diff --git a/docs/sphinx/source/_images/FSLR_irrad_shade_loss_slope_terrain.png b/docs/sphinx/source/_images/FSLR_irrad_shade_loss_slope_terrain.png
new file mode 100644
index 0000000000..d2f01c2e88
Binary files /dev/null and b/docs/sphinx/source/_images/FSLR_irrad_shade_loss_slope_terrain.png differ
diff --git a/docs/sphinx/source/reference/effects_on_pv_system_output/shading.rst b/docs/sphinx/source/reference/effects_on_pv_system_output/shading.rst
index a68dd94b2a..189f597dce 100644
--- a/docs/sphinx/source/reference/effects_on_pv_system_output/shading.rst
+++ b/docs/sphinx/source/reference/effects_on_pv_system_output/shading.rst
@@ -8,4 +8,7 @@ Shading
shading.masking_angle
shading.masking_angle_passias
- shading.sky_diffuse_passias
\ No newline at end of file
+ shading.sky_diffuse_passias
+ shading.tracker_shaded_fraction
+ shading.linear_shade_loss
+
\ No newline at end of file
diff --git a/docs/sphinx/source/whatsnew/v0.9.6.rst b/docs/sphinx/source/whatsnew/v0.9.6.rst
index 7d1271086f..e09ff4eb1c 100644
--- a/docs/sphinx/source/whatsnew/v0.9.6.rst
+++ b/docs/sphinx/source/whatsnew/v0.9.6.rst
@@ -11,12 +11,16 @@ Deprecations
Enhancements
~~~~~~~~~~~~
-
+* added functions `pvlib.shading.tracker_shaded_fraction` and
+ `pvlib.shading.linear_shade_loss` to calculate row-to-row shade and apply
+ linear shade loss for thin film CdTe modules like First Solar.
+ (:issue:`1689`, :issue:`1690`, :pull:`1725`)
Bug fixes
~~~~~~~~~
* `data` can no longer be left unspecified in
- :py:meth:`pvlib.modelchain.ModelChain.run_model_from_effective_irradiance`. (:issue:`1713`, :pull:`1720`)
+ :py:meth:`pvlib.modelchain.ModelChain.run_model_from_effective_irradiance`.
+ (:issue:`1713`, :pull:`1720`)
Testing
~~~~~~~
@@ -41,6 +45,6 @@ Contributors
* Lakshya Garg (:ghuser:`Lakshyadevelops`)
* Adam R. Jensen (:ghuser:`adamrjensen`)
* Siddharth Kaul (:ghuser:`k10blogger`)
+* Mark A. Mikofski (:ghuser:`mikofski`)
* Kshitiz Gupta (:ghuser:`kshitiz305`)
* Stefan de Lange (:ghuser:`langestefan`)
-
diff --git a/pvlib/shading.py b/pvlib/shading.py
index 01d725207c..9e511d600e 100644
--- a/pvlib/shading.py
+++ b/pvlib/shading.py
@@ -191,3 +191,117 @@ def sky_diffuse_passias(masking_angle):
Available at https://www.nrel.gov/docs/fy18osti/67399.pdf
"""
return 1 - cosd(masking_angle/2)**2
+
+
+def tracker_shaded_fraction(tracker_theta, gcr, projected_solar_zenith,
+ cross_axis_slope=0):
+ r"""
+ Shaded fraction for trackers with a common angle on an east-west slope.
+
+ Parameters
+ ----------
+ tracker_theta : numeric
+ The tracker rotation angle in degrees from horizontal.
+ gcr : float
+ The ground coverage ratio as a fraction equal to the collector width
+ over the horizontal row-to-row pitch.
+ projected_solar_zenith : numeric
+ Zenith angle in degrees of the solar vector projected into the plane
+ perpendicular to the tracker axes.
+ cross_axis_slope : float, default 0
+ Angle of the plane containing the tracker axes in degrees from
+ horizontal.
+
+ Returns
+ -------
+ shaded_fraction : numeric
+ The fraction of the collector width shaded by an adjacent row. A
+ value of 1 is completely shaded and zero is no shade.
+
+ See also
+ --------
+ pvlib.shading.linear_shade_loss
+
+
+ The shaded fraction is derived using trigonometery and similar triangles
+ from the tracker rotation :math:`\beta`, the ground slope :math:`\theta_g`,
+ the projected solar zenith (psz) :math:`\theta`, the collector width
+ :math:`L`, the row-to-row pitch :math:`P`, and the shadow length :math:`z`
+ as shown in the image below.
+
+ .. image:: /_images/FSLR_irrad_shade_loss_slope_terrain.png
+
+ The ratio of the shadow length to the pitch, :math:`z/P`, is given by the
+ following relation where the ground coverage ratio (GCR) is :math:`L/P`:
+
+ .. math::
+ \frac{z/P}{\sin{\left(\frac{\pi}{2}-\beta+\theta\right)}}
+ = \frac{GCR}{\sin{\left(\frac{\pi}{2}-\theta-\theta_g\right)}}
+
+ Then the shaded fraction :math:`w/L` is derived from :math:`z/P` as
+ follows:
+
+ .. math::
+ \frac{w}{L} = 1 - \frac{P}{z\cos{\theta_g}}
+
+ Finally, shade is zero if :math:`z\cos{\theta_g}/P \le 1`.
+
+ References
+ ----------
+ Mark A. Mikofski, "First Solar Irradiance Shade Losses on Sloped Terrain,"
+ PVPMC, 2023
+ """
+ theta_g_rad = np.radians(cross_axis_slope)
+ # angle opposite shadow cast on the ground, z
+ angle_z = (
+ np.pi / 2 - np.radians(tracker_theta)
+ + np.radians(projected_solar_zenith))
+ # angle opposite the collector width, L
+ angle_gcr = (
+ np.pi / 2 - np.radians(projected_solar_zenith)
+ - theta_g_rad)
+ # ratio of shadow, z, to pitch, P
+ zp = gcr * np.sin(angle_z) / np.sin(angle_gcr)
+ # there's only row-to-row shade loss if the shadow on the ground, z, is
+ # longer than row-to-row pitch projected on the ground, P*cos(theta_g)
+ zp_cos_g = zp*np.cos(theta_g_rad)
+ # shaded fraction (fs)
+ fs = np.where(zp_cos_g <= 1, 0, 1 - 1/zp_cos_g)
+ return fs
+
+
+def linear_shade_loss(shaded_fraction, diffuse_fraction):
+ """
+ Fraction of power lost to linear shade loss applicable to monolithic thin
+ film modules like First Solar CdTe, where the shadow is perpendicular to
+ cell scribe lines.
+
+ Parameters
+ ----------
+ shaded_fraction : numeric
+ The fraction of the collector width shaded by an adjacent row. A
+ value of 1 is completely shaded and zero is no shade.
+ diffuse_fraction : numeric
+ The ratio of diffuse plane of array (poa) irradiance to global poa.
+ A value of 1 is completely diffuse and zero is no diffuse.
+
+ Returns
+ -------
+ linear_shade_loss : numeric
+ The fraction of power lost due to linear shading. A value of 1 is all
+ power lost and zero is no loss.
+
+ See also
+ --------
+ pvlib.shading.tracker_shaded_fraction
+
+ Example
+ -------
+ >>> from pvlib import shading
+ >>> fs = shading.tracker_shaded_fraction(45.0, 0.8, 45.0, 0)
+ >>> loss = shading.linear_shade_loss(fs, 0.2)
+ >>> P_no_shade = 100 # [kWdc] DC output from modules
+ >>> P_linear_shade = P_no_shade * (1-loss) # [kWdc] output after loss
+ # 90.71067811865476 [kWdc]
+ """
+ return shaded_fraction * (1 - diffuse_fraction)
diff --git a/pvlib/tests/test_shading.py b/pvlib/tests/test_shading.py
index 0558cb76ad..a2d90b89aa 100644
--- a/pvlib/tests/test_shading.py
+++ b/pvlib/tests/test_shading.py
@@ -76,3 +76,46 @@ def test_sky_diffuse_passias_scalar(average_masking_angle, shading_loss):
for angle, loss in zip(average_masking_angle, shading_loss):
actual_loss = shading.sky_diffuse_passias(angle)
assert np.isclose(loss, actual_loss)
+
+
+@pytest.fixture
+def expected_fs():
+ # trivial case, 80% gcr, no slope, trackers & psz at 45-deg
+ z0 = np.sqrt(2*0.8*0.8)
+ # another trivial case, 60% gcr, no slope, trackers & psz at 60-deg
+ z1 = 2*0.6
+ # 30-deg isosceles, 60% gcr, no slope, 30-deg trackers, psz at 60-deg
+ z2 = 0.6*np.sqrt(3)
+ z = np.array([z0, z1, z2])
+ return 1 - 1/z
+
+
+def test_tracker_shade_fraction(expected_fs):
+ """closes gh1690"""
+ fs = shading.tracker_shaded_fraction(45.0, 0.8, 45.0)
+ assert np.isclose(fs, expected_fs[0])
+ # same trivial case with 40%, shadow is only 0.565-m long < 1-m r2r P
+ zero_fs = shading.tracker_shaded_fraction(45.0, 0.4, 45.0)
+ assert np.isclose(zero_fs, 0)
+ # test vectors
+ tracker_theta = [45.0, 60.0, 30.0]
+ gcr = [0.8, 0.6, 0.6]
+ psz = [45.0, 60.0, 60.0]
+ slope = [0]*3
+ fs_vec = shading.tracker_shaded_fraction(
+ tracker_theta, gcr, psz, slope)
+ assert np.allclose(fs_vec, expected_fs)
+
+
+def test_linear_shade_loss(expected_fs):
+ loss = shading.linear_shade_loss(expected_fs[0], 0.2)
+ assert np.isclose(loss, 0.09289321881345258)
+ # if no diffuse, shade fraction is the loss
+ loss_no_df = shading.linear_shade_loss(expected_fs[0], 0)
+ assert np.isclose(loss_no_df, expected_fs[0])
+ # if all diffuse, no shade loss
+ no_loss = shading.linear_shade_loss(expected_fs[0], 1.0)
+ assert np.isclose(no_loss, 0)
+ vec_loss = shading.linear_shade_loss(expected_fs, 0.2)
+ expected_loss = np.array([0.09289322, 0.13333333, 0.03019964])
+ assert np.allclose(vec_loss, expected_loss)