From f673ac5410f8beeb9704da2ffd77c04894321247 Mon Sep 17 00:00:00 2001 From: Kevin Anderson Date: Tue, 8 Sep 2020 09:20:51 -0600 Subject: [PATCH 01/10] Create plot_backtracking_sloped_terrain.py --- .../plot_backtracking_sloped_terrain.py | 122 ++++++++++++++++++ 1 file changed, 122 insertions(+) create mode 100644 docs/examples/plot_backtracking_sloped_terrain.py diff --git a/docs/examples/plot_backtracking_sloped_terrain.py b/docs/examples/plot_backtracking_sloped_terrain.py new file mode 100644 index 0000000000..d8d71b0810 --- /dev/null +++ b/docs/examples/plot_backtracking_sloped_terrain.py @@ -0,0 +1,122 @@ +""" +Backtracking on sloped terrain +============================== + +Modeling backtracking for single-axis tracker arrays built on sloped terrain. +""" + +# %% +# Tracker systems avoid row-to-row shading when the sun is low in the sky +# by backtracking. The backtracking strategy orients the modules exactly +# on the boundary between shaded and unshaded so that the modules are oriented +# as much towards the sun as possible while still remaining unshaded. +# Unlike the truetracking calculation (which only depends on solar position), +# calculating the backtracking angle requires knowledge of the relative spacing +# of adjacent tracker rows. This example shows how the backtracking angle +# changes based on a vertical offset between rows caused by sloped terrain. +# It uses :py:func:`pvlib.tracking.calc_axis_tilt` and +# :py:func:`pvlib.tracking.calc_cross_axis_tilt` to calculate the necessary +# array geometry parameters and :py:func:`pvlib.tracking.singleaxis` to +# calculate the backtracking angles. +# +# First, let's plot the simple case where the tracker axes are at right angles +# to the direction of the slope. In this case, the cross-axis tilt angle +# is the same as the slope of the terrain and the tracker axis itself is +# horizontal. + +from pvlib import solarposition, tracking +import pandas as pd +import matplotlib.pyplot as plt + +# PV system parameters +tz = 'US/Eastern' +lat, lon = 40, -80 +gcr = 0.4 + +# calculate the solar position +times = pd.date_range('2019-01-01 06:00', '2019-01-01 18:00', closed='left', + freq='1min', tz=tz) +solpos = solarposition.get_solarposition(times, lat, lon) + +# compare the backtracking angle at various terrain slopes +fig, ax = plt.subplots() +for cross_axis_tilt in [0, 5, 10]: + tracker_data = tracking.singleaxis( + apparent_zenith=solpos['apparent_zenith'], + apparent_azimuth=solpos['azimuth'], + axis_tilt=0, # flat because the axis is perpendicular to the slope + axis_azimuth=180, # N-S axis, azimuth facing south + max_angle=90, + backtrack=True, + gcr=gcr, + cross_axis_tilt=cross_axis_tilt) + + backtracking_position = tracker_data['tracker_theta'].fillna(0) + label = r'$\beta_c$: {}°'.format(cross_axis_tilt) + backtracking_position.plot(label=label, ax=ax) + +plt.legend() +plt.title('Backtracking Curves') +plt.show() + +# %% +# This plot shows how backtracking changes based on the slope between rows. +# For example, unlike the flat-terrain backtracking curve, the sloped-terrain +# curves do not approach zero at the end of the day. Because of the vertical +# offset between rows introduced by the sloped terrain, the trackers can be +# slightly tilted without shading each other: +# +# TODO: RHR image +# +# TODO: talk about RHR +# +# Now let's examine the general case where the terrain slope makes an +# inconvenient angle to the tracker axes. For example, consider an array +# with north-south axes on terrain that slopes down to the south-south-east. +# Assuming the axes are installed parallel to the ground, the northern ends +# of the axes will be higher than the southern ends. But because the slope +# isn't purely parallel or perpendicular to the axes, the axis tilt and +# cross-axis tilt angles are not immediately obvious. We can use pvlib +# to calculate them for us: + +slope_azimuth = 155 # terrain slopes down to the south-south-east +slope_tilt = 10 # terrain is sloped at 10 degrees from horizontal +axis_azimuth = 180 # tracker axis is still N-S + +# calculate the tracker axis tilt, assuming that the axis follows the terrain: +axis_tilt = tracking.calc_axis_tilt(slope_azimuth, slope_tilt, axis_azimuth) + +# calculate the cross-axis tilt: +cross_axis_tilt = tracking.calc_cross_axis_tilt(slope_azimuth, + slope_tilt, + axis_azimuth, + axis_tilt) + +print('Axis tilt:', '{:0.01f}°'.format(axis_tilt)) +print('Cross-axis tilt:', '{:0.01f}°'.format(cross_axis_tilt)) + +# %% +# And now we can pass use these values to generate the tracker curve as +# before: + +tracker_data = tracking.singleaxis( + apparent_zenith=solpos['apparent_zenith'], + apparent_azimuth=solpos['azimuth'], + axis_tilt=axis_tilt, # no longer flat because the terrain imparts a tilt + axis_azimuth=axis_azimuth, + max_angle=90, + backtrack=True, + gcr=gcr, + cross_axis_tilt=cross_axis_tilt) + +backtracking_position = tracker_data['tracker_theta'].fillna(0) +backtracking_position.plot() + +title_template = 'Axis tilt: {:0.01f}° Cross-axis tilt: {:0.01f}°' +plt.title(title_template.format(axis_tilt, cross_axis_tilt)) +plt.show() + +# %% +# Note that the backtracking curve is roughly mirrored compared with the +# earlier example -- it is because the terrain is now sloped somewhat to the +# east instead of west. From f84fb40b5c517e69023de5d5ffbf4dce1f08d72c Mon Sep 17 00:00:00 2001 From: Kevin Anderson Date: Tue, 6 Oct 2020 20:40:46 -0600 Subject: [PATCH 02/10] add angle convention images --- .../plot_backtracking_sloped_terrain.py | 70 +++++++++++++++--- .../_images/ground_slope_angle_convention.png | Bin 0 -> 14810 bytes .../tracker_azimuth_angle_convention.png | Bin 0 -> 39455 bytes .../tracker_rotation_angle_convention.png | Bin 0 -> 126770 bytes 4 files changed, 58 insertions(+), 12 deletions(-) create mode 100644 docs/sphinx/source/_images/ground_slope_angle_convention.png create mode 100644 docs/sphinx/source/_images/tracker_azimuth_angle_convention.png create mode 100644 docs/sphinx/source/_images/tracker_rotation_angle_convention.png diff --git a/docs/examples/plot_backtracking_sloped_terrain.py b/docs/examples/plot_backtracking_sloped_terrain.py index d8d71b0810..b207682149 100644 --- a/docs/examples/plot_backtracking_sloped_terrain.py +++ b/docs/examples/plot_backtracking_sloped_terrain.py @@ -2,7 +2,7 @@ Backtracking on sloped terrain ============================== -Modeling backtracking for single-axis tracker arrays built on sloped terrain. +Modeling backtracking for single-axis tracker arrays on sloped terrain. """ # %% @@ -19,7 +19,59 @@ # array geometry parameters and :py:func:`pvlib.tracking.singleaxis` to # calculate the backtracking angles. # -# First, let's plot the simple case where the tracker axes are at right angles +# Angle conventions +# ----------------- +# +# First let's go over the sign conventions used for angles. In contrast to +# fixed-tilt arrays, the convention for the azimuth angle of a single-axis +# tracker array is along the tracker axis. Note that the axis azimuth is +# a property of the array and is distinct from the azimuth of the panel +# orientation, which changes based on tracker angle. +# Because the tracker axis points in two directions, there are two choices for +# the axis azimuth angle, and by convention (at least in the northern +# hemisphere), the more southward angle is chosen: +# +# .. image:: ../_images/tracker_azimuth_angle_convention.png +# :alt: Image showing the azimuth convention for single-axis tracker arrays. +# :width: 500 +# :align: center +# +# Note that, as with fixed-tilt arrays, the axis azimuth is determined as the +# angle clockwise from north. +# +# Using the axis azimuth convention above, the sign convention for tracker +# rotations is given by the +# `right-hand rule `_. +# Point the right hand thumb along the axis in the direction of the axis +# azimuth and the fingers curl in the direction of positive rotation angle: +# +# .. image:: ../_images/tracker_rotation_angle_convention.png +# :alt: Image showing the rotation sign convention for single-axis trackers. +# :width: 500 +# :align: center +# +# So for an array with ``axis_azimuth=180`` (tracker axis aligned perfectly +# north-south), pointing the right-hand thumb along the axis azimuth has the +# fingers curling towards the west, meaning rotations towards the west are +# positive and rotations towards the east are negative. +# +# The sign convention for ground slope follows the same convention -- align +# the right-hand thumb along the tracker axis in the direction of the axis +# azimuth and the fingers curl towards positive angles. So in this example, +# with the axis azimuth coming out of the page, an east-facing slope is a +# negative rotation from horizontal: +# +# .. image:: ../_images/ground_slope_angle_convention.png +# :alt: Image showing the ground slope sign convention. +# :width: 500 +# :align: center +# + +# %% +# Rotation curves +# --------------- +# +# Now, let's plot the simple case where the tracker axes are at right angles # to the direction of the slope. In this case, the cross-axis tilt angle # is the same as the slope of the terrain and the tracker axis itself is # horizontal. @@ -52,7 +104,7 @@ cross_axis_tilt=cross_axis_tilt) backtracking_position = tracker_data['tracker_theta'].fillna(0) - label = r'$\beta_c$: {}°'.format(cross_axis_tilt) + label = 'cross-axis tilt: {}°'.format(cross_axis_tilt) backtracking_position.plot(label=label, ax=ax) plt.legend() @@ -64,11 +116,7 @@ # For example, unlike the flat-terrain backtracking curve, the sloped-terrain # curves do not approach zero at the end of the day. Because of the vertical # offset between rows introduced by the sloped terrain, the trackers can be -# slightly tilted without shading each other: -# -# TODO: RHR image -# -# TODO: talk about RHR +# slightly tilted without shading each other. # # Now let's examine the general case where the terrain slope makes an # inconvenient angle to the tracker axes. For example, consider an array @@ -87,10 +135,8 @@ axis_tilt = tracking.calc_axis_tilt(slope_azimuth, slope_tilt, axis_azimuth) # calculate the cross-axis tilt: -cross_axis_tilt = tracking.calc_cross_axis_tilt(slope_azimuth, - slope_tilt, - axis_azimuth, - axis_tilt) +cross_axis_tilt = tracking.calc_cross_axis_tilt(slope_azimuth, slope_tilt, + axis_azimuth, axis_tilt) print('Axis tilt:', '{:0.01f}°'.format(axis_tilt)) print('Cross-axis tilt:', '{:0.01f}°'.format(cross_axis_tilt)) diff --git a/docs/sphinx/source/_images/ground_slope_angle_convention.png b/docs/sphinx/source/_images/ground_slope_angle_convention.png new file mode 100644 index 0000000000000000000000000000000000000000..f0351c04bf0369fd88919fdc8d7c860b2d799af0 GIT binary patch literal 14810 zcmeHuX*`tw`|pjYEG>3gDElBJOJu2#u^Thi$dWxIOJy%n_7I6g_8Gfu$rhnV3ZqaI zErulf&be;i@9+H2|2#Oa^WZ!@4|-+p<@32d*YdvBJHkNk0uwzqJ%S)iSWPt?g6tYc z5UP)RsNsqyac?sGN9BdPa1JSXcbEb{b~&EaJ&PdaaSR(awD5cHRZTN51liY${-f&f 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zSogoz?et(3jeqIJtY>r!_p~Tn&A&loKEV=zXQK>8$|vAXrEuyKMc!=)qa0I=Rozul ztjLbFre>?2w{Y~8jWSwW_#UcfsETqzywGBY9M5BTBD`+)R-}Gv1v|AshG# zy&ILnLco2>aOo2+U*U5jC#K-UODpagD%+gKTMmXVDPkT9)iWcw92qQKxdYKUJBr~6 ze0adBMXB?aSE$~)^oeaB{NeXz Date: Tue, 6 Oct 2020 20:51:30 -0600 Subject: [PATCH 03/10] whatsnew --- docs/sphinx/source/whatsnew/v0.8.1.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/sphinx/source/whatsnew/v0.8.1.rst b/docs/sphinx/source/whatsnew/v0.8.1.rst index 4bc09643ac..ae40d74326 100644 --- a/docs/sphinx/source/whatsnew/v0.8.1.rst +++ b/docs/sphinx/source/whatsnew/v0.8.1.rst @@ -26,7 +26,7 @@ Testing Documentation ~~~~~~~~~~~~~ - +* Add gallery example about backtracking on sloped terrain. (:pull:`1077`) Requirements ~~~~~~~~~~~~ From 9d24f613dce6060c2ec248b186f4e8a80a04d5ac Mon Sep 17 00:00:00 2001 From: Kevin Anderson <57452607+kanderso-nrel@users.noreply.github.com> Date: Wed, 7 Oct 2020 20:42:53 -0600 Subject: [PATCH 04/10] Apply suggestions from code review Co-authored-by: Cliff Hansen --- docs/examples/plot_backtracking_sloped_terrain.py | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/docs/examples/plot_backtracking_sloped_terrain.py b/docs/examples/plot_backtracking_sloped_terrain.py index b207682149..62b160f4ae 100644 --- a/docs/examples/plot_backtracking_sloped_terrain.py +++ b/docs/examples/plot_backtracking_sloped_terrain.py @@ -6,8 +6,8 @@ """ # %% -# Tracker systems avoid row-to-row shading when the sun is low in the sky -# by backtracking. The backtracking strategy orients the modules exactly +# Tracker systems use backtracking to avoid row-to-row shading when the +# sun is low in the sky. The backtracking strategy orients the modules exactly # on the boundary between shaded and unshaded so that the modules are oriented # as much towards the sun as possible while still remaining unshaded. # Unlike the truetracking calculation (which only depends on solar position), @@ -23,10 +23,10 @@ # ----------------- # # First let's go over the sign conventions used for angles. In contrast to -# fixed-tilt arrays, the convention for the azimuth angle of a single-axis -# tracker array is along the tracker axis. Note that the axis azimuth is +# fixed-tilt arrays where the azimuth is that of the normal to the panels, the convention +# for the azimuth of a single-axis tracker is along the tracker axis. Note that the axis azimuth is # a property of the array and is distinct from the azimuth of the panel -# orientation, which changes based on tracker angle. +# orientation, which changes based on tracker rotation angle. # Because the tracker axis points in two directions, there are two choices for # the axis azimuth angle, and by convention (at least in the northern # hemisphere), the more southward angle is chosen: @@ -58,7 +58,7 @@ # The sign convention for ground slope follows the same convention -- align # the right-hand thumb along the tracker axis in the direction of the axis # azimuth and the fingers curl towards positive angles. So in this example, -# with the axis azimuth coming out of the page, an east-facing slope is a +# with the axis azimuth coming out of the page, an east-facing, downward slope is a # negative rotation from horizontal: # # .. image:: ../_images/ground_slope_angle_convention.png From 3b75bb38807b67d1bb965018f684b6f4a5b05ceb Mon Sep 17 00:00:00 2001 From: Kevin Anderson Date: Wed, 7 Oct 2020 21:00:19 -0600 Subject: [PATCH 05/10] new images --- .../tracker_azimuth_angle_convention.png | Bin 39455 -> 39690 bytes .../tracker_rotation_angle_convention.png | Bin 126770 -> 110289 bytes 2 files changed, 0 insertions(+), 0 deletions(-) diff --git a/docs/sphinx/source/_images/tracker_azimuth_angle_convention.png b/docs/sphinx/source/_images/tracker_azimuth_angle_convention.png index 465481152c5ff3bf503a26ad4734feeefc12c307..2c7124bbf18e6d86727d00bdf54def3585898ef5 100644 GIT binary patch literal 39690 zcmYIv1yqz>)HNU>p{PhBAulNOT(HJF&wcJW`|PvNzVFpkWFHVv5ny0oJdl@rqk(~em4$(UIdLBg_|25L 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zSogoz?et(3jeqIJtY>r!_p~Tn&A&loKEV=zXQK>8$|vAXrEuyKMc!=)qa0I=Rozul ztjLbFre>?2w{Y~8jWSwW_#UcfsETqzywGBY9M5BTBD`+)R-}Gv1v|AshG# zy&ILnLco2>aOo2+U*U5jC#K-UODpagD%+gKTMmXVDPkT9)iWcw92qQKxdYKUJBr~6 ze0adBMXB?aSE$~)^oeaB{NeXz Date: Wed, 7 Oct 2020 21:04:55 -0600 Subject: [PATCH 06/10] reflow text for 80char limit --- .../plot_backtracking_sloped_terrain.py | 18 +++++++++--------- 1 file changed, 9 insertions(+), 9 deletions(-) diff --git a/docs/examples/plot_backtracking_sloped_terrain.py b/docs/examples/plot_backtracking_sloped_terrain.py index 62b160f4ae..aa75091425 100644 --- a/docs/examples/plot_backtracking_sloped_terrain.py +++ b/docs/examples/plot_backtracking_sloped_terrain.py @@ -23,13 +23,13 @@ # ----------------- # # First let's go over the sign conventions used for angles. In contrast to -# fixed-tilt arrays where the azimuth is that of the normal to the panels, the convention -# for the azimuth of a single-axis tracker is along the tracker axis. Note that the axis azimuth is -# a property of the array and is distinct from the azimuth of the panel -# orientation, which changes based on tracker rotation angle. -# Because the tracker axis points in two directions, there are two choices for -# the axis azimuth angle, and by convention (at least in the northern -# hemisphere), the more southward angle is chosen: +# fixed-tilt arrays where the azimuth is that of the normal to the panels, the +# convention for the azimuth of a single-axis tracker is along the tracker +# axis. Note that the axis azimuth is a property of the array and is distinct +# from the azimuth of the panel orientation, which changes based on tracker +# rotation angle. Because the tracker axis points in two directions, there are +# two choices for the axis azimuth angle, and by convention (at least in the +# northern hemisphere), the more southward angle is chosen: # # .. image:: ../_images/tracker_azimuth_angle_convention.png # :alt: Image showing the azimuth convention for single-axis tracker arrays. @@ -58,8 +58,8 @@ # The sign convention for ground slope follows the same convention -- align # the right-hand thumb along the tracker axis in the direction of the axis # azimuth and the fingers curl towards positive angles. So in this example, -# with the axis azimuth coming out of the page, an east-facing, downward slope is a -# negative rotation from horizontal: +# with the axis azimuth coming out of the page, an east-facing, downward slope +# is a negative rotation from horizontal: # # .. image:: ../_images/ground_slope_angle_convention.png # :alt: Image showing the ground slope sign convention. From 186232c45414afd8e896ee4f9328bab8f96acdc5 Mon Sep 17 00:00:00 2001 From: Kevin Anderson Date: Wed, 7 Oct 2020 21:16:11 -0600 Subject: [PATCH 07/10] text improvements --- .../examples/plot_backtracking_sloped_terrain.py | 16 ++++++++++++---- 1 file changed, 12 insertions(+), 4 deletions(-) diff --git a/docs/examples/plot_backtracking_sloped_terrain.py b/docs/examples/plot_backtracking_sloped_terrain.py index aa75091425..37c05f8ae9 100644 --- a/docs/examples/plot_backtracking_sloped_terrain.py +++ b/docs/examples/plot_backtracking_sloped_terrain.py @@ -37,7 +37,10 @@ # :align: center # # Note that, as with fixed-tilt arrays, the axis azimuth is determined as the -# angle clockwise from north. +# angle clockwise from north. The azimuth of the terrain's slope is also +# determined as an angle clockwise from north, pointing in the direction +# of falling slope. So for example, a hillside that slopes down to the east +# has an azimuth of 90 degrees. # # Using the axis azimuth convention above, the sign convention for tracker # rotations is given by the @@ -55,7 +58,9 @@ # fingers curling towards the west, meaning rotations towards the west are # positive and rotations towards the east are negative. # -# The sign convention for ground slope follows the same convention -- align +# The ground slope itself is always positive, but the component of the slope +# perpendicular to the tracker axes can be positive or negative. The convention +# for the cross-axis slope angle follows the right-hand rule: align # the right-hand thumb along the tracker axis in the direction of the axis # azimuth and the fingers curl towards positive angles. So in this example, # with the axis azimuth coming out of the page, an east-facing, downward slope @@ -127,8 +132,11 @@ # cross-axis tilt angles are not immediately obvious. We can use pvlib # to calculate them for us: -slope_azimuth = 155 # terrain slopes down to the south-south-east -slope_tilt = 10 # terrain is sloped at 10 degrees from horizontal +# terrain slopes 10 degrees downward to the south-south-east. note: because +# slope_azimuth is defined in the direction of falling slope, slope_tilt is +# always positive. +slope_azimuth = 155 +slope_tilt = 10 axis_azimuth = 180 # tracker axis is still N-S # calculate the tracker axis tilt, assuming that the axis follows the terrain: From 3320e192b48a680ddf0b3a17c105bcdee92a5847 Mon Sep 17 00:00:00 2001 From: Kevin Anderson Date: Thu, 8 Oct 2020 18:05:42 -0600 Subject: [PATCH 08/10] truetrack -> true-track --- docs/examples/plot_backtracking_sloped_terrain.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/examples/plot_backtracking_sloped_terrain.py b/docs/examples/plot_backtracking_sloped_terrain.py index 37c05f8ae9..09e3dd329b 100644 --- a/docs/examples/plot_backtracking_sloped_terrain.py +++ b/docs/examples/plot_backtracking_sloped_terrain.py @@ -10,7 +10,7 @@ # sun is low in the sky. The backtracking strategy orients the modules exactly # on the boundary between shaded and unshaded so that the modules are oriented # as much towards the sun as possible while still remaining unshaded. -# Unlike the truetracking calculation (which only depends on solar position), +# Unlike the true-tracking calculation (which only depends on solar position), # calculating the backtracking angle requires knowledge of the relative spacing # of adjacent tracker rows. This example shows how the backtracking angle # changes based on a vertical offset between rows caused by sloped terrain. From cbb8fd1817ce64ae7a232b829b556b056d708720 Mon Sep 17 00:00:00 2001 From: Kevin Anderson Date: Thu, 8 Oct 2020 18:07:15 -0600 Subject: [PATCH 09/10] add comment per wholmgren's suggestion --- docs/examples/plot_backtracking_sloped_terrain.py | 1 + 1 file changed, 1 insertion(+) diff --git a/docs/examples/plot_backtracking_sloped_terrain.py b/docs/examples/plot_backtracking_sloped_terrain.py index 09e3dd329b..5fc5f47c12 100644 --- a/docs/examples/plot_backtracking_sloped_terrain.py +++ b/docs/examples/plot_backtracking_sloped_terrain.py @@ -108,6 +108,7 @@ gcr=gcr, cross_axis_tilt=cross_axis_tilt) + # tracker rotation is undefined at night backtracking_position = tracker_data['tracker_theta'].fillna(0) label = 'cross-axis tilt: {}°'.format(cross_axis_tilt) backtracking_position.plot(label=label, ax=ax) From 5dd6d4688eac6f41b2a132c48b976dbdf125562a Mon Sep 17 00:00:00 2001 From: Kevin Anderson Date: Thu, 8 Oct 2020 18:07:54 -0600 Subject: [PATCH 10/10] rename file --- ..._terrain.py => plot_single_axis_tracking_on_sloped_terrain.py} | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename docs/examples/{plot_backtracking_sloped_terrain.py => plot_single_axis_tracking_on_sloped_terrain.py} (100%) diff --git a/docs/examples/plot_backtracking_sloped_terrain.py b/docs/examples/plot_single_axis_tracking_on_sloped_terrain.py similarity index 100% rename from docs/examples/plot_backtracking_sloped_terrain.py rename to docs/examples/plot_single_axis_tracking_on_sloped_terrain.py