
'GHI':('x>=0'),
'SunZen':('x>=0'),
'SunAz':('x>=-180')
}
var=pvl_tools.Parse(Vars,Expect)
GHI[GHI < DHI]=DHI
GHI[GHI < 1e-06]=1e-06
COSTT=pvl_tools.cosd(SurfTilt)*pvl_tools.cosd(SunZen) + pvl_tools.sind(SurfTilt)*pvl_tools.sind(SunZen)*pvl_tools.cosd(SunAz - SurfAz)
F=1 - ((DHI / GHI) ** 2)
SkyDiffuse=DHI*((0.5*((1 + pvl_tools.cosd(SurfTilt)))))*((1 + F*(((pvl_tools.sind(SurfTilt / 2)) ** 3))))*((1 + F*(((COSTT) ** 2))*(((pvl_tools.sind(SunZen)) ** 3))))
return SkyDiffuse
def pvl_clearsky_ineichen(Time,Location,LinkeTurbidity=-999):
'''
Determine clear sky GHI, DNI, and DHI from Ineichen/Perez model
Implements the Ineichen and Perez clear sky model for global horizontal
irradiance (GHI), direct normal irradiance (DNI), and calculates
the clear-sky diffuse horizontal (DHI) component as the difference
between GHI and DNI*cos(zenith) as presented in [1, 2]. A report on clear
sky models found the Ineichen/Perez model to have excellent performance
with a minimal input data set [3]. Default values for Linke turbidity
provided by SoDa [4, 5].
Parameters
----------
Time : Dataframe.index
A timezone aware pandas dataframe index.
Location : dict
latitude
vector or scalar latitude in decimal degrees (positive is
northern hemisphere)
longitude
vector or scalar longitude in decimal degrees (positive is
east of prime meridian)
altitude
an optional component of the Location struct, not
used in the ephemeris code directly, but it may be used to calculate
standard site pressure (see pvl_alt2pres function)
TZ
Time Zone offset from UTC
Other Parameters
----------------
LinkeTurbidityInput : Optional, float or DataFrame
An optional input to provide your own Linke
turbidity. If this input is omitted, the default Linke turbidity
maps will be used. LinkeTurbidityInput may be a float or
dataframe of Linke turbidities. If dataframe is provided, the same
turbidity will be used for all time/location sets. If a dataframe is
provided, it must be of the same size as any time/location dataframes
and each element of the dataframe corresponds to any time and location
elements.
Returns
-------
ClearSkyGHI : Dataframe
the modeled global horizonal irradiance in W/m^2 provided
by the Ineichen clear-sky model.
ClearSkyDNI : Dataframe
the modeled direct normal irradiance in W/m^2 provided
by the Ineichen clear-sky model.
ClearSkyDHI : Dataframe
the calculated diffuse horizonal irradiance in W/m^2
provided by the Ineichen clear-sky model.
Notes
-----
This implementation of the Ineichen model requires a number of other
PV_LIB functions including pvl_ephemeris, pvl_date2doy,
pvl_extraradiation, pvl_absoluteairmass, pvl_relativeairmass, and
pvl_alt2pres. It also requires the file "LinkeTurbidities.mat" to be
in the working directory. If you are using pvl_ineichen
in a loop, it may be faster to load LinkeTurbidities.mat outside of
the loop and feed it into pvl_ineichen as a variable, rather than
having pvl_ineichen open the file each time it is called (or utilize
column vectors of time/location instead of a loop).
Initial implementation of this algorithm by Matthew Reno.
References
----------
[1] P. Ineichen and R. Perez, "A New airmass independent formulation for
the Linke turbidity coefficient", Solar Energy, vol 73, pp. 151-157, 2002.
[2] R. Perez et. al., "A New Operational Model for Satellite-Derived
Irradiances: Description and Validation", Solar Energy, vol 73, pp.
307-317, 2002.
[3] M. Reno, C. Hansen, and J. Stein, "Global Horizontal Irradiance Clear
Sky Models: Implementation and Analysis", Sandia National
Laboratories, SAND2012-2389, 2012.
[4] http://www.soda-is.com/eng/services/climat_free_eng.php#c5 (obtained
July 17, 2012).
[5] J. Remund, et. al., "Worldwide Linke Turbidity Information", Proc.
ISES Solar World Congress, June 2003. Goteborg, Sweden.
See Also
--------
pvl_maketimestruct
pvl_makelocationstruct
pvl_ephemeris
pvl_haurwitz
'''
Vars=locals()
Expect={'Time':(''),
'Location':(''),
'LinkeTurbidity':('optional')}
var=pvl_tools.Parse(Vars,Expect)
I0=pvl_extraradiation.pvl_extraradiation(var.Time.dayofyear)
__,__,ApparentSunElevation,__,__=pvl_ephemeris.pvl_ephemeris(var.Time,var.Location,pvl_alt2pres.pvl_alt2pres(var.Location['altitude'])) # nargout=4
ApparentZenith=90 - ApparentSunElevation
ApparentZenith[ApparentZenith>=90]=90
if LinkeTurbidity==-999:
# The .mat file 'LinkeTurbidities.mat' contains a single 2160 x 4320 x 12
# matrix of type uint8 called 'LinkeTurbidity'. The rows represent global
# latitudes from 90 to -90 degrees; the columns represent global longitudes
# from -180 to 180; and the depth (third dimension) represents months of
# the year from January (1) to December (12). To determine the Linke
# turbidity for a position on the Earth's surface for a given month do the
# following: LT = LinkeTurbidity(LatitudeIndex, LongitudeIndex, month). Note that the numbers within the matrix are 20 * Linke
# Turbidity, so divide the number from the file by 20 to get the
# turbidity.
mat = scipy.io.loadmat('LinkeTurbidities.mat')
LinkeTurbidity=mat['LinkeTurbidity']
LatitudeIndex=np.round_(LinearlyScale(Location['latitude'],90,- 90,1,2160))
LongitudeIndex=np.round_(LinearlyScale(Location['longitude'],- 180,180,1,4320))
g=LinkeTurbidity[LatitudeIndex][LongitudeIndex]
ApplyMonth=lambda x:g[x[0]-1]
LT=pd.DataFrame(Time.month)
LT.index=Time
LT=LT.apply(ApplyMonth,axis=1)
TL=LT / float(20)
else:
TL=var.LinkeTurbidity
# Get the absolute airmass assuming standard local pressure (per
# pvl_alt2pres) using Kasten and Young's 1989 formula for airmass.
AMabsolute=pvl_absoluteairmass.pvl_absoluteairmass(AMrelative=pvl_relativeairmass.pvl_relativeairmass(ApparentZenith,model='kastenyoung1989'),Pressure=pvl_alt2pres.pvl_alt2pres(var.Location['altitude']))
fh1=np.exp(var.Location['altitude']*((- 1 / 8000)))
fh2=np.exp(var.Location['altitude']*((- 1 / 1250)))
cg1=(5.09e-05*(var.Location['altitude']) + 0.868)
cg2=3.92e-05*(var.Location['altitude']) + 0.0387
# Dan's note on the TL correction: By my reading of the publication on
# pages 151-157, Ineichen and Perez introduce (among other things) three
# things. 1) Beam model in eqn. 8, 2) new turbidity factor in eqn 9 and
# appendix A, and 3) Global horizontal model in eqn. 11. They do NOT appear
# to use the new turbidity factor (item 2 above) in either the beam or GHI
# models. The phrasing of appendix A seems as if there are two separate
# corrections, the first correction is used to correct the beam/GHI models,
# and the second correction is used to correct the revised turibidity
# factor. In my estimation, there is no need to correct the turbidity
# factor used in the beam/GHI models.
# Create the corrected TL for TL < 2
# TLcorr = TL;
# TLcorr(TL < 2) = TLcorr(TL < 2) - 0.25 .* (2-TLcorr(TL < 2)) .^ (0.5);
# This equation is found in Solar Energy 73, pg 311. It is slightly
# different than the equation given in Solar Energy 73, pg 156. We used the
# equation from pg 311 because of the existence of known typos in the pg 156
# publication (notably the fh2-(TL-1) should be fh2 * (TL-1)).
ClearSkyGHI=cg1*(I0)*(pvl_tools.cosd(ApparentZenith))*(np.exp(- cg2*(AMabsolute)*((fh1 + fh2*((TL - 1))))))*(np.exp(0.01*((AMabsolute) ** (1.8))))
ClearSkyGHI[ClearSkyGHI < 0]=0
b=0.664 + 0.163 / fh1
BncI=b*(I0)*(np.exp(- 0.09*(AMabsolute)*((TL - 1))))
ClearSkyDNI=np.min(BncI,ClearSkyGHI*((1 - (0.1 - 0.2*(np.exp(- TL))) / (0.1 + 0.882 / fh1))) / pvl_tools.cosd(ApparentZenith))
#ClearSkyDNI=ClearSkyGHI*((1 - (0.1 - 0.2*(np.exp(- TL))) / (0.1 + 0.882 / fh1))) / pvl_tools.cosd(ApparentZenith)
ClearSkyDHI=ClearSkyGHI - ClearSkyDNI*(pvl_tools.cosd(ApparentZenith))
return ClearSkyGHI,ClearSkyDNI,ClearSkyDHI,BncI
def pvl_perez(SurfTilt, SurfAz, DHI, DNI, HExtra, SunZen, SunAz, AM,modelt='allsitescomposite1990'):
'''
Determine diffuse irradiance from the sky on a tilted surface using one of the Perez models
Perez models determine 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, extraterrestrial
irradiance, sun zenith angle, sun azimuth angle, and relative (not
pressure-corrected) airmass. Optionally a selector may be used to use
any of Perez's model coefficient sets.
Parameters
----------
SurfTilt : float or DataFrame
Surface tilt angles in decimal degrees.
SurfTilt must be >=0 and <=180. The tilt angle is defined as
degrees from horizontal (e.g. surface facing up = 0, surface facing
horizon = 90)
SurfAz : float or DataFrame
Surface azimuth angles in decimal degrees.
SurfAz must be >=0 and <=360. The Azimuth convention is defined
as degrees east of north (e.g. North = 0, South=180 East = 90, West = 270).
DHI : float or DataFrame
diffuse horizontal irradiance in W/m^2.
DHI must be >=0.
DNI : float or DataFrame
direct normal irradiance in W/m^2.
DNI must be >=0.
HExtra : float or DataFrame
extraterrestrial normal irradiance in W/m^2.
HExtra must be >=0.
SunZen : float or DataFrame
apparent (refraction-corrected) zenith
angles in decimal degrees.
SunZen must be >=0 and <=180.
SunAz : float or DataFrame
Sun azimuth angles in decimal degrees.
SunAz must be >=0 and <=360. The Azimuth convention is defined
as degrees east of north (e.g. North = 0, East = 90, West = 270).
AM : float or DataFrame
relative (not pressure-corrected) airmass
values. If AM is a DataFrame it must be of the same size as all other
DataFrame inputs. AM must be >=0 (careful using the 1/sec(z) model of AM
generation)
Other Parameters
----------------
model : string (optional, default='allsitescomposite1990')
a character string which selects the desired set of Perez
coefficients. If model is not provided as an input, the default,
'1990' will be used.
All possible model selections are:
* '1990'
* 'allsitescomposite1990' (same as '1990')
* 'allsitescomposite1988'
* 'sandiacomposite1988'
* 'usacomposite1988'
* 'france1988'
* 'phoenix1988'
* 'elmonte1988'
* 'osage1988'
* 'albuquerque1988'
* 'capecanaveral1988'
* 'albany1988'
Returns
--------
SkyDiffuse : float or DataFrame
the diffuse component of the solar radiation on an
arbitrarily tilted surface defined by the Perez model as given in
reference [3].
SkyDiffuse is the diffuse component ONLY and does not include the ground
reflected irradiance or the irradiance due to the beam.
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] Perez, R., Seals, R., Ineichen, P., Stewart, R., Menicucci, D., 1987. A new
simplified version of the Perez diffuse irradiance model for tilted
surfaces. Solar Energy 39(3), 221-232.
[3] Perez, R., Ineichen, P., Seals, R., Michalsky, J., Stewart, R., 1990.
Modeling daylight availability and irradiance components from direct
and global irradiance. Solar Energy 44 (5), 271-289.
[4] Perez, R. et. al 1988. "The Development and Verification of the
Perez Diffuse Radiation Model". SAND88-7030
See also
--------
pvl_ephemeris
pvl_extraradiation
pvl_isotropicsky
pvl_haydavies1980
pvl_reindl1990
pvl_klucher1979
pvl_kingdiffuse
pvl_relativeairmass
'''
Vars=locals()
Expect={'SurfTilt':('num','x>=0'),
'SurfAz':('x>=-180'),
'DHI':('x>=0'),
'DNI':('x>=0'),
'HExtra':('x>=0'),
'SunZen':('x>=0'),
'SunAz':('x>=-180'),
'AM':('x>=0'),
'modelt': ('default','default=allsitescomposite1990')}
var=pvl_tools.Parse(Vars,Expect)
kappa = 1.041 #for SunZen in radians
z = var.SunZen*np.pi/180# # convert to radians
Dhfilter = var.DHI > 0
e = ((var.DHI[Dhfilter] + var.DNI[Dhfilter])/var.DHI[Dhfilter]+kappa*z[Dhfilter]**3)/(1+kappa*z[Dhfilter]**3).reindex_like(var.SunZen)
ebin = pd.Series(np.zeros(var.DHI.shape[0]),index=e.index)
# Select which bin e falls into
ebin[(e<1.065)]= 1
ebin[(e>=1.065) & (e<1.23)]= 2
ebin[(e>=1.23) & (e<1.5)]= 3
ebin[(e>=1.5) & (e<1.95)]= 4
ebin[(e>=1.95) & (e<2.8)]= 5
ebin[(e>=2.8) & (e<4.5)]= 6
ebin[(e>=4.5) & (e<6.2)]= 7
ebin[e>=6.2] = 8
ebinfilter=ebin>0
ebin=ebin-1 #correct for 0 indexing
ebin[ebinfilter==False]=np.NaN
ebin=ebin.dropna().astype(int)
# This is added because in cases where the sun is below the horizon
# (var.SunZen > 90) but there is still diffuse horizontal light (var.DHI>0), it is
# possible that the airmass (var.AM) could be NaN, which messes up later
# calculations. Instead, if the sun is down, and there is still var.DHI, we set
# the airmass to the airmass value on the horizon (approximately 37-38).
#var.AM(var.SunZen >=90 & var.DHI >0) = 37;
var.HExtra[var.HExtra==0]=.00000001 #very hacky, fix this
delt = var.DHI*var.AM/var.HExtra
#
# The various possible sets of Perez coefficients are contained
# in a subfunction to clean up the code.
F1c,F2c = GetPerezCoefficients(var.modelt)
F1= F1c[ebin,0] + F1c[ebin,1]*delt[ebinfilter] + F1c[ebin,2]*z[ebinfilter]
F1[F1<0]=0;
F1=F1.astype(float)
F2= F2c[ebin,0] + F2c[ebin,1]*delt[ebinfilter] + F2c[ebin,2]*z[ebinfilter]
F2[F2<0]=0
F2=F2.astype(float)
A = pvl_tools.cosd(var.SurfTilt)*pvl_tools.cosd(var.SunZen) + pvl_tools.sind(var.SurfTilt)*pvl_tools.sind(var.SunZen)*pvl_tools.cosd(var.SunAz-var.SurfAz); #removed +180 from azimuth modifier: Rob Andrews October 19th 2012
A[A < 0] = 0
B = pvl_tools.cosd(var.SunZen);
B[B < pvl_tools.cosd(85)] = pvl_tools.cosd(85)
#Calculate Diffuse POA from sky dome
#SkyDiffuse = pd.Series(np.zeros(var.DHI.shape[0]),index=data.index)
SkyDiffuse = var.DHI[ebinfilter]*( 0.5* (1-F1[ebinfilter])*(1+pvl_tools.cosd(var.SurfTilt))+F1[ebinfilter] * A[ebinfilter]/ B[ebinfilter] + F2[ebinfilter]* pvl_tools.sind(var.SurfTilt))
SkyDiffuse[SkyDiffuse <= 0]= 0
return pd.DataFrame({'In_Plane_SkyDiffuse':SkyDiffuse})
def pvl_reindl1990(SurfTilt, SurfAz, DHI, DNI, GHI, HExtra, SunZen, SunAz):
'''
Determine diffuse irradiance from the sky on a tilted surface using Reindl's 1990 model
Reindl's 1990 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
horizontal irradiance, extraterrestrial irradiance, sun zenith angle,
and sun azimuth angle.
Parameters
----------
SurfTilt : DataFrame
Surface tilt angles in decimal degrees.
SurfTilt must be >=0 and <=180. The tilt angle is defined as
degrees from horizontal (e.g. surface facing up = 0, surface facing
horizon = 90)
SurfAz : DataFrame
Surface azimuth angles in decimal degrees.
SurfAz must be >=0 and <=360. The Azimuth convention is defined
as degrees east of north (e.g. North = 0, South=180 East = 90, West = 270).
DHI : DataFrame
diffuse horizontal irradiance in W/m^2.
DHI must be >=0.
DNI : DataFrame
direct normal irradiance in W/m^2.
DNI must be >=0.
GHI: DataFrame
Global irradiance in W/m^2.
GHI must be >=0.
HExtra : DataFrame
extraterrestrial normal irradiance in W/m^2.
HExtra must be >=0.
SunZen : DataFrame
apparent (refraction-corrected) zenith
angles in decimal degrees.
SunZen must be >=0 and <=180.
SunAz : DataFrame
Sun azimuth angles in decimal degrees.
SunAz must be >=0 and <=360. The Azimuth convention is defined
as degrees east of north (e.g. North = 0, East = 90, West = 270).
Returns
-------
SkyDiffuse : DataFrame
the diffuse component of the solar radiation on an
arbitrarily tilted surface defined by the Reindl model as given in
Loutzenhiser et. al (2007) equation 8.
SkyDiffuse is the diffuse component ONLY and does not include the ground
reflected irradiance or the irradiance due to the beam.
SkyDiffuse is a column vector vector with a number of elements equal to
the input vector(s).
Notes
-----
The POAskydiffuse 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.
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 fraction
correlations. Solar Energy 45(1), 1-7.
[3] Reindl, D.T., Beckmann, W.A., Duffie, J.A., 1990b. Evaluation of hourly
tilted surface radiation models. Solar Energy 45(1), 9-17.
See Also
---------
pvl_ephemeris
pvl_extraradiation
pvl_isotropicsky
pvl_haydavies1980
pvl_perez
pvl_klucher1979
pvl_kingdiffuse
'''
Vars = locals()
Expect = {
'SurfTilt': ('num', 'x>=0'),
'SurfAz': ('num', 'x>=-180'),
'DHI': ('num', 'x>=0'),
'DNI': ('num', 'x>=0'),
'GHI': ('num', 'x>=0'),
'HExtra': ('num', 'x>=0'),
'SunZen': ('num', 'x>=0'),
'SunAz': ('num', 'x>=-180'),
}
var = pvl_tools.Parse(Vars, Expect)
small = 1e-06
COSTT = pvl_tools.cosd(SurfTilt) * pvl_tools.cosd(SunZen) + pvl_tools.sind(
SurfTilt) * pvl_tools.sind(SunZen) * pvl_tools.cosd(SunAz - SurfAz)
RB = np.max(COSTT, 0) / np.max(pvl_tools.cosd(SunZen), 0.01745)
AI = DNI / HExtra
GHI[GHI < small] = small
HB = DNI * (pvl_tools.cosd(SunZen))
HB[HB < 0] = 0
GHI[GHI < 0] = 0
F = np.sqrt(HB / GHI)
SCUBE = (pvl_tools.sind(SurfTilt * (0.5)))**3
SkyDiffuse = DHI * ((AI * (RB) + (1 - AI) * (0.5) *
((1 + pvl_tools.cosd(SurfTilt))) * ((1 + F *
(SCUBE)))))
return SkyDiffuse
def pvl_perez(SurfTilt,
SurfAz,
DHI,
DNI,
HExtra,
SunZen,
SunAz,
AM,
modelt='allsitescomposite1990'):
'''
Determine diffuse irradiance from the sky on a tilted surface using one of the Perez models
Perez models determine 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, extraterrestrial
irradiance, sun zenith angle, sun azimuth angle, and relative (not
pressure-corrected) airmass. Optionally a selector may be used to use
any of Perez's model coefficient sets.
Parameters
----------
SurfTilt : float or DataFrame
Surface tilt angles in decimal degrees.
SurfTilt must be >=0 and <=180. The tilt angle is defined as
degrees from horizontal (e.g. surface facing up = 0, surface facing
horizon = 90)
SurfAz : float or DataFrame
Surface azimuth angles in decimal degrees.
SurfAz must be >=0 and <=360. The Azimuth convention is defined
as degrees east of north (e.g. North = 0, South=180 East = 90, West = 270).
DHI : float or DataFrame
diffuse horizontal irradiance in W/m^2.
DHI must be >=0.
DNI : float or DataFrame
direct normal irradiance in W/m^2.
DNI must be >=0.
HExtra : float or DataFrame
extraterrestrial normal irradiance in W/m^2.
HExtra must be >=0.
SunZen : float or DataFrame
apparent (refraction-corrected) zenith
angles in decimal degrees.
SunZen must be >=0 and <=180.
SunAz : float or DataFrame
Sun azimuth angles in decimal degrees.
SunAz must be >=0 and <=360. The Azimuth convention is defined
as degrees east of north (e.g. North = 0, East = 90, West = 270).
AM : float or DataFrame
relative (not pressure-corrected) airmass
values. If AM is a DataFrame it must be of the same size as all other
DataFrame inputs. AM must be >=0 (careful using the 1/sec(z) model of AM
generation)
Other Parameters
----------------
model : string (optional, default='allsitescomposite1990')
a character string which selects the desired set of Perez
coefficients. If model is not provided as an input, the default,
'1990' will be used.
All possible model selections are:
* '1990'
* 'allsitescomposite1990' (same as '1990')
* 'allsitescomposite1988'
* 'sandiacomposite1988'
* 'usacomposite1988'
* 'france1988'
* 'phoenix1988'
* 'elmonte1988'
* 'osage1988'
* 'albuquerque1988'
* 'capecanaveral1988'
* 'albany1988'
Returns
--------
SkyDiffuse : float or DataFrame
the diffuse component of the solar radiation on an
arbitrarily tilted surface defined by the Perez model as given in
reference [3].
SkyDiffuse is the diffuse component ONLY and does not include the ground
reflected irradiance or the irradiance due to the beam.
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] Perez, R., Seals, R., Ineichen, P., Stewart, R., Menicucci, D., 1987. A new
simplified version of the Perez diffuse irradiance model for tilted
surfaces. Solar Energy 39(3), 221-232.
[3] Perez, R., Ineichen, P., Seals, R., Michalsky, J., Stewart, R., 1990.
Modeling daylight availability and irradiance components from direct
and global irradiance. Solar Energy 44 (5), 271-289.
[4] Perez, R. et. al 1988. "The Development and Verification of the
Perez Diffuse Radiation Model". SAND88-7030
See also
--------
pvl_ephemeris
pvl_extraradiation
pvl_isotropicsky
pvl_haydavies1980
pvl_reindl1990
pvl_klucher1979
pvl_kingdiffuse
pvl_relativeairmass
'''
Vars = locals()
Expect = {
'SurfTilt': ('num', 'x>=0'),
'SurfAz': ('x>=-180'),
'DHI': ('x>=0'),
'DNI': ('x>=0'),
'HExtra': ('x>=0'),
'SunZen': ('x>=0'),
'SunAz': ('x>=-180'),
'AM': ('x>=0'),
'modelt': ('default', 'default=allsitescomposite1990')
}
var = pvl_tools.Parse(Vars, Expect)
kappa = 1.041 #for SunZen in radians
z = var.SunZen * np.pi / 180 # # convert to radians
Dhfilter = var.DHI > 0
e = ((var.DHI[Dhfilter] + var.DNI[Dhfilter]) / var.DHI[Dhfilter] +
kappa * z[Dhfilter]**3) / (1 + kappa * z[Dhfilter]**3).reindex_like(
var.SunZen)
ebin = pd.Series(np.zeros(var.DHI.shape[0]), index=e.index)
# Select which bin e falls into
ebin[(e < 1.065)] = 1
ebin[(e >= 1.065) & (e < 1.23)] = 2
ebin[(e >= 1.23) & (e < 1.5)] = 3
ebin[(e >= 1.5) & (e < 1.95)] = 4
ebin[(e >= 1.95) & (e < 2.8)] = 5
ebin[(e >= 2.8) & (e < 4.5)] = 6
ebin[(e >= 4.5) & (e < 6.2)] = 7
ebin[e >= 6.2] = 8
ebinfilter = ebin > 0
ebin = ebin - 1 #correct for 0 indexing
ebin[ebinfilter == False] = np.NaN
ebin = ebin.dropna().astype(int)
# This is added because in cases where the sun is below the horizon
# (var.SunZen > 90) but there is still diffuse horizontal light (var.DHI>0), it is
# possible that the airmass (var.AM) could be NaN, which messes up later
# calculations. Instead, if the sun is down, and there is still var.DHI, we set
# the airmass to the airmass value on the horizon (approximately 37-38).
#var.AM(var.SunZen >=90 & var.DHI >0) = 37;
var.HExtra[var.HExtra == 0] = .00000001 #very hacky, fix this
delt = var.DHI * var.AM / var.HExtra
#
# The various possible sets of Perez coefficients are contained
# in a subfunction to clean up the code.
F1c, F2c = GetPerezCoefficients(var.modelt)
F1 = F1c[ebin,
0] + F1c[ebin, 1] * delt[ebinfilter] + F1c[ebin,
2] * z[ebinfilter]
F1[F1 < 0] = 0
F1 = F1.astype(float)
F2 = F2c[ebin,
0] + F2c[ebin, 1] * delt[ebinfilter] + F2c[ebin,
2] * z[ebinfilter]
F2[F2 < 0] = 0
F2 = F2.astype(float)
A = pvl_tools.cosd(var.SurfTilt) * pvl_tools.cosd(
var.SunZen) + pvl_tools.sind(var.SurfTilt) * pvl_tools.sind(
var.SunZen) * pvl_tools.cosd(var.SunAz - var.SurfAz)
#removed +180 from azimuth modifier: Rob Andrews October 19th 2012
A[A < 0] = 0
B = pvl_tools.cosd(var.SunZen)
B[B < pvl_tools.cosd(85)] = pvl_tools.cosd(85)
#Calculate Diffuse POA from sky dome
#SkyDiffuse = pd.Series(np.zeros(var.DHI.shape[0]),index=data.index)
SkyDiffuse = var.DHI[ebinfilter] * (
0.5 * (1 - F1[ebinfilter]) *
(1 + pvl_tools.cosd(var.SurfTilt)) + F1[ebinfilter] * A[ebinfilter] /
B[ebinfilter] + F2[ebinfilter] * pvl_tools.sind(var.SurfTilt))
SkyDiffuse[SkyDiffuse <= 0] = 0
return pd.DataFrame({'In_Plane_SkyDiffuse': SkyDiffuse})
def pvl_physicaliam(K, L, n, theta):
'''
Determine the incidence angle modifier using refractive
index, glazing thickness, and extinction coefficient
pvl_physicaliam calculates the incidence angle modifier as described in
De Soto et al. "Improvement and validation of a model for photovoltaic
array performance", section 3. The calculation is based upon a physical
model of absorbtion and transmission through a cover. Required
information includes, incident angle, cover extinction coefficient,
cover thickness
Note: The authors of this function believe that eqn. 14 in [1] is
incorrect. This function uses the following equation in its place:
theta_r = arcsin(1/n * sin(theta))
Parameters
----------
K : float
The glazing extinction coefficient in units of 1/meters. Reference
[1] indicates that a value of 4 is reasonable for "water white"
glass. K must be a numeric scalar or vector with all values >=0. If K
is a vector, it must be the same size as all other input vectors.
L : float
The glazing thickness in units of meters. Reference [1] indicates
that 0.002 meters (2 mm) is reasonable for most glass-covered
PV panels. L must be a numeric scalar or vector with all values >=0.
If L is a vector, it must be the same size as all other input vectors.
n : float
The effective index of refraction (unitless). Reference [1]
indicates that a value of 1.526 is acceptable for glass. n must be a
numeric scalar or vector with all values >=0. If n is a vector, it
must be the same size as all other input vectors.
theta :float
The angle of incidence between the module normal vector and the
sun-beam vector in degrees. Theta must be a numeric scalar or vector.
For any values of theta where abs(theta)>90, IAM is set to 0. For any
values of theta where -90 < theta < 0, theta is set to abs(theta) and
evaluated. A warning will be generated if any(theta<0 or theta>90).
Returns
-------
IAM : float
The incident angle modifier as specified in eqns. 14-16 of [1].
IAM is a column vector with the same number of elements as the
largest input vector.
References
----------
[1] W. De Soto et al., "Improvement and validation of a model for
photovoltaic array performance", Solar Energy, vol 80, pp. 78-88,
2006.
[2] Duffie, John A. & Beckman, William A.. (2006). Solar Engineering
of Thermal Processes, third edition. [Books24x7 version] Available
from http://common.books24x7.com/toc.aspx?bookid=17160.
See Also
--------
pvl_getaoi
pvl_ephemeris
pvl_spa
pvl_ashraeiam
'''
Vars = locals()
Expect = {'K': 'x >= 0', 'L': 'x >= 0', 'n': 'x >= 0', 'theta': 'num'}
var = pvl_tools.Parse(Vars, Expect)
if any((var.theta < 0) | (var.theta >= 90)):
print(
'Input incident angles <0 or >=90 detected For input angles with absolute value greater than 90, the '
+
'modifier is set to 0. For input angles between -90 and 0, the ' +
'angle is changed to its absolute value and evaluated.')
var.theta[(var.theta < 0) |
(var.theta >= 90)] = abs((var.theta < 0) | (var.theta >= 90))
thetar_deg = pvl_tools.asind(1.0 / n * (pvl_tools.sind(theta)))
tau = np.exp(-1.0 * (K * (L) / pvl_tools.cosd(thetar_deg))) * ((1 - 0.5 * (
(((pvl_tools.sind(thetar_deg - theta))**2) /
((pvl_tools.sind(thetar_deg + theta))**2) +
((pvl_tools.tand(thetar_deg - theta))**2) /
((pvl_tools.tand(thetar_deg + theta))**2)))))
zeroang = 1e-06
thetar_deg0 = pvl_tools.asind(1.0 / n * (pvl_tools.sind(zeroang)))
tau0 = np.exp(-1.0 * (K * (L) / pvl_tools.cosd(thetar_deg0))) * (
(1 - 0.5 * ((((pvl_tools.sind(thetar_deg0 - zeroang))**2) /
((pvl_tools.sind(thetar_deg0 + zeroang))**2) +
((pvl_tools.tand(thetar_deg0 - zeroang))**2) /
((pvl_tools.tand(thetar_deg0 + zeroang))**2)))))
IAM = tau / tau0
IAM[theta == 0] = 1
IAM[abs(theta) > 90 | (IAM < 0)] = 0
return IAM
def pvl_haydavies1980(SurfTilt, SurfAz, DHI, DNI, HExtra, SunZen, SunAz):
'''
Determine diffuse irradiance from the sky on a tilted surface using Hay & Davies' 1980 model
Hay and Davies' 1980 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,
extraterrestrial irradiance, sun zenith angle, and sun azimuth angle.
Parameters
----------
SurfTilt : float or DataFrame
Surface tilt angles in decimal degrees.
SurfTilt must be >=0 and <=180. The tilt angle is defined as
degrees from horizontal (e.g. surface facing up = 0, surface facing
horizon = 90)
SurfAz : float or DataFrame
Surface azimuth angles in decimal degrees.
SurfAz must be >=0 and <=360. The Azimuth convention is defined
as degrees east of north (e.g. North = 0, South=180 East = 90, West = 270).
DHI : float or DataFrame
diffuse horizontal irradiance in W/m^2.
DHI must be >=0.
DNI : float or DataFrame
direct normal irradiance in W/m^2.
DNI must be >=0.
HExtra : float or DataFrame
extraterrestrial normal irradiance in W/m^2.
HExtra must be >=0.
SunZen : float or DataFrame
apparent (refraction-corrected) zenith
angles in decimal degrees.
SunZen must be >=0 and <=180.
SunAz : float or DataFrame
Sun azimuth angles in decimal degrees.
SunAz must be >=0 and <=360. The Azimuth convention is defined
as degrees east of north (e.g. North = 0, East = 90, West = 270).
Returns
--------
SkyDiffuse : float or DataFrame
the diffuse component of the solar radiation on an
arbitrarily tilted surface defined by the Perez model as given in
reference [3].
SkyDiffuse is the diffuse component ONLY and does not include the ground
reflected irradiance or the irradiance due to the beam.
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] Hay, J.E., Davies, J.A., 1980. Calculations of the solar radiation incident
on an inclined surface. In: Hay, J.E., Won, T.K. (Eds.), Proc. of First
Canadian Solar Radiation Data Workshop, 59. Ministry of Supply
and Services, Canada.
See Also
--------
pvl_ephemeris
pvl_extraradiation
pvl_isotropicsky
pvl_reindl1990
pvl_perez
pvl_klucher1979
pvl_kingdiffuse
pvl_spa
'''
Vars = locals()
Expect = {
'SurfTilt': ('num', 'x>=0'),
'SurfAz': ('x>=-180'),
'DHI': ('x>=0'),
'DNI': ('x>=0'),
'HExtra': ('x>=0'),
'SunZen': ('x>=0'),
'SunAz': ('x>=-180'),
}
var = pvl_tools.Parse(Vars, Expect)
COSTT = pvl_tools.cosd(SurfTilt) * pvl_tools.cosd(SunZen) + pvl_tools.sind(
SurfTilt) * pvl_tools.sind(SunZen) * pvl_tools.cosd(SunAz - SurfAz)
RB = np.max(COSTT, 0) / np.max(pvl_tools.cosd(SunZen), 0.01745)
AI = DNI / HExtra
SkyDiffuse = DHI * ((AI * (RB) + (1 - AI) * (0.5) *
((1 + pvl_tools.cosd(SurfTilt)))))
return SkyDiffuse
def pvl_physicaliam(K,L,n,theta):
'''
Determine the incidence angle modifier using refractive
index, glazing thickness, and extinction coefficient
pvl_physicaliam calculates the incidence angle modifier as described in
De Soto et al. "Improvement and validation of a model for photovoltaic
array performance", section 3. The calculation is based upon a physical
model of absorbtion and transmission through a cover. Required
information includes, incident angle, cover extinction coefficient,
cover thickness
Note: The authors of this function believe that eqn. 14 in [1] is
incorrect. This function uses the following equation in its place:
theta_r = arcsin(1/n * sin(theta))
Parameters
----------
K : float
The glazing extinction coefficient in units of 1/meters. Reference
[1] indicates that a value of 4 is reasonable for "water white"
glass. K must be a numeric scalar or vector with all values >=0. If K
is a vector, it must be the same size as all other input vectors.
L : float
The glazing thickness in units of meters. Reference [1] indicates
that 0.002 meters (2 mm) is reasonable for most glass-covered
PV panels. L must be a numeric scalar or vector with all values >=0.
If L is a vector, it must be the same size as all other input vectors.
n : float
The effective index of refraction (unitless). Reference [1]
indicates that a value of 1.526 is acceptable for glass. n must be a
numeric scalar or vector with all values >=0. If n is a vector, it
must be the same size as all other input vectors.
theta :float
The angle of incidence between the module normal vector and the
sun-beam vector in degrees. Theta must be a numeric scalar or vector.
For any values of theta where abs(theta)>90, IAM is set to 0. For any
values of theta where -90 < theta < 0, theta is set to abs(theta) and
evaluated. A warning will be generated if any(theta<0 or theta>90).
Returns
-------
IAM : float
The incident angle modifier as specified in eqns. 14-16 of [1].
IAM is a column vector with the same number of elements as the
largest input vector.
References
----------
[1] W. De Soto et al., "Improvement and validation of a model for
photovoltaic array performance", Solar Energy, vol 80, pp. 78-88,
2006.
[2] Duffie, John A. & Beckman, William A.. (2006). Solar Engineering
of Thermal Processes, third edition. [Books24x7 version] Available
from http://common.books24x7.com/toc.aspx?bookid=17160.
See Also
--------
pvl_getaoi
pvl_ephemeris
pvl_spa
pvl_ashraeiam
'''
Vars=locals()
Expect={'K':'x >= 0',
'L':'x >= 0',
'n':'x >= 0',
'theta':'num'}
var=pvl_tools.Parse(Vars,Expect)
if any((var.theta < 0) | (var.theta >= 90)):
print('Input incident angles <0 or >=90 detected For input angles with absolute value greater than 90, the ' + 'modifier is set to 0. For input angles between -90 and 0, the ' + 'angle is changed to its absolute value and evaluated.')
var.theta[(var.theta < 0) | (var.theta >= 90)]=abs((var.theta < 0) | (var.theta >= 90))
thetar_deg=pvl_tools.asind(1.0 / n*(pvl_tools.sind(theta)))
tau=np.exp(- 1.0 * (K*(L) / pvl_tools.cosd(thetar_deg)))*((1 - 0.5*((((pvl_tools.sind(thetar_deg - theta)) ** 2) / ((pvl_tools.sind(thetar_deg + theta)) ** 2) + ((pvl_tools.tand(thetar_deg - theta)) ** 2) / ((pvl_tools.tand(thetar_deg + theta)) ** 2)))))
zeroang=1e-06
thetar_deg0=pvl_tools.asind(1.0 / n*(pvl_tools.sind(zeroang)))
tau0=np.exp(- 1.0 * (K*(L) / pvl_tools.cosd(thetar_deg0)))*((1 - 0.5*((((pvl_tools.sind(thetar_deg0 - zeroang)) ** 2) / ((pvl_tools.sind(thetar_deg0 + zeroang)) ** 2) + ((pvl_tools.tand(thetar_deg0 - zeroang)) ** 2) / ((pvl_tools.tand(thetar_deg0 + zeroang)) ** 2)))))
IAM=tau / tau0
IAM[theta == 0]=1
IAM[abs(theta) > 90 | (IAM < 0)]=0
return IAM
