This tutorial introduces the pvlib.tracking module. This module currently only contains one function, tracking.singleaxis, but we hope to add dual axis tracking support in the future.
The tracking.singleaxis function is a port of the PVLIB MATLAB file pvl_singleaxis.m. The algorithm is based on Lorenzo et al, Tracking and back-tracking, Prog. in Photovoltaics: Research and Applications, 19, 747-753 (2011). Most of the Python and MATLAB algorithms are identical except for name changes to conform to the PEP8 Python style guide. There are few spots, noteably in the calculation of surface_azimuth, that our implementation differs from the MATLAB implementation.
Table of contents:
tracking.singleaxis function to explore the impacts of tracker tilt, tracker azimuth, and backtracking.This tutorial requires pvlib >= 0.6.0.
This tutorial was written by
pvl_singleaxis.m, presumably written by the PVLIB_MATLAB team at Sandia National Laboratory.Standard scientific Python imports.
In [1]:
# plotting modules
%matplotlib inline
import matplotlib.pyplot as plt
# built in python modules
import datetime
# python add-ons
import numpy as np
import pandas as pd
In [2]:
import pvlib
from pvlib.tools import cosd, sind
from pvlib.location import Location
Make some pvlib Location objects. These are the standard inputs to the solar position calculator.
In [3]:
tus = Location(32.2, -111, 'US/Arizona', 700, 'Tucson')
print(tus)
johannesburg = Location(-26.2044, 28.0456, 'Africa/Johannesburg', 1753, 'Johannesburg')
print(johannesburg)
Calculate solar position at those locations. To start, we'll choose times near an equinox. Later, we'll test against times near a solstice.
In [4]:
times = pd.date_range(start=datetime.datetime(2014,3,23), end=datetime.datetime(2014,3,24), freq='5Min')
ephem_tus = pvlib.solarposition.get_solarposition(times.tz_localize(tus.tz), tus.latitude, tus.longitude)
ephem_joh = pvlib.solarposition.get_solarposition(times.tz_localize(johannesburg.tz),
johannesburg.latitude, johannesburg.longitude)
ephemout = ephem_tus # default for notebook
The steps of the tracking algorithm are:
First, define the input parameters. From the tracking.singleaxis docstring...
In [5]:
help(pvlib.tracking.singleaxis)
In [6]:
azimuth = ephemout['azimuth']
apparent_azimuth = ephemout['azimuth']
apparent_zenith = ephemout['apparent_zenith']
axis_tilt = 10
axis_azimuth = 170
latitude = 32
max_angle = 65
backtrack = True
gcr = 2.0/7.0
times = azimuth.index
The reference that this algorithm is based on used an Earth coordinate system where y points south. So, we first transform our solar position vector to this new coordiante system.
In [7]:
az = apparent_azimuth - 180
apparent_elevation = 90 - apparent_zenith
x = cosd(apparent_elevation) * sind(az)
y = cosd(apparent_elevation) * cosd(az)
z = sind(apparent_elevation)
earth_coords = pd.DataFrame({'x':x,'y':y,'z':z})
earth_coords.plot()
plt.title('sun position in Earth coordinate system');
Transform solar vector to panel coordinate system. For North-South oriented trackers parallel to the ground, the only difference is the sign of the x component. The x components are the same if axis_azimuth=180 and opposite if axis_azimuth=0.
In [8]:
axis_azimuth_south = axis_azimuth - 180
print('cos(axis_azimuth_south)={}, sin(axis_azimuth_south)={}'
.format(cosd(axis_azimuth_south), sind(axis_azimuth_south)))
print('cos(axis_tilt)={}, sin(axis_tilt)={}'
.format(cosd(axis_tilt), sind(axis_tilt)))
xp = x*cosd(axis_azimuth_south) - y*sind(axis_azimuth_south);
yp = (x*cosd(axis_tilt)*sind(axis_azimuth_south) +
y*cosd(axis_tilt)*cosd(axis_azimuth_south) -
z*sind(axis_tilt))
zp = (x*sind(axis_tilt)*sind(axis_azimuth_south) +
y*sind(axis_tilt)*cosd(axis_azimuth_south) +
z*cosd(axis_tilt))
panel_coords = pd.DataFrame({'x':xp,'y':yp,'z':zp})
panel_coords.plot()
plt.title('sun position in panel coordinate system');
The ideal tracking angle wid is the rotation to place the sun position
vector (xp, yp, zp) in the (y, z) plane; i.e. normal to the panel and
containing 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.
We use arctan2, but PVLIB MATLAB uses arctan. Here prove that we get the same result.
In [9]:
# Calculate angle from x-y plane to projection of sun vector onto x-z plane
# and then obtain wid by translating tmp to convention for rotation angles.
wid = pd.Series(90 - np.degrees(np.arctan2(zp, xp)), index=times)
# filter for sun above panel horizon
wid[zp <= 0] = np.nan
wid.plot(label='tracking angle')
ephemout['apparent_elevation'].plot(label='apparent elevation')
plt.legend()
plt.title('Ideal tracking angle without backtracking');
arctan version
In [10]:
tmp = np.degrees(np.arctan(zp/xp)) # angle from x-y plane to projection of sun vector onto x-z plane
# Obtain wid by translating tmp to convention for rotation angles.
# Have to account for which quadrant of the x-z plane in which the sun
# vector lies. Complete solution here but probably not necessary to
# consider QIII and QIV.
wid = pd.Series(index=times, dtype=float)
wid[(xp>=0) & (zp>=0)] = 90 - tmp[(xp>=0) & (zp>=0)]; # QI
wid[(xp<0) & (zp>=0)] = -90 - tmp[(xp<0) & (zp>=0)]; # QII
wid[(xp<0) & (zp<0)] = -90 - tmp[(xp<0) & (zp<0)]; # QIII
wid[(xp>=0) & (zp<0)] = 90 - tmp[(xp>=0) & (zp<0)]; # QIV
# filter for sun above panel horizon
wid[zp <= 0] = np.nan
wid.plot(label='tracking angle')
ephemout['apparent_elevation'].plot(label='apparent elevation')
plt.legend()
plt.title('Ideal tracking angle without backtracking');
Account for backtracking; modified from [1] to account for rotation angle convention being used here.
In [11]:
if backtrack:
axes_distance = 1/gcr
temp = np.minimum(axes_distance*cosd(wid), 1)
# backtrack angle
# (always positive b/c acosd returns values between 0 and 180)
wc = np.degrees(np.arccos(temp))
v = wid < 0
widc = pd.Series(index=times, dtype=float)
widc[~v] = wid[~v] - wc[~v]; # Eq 4 applied when wid in QI
widc[v] = wid[v] + wc[v]; # Eq 4 applied when wid in QIV
else:
widc = wid
widc.plot(label='tracking angle')
#pyephemout['apparent_elevation'].plot(label='apparent elevation')
plt.legend(loc=2)
plt.title('Ideal tracking angle with backtracking');
Compare tracking angle with and without backtracking.
In [12]:
tracking_angles = pd.DataFrame({'with backtracking':widc,'without backtracking':wid})
tracking_angles.plot()
#pyephemout['apparent_elevation'].plot(label='apparent elevation')
plt.legend();
Apply angle restriction.
In [13]:
tracker_theta = widc.copy()
tracker_theta[tracker_theta > max_angle] = max_angle
tracker_theta[tracker_theta < -max_angle] = -max_angle
tracking_angles['with restriction'] = tracker_theta
tracking_angles.plot();
Calculate panel normal vector in panel x, y, z coordinates.
y-axis is axis of tracker rotation. tracker_theta is a compass angle
(clockwise is positive) rather than a trigonometric angle.
In [14]:
panel_norm = np.array([sind(tracker_theta),
tracker_theta*0,
cosd(tracker_theta)])
panel_norm_df = pd.DataFrame(panel_norm.T, columns=('x','y','z'), index=times)
panel_norm_df.plot()
plt.title('panel normal vector components in panel coordinate system')
plt.legend();
sun position in vector format in panel-oriented x, y, z coordinates. We've already seen this above, but it's good to look at it again after calculating the tracker normal vector.
In [15]:
sun_vec = np.array([xp, yp, zp])
panel_coords = pd.DataFrame(sun_vec.T, columns=('x','y','z'), index=times)
panel_coords.plot()
plt.title('sun position in panel coordinate system');
Calculate angle-of-incidence on panel
In [16]:
aoi = np.degrees(np.arccos(np.abs(np.sum(sun_vec*panel_norm, axis=0))))
aoi = pd.Series(aoi, index=times)
aoi.plot()
plt.title('angle of incidence');
The power produced by the tracker will be primarily determined by the cosine of the angle of incidence.
In [17]:
cosd(aoi).plot();
Calculate panel tilt surface_tilt and azimuth surface_azimuth
in a coordinate system where the panel tilt is the
angle from horizontal, and the panel azimuth is
the compass angle (clockwise from north) to the projection
of the panel's normal to the earth's surface.
These outputs are provided for convenience and comparison
with other PV software which use these angle conventions.
Project normal vector to earth surface. First rotate about x-axis by angle -axis_tilt so that y-axis is also parallel to earth surface, then project.
In [18]:
# Calculate standard rotation matrix
print('cos(axis_azimuth_south)={}, sin(axis_azimuth_south)={}'
.format(cosd(axis_azimuth_south), sind(axis_azimuth_south)))
print('cos(axis_tilt)={}, sin(axis_tilt)={}'
.format(cosd(axis_tilt), sind(axis_tilt)))
rot_x = np.array([[1, 0, 0],
[0, cosd(-axis_tilt), -sind(-axis_tilt)],
[0, sind(-axis_tilt), cosd(-axis_tilt)]])
# panel_norm_earth contains the normal vector expressed in earth-surface coordinates
# (z normal to surface, y aligned with tracker axis parallel to earth)
panel_norm_earth = np.dot(rot_x, panel_norm).T
# projection to plane tangent to earth surface,
# in earth surface coordinates
projected_normal = np.array([panel_norm_earth[:,0], panel_norm_earth[:,1], panel_norm_earth[:,2]*0]).T
# calculate magnitudes
panel_norm_earth_mag = np.sqrt(np.nansum(panel_norm_earth**2, axis=1))
projected_normal_mag = np.sqrt(np.nansum(projected_normal**2, axis=1))
#print('panel_norm_earth_mag={}, projected_normal_mag={}'.format(panel_norm_earth_mag, projected_normal_mag))
projected_normal = (projected_normal.T / projected_normal_mag).T
panel_norm_earth_df = pd.DataFrame(panel_norm_earth, columns=('x','y','z'), index=times)
panel_norm_earth_df.plot()
plt.title('panel normal vector components in Earth coordinate system')
projected_normal_df = pd.DataFrame(projected_normal, columns=('x','y','z'), index=times)
projected_normal_df.plot()
plt.title('panel normal vector projected to surface in Earth coordinate system');
Calculate surface_azimuth. This takes a few steps. We need to take the arctan, rotate from the panel system to the south-facing Earth system and then rotate the Earth system to a north-facing Earth system. We use the arctan2 function, but PVLIB MATLAB uses arctan.
In [19]:
# calculation of surface_azimuth
# 1. Find the angle.
surface_azimuth = pd.Series(np.degrees(np.arctan2(projected_normal[:,1], projected_normal[:,0])), index=times)
surface_azimuth.plot(label='orig')
# 2. Rotate 0 reference from panel's x axis to it's y axis and
# then back to North.
surface_azimuth = 90 - surface_azimuth + axis_azimuth
# 3. Map azimuth into [0,360) domain.
surface_azimuth[surface_azimuth<0] += 360
surface_azimuth[surface_azimuth>=360] -= 360
surface_azimuth.plot(label='compass angle north')
plt.legend();
arctan version
In [20]:
# calculation of surface_azimuth
# 1. Find the angle.
surface_azimuth = pd.Series(np.degrees(np.arctan(projected_normal[:,1]/projected_normal[:,0])), index=times)
surface_azimuth.plot(label='orig')
# 2. Clean up atan when x-coord or y-coord is zero
surface_azimuth[(projected_normal[:,0]==0) & (projected_normal[:,1]>0)] = 90
surface_azimuth[(projected_normal[:,0]==0) & (projected_normal[:,1]<0)] = -90
surface_azimuth[(projected_normal[:,1]==0) & (projected_normal[:,0]>0)] = 0
surface_azimuth[(projected_normal[:,1]==0) & (projected_normal[:,0]<0)] = 180
surface_azimuth.plot(label='x or y 0 corrected')
# 3. Correct atan for QII and QIII
surface_azimuth[(projected_normal[:,0]<0) & (projected_normal[:,1]>0)] += 180 # QII
surface_azimuth[(projected_normal[:,0]<0) & (projected_normal[:,1]<0)] += 180 # QIII
surface_azimuth.plot(label='q2, q3 corrected')
# 4. Skip to below
# From PVLIB MATLAB...
# at this point surface_azimuth contains angles between -90 and +270,
# where 0 is along the positive x-axis,
# the y-axis is in the direction of the tracker azimuth,
# and positive angles are rotations from the positive x axis towards
# the positive y-axis.
# Adjust to compass angles
# (clockwise rotation from 0 along the positive y-axis)
# surface_azimuth[surface_azimuth<=90] = 90 - surface_azimuth[surface_azimuth<=90]
# surface_azimuth[surface_azimuth>90] = 450 - surface_azimuth[surface_azimuth>90]
# finally rotate to align y-axis with true north
# PVLIB_MATLAB has this latitude correction,
# but I don't think it's latitude dependent if you always
# specify axis_azimuth with respect to North.
# if latitude > 0 or True:
# surface_azimuth = surface_azimuth - axis_azimuth
# else:
# surface_azimuth = surface_azimuth - axis_azimuth - 180
# surface_azimuth[surface_azimuth<0] = 360 + surface_azimuth[surface_azimuth<0]
# the commented code above is mostly part of PVLIB_MATLAB.
# My (wholmgren) take is that it can be done more simply.
# Say that we're pointing along the postive x axis (likely west).
# We just need to rotate 90 degrees to get from the x axis
# to the y axis (likely south),
# and then add the axis_azimuth to get back to North.
# Anything left over is the azimuth that we want,
# and we can map it into the [0,360) domain.
# 4. Rotate 0 reference from panel's x axis to it's y axis and
# then back to North.
surface_azimuth = 90 - surface_azimuth + axis_azimuth
# 5. Map azimuth into [0,360) domain.
surface_azimuth[surface_azimuth<0] += 360
surface_azimuth[surface_azimuth>=360] -= 360
surface_azimuth.plot(label='compass angle north')
plt.legend();
The final surface_azimuth is given by the curve labeled "compass angle north". This is in degrees East of North.
Calculate surface_tilt.
In [21]:
surface_tilt = (90 - np.degrees(np.arccos(
pd.DataFrame(panel_norm_earth * projected_normal, index=times).sum(axis=1))))
surface_tilt.plot();
According to the MATLAB code, surface_tilt is "The angle between the panel surface and the earth surface, accounting for panel rotation."
With backtracking
In [22]:
tracker_data = pvlib.tracking.singleaxis(ephemout['apparent_zenith'], ephemout['azimuth'],
axis_tilt=0, axis_azimuth=180, max_angle=90,
backtrack=True, gcr=2.0/7.0)
In [23]:
tracker_data.plot();
Without backtracking
In [24]:
tracker_data = pvlib.tracking.singleaxis(ephemout['apparent_zenith'], ephemout['azimuth'],
axis_tilt=0, axis_azimuth=180, max_angle=90,
backtrack=False, gcr=2.0/7.0)
tracker_data.plot();
Explore ground cover ratio
In [25]:
aois = pd.DataFrame(index=ephemout.index)
for gcr in np.linspace(0, 1, 6):
tracker_data = pvlib.tracking.singleaxis(ephemout['apparent_zenith'], ephemout['azimuth'],
axis_tilt=0, axis_azimuth=180, max_angle=90,
backtrack=True, gcr=gcr)
aois[gcr] = tracker_data['aoi']
In [26]:
aois.plot();
Ensure that max_angle works.
In [27]:
tracker_data = pvlib.tracking.singleaxis(ephemout['apparent_zenith'], ephemout['azimuth'],
axis_tilt=0, axis_azimuth=180, max_angle=45,
backtrack=True, gcr=2.0/7.0)
tracker_data.plot();
Play with axis_tilt.
In [28]:
aois = pd.DataFrame(index=ephemout.index)
tilts = pd.DataFrame(index=ephemout.index)
azis = pd.DataFrame(index=ephemout.index)
thetas = pd.DataFrame(index=ephemout.index)
for tilt in np.linspace(0, 90, 7):
tracker_data = pvlib.tracking.singleaxis(ephemout['apparent_zenith'], ephemout['azimuth'],
axis_tilt=tilt, axis_azimuth=180, max_angle=90,
backtrack=True, gcr=2/7.)
aois[tilt] = tracker_data['aoi']
tilts[tilt] = tracker_data['surface_tilt']
azis[tilt] = tracker_data['surface_azimuth']
thetas[tilt] = tracker_data['tracker_theta']
fig, axes = plt.subplots(2, 2, figsize=(16,12), sharex=True)
ax = axes[0,0]
aois.plot(ax=ax)
ax.set_ylim(0,90)
ax.set_title('aoi')
ax = axes[0,1]
thetas.plot(ax=ax)
ax.set_ylim(-90,90)
ax.set_title('tracker theta')
ax = axes[1,1]
tilts.plot(ax=ax)
ax.set_title('surface tilt')
ax.set_ylim(0,90)
ax = axes[1,0]
azis.plot(ax=ax)
ax.set_title('surface azimuth')
ax.set_ylim(0,360);
#ax.hlines([0, 90, 180, 270, 360], *ax.get_xlim(), colors='0.25', lw=1, alpha=0.25)
The simple case of axis_tilt = 0 shows the panels pointing directly East in the morning and directly West in the afternoon. If axis_tilt > 0 then the panels always point South of East and South of West. The panels point towards South near sunrise, rotate towards East in mid-morning, then back towards Sorth around noon, continuing towards West in the mid-afternoon, and finally back towards Sorth near sunset.
Next, what happens if we try to point the panels North?
In [29]:
aois = pd.DataFrame(index=ephemout.index)
tilts = pd.DataFrame(index=ephemout.index)
azis = pd.DataFrame(index=ephemout.index)
thetas = pd.DataFrame(index=ephemout.index)
for tilt in np.linspace(0, -90, 7):
tracker_data = pvlib.tracking.singleaxis(ephemout['apparent_zenith'], ephemout['azimuth'],
axis_tilt=tilt, axis_azimuth=180, max_angle=90,
backtrack=True, gcr=2/7.)
aois[tilt] = tracker_data['aoi']
tilts[tilt] = tracker_data['surface_tilt']
azis[tilt] = tracker_data['surface_azimuth']
thetas[tilt] = tracker_data['tracker_theta']
fig, axes = plt.subplots(2, 2, figsize=(16,12), sharex=True)
ax = axes[0,0]
aois.plot(ax=ax)
ax.set_ylim(0,90)
ax.set_title('aoi')
ax = axes[0,1]
thetas.plot(ax=ax)
ax.set_ylim(-90,90)
ax.set_title('tracker theta')
ax = axes[1,1]
tilts.plot(ax=ax)
ax.set_title('surface tilt')
ax.set_ylim(0,90)
ax = axes[1,0]
azis.plot(ax=ax)
ax.set_title('surface azimuth')
ax.set_ylim(0,360);
#ax.hlines([0, 90, 180, 270, 360], *ax.get_xlim(), colors='0.25', lw=1, alpha=0.25)
The 0 tilt case is repeated for reference. For small Northward tilts, such as -15, the panels point towards North near sunrise, rotate towards the east in mid-morning, then back towards North around noon, continuing towards West in the mid-afternoon, and finally back towards North near sunset.
The algorithm returns nan for larger Northward tilts at midday since the beam component of the irradiance would be 0.
Play with axis_azimuth.
In [30]:
aois = pd.DataFrame(index=ephemout.index)
tilts = pd.DataFrame(index=ephemout.index)
azis = pd.DataFrame(index=ephemout.index)
thetas = pd.DataFrame(index=ephemout.index)
for azi in np.linspace(90, 270, 5):
tracker_data = pvlib.tracking.singleaxis(ephemout['apparent_zenith'], ephemout['azimuth'],
axis_tilt=0, axis_azimuth=azi, max_angle=90,
backtrack=True, gcr=2/7.)
aois[azi] = tracker_data['aoi']
tilts[azi] = tracker_data['surface_tilt']
azis[azi] = tracker_data['surface_azimuth']
thetas[azi] = tracker_data['tracker_theta']
fig, axes = plt.subplots(2, 2, figsize=(16,12), sharex=True)
ax=axes[0,0]
aois.plot(ax=ax)
ax.set_ylim(0,90)
ax.set_title('aoi')
ax=axes[0,1]
thetas.plot(ax=ax)
ax.set_ylim(-90,90)
ax.set_title('tracker theta')
ax=axes[1,1]
tilts.plot(ax=ax)
ax.set_title('surface tilt')
ax.set_ylim(0,90)
ax=axes[1,0]
azis.plot(ax=ax)
ax.set_title('surface azimuth')
ax.set_ylim(0,360);
This discussion of the axis_azimuth parameter assumes axis_tilt=0 and no backtracking.
Say that your axis_azimuth=90 or 270. Your surface_azimuth has no choice but to point to North (0), or South (180). Near the equinox, the solar azimuth is very nearly 90 at sunrise and sunset, so the surface_tilt is going to be poorly defined until the sun is a bit above the horizon. At midday, the surface_azimuth should definitely point South (180), surface_tilt will very nearly equal the latitude, and AOI should be nearly 0.
Next, let's study the axis_azimuth=135 case. This corresponds to a tracker oriented from SSE-NNW. At sunrise, on the equinox, the tracker is going to point East of North by 45 degrees. Sometime before solar noon, the panels should lay flat, and then point West of South by 45 degrees, or East of North by 225.
Test the southern hemispere.
In [31]:
tracker_data = pvlib.tracking.singleaxis(ephem_joh['apparent_zenith'], ephem_joh['azimuth'],
axis_tilt=0, axis_azimuth=0, max_angle=90,
backtrack=True, gcr=2.0/7.0)
tracker_data.plot();
Test different seasons.
In [32]:
times = pd.date_range(start=datetime.datetime(2014,3,23), end=datetime.datetime(2014,3,24), freq='5Min')
ephem_tus = pvlib.solarposition.get_solarposition(times.tz_localize(tus.tz), tus.latitude, tus.longitude)
ephem_joh = pvlib.solarposition.get_solarposition(times.tz_localize(johannesburg.tz),
johannesburg.latitude, johannesburg.longitude)
tracker_data = pvlib.tracking.singleaxis(ephem_tus['apparent_zenith'], ephem_tus['azimuth'],
axis_tilt=0, axis_azimuth=0, max_angle=90,
backtrack=True, gcr=2.0/7.0)
tracker_data.plot()
plt.title('Tucson, March')
plt.ylim(-100,100)
tracker_data = pvlib.tracking.singleaxis(ephem_joh['apparent_zenith'], ephem_joh['azimuth'],
axis_tilt=0, axis_azimuth=0, max_angle=90,
backtrack=True, gcr=2.0/7.0)
tracker_data.plot()
plt.title('Johannesburg, March')
plt.ylim(-100,100);
In [33]:
times = pd.date_range(start=datetime.datetime(2014,6,23), end=datetime.datetime(2014,6,24), freq='5Min')
ephem_tus = pvlib.solarposition.get_solarposition(times.tz_localize(tus.tz), tus.latitude, tus.longitude)
ephem_joh = pvlib.solarposition.get_solarposition(times.tz_localize(johannesburg.tz),
johannesburg.latitude, johannesburg.longitude)
tracker_data = pvlib.tracking.singleaxis(ephem_tus['apparent_zenith'], ephem_tus['azimuth'],
axis_tilt=0, axis_azimuth=0, max_angle=90,
backtrack=True, gcr=2.0/7.0)
tracker_data.plot()
plt.title('Tucson, June')
plt.ylim(-100,100)
tracker_data = pvlib.tracking.singleaxis(ephem_joh['apparent_zenith'], ephem_joh['azimuth'],
axis_tilt=0, axis_azimuth=0, max_angle=90,
backtrack=True, gcr=2.0/7.0)
tracker_data.plot()
plt.title('Johannesburg, June')
plt.ylim(-100,100);
In [34]:
times = pd.date_range(start=datetime.datetime(2014,12,23), end=datetime.datetime(2014,12,24), freq='5Min')
ephem_tus = pvlib.solarposition.get_solarposition(times.tz_localize(tus.tz), tus.latitude, tus.longitude)
ephem_joh = pvlib.solarposition.get_solarposition(times.tz_localize(johannesburg.tz),
johannesburg.latitude, johannesburg.longitude)
tracker_data = pvlib.tracking.singleaxis(ephem_tus['apparent_zenith'], ephem_tus['azimuth'],
axis_tilt=0, axis_azimuth=0, max_angle=90,
backtrack=True, gcr=2.0/7.0)
tracker_data.plot()
plt.title('Tucson, December')
plt.ylim(-100,100)
tracker_data = pvlib.tracking.singleaxis(ephem_joh['apparent_zenith'], ephem_joh['azimuth'],
axis_tilt=0, axis_azimuth=0, max_angle=90,
backtrack=True, gcr=2.0/7.0)
tracker_data.plot()
plt.title('Johannesburg, December')
plt.ylim(-100,100);
In [35]:
times = pd.date_range(start=datetime.datetime(2014,12,23), end=datetime.datetime(2014,12,24), freq='5Min')
ephem_tus = pvlib.solarposition.get_solarposition(times.tz_localize(tus.tz), tus.latitude, tus.longitude)
ephem_joh = pvlib.solarposition.get_solarposition(times.tz_localize(johannesburg.tz),
johannesburg.latitude, johannesburg.longitude)
tracker_data = pvlib.tracking.singleaxis(ephem_tus['apparent_zenith'], ephem_tus['azimuth'],
axis_tilt=0, axis_azimuth=0, max_angle=90,
backtrack=False, gcr=2.0/7.0)
tracker_data['aoi'].plot()
plt.title('Tucson, December, no backtrack')
tracker_data = pvlib.tracking.singleaxis(ephem_joh['apparent_zenith'], ephem_joh['azimuth'],
axis_tilt=0, axis_azimuth=0, max_angle=90,
backtrack=False, gcr=2.0/7.0)
plt.figure()
tracker_data['aoi'].plot()
plt.title('Johannesburg, December, no backtrack');
In [36]:
times = pd.date_range(start=datetime.datetime(2014,5,5), end=datetime.datetime(2014,5,6), freq='5Min')
ephem_tus = pvlib.solarposition.get_solarposition(times.tz_localize(tus.tz), tus.latitude, tus.longitude)
ephem_joh = pvlib.solarposition.get_solarposition(times.tz_localize(johannesburg.tz),
johannesburg.latitude, johannesburg.longitude)
tracker_data = pvlib.tracking.singleaxis(ephem_tus['apparent_zenith'], ephem_tus['azimuth'],
axis_tilt=0, axis_azimuth=0, max_angle=90,
backtrack=False, gcr=2.0/7.0)
tracker_data['aoi'].plot()
plt.title('Tucson, May, no backtrack')
tracker_data = pvlib.tracking.singleaxis(ephem_joh['apparent_zenith'], ephem_joh['azimuth'],
axis_tilt=0, axis_azimuth=0, max_angle=90,
backtrack=False, gcr=2.0/7.0)
plt.figure()
tracker_data['aoi'].plot()
plt.title('Johannesburg, May, no backtrack');
Finally, we'll put the tracker data together with the irradiance algorithms to determine plane-of-array irradiance.
In [37]:
times = pd.date_range(start=datetime.datetime(2014,3,23), end=datetime.datetime(2014,3,24), freq='5Min')
ephem_tus = pvlib.solarposition.get_solarposition(times.tz_localize(tus.tz), tus.latitude, tus.longitude)
ephem_joh = pvlib.solarposition.get_solarposition(times.tz_localize(johannesburg.tz),
johannesburg.latitude, johannesburg.longitude)
tracker_data = pvlib.tracking.singleaxis(ephem_tus['apparent_zenith'], ephem_tus['azimuth'],
axis_tilt=0, axis_azimuth=0, max_angle=90,
backtrack=True, gcr=2.0/7.0)
tracker_data.plot()
plt.ylim(-100,100);
In [38]:
irrad_data = tus.get_clearsky(times.tz_localize(tus.tz))
dni_et = pvlib.irradiance.get_extra_radiation(irrad_data.index, method='asce')
irrad_data.plot()
dni_et.plot(label='DNI ET');
In [39]:
ground_irrad = pvlib.irradiance.get_ground_diffuse(tracker_data['surface_tilt'], irrad_data['ghi'], albedo=.25)
ground_irrad.plot();
In [40]:
ephem_data = ephem_tus
haydavies_diffuse = pvlib.irradiance.haydavies(tracker_data['surface_tilt'], tracker_data['surface_azimuth'],
irrad_data['dhi'], irrad_data['dni'], dni_et,
ephem_data['apparent_zenith'], ephem_data['azimuth'])
haydavies_diffuse.plot(label='haydavies diffuse');
In [41]:
global_in_plane = cosd(tracker_data['aoi'])*irrad_data['dni'] + haydavies_diffuse + ground_irrad
global_in_plane.plot();
Do it again for another time of year.
In [42]:
times = pd.date_range(start=datetime.datetime(2014,6,23), end=datetime.datetime(2014,6,24), freq='5Min')
ephem_tus = pvlib.solarposition.get_solarposition(times.tz_localize(tus.tz), tus.latitude, tus.longitude)
ephem_joh = pvlib.solarposition.get_solarposition(times.tz_localize(johannesburg.tz),
johannesburg.latitude, johannesburg.longitude)
tracker_data = pvlib.tracking.singleaxis(ephem_tus['apparent_zenith'], ephem_tus['azimuth'],
axis_tilt=0, axis_azimuth=0, max_angle=90,
backtrack=True, gcr=2.0/7.0)
tracker_data.plot()
plt.ylim(-100,100)
irrad_data = tus.get_clearsky(times.tz_localize(tus.tz))
dni_et = pvlib.irradiance.get_extra_radiation(irrad_data.index, method='asce')
plt.figure()
irrad_data.plot()
dni_et.plot(label='DNI ET')
ground_irrad = pvlib.irradiance.get_ground_diffuse(tracker_data['surface_tilt'], irrad_data['ghi'], albedo=.25)
ground_irrad.plot()
ephem_data = ephem_tus
haydavies_diffuse = pvlib.irradiance.haydavies(tracker_data['surface_tilt'], tracker_data['surface_azimuth'],
irrad_data['dhi'], irrad_data['dni'], dni_et,
ephem_data['apparent_zenith'], ephem_data['azimuth'])
haydavies_diffuse.plot(label='haydavies diffuse')
global_in_plane = cosd(tracker_data['aoi'])*irrad_data['dni'] + haydavies_diffuse + ground_irrad
global_in_plane.plot(label='global in plane')
plt.legend();
In [43]:
times = pd.date_range(start=datetime.datetime(2014,12,23), end=datetime.datetime(2014,12,24), freq='5Min')
ephem_tus = pvlib.solarposition.get_solarposition(times.tz_localize(tus.tz), tus.latitude, tus.longitude)
ephem_joh = pvlib.solarposition.get_solarposition(times.tz_localize(johannesburg.tz),
johannesburg.latitude, johannesburg.longitude)
tracker_data = pvlib.tracking.singleaxis(ephem_tus['apparent_zenith'], ephem_tus['azimuth'],
axis_tilt=0, axis_azimuth=0, max_angle=90,
backtrack=True, gcr=2.0/7.0)
tracker_data.plot()
plt.ylim(-100,100)
irrad_data = tus.get_clearsky(times.tz_localize(tus.tz))
dni_et = pvlib.irradiance.get_extra_radiation(irrad_data.index, method='asce')
plt.figure()
irrad_data.plot()
dni_et.plot(label='DNI ET')
ground_irrad = pvlib.irradiance.get_ground_diffuse(tracker_data['surface_tilt'], irrad_data['ghi'], albedo=.25)
ground_irrad.plot()
ephem_data = ephem_tus
haydavies_diffuse = pvlib.irradiance.haydavies(tracker_data['surface_tilt'], tracker_data['surface_azimuth'],
irrad_data['dhi'], irrad_data['dni'], dni_et,
ephem_data['apparent_zenith'], ephem_data['azimuth'])
haydavies_diffuse.plot(label='haydavies diffuse')
global_in_plane = cosd(tracker_data['aoi'])*irrad_data['dni'] + haydavies_diffuse + ground_irrad
global_in_plane.plot(label='global in plane')
plt.legend();
In [44]:
abq = Location(35, -106, 'US/Mountain', 0, 'Albuquerque')
print(abq)
In [45]:
times = pd.date_range(start=datetime.datetime(2014,6,1), end=datetime.datetime(2014,6,2), freq='5Min')
ephem_abq = abq.get_solarposition(times.tz_localize(abq.tz))
tracker_data = pvlib.tracking.singleaxis(ephem_abq['apparent_zenith'], ephem_abq['azimuth'],
axis_tilt=0, axis_azimuth=180, max_angle=45,
backtrack=False, gcr=2.0/7.0)
tracker_data.plot()
plt.ylim(-100,100)
plt.title('June 1, Albuquerque, NS Horizontal Single-Axis, no backtrack');
In [46]:
times = pd.date_range(start=datetime.datetime(2014,6,1), end=datetime.datetime(2014,6,2), freq='5Min')
ephem_abq = abq.get_solarposition(times.tz_localize(abq.tz))
tracker_data = pvlib.tracking.singleaxis(ephem_abq['apparent_zenith'], ephem_abq['azimuth'],
axis_tilt=0, axis_azimuth=180, max_angle=45,
backtrack=True, gcr=.3)
tracker_data.plot()
plt.ylim(-100,100)
plt.title('June 1, Albuquerque, NS Horizontal Single-Axis, with backtracking');
In [47]:
times = pd.date_range(start=datetime.datetime(2014,6,1), end=datetime.datetime(2014,6,2), freq='5Min')
ephem_abq = abq.get_solarposition(times.tz_localize(abq.tz))
tracker_data = pvlib.tracking.singleaxis(ephem_abq['apparent_zenith'], ephem_abq['azimuth'],
axis_tilt=20, axis_azimuth=180, max_angle=45,
backtrack=True, gcr=.3)
tracker_data.plot()
plt.ylim(-50,300)
plt.title('June 1, Albuquerque, 20 deg S-Tilted Single-Axis, with backtracking');
test solar noon
In [48]:
apparent_zenith = pd.Series([10])
apparent_azimuth = pd.Series([180])
tracker_data = pvlib.tracking.singleaxis(apparent_zenith, apparent_azimuth,
axis_tilt=0, axis_azimuth=0, max_angle=90,
backtrack=True, gcr=2.0/7.0)
tracker_data
Out[48]:
In [49]:
apparent_zenith = pd.Series([60])
apparent_azimuth = pd.Series([90])
tracker_data = pvlib.tracking.singleaxis(apparent_zenith, apparent_azimuth,
axis_tilt=0, axis_azimuth=180, max_angle=90,
backtrack=True, gcr=2.0/7.0)
tracker_data
Out[49]:
In [50]:
apparent_zenith = pd.Series([60])
apparent_azimuth = pd.Series([90])
tracker_data = pvlib.tracking.singleaxis(apparent_zenith, apparent_azimuth,
axis_tilt=0, axis_azimuth=0, max_angle=90,
backtrack=True, gcr=2.0/7.0)
tracker_data
Out[50]:
Test max
In [51]:
apparent_zenith = pd.Series([60])
apparent_azimuth = pd.Series([90])
tracker_data = pvlib.tracking.singleaxis(apparent_zenith, apparent_azimuth,
axis_tilt=0, axis_azimuth=0, max_angle=45,
backtrack=True, gcr=2.0/7.0)
tracker_data
Out[51]:
Test backtrack bool
In [52]:
apparent_zenith = pd.Series([80])
apparent_azimuth = pd.Series([90])
tracker_data = pvlib.tracking.singleaxis(apparent_zenith, apparent_azimuth,
axis_tilt=0, axis_azimuth=0, max_angle=90,
backtrack=False, gcr=2.0/7.0)
tracker_data
Out[52]:
In [53]:
apparent_zenith = pd.Series([80])
apparent_azimuth = pd.Series([90])
tracker_data = pvlib.tracking.singleaxis(apparent_zenith, apparent_azimuth,
axis_tilt=0, axis_azimuth=0, max_angle=90,
backtrack=True, gcr=2.0/7.0)
tracker_data
Out[53]:
Test axis_tilt
In [54]:
apparent_zenith = pd.Series([30])
apparent_azimuth = pd.Series([135])
tracker_data = pvlib.tracking.singleaxis(apparent_zenith, apparent_azimuth,
axis_tilt=30, axis_azimuth=180, max_angle=90,
backtrack=True, gcr=2.0/7.0)
tracker_data
Out[54]:
In [55]:
apparent_zenith = pd.Series([30])
apparent_azimuth = pd.Series([135])
tracker_data = pvlib.tracking.singleaxis(apparent_zenith, apparent_azimuth,
axis_tilt=30, axis_azimuth=0, max_angle=90,
backtrack=True, gcr=2.0/7.0)
tracker_data
Out[55]:
Test axis_azimuth
In [56]:
apparent_zenith = pd.Series([30])
apparent_azimuth = pd.Series([90])
tracker_data = pvlib.tracking.singleaxis(apparent_zenith, apparent_azimuth,
axis_tilt=0, axis_azimuth=90, max_angle=90,
backtrack=True, gcr=2.0/7.0)
tracker_data
Out[56]:
In [57]:
apparent_zenith = pd.Series([30])
apparent_azimuth = pd.Series([180])
tracker_data = pvlib.tracking.singleaxis(apparent_zenith, apparent_azimuth,
axis_tilt=0, axis_azimuth=90, max_angle=90,
backtrack=True, gcr=2.0/7.0)
tracker_data
Out[57]:
In [58]:
apparent_zenith = pd.Series([30])
apparent_azimuth = pd.Series([180])
tracker_data = pvlib.tracking.singleaxis(apparent_zenith, apparent_azimuth,
axis_tilt=0, axis_azimuth=90, max_angle=90,
backtrack=True, gcr=2.0/7.0)
tracker_data
Out[58]:
In [59]:
apparent_zenith = pd.Series([30])
apparent_azimuth = pd.Series([150])
tracker_data = pvlib.tracking.singleaxis(apparent_zenith, apparent_azimuth,
axis_tilt=0, axis_azimuth=170, max_angle=90,
backtrack=True, gcr=2.0/7.0)
tracker_data
Out[59]:
In [60]:
apparent_zenith = pd.Series([30])
apparent_azimuth = pd.Series([180])
tracker_data = pvlib.tracking.singleaxis(apparent_zenith, apparent_azimuth,
axis_tilt=0, axis_azimuth=170, max_angle=90,
backtrack=True, gcr=2.0/7.0)
tracker_data
Out[60]:
In [61]:
apparent_zenith = pd.Series([10])
apparent_azimuth = pd.Series([180])
tracker_data = pvlib.tracking.singleaxis(apparent_zenith, apparent_azimuth,
axis_tilt=0, axis_azimuth=0, max_angle=90,
backtrack=True, gcr=2.0/7.0)
tracker_data
Out[61]:
This is supposed to fail...
In [62]:
# NBVAL_RAISES_EXCEPTION
apparent_zenith = pd.Series([10])
apparent_azimuth = pd.Series([180,90])
tracker_data = pvlib.tracking.singleaxis(apparent_zenith, apparent_azimuth,
axis_tilt=0, axis_azimuth=0, max_angle=90,
backtrack=True, gcr=2.0/7.0)
tracker_data
In [ ]: