def get_aoi(self, surface_tilt, surface_azimuth, solar_zenith,
solar_azimuth):
"""Get the angle of incidence on the system.
For a given set of solar zenith and azimuth angles, the
surface tilt and azimuth parameters are typically determined
by :py:method:`~SingleAxisTracker.singleaxis`. The
:py:method:`~SingleAxisTracker.singleaxis` method also returns
the angle of incidence, so this method is only needed
if using a different tracking algorithm.
Parameters
----------
surface_tilt : numeric
Panel tilt from horizontal.
surface_azimuth : numeric
Panel azimuth from north
solar_zenith : float or Series.
Solar zenith angle.
solar_azimuth : float or Series.
Solar azimuth angle.
Returns
-------
aoi : Series
The angle of incidence in degrees from normal.
"""
aoi = irradiance.aoi(surface_tilt, surface_azimuth,
solar_zenith, solar_azimuth)
return aoi
def get_aoi(self, surface_tilt, surface_azimuth, solar_zenith,
solar_azimuth):
"""Get the angle of incidence on the system.
For a given set of solar zenith and azimuth angles, the
surface tilt and azimuth parameters are typically determined
by :py:method:`~SingleAxisTracker.singleaxis`. The
:py:method:`~SingleAxisTracker.singleaxis` method also returns
the angle of incidence, so this method is only needed
if using a different tracking algorithm.
Parameters
----------
surface_tilt : numeric
Panel tilt from horizontal.
surface_azimuth : numeric
Panel azimuth from north
solar_zenith : float or Series.
Solar zenith angle.
solar_azimuth : float or Series.
Solar azimuth angle.
Returns
-------
aoi : Series
The angle of incidence in degrees from normal.
"""
aoi = irradiance.aoi(surface_tilt, surface_azimuth, solar_zenith,
solar_azimuth)
return aoi
def _shaded_fraction(solar_zenith, solar_azimuth, surface_tilt,
surface_azimuth, gcr):
"""
Calculate fraction (from the bottom) of row slant height that is shaded
from direct irradiance by the row in front toward the sun.
See [1], Eq. 14 and also [2], Eq. 32.
.. math::
F_x = \\max \\left( 0, \\min \\left(\\frac{\\text{GCR} \\cos \\theta
+ \\left( \\text{GCR} \\sin \\theta - \\tan \\beta_{c} \\right)
\\tan Z - 1}
{\\text{GCR} \\left( \\cos \\theta + \\sin \\theta \\tan Z \\right)},
1 \\right) \\right)
Parameters
----------
solar_zenith : numeric
Apparent (refraction-corrected) solar zenith. [degrees]
solar_azimuth : numeric
Solar azimuth. [degrees]
surface_tilt : numeric
Row tilt from horizontal, e.g. surface facing up = 0, surface facing
horizon = 90. [degrees]
surface_azimuth : numeric
Azimuth angle of the row surface. North=0, East=90, South=180,
West=270. [degrees]
gcr : numeric
Ground coverage ratio, which is the ratio of row slant length to row
spacing (pitch). [unitless]
Returns
-------
f_x : numeric
Fraction of row slant height from the bottom that is shaded from
direct irradiance.
References
----------
.. [1] Mikofski, M., Darawali, R., Hamer, M., Neubert, A., and Newmiller,
J. "Bifacial Performance Modeling in Large Arrays". 2019 IEEE 46th
Photovoltaic Specialists Conference (PVSC), 2019, pp. 1282-1287.
:doi:`10.1109/PVSC40753.2019.8980572`.
.. [2] Kevin Anderson and Mark Mikofski, "Slope-Aware Backtracking for
Single-Axis Trackers", Technical Report NREL/TP-5K00-76626, July 2020.
https://www.nrel.gov/docs/fy20osti/76626.pdf
"""
tan_phi = utils._solar_projection_tangent(solar_zenith, solar_azimuth,
surface_azimuth)
# length of shadow behind a row as a fraction of pitch
x = gcr * (sind(surface_tilt) * tan_phi + cosd(surface_tilt))
f_x = 1 - 1. / x
# set f_x to be 1 when sun is behind the array
ao = aoi(surface_tilt, surface_azimuth, solar_zenith, solar_azimuth)
f_x = np.where(ao < 90, f_x, 1.)
# when x < 1, the shadow is not long enough to fall on the row surface
f_x = np.where(x > 1., f_x, 0.)
return f_x
def test_aoi_and_aoi_projection(surface_tilt, surface_azimuth, solar_zenith,
solar_azimuth, aoi_expected,
aoi_proj_expected):
aoi = irradiance.aoi(surface_tilt, surface_azimuth, solar_zenith,
solar_azimuth)
assert_allclose(aoi, aoi_expected, atol=1e-6)
aoi_projection = irradiance.aoi_projection(surface_tilt, surface_azimuth,
solar_zenith, solar_azimuth)
assert_allclose(aoi_projection, aoi_proj_expected, atol=1e-6)
def test_aoi_and_aoi_projection(surface_tilt, surface_azimuth, solar_zenith,
solar_azimuth, aoi_expected,
aoi_proj_expected):
aoi = irradiance.aoi(surface_tilt, surface_azimuth, solar_zenith,
solar_azimuth)
assert_allclose(aoi, aoi_expected, atol=1e-6)
aoi_projection = irradiance.aoi_projection(
surface_tilt, surface_azimuth, solar_zenith, solar_azimuth)
assert_allclose(aoi_projection, aoi_proj_expected, atol=1e-6)
def test_globalinplane():
aoi = irradiance.aoi(40, 180, ephem_data['apparent_zenith'],
ephem_data['azimuth'])
airmass = atmosphere.relativeairmass(ephem_data['apparent_zenith'])
gr_sand = irradiance.grounddiffuse(40, ghi, surface_type='sand')
diff_perez = irradiance.perez(
40, 180, irrad_data['dhi'], irrad_data['dni'], dni_et,
ephem_data['apparent_zenith'], ephem_data['azimuth'], airmass)
irradiance.globalinplane(
aoi=aoi, dni=irrad_data['dni'], poa_sky_diffuse=diff_perez,
poa_ground_diffuse=gr_sand)
def test_globalinplane():
aoi = irradiance.aoi(40, 180, ephem_data['apparent_zenith'],
ephem_data['apparent_azimuth'])
airmass = atmosphere.relativeairmass(ephem_data['apparent_zenith'])
gr_sand = irradiance.grounddiffuse(40, ghi, surface_type='sand')
diff_perez = irradiance.perez(
40, 180, irrad_data['dhi'], irrad_data['dni'], dni_et,
ephem_data['apparent_zenith'], ephem_data['apparent_azimuth'], airmass)
irradiance.globalinplane(
aoi=aoi, dni=irrad_data['dni'], poa_sky_diffuse=diff_perez,
poa_ground_diffuse=gr_sand)
def test_globalinplane():
AOI = irradiance.aoi(40, 180, ephem_data['apparent_zenith'],
ephem_data['apparent_azimuth'])
AM = atmosphere.relativeairmass(ephem_data['apparent_zenith'])
gr_sand = irradiance.grounddiffuse(40, ghi, surface_type='sand')
diff_perez = irradiance.perez(
40, 180, irrad_data['DHI'], irrad_data['DNI'], dni_et,
ephem_data['apparent_zenith'], ephem_data['apparent_azimuth'], AM)
irradiance.globalinplane(
AOI=AOI, DNI=irrad_data['DNI'], In_Plane_SkyDiffuse=diff_perez,
GR=gr_sand)
def setup(self):
self.times = pd.date_range(start='20180601', freq='1min',
periods=14400)
self.days = pd.date_range(start='20180601', freq='d', periods=30)
self.location = location.Location(40, -80)
self.solar_position = self.location.get_solarposition(self.times)
self.clearsky_irradiance = self.location.get_clearsky(self.times)
self.tilt = 20
self.azimuth = 180
self.aoi = irradiance.aoi(self.tilt, self.azimuth,
self.solar_position.apparent_zenith,
self.solar_position.azimuth)
def test_globalinplane():
AOI = irradiance.aoi(40, 180, ephem_data['apparent_zenith'],
ephem_data['apparent_azimuth'])
AM = atmosphere.relativeairmass(ephem_data['apparent_zenith'])
gr_sand = irradiance.grounddiffuse(40, ghi, surface_type='sand')
diff_perez = irradiance.perez(40, 180, irrad_data['DHI'],
irrad_data['DNI'], dni_et,
ephem_data['apparent_zenith'],
ephem_data['apparent_azimuth'], AM)
irradiance.globalinplane(AOI=AOI,
DNI=irrad_data['DNI'],
In_Plane_SkyDiffuse=diff_perez,
GR=gr_sand)
def get_perfect_voltage_for_a_day(start, freq):
"""This method is used to build a pandas serie with voltage values.
This serie has DateTime index and contains a value for every "freq"
seconds during 24 hours starting from "start" date.
There are several assumptions:
1. Location is Munich
2. A battery is pointing to the south, amount of blocks is 20
3. Sandia Module database is used
4. pvlib library is heavily used
:param start: datetime. First timestamp in result series
:param freq: str. How often voltage should be sampled
:return: voltage : Series
"""
surface_tilt = _munich_location.latitude
surface_azimuth = 180 # pointing south
date_range = pd.date_range(start=start,
end=start + dt.timedelta(
hours=23, minutes=59, seconds=59),
freq=freq, tz=_munich_location.tz)
clearsky_estimations = _munich_location.get_clearsky(date_range)
dni_extra = irradiance.extraradiation(date_range)
solar_position = solarposition.get_solarposition(
date_range, _munich_location.latitude, _munich_location.longitude)
airmass = atmosphere.relativeairmass(solar_position['apparent_zenith'])
pressure = atmosphere.alt2pres(_munich_location.altitude)
am_abs = atmosphere.absoluteairmass(airmass, pressure)
total_irrad = irradiance.total_irrad(surface_tilt,
surface_azimuth,
solar_position['apparent_zenith'],
solar_position['azimuth'],
clearsky_estimations['dni'],
clearsky_estimations['ghi'],
clearsky_estimations['dhi'],
dni_extra=dni_extra,
model='haydavies')
temps = pvsystem.sapm_celltemp(total_irrad['poa_global'], 0, 15)
aoi = irradiance.aoi(surface_tilt, surface_azimuth,
solar_position['apparent_zenith'],
solar_position['azimuth'])
# add 0.0001 to avoid np.log(0) and warnings about that
effective_irradiance = pvsystem.sapm_effective_irradiance(
total_irrad['poa_direct'], total_irrad['poa_diffuse'], am_abs,
aoi, _sandia_module) + 0.0001
sapm = pvsystem.sapm(effective_irradiance, temps['temp_cell'],
_sandia_module)
return sapm['p_mp'] * _module_count
def tilt_irr(self,
surface_tilt=None,
surface_azimuth=180,
include_solar_pos=False) -> pd.DataFrame:
"""
Calculate the irradiances(DNI) and angle of incidence (aoi) on a tilted surface
:param surface_tilt: The surface tilt angle (in degree).
:param surface_azimuth: The azimuth angle of the surface. Default is 180 degrees.
:param include_solar_pos: whether to include solar position in the output dataframe.
:return: a dataframe with calculated solar incidence.
"""
if surface_tilt is None:
surface_tilt = self.latitude
ngo = Location(latitude=self.latitude,
longitude=self.longitude,
altitude=0,
tz='Japan')
solar_pos = ngo.get_solarposition(
pd.DatetimeIndex(self.hour_df['avg_time']))
dni_arr = self.get_DNI()
irrad_df = total_irrad(surface_tilt=surface_tilt,
surface_azimuth=surface_azimuth,
apparent_zenith=solar_pos['apparent_zenith'],
azimuth=solar_pos['azimuth'],
dni=dni_arr,
ghi=self.hour_df['GHI'],
dhi=self.hour_df['dHI'])
irrad_df['aoi'] = aoi(surface_tilt, surface_azimuth,
solar_pos['zenith'], solar_pos['azimuth'])
irrad_df['DNI'] = dni_arr
n_df = pd.concat([self.hour_df, irrad_df], axis=1)
if include_solar_pos:
n_df = pd.concat([n_df, solar_pos], axis=1)
return n_df
def get_aoi(self, solar_zenith, solar_azimuth):
"""
Get the angle of incidence on the Static CPV System.
Parameters
----------
solar_zenith : float or Series.
Solar zenith angle.
solar_azimuth : float or Series.
Solar azimuth angle.
Returns
-------
aoi : Series
The angle of incidence
"""
aoi = irradiance.aoi(self.surface_tilt, self.surface_azimuth,
solar_zenith, solar_azimuth)
return aoi
def _get_poa(data, solar_position):
"""
Return the radiation adjusted to
Plane of Array (SkyDiffuse, GroundDiffuse, Total).
"""
extra_radiation = get_extra_radiation(data.data.index)
# Best orientation for pv system
surface_tilt = _surface_tilt(data.latitude)
surface_azimuth = _surface_azimuth(data.latitude)
# Sky Diffuse radiation (From PvLib)
poa_diffuse = haydavies(surface_tilt=surface_tilt,
surface_azimuth=surface_azimuth,
dhi=data.data['Gd(h)'],
dni=data.data['Gb(n)'],
dni_extra=extra_radiation,
solar_zenith=solar_position.apparent_zenith,
solar_azimuth=solar_position.azimuth)
# Ground Diffuse radiation (From PvLib)
poa_ground = get_ground_diffuse(data.latitude,
data.data['G(h)'],
surface_type='urban')
# Angle of incidence at best orientation
_aoi = aoi(surface_tilt=surface_tilt,
surface_azimuth=surface_azimuth,
solar_zenith=solar_position.apparent_zenith,
solar_azimuth=solar_position.apparent_zenith)
# Total radiation at plane of the pv array.
poa_total = poa_components(aoi=_aoi,
dni=data.data['Gb(n)'],
poa_sky_diffuse=poa_diffuse,
poa_ground_diffuse=poa_ground)
return poa_total, _aoi
def test_poa_components(irrad_data, ephem_data, dni_et, relative_airmass):
aoi = irradiance.aoi(40, 180, ephem_data['apparent_zenith'],
ephem_data['azimuth'])
gr_sand = irradiance.get_ground_diffuse(40,
irrad_data['ghi'],
surface_type='sand')
diff_perez = irradiance.perez(40, 180, irrad_data['dhi'],
irrad_data['dni'], dni_et,
ephem_data['apparent_zenith'],
ephem_data['azimuth'], relative_airmass)
out = irradiance.poa_components(aoi, irrad_data['dni'], diff_perez,
gr_sand)
expected = pd.DataFrame(np.array(
[[0., -0., 0., 0., 0.],
[35.19456561, 0., 35.19456561, 31.4635077, 3.73105791],
[956.18253696, 798.31939281, 157.86314414, 109.08433162, 48.77881252],
[90.99624896, 33.50143401, 57.49481495, 45.45978964, 12.03502531]]),
columns=[
'poa_global', 'poa_direct', 'poa_diffuse',
'poa_sky_diffuse', 'poa_ground_diffuse'
],
index=irrad_data.index)
assert_frame_equal(out, expected)
def test_poa_components(irrad_data, ephem_data, dni_et, relative_airmass):
aoi = irradiance.aoi(40, 180, ephem_data['apparent_zenith'],
ephem_data['azimuth'])
gr_sand = irradiance.get_ground_diffuse(40, irrad_data['ghi'],
surface_type='sand')
diff_perez = irradiance.perez(
40, 180, irrad_data['dhi'], irrad_data['dni'], dni_et,
ephem_data['apparent_zenith'], ephem_data['azimuth'], relative_airmass)
out = irradiance.poa_components(
aoi, irrad_data['dni'], diff_perez, gr_sand)
expected = pd.DataFrame(np.array(
[[ 0. , -0. , 0. , 0. ,
0. ],
[ 35.19456561, 0. , 35.19456561, 31.4635077 ,
3.73105791],
[956.18253696, 798.31939281, 157.86314414, 109.08433162,
48.77881252],
[ 90.99624896, 33.50143401, 57.49481495, 45.45978964,
12.03502531]]),
columns=['poa_global', 'poa_direct', 'poa_diffuse', 'poa_sky_diffuse',
'poa_ground_diffuse'],
index=irrad_data.index)
assert_frame_equal(out, expected)
from nose.tools import assert_equals, assert_almost_equals
from pandas.util.testing import assert_series_equal, assert_frame_equal
from pvlib import tmy
from pvlib import pvsystem
from pvlib import clearsky
from pvlib import irradiance
from pvlib import atmosphere
from pvlib import solarposition
from pvlib.location import Location
tus = Location(32.2, -111, "US/Arizona", 700, "Tucson")
times = pd.date_range(start=datetime.datetime(2014, 1, 1), end=datetime.datetime(2014, 1, 2), freq="1Min")
ephem_data = solarposition.get_solarposition(times, tus, method="pyephem")
irrad_data = clearsky.ineichen(times, tus, linke_turbidity=3, solarposition_method="pyephem")
aoi = irradiance.aoi(0, 0, ephem_data["apparent_zenith"], ephem_data["apparent_azimuth"])
am = atmosphere.relativeairmass(ephem_data.apparent_zenith)
meta = {"latitude": 37.8, "longitude": -122.3, "altitude": 10, "Name": "Oakland", "State": "CA", "TZ": -8}
pvlib_abspath = os.path.dirname(os.path.abspath(inspect.getfile(tmy)))
tmy3_testfile = os.path.join(pvlib_abspath, "data", "703165TY.csv")
tmy2_testfile = os.path.join(pvlib_abspath, "data", "12839.tm2")
tmy3_data, tmy3_metadata = tmy.readtmy3(tmy3_testfile)
tmy2_data, tmy2_metadata = tmy.readtmy2(tmy2_testfile)
def test_systemdef_tmy3():
expected = {
from pvlib import tmy
from pvlib import pvsystem
from pvlib import clearsky
from pvlib import irradiance
from pvlib import atmosphere
from pvlib import solarposition
from pvlib.location import Location
tus = Location(32.2, -111, 'US/Arizona', 700, 'Tucson')
times = pd.date_range(start=datetime.datetime(2014,1,1),
end=datetime.datetime(2014,1,2), freq='1Min')
ephem_data = solarposition.get_solarposition(times, tus, method='pyephem')
irrad_data = clearsky.ineichen(times, tus, linke_turbidity=3,
solarposition_method='pyephem')
aoi = irradiance.aoi(0, 0, ephem_data['apparent_zenith'],
ephem_data['apparent_azimuth'])
am = atmosphere.relativeairmass(ephem_data.apparent_zenith)
meta = {'latitude': 37.8,
'longitude': -122.3,
'altitude': 10,
'Name': 'Oakland',
'State': 'CA',
'TZ': -8}
pvlib_abspath = os.path.dirname(os.path.abspath(inspect.getfile(tmy)))
tmy3_testfile = os.path.join(pvlib_abspath, 'data', '703165TY.csv')
tmy2_testfile = os.path.join(pvlib_abspath, 'data', '12839.tm2')
tmy3_data, tmy3_metadata = tmy.readtmy3(tmy3_testfile)
def calculate_overcast_spectrl2():
"""
This example will loop over a range of cloud covers and latitudes
(at longitude=0) for a specific date and calculate the spectral
irradiance with and without accounting for clouds. Clouds are accounted for
by applying the cloud opacity factor defined in [1]. Several steps
are required:
1. Calculate the atmospheric and solar conditions for the
location and time
2. Calculate the spectral irradiance using `pvlib.spectrum.spectrl2`
for clear sky conditions
3. Calculate the dni, dhi, and ghi for cloudy conditions using
`pvlib.irradiance.campbell_norman`
4. Determine total in-plane irradiance and its beam,
sky diffuse and ground
reflected components for cloudy conditions -
`pvlib.irradiance.get_total_irradiance`
5. Calculate the dni, dhi, and ghi for clear sky conditions
using `pvlib.irradiance.campbell_norman`
6. Determine total in-plane irradiance and its beam,
sky diffuse and ground
reflected components for clear sky conditions -
`pvlib.irradiance.get_total_irradiance`
7. Calculate the cloud opacity factor [1] and scale the
spectral results from step 4 - func cloud_opacity_factor
8. Plot the results - func plot_spectral_irradiance
"""
month = 2
hour_of_day = 12
altitude = 0.0
longitude = 0.0
latitudes = [10, 40]
# cloud cover in fraction units
cloud_covers = [0.2, 0.5]
water_vapor_content = 0.5
tau500 = 0.1
ground_albedo = 0.06
ozone = 0.3
surface_tilt = 0.0
ctime, pv_system = setup_pv_system(month, hour_of_day)
for cloud_cover in cloud_covers:
for latitude in latitudes:
sol = get_solarposition(ctime, latitude, longitude)
az = sol['apparent_zenith'].to_numpy()
airmass_relative = get_relative_airmass(az,
model='kastenyoung1989')
pressure = pvlib.atmosphere.alt2pres(altitude)
az = sol['apparent_zenith'].to_numpy()
azimuth = sol['azimuth'].to_numpy()
surface_azimuth = pv_system['surface_azimuth']
transmittance = (1.0 - cloud_cover) * 0.75
calc_aoi = aoi(surface_tilt, surface_azimuth, az, azimuth)
# day of year is an int64index array so access first item
day_of_year = ctime.dayofyear[0]
spectra = pvlib.spectrum.spectrl2(
apparent_zenith=az,
aoi=calc_aoi,
surface_tilt=surface_tilt,
ground_albedo=ground_albedo,
surface_pressure=pressure,
relative_airmass=airmass_relative,
precipitable_water=water_vapor_content,
ozone=ozone,
aerosol_turbidity_500nm=tau500,
dayofyear=day_of_year)
irrads_clouds = campbell_norman(sol['zenith'].to_numpy(),
transmittance)
# Convert the irradiance to a plane with tilt zero
# horizontal to the earth. This is done applying
# tilt=0 to POA calculations using the output from
# `campbell_norman`. The POA calculations include
# calculating sky and ground diffuse light where
# specific models can be selected (we use default).
poa_irr_clouds = get_total_irradiance(
surface_tilt=surface_tilt,
surface_azimuth=pv_system['surface_azimuth'],
dni=irrads_clouds['dni'],
ghi=irrads_clouds['ghi'],
dhi=irrads_clouds['dhi'],
solar_zenith=sol['apparent_zenith'],
solar_azimuth=sol['azimuth'])
show_info(latitude, poa_irr_clouds)
zen = sol['zenith'].to_numpy()
irr_clearsky = campbell_norman(zen, transmittance=0.75)
poa_irr_clearsky = get_total_irradiance(
surface_tilt=surface_tilt,
surface_azimuth=pv_system['surface_azimuth'],
dni=irr_clearsky['dni'],
ghi=irr_clearsky['ghi'],
dhi=irr_clearsky['dhi'],
solar_zenith=sol['apparent_zenith'],
solar_azimuth=sol['azimuth'])
show_info(latitude, poa_irr_clearsky)
poa_dr = poa_irr_clouds['poa_direct'].values
poa_diff = poa_irr_clouds['poa_diffuse'].values
poa_global = poa_irr_clouds['poa_global'].values
f_dir, f_diff = cloud_opacity_factor(poa_dr, poa_diff, poa_global,
spectra)
plot_spectral_irr(spectra,
f_dir,
f_diff,
lat=latitude,
doy=day_of_year,
year=ctime.year[0],
clouds=cloud_cover)
def __init__(self, panel=None, forecast_length=7, forecast_model=None):
self.forecast_length = forecast_length
if panel == None:
self.panel = Panel()
else:
self.panel = panel
if forecast_model == None:
self.fm = GFS()
else:
self.fm = forecast_model
self.start = pd.Timestamp(datetime.date.today(),
tz=self.panel.tz) # today's date
self.end = self.start + pd.Timedelta(
days=forecast_length) # days from today
print(
"getting processed data with lat: %s, lng: %s, start:%s, end:%s" %
(self.panel.latitude, self.panel.longitude, self.start, self.end))
# get forecast data
forecast_data = self.fm.get_processed_data(self.panel.latitude,
self.panel.longitude,
self.start, self.end)
ghi = forecast_data['ghi']
# get solar position
time = forecast_data.index
a_point = self.fm.location
solpos = a_point.get_solarposition(time)
# get PV(photovoltaic device) modules
sandia_modules = pvsystem.retrieve_sam('SandiaMod')
sandia_module = sandia_modules.Canadian_Solar_CS5P_220M___2009_
dni_extra = irradiance.get_extra_radiation(
self.fm.time) # extra terrestrial radiation
airmass = atmosphere.get_relative_airmass(solpos['apparent_zenith'])
# POA: Plane Of Array: an image sensing device consisting of an array
# (typically rectangular) of light-sensing pixels at the focal plane of a lens.
# https://en.wikipedia.org/wiki/Staring_array
# Diffuse sky radiation is solar radiation reaching the Earth's surface after
# having been scattered from the direct solar beam by molecules or particulates
# in the atmosphere.
# https://en.wikipedia.org/wiki/Diffuse_sky_radiation
poa_sky_diffuse = irradiance.haydavies(self.panel.surface_tilt,
self.panel.surface_azimuth,
forecast_data['dhi'],
forecast_data['dni'], dni_extra,
solpos['apparent_zenith'],
solpos['azimuth'])
# Diffuse reflection is the reflection of light or other waves or particles
# from a surface such that a ray incident on the surface is scattered at many
# angles rather than at just one angle as in the case of specular reflection.
poa_ground_diffuse = irradiance.get_ground_diffuse(
self.panel.surface_tilt, ghi, albedo=self.panel.albedo)
# AOI: Angle Of Incidence
aoi = irradiance.aoi(self.panel.surface_tilt,
self.panel.surface_azimuth,
solpos['apparent_zenith'], solpos['azimuth'])
# irradiance is the radiant flux (power) received by a surface per unit area
# https://en.wikipedia.org/wiki/Irradiance
poa_irrad = irradiance.poa_components(aoi, forecast_data['dni'],
poa_sky_diffuse,
poa_ground_diffuse)
temperature = forecast_data['temp_air']
wnd_spd = forecast_data['wind_speed']
# pvtemps: pv temperature
pvtemps = pvsystem.sapm_celltemp(poa_irrad['poa_global'], wnd_spd,
temperature)
# irradiance actually used by PV
effective_irradiance = pvsystem.sapm_effective_irradiance(
poa_irrad.poa_direct, poa_irrad.poa_diffuse, airmass, aoi,
sandia_module)
# SAPM: Sandia PV Array Performance Model
# https://pvpmc.sandia.gov/modeling-steps/2-dc-module-iv/point-value-models/sandia-pv-array-performance-model/
self.sapm_out = pvsystem.sapm(effective_irradiance,
pvtemps['temp_cell'], sandia_module)
sapm_inverters = pvsystem.retrieve_sam('sandiainverter')
sapm_inverter = sapm_inverters[
'ABB__MICRO_0_25_I_OUTD_US_208_208V__CEC_2014_']
self.ac_power = pvsystem.snlinverter(self.sapm_out.v_mp,
self.sapm_out.p_mp, sapm_inverter)
def get_angle_of_incidence(surface_tilt, surface_azimuth, solpos):
# Calculate AOI
aoi = irradiance.aoi(surface_tilt, surface_azimuth, solpos['apparent_zenith'], solpos['azimuth'])
return aoi
import matplotlib.pyplot as plt
# assumptions from the technical report:
lat = 37
lon = -100
tilt = 37
azimuth = 180
pressure = 101300 # sea level, roughly
water_vapor_content = 0.5 # cm
tau500 = 0.1
ozone = 0.31 # atm-cm
albedo = 0.2
times = pd.date_range('1984-03-20 06:17', freq='h', periods=6, tz='Etc/GMT+7')
solpos = solarposition.get_solarposition(times, lat, lon)
aoi = irradiance.aoi(tilt, azimuth, solpos.apparent_zenith, solpos.azimuth)
# The technical report uses the 'kasten1966' airmass model, but later
# versions of SPECTRL2 use 'kastenyoung1989'. Here we use 'kasten1966'
# for consistency with the technical report.
relative_airmass = atmosphere.get_relative_airmass(solpos.apparent_zenith,
model='kasten1966')
# %%
# With all the necessary inputs in hand we can model spectral irradiance using
# :py:func:`pvlib.spectrum.spectrl2`. Note that because we are calculating
# the spectra for more than one set of conditions, we will get back 2-D
# arrays (one dimension for wavelength, one for time).
spectra = spectrum.spectrl2(
apparent_zenith=solpos.apparent_zenith,
def time_aoi(self):
irradiance.aoi(self.tilt, self.azimuth,
self.solar_position.apparent_zenith,
self.solar_position.azimuth)
# retrieve time and location parameters
time = forecast_data.index
a_point = fm.location
solpos = a_point.get_solarposition(time)
dni_extra = irradiance.get_extra_radiation(fm.time)
airmass = atmosphere.get_relative_airmass(solpos['apparent_zenith'])
poa_sky_diffuse = irradiance.haydavies(surface_tilt, surface_azimuth,
forecast_data['dhi'], forecast_data['dni'], dni_extra,
solpos['apparent_zenith'], solpos['azimuth'])
poa_ground_diffuse = irradiance.get_ground_diffuse(surface_tilt, ghi, albedo=albedo)
aoi = irradiance.aoi(surface_tilt, surface_azimuth, solpos['apparent_zenith'], solpos['azimuth'])
poa_irrad = irradiance.poa_components(aoi, forecast_data['dni'], poa_sky_diffuse,
poa_ground_diffuse)
temperature = forecast_data['temp_air']
wnd_spd = forecast_data['wind_speed']
pvtemps = pvsystem.sapm_celltemp(poa_irrad['poa_global'], wnd_spd, temperature)
effective_irradiance = pvsystem.sapm_effective_irradiance(poa_irrad.poa_direct,
poa_irrad.poa_diffuse, airmass, aoi, sandia_module)
sapm_out = pvsystem.sapm(effective_irradiance, pvtemps['temp_cell'], sandia_module)
# print(sapm_out.head())
print(sapm_out['p_mp'])
plot = "pop"
# sapm_out[['p_mp']].plot()
def singleaxis(apparent_zenith, apparent_azimuth,
axis_tilt=0, axis_azimuth=0, max_angle=90,
backtrack=True, gcr=2.0/7.0, cross_axis_tilt=0):
"""
Determine the rotation angle of a single-axis tracker when given particular
solar zenith and azimuth angles.
See [1]_ for details about the equations. Backtracking may be specified,
and if so, a ground coverage ratio is required.
Rotation angle is determined in a right-handed coordinate system. The
tracker `axis_azimuth` defines the positive y-axis, the positive x-axis is
90 degrees clockwise from the y-axis and parallel to the Earth's surface,
and the positive z-axis is normal to both x & y-axes and oriented skyward.
Rotation angle `tracker_theta` is a right-handed rotation around the y-axis
in the x, y, z coordinate system and indicates tracker position relative to
horizontal. For example, if tracker `axis_azimuth` is 180 (oriented south)
and `axis_tilt` is zero, then a `tracker_theta` of zero is horizontal, a
`tracker_theta` of 30 degrees is a rotation of 30 degrees towards the west,
and a `tracker_theta` of -90 degrees is a rotation to the vertical plane
facing east.
Parameters
----------
apparent_zenith : float, 1d array, or Series
Solar apparent zenith angles in decimal degrees.
apparent_azimuth : float, 1d array, or Series
Solar apparent azimuth angles in decimal degrees.
axis_tilt : float, default 0
The tilt of the axis of rotation (i.e, the y-axis defined by
axis_azimuth) with respect to horizontal, in decimal degrees.
axis_azimuth : float, default 0
A value denoting the compass direction along which the axis of
rotation lies. Measured in decimal degrees east of north.
max_angle : float, default 90
A value denoting the maximum rotation angle, in decimal degrees,
of the one-axis tracker from its horizontal position (horizontal
if axis_tilt = 0). A max_angle of 90 degrees allows the tracker
to rotate to a vertical position to point the panel towards a
horizon. max_angle of 180 degrees allows for full rotation.
backtrack : bool, default True
Controls whether the tracker has the capability to "backtrack"
to avoid row-to-row shading. False denotes no backtrack
capability. True denotes backtrack capability.
gcr : float, default 2.0/7.0
A value denoting the ground coverage ratio of a tracker system
which utilizes backtracking; i.e. the ratio between the PV array
surface area to total ground area. A tracker system with modules
2 meters wide, centered on the tracking axis, with 6 meters
between the tracking axes has a gcr of 2/6=0.333. If gcr is not
provided, a gcr of 2/7 is default. gcr must be <=1.
cross_axis_tilt : float, default 0.0
The angle, relative to horizontal, of the line formed by the
intersection between the slope containing the tracker axes and a plane
perpendicular to the tracker axes. Cross-axis tilt should be specified
using a right-handed convention. For example, trackers with axis
azimuth of 180 degrees (heading south) will have a negative cross-axis
tilt if the tracker axes plane slopes down to the east and positive
cross-axis tilt if the tracker axes plane slopes up to the east. Use
:func:`~pvlib.tracking.calc_cross_axis_tilt` to calculate
`cross_axis_tilt`. [degrees]
Returns
-------
dict or DataFrame with the following columns:
* `tracker_theta`: The rotation angle of the tracker is a right-handed
rotation defined by `axis_azimuth`.
tracker_theta = 0 is horizontal. [degrees]
* `aoi`: The angle-of-incidence of direct irradiance onto the
rotated panel surface. [degrees]
* `surface_tilt`: The angle between the panel surface and the earth
surface, accounting for panel rotation. [degrees]
* `surface_azimuth`: The azimuth of the rotated panel, determined by
projecting the vector normal to the panel's surface to the earth's
surface. [degrees]
See also
--------
pvlib.tracking.calc_axis_tilt
pvlib.tracking.calc_cross_axis_tilt
pvlib.tracking.calc_surface_orientation
References
----------
.. [1] Kevin Anderson and Mark Mikofski, "Slope-Aware Backtracking for
Single-Axis Trackers", Technical Report NREL/TP-5K00-76626, July 2020.
https://www.nrel.gov/docs/fy20osti/76626.pdf
"""
# MATLAB to Python conversion by
# Will Holmgren (@wholmgren), U. Arizona. March, 2015.
if isinstance(apparent_zenith, pd.Series):
index = apparent_zenith.index
else:
index = None
# convert scalars to arrays
apparent_azimuth = np.atleast_1d(apparent_azimuth)
apparent_zenith = np.atleast_1d(apparent_zenith)
if apparent_azimuth.ndim > 1 or apparent_zenith.ndim > 1:
raise ValueError('Input dimensions must not exceed 1')
# Calculate sun position x, y, z using coordinate system as in [1], Eq 1.
# NOTE: solar elevation = 90 - solar zenith, then use trig identities:
# sin(90-x) = cos(x) & cos(90-x) = sin(x)
sin_zenith = sind(apparent_zenith)
x = sin_zenith * sind(apparent_azimuth)
y = sin_zenith * cosd(apparent_azimuth)
z = cosd(apparent_zenith)
# Assume the tracker reference frame is right-handed. Positive y-axis is
# oriented along tracking axis; from north, the y-axis is rotated clockwise
# by the axis azimuth and tilted from horizontal by the axis tilt. The
# positive x-axis is 90 deg clockwise from the y-axis and parallel to
# horizontal (e.g., if the y-axis is south, the x-axis is west); the
# positive z-axis is normal to the x and y axes, pointed upward.
# Calculate sun position (xp, yp, zp) in tracker coordinate system using
# [1] Eq 4.
cos_axis_azimuth = cosd(axis_azimuth)
sin_axis_azimuth = sind(axis_azimuth)
cos_axis_tilt = cosd(axis_tilt)
sin_axis_tilt = sind(axis_tilt)
xp = x*cos_axis_azimuth - y*sin_axis_azimuth
# not necessary to calculate y'
# yp = (x*cos_axis_tilt*sin_axis_azimuth
# + y*cos_axis_tilt*cos_axis_azimuth
# - z*sin_axis_tilt)
zp = (x*sin_axis_tilt*sin_axis_azimuth
+ y*sin_axis_tilt*cos_axis_azimuth
+ z*cos_axis_tilt)
# The ideal tracking angle wid is the rotation to place the sun position
# vector (xp, yp, zp) in the (y, z) plane, which is normal to the panel and
# contains the axis of rotation. wid = 0 indicates that the panel is
# horizontal. Here, our convention is that a clockwise rotation is
# positive, to view rotation angles in the same frame of reference as
# azimuth. For example, for a system with tracking axis oriented south, a
# rotation toward the east is negative, and a rotation to the west is
# positive. This is a right-handed rotation around the tracker y-axis.
# Calculate angle from x-y plane to projection of sun vector onto x-z plane
# using [1] Eq. 5.
wid = np.degrees(np.arctan2(xp, zp))
# filter for sun above panel horizon
zen_gt_90 = apparent_zenith > 90
wid[zen_gt_90] = np.nan
# Account for backtracking
if backtrack:
# distance between rows in terms of rack lengths relative to cross-axis
# tilt
axes_distance = 1/(gcr * cosd(cross_axis_tilt))
# NOTE: account for rare angles below array, see GH 824
temp = np.abs(axes_distance * cosd(wid - cross_axis_tilt))
# backtrack angle using [1], Eq. 14
with np.errstate(invalid='ignore'):
wc = np.degrees(-np.sign(wid)*np.arccos(temp))
# NOTE: in the middle of the day, arccos(temp) is out of range because
# there's no row-to-row shade to avoid, & backtracking is unnecessary
# [1], Eqs. 15-16
with np.errstate(invalid='ignore'):
tracker_theta = wid + np.where(temp < 1, wc, 0)
else:
tracker_theta = wid
# NOTE: max_angle defined relative to zero-point rotation, not the
# system-plane normal
tracker_theta = np.clip(tracker_theta, -max_angle, max_angle)
# Calculate auxiliary angles
surface = calc_surface_orientation(tracker_theta, axis_tilt, axis_azimuth)
surface_tilt = surface['surface_tilt']
surface_azimuth = surface['surface_azimuth']
aoi = irradiance.aoi(surface_tilt, surface_azimuth,
apparent_zenith, apparent_azimuth)
# Bundle DataFrame for return values and filter for sun below horizon.
out = {'tracker_theta': tracker_theta, 'aoi': aoi,
'surface_azimuth': surface_azimuth, 'surface_tilt': surface_tilt}
if index is not None:
out = pd.DataFrame(out, index=index)
out[zen_gt_90] = np.nan
else:
out = {k: np.where(zen_gt_90, np.nan, v) for k, v in out.items()}
return out
def simulate_power_by_station(station_index, surface_tilt, surface_azimuth,
pv_module, tcell_model_parameters, ghi, tamb,
wspd, albedo, days, lead_times, air_mass,
dni_extra, zenith, apparent_zenith, azimuth):
"""
This is the worker function for simulating power at a specified location. This function should be used inside
of `simulate_power` and direct usage is discouraged.
:param station_index: A station index
:param ghi: See `simulate_power`
:param tamb: See `simulate_power`
:param wspd: See `simulate_power`
:param albedo: See `simulate_power`
:param days: See `simulate_power`
:param lead_times: See `simulate_power`
:param air_mass: See `simulate_power`
:param dni_extra: See `simulate_power`
:param zenith: See `simulate_power`
:param apparent_zenith: See `simulate_power`
:param azimuth: See `simulate_power`
:param surface_tilt: See `simulate_power`
:param surface_azimuth: See `simulate_power`
:param pv_module: A PV module name
:param tcell_model_parameters: A cell module name
:return: A list with power, cell temperature, and the effective irradiance
"""
# Sanity check
assert 0 <= station_index < ghi.shape[3], 'Invalid station index'
# Determine the dimensions
num_analogs = ghi.shape[0]
num_lead_times = ghi.shape[1]
num_days = ghi.shape[2]
# Initialization
p_mp = np.zeros((num_analogs, num_lead_times, num_days))
tcell = np.zeros((num_analogs, num_lead_times, num_days))
effective_irradiance = np.zeros((num_analogs, num_lead_times, num_days))
pv_module = pvsystem.retrieve_sam("SandiaMod")[pv_module]
tcell_model_parameters = temperature.TEMPERATURE_MODEL_PARAMETERS["sapm"][
tcell_model_parameters]
for day_index in range(num_days):
for lead_time_index in range(num_lead_times):
# Determine the current time
current_posix = days[day_index] + lead_times[lead_time_index]
current_time = pd.Timestamp(current_posix, tz="UTC", unit='s')
for analog_index in range(num_analogs):
ghi_ = ghi[analog_index, lead_time_index, day_index,
station_index]
if ghi_ == 0:
continue
albedo_ = albedo[analog_index, lead_time_index, day_index,
station_index]
wspd_ = wspd[analog_index, lead_time_index, day_index,
station_index]
tamb_ = tamb[analog_index, lead_time_index, day_index,
station_index]
air_mass_ = air_mass[lead_time_index, day_index, station_index]
dni_extra_ = dni_extra[lead_time_index, day_index,
station_index]
zenith_ = zenith[lead_time_index, day_index, station_index]
apparent_zenith_ = apparent_zenith[lead_time_index, day_index,
station_index]
azimuth_ = azimuth[lead_time_index, day_index, station_index]
##########################################################################################
# #
# Core procedures of simulating power at one location #
# #
##########################################################################################
# Decompose DNI from GHI
dni_dict = irradiance.disc(ghi_, zenith_, current_time)
# Calculate POA sky diffuse
poa_sky_diffuse = irradiance.haydavies(
surface_tilt, surface_azimuth, ghi_, dni_dict["dni"],
dni_extra_, apparent_zenith_, azimuth_)
# Calculate POA ground diffuse
poa_ground_diffuse = irradiance.get_ground_diffuse(
surface_tilt, ghi_, albedo_)
# Calculate angle of incidence
aoi = irradiance.aoi(surface_tilt, surface_azimuth,
apparent_zenith_, azimuth_)
# Calculate POA total
poa_irradiance = irradiance.poa_components(
aoi, dni_dict["dni"], poa_sky_diffuse, poa_ground_diffuse)
# Calculate cell temperature
tcell[analog_index, lead_time_index,
day_index] = pvsystem.temperature.sapm_cell(
poa_irradiance['poa_global'], tamb_, wspd_,
tcell_model_parameters['a'],
tcell_model_parameters['b'],
tcell_model_parameters["deltaT"])
# Calculate effective irradiance
effective_irradiance[
analog_index, lead_time_index,
day_index] = pvsystem.sapm_effective_irradiance(
poa_irradiance['poa_direct'],
poa_irradiance['poa_diffuse'], air_mass_, aoi,
pv_module)
# Calculate power
sapm_out = pvsystem.sapm(
effective_irradiance[analog_index, lead_time_index,
day_index],
tcell[analog_index, lead_time_index, day_index], pv_module)
# Save output to numpy
p_mp[analog_index, lead_time_index,
day_index] = sapm_out["p_mp"]
return [p_mp, tcell, effective_irradiance]
def AOI(surf_tilt, surf_azm, solpos):
aoi = irradiance.aoi(surf_tilt, surf_azm, solpos['apparent_zenith'],
solpos['azimuth'])
return (aoi)
latitude=latitude,
longitude=longitude,
method='nrel_numpy')
# Compute the diffuse irradiance on the panel, reflected from the ground:
S_d_reflect = irradiance.grounddiffuse(surface_tilt,
I_hor,
albedo=0.25,
surface_type=None)
# Compute the diffuse irradiance on the panel, from the sky:
S_d_sky = irradiance.klucher(surface_tilt, surface_azimuth, I_d_hor, I_hor,
ephem_data['zenith'], ephem_data['azimuth'])
# Compute the angles between the panel and the sun:
aoi = irradiance.aoi(surface_tilt, surface_azimuth, ephem_data['zenith'],
ephem_data['azimuth'])
# Compute the global irradiance on the panel:
S = irradiance.globalinplane(aoi, DNI, S_d_sky, S_d_reflect)
# Second case: with tracking (axis is supposed to be north-south):
S_track = tracking.singleaxis(ephem_data['apparent_zenith'],
ephem_data['azimuth'],
axis_tilt=0,
axis_azimuth=0,
max_angle=360,
backtrack=True)
S['Direct with tracking'] = DNI * np.cos(np.radians(S_track.aoi))
