[Reviewed] PV horizontal tracking

RELEASE_NOTES.rst

@@ -13,7 +13,7 @@ Upcoming Release
 ================
 
 * With this release, we change the license from copyleft GPLv3 to the more liberal MIT license with the consent of all major contributors `#263 <https://github.com/PyPSA/atlite/pull/263>`_.
-* Added 1-axis vertical and 2-axis tracking option for solar pv and trigon_model = "simple"
+* Added 1-axis horizontal, 1-axis tilted horizontal, 1-axis vertical, and 2-axis tracking options for solar PV; e.g. ``cutout.pv(tracking='horizontal')``.
 * Added small documentation for get_windturbineconfig
 * The deprecated functions `grid_cells` and `grid_coordinates` were removed.
 * Feature: Cutouts are now compressed differently during the `.prepare(...)` step using the native compression feature of netCDF files.

atlite/convert.py

@@ -560,8 +560,10 @@ def pv(cutout, panel, orientation, tracking=None, clearsky_model=None, **params)
         'atlite.pv.orientation.make_*' functions.
     tracking : None or str:
         None for no tracking, default
+        'horizontal' for 1-axis horizontal tracking
+        'tilted_horizontal' for 1-axis horizontal tracking with tilted axis
         'vertical' for 1-axis vertical tracking
-        'vh' for 2-axis tracking
+        'dual' for 2-axis tracking
     clearsky_model : str or None
         Either the 'simple' or the 'enhanced' Reindl clearsky
         model. The default choice of None will choose dependending on

atlite/pv/irradiation.py

@@ -180,9 +180,9 @@ def clip(influx, influx_max):
         )
     if trigon_model == "simple":
         k = surface_orientation["cosincidence"] / sin(solar_position["altitude"])
-        if tracking != "vh":
+        if tracking != "dual":
             cos_surface_slope = cos(surface_orientation["slope"])
-        elif tracking == "vh":
+        elif tracking == "dual":
             cos_surface_slope = sin(solar_position["altitude"])
 
         influx = direct + diffuse

atlite/pv/orientation.py

@@ -97,6 +97,9 @@ def SurfaceOrientation(ds, solar_position, orientation, tracking=None):
     ----------
     [1] Sproul, A. B., Derivation of the solar geometric relationships using
     vector analysis, Renewable Energy, 32(7), 1187–1205 (2007).
+    [2] Marion, William F., and Aron P. Dobos. Rotation angle for the optimum
+    tracking of one-axis trackers. No. NREL/TP-6A20-58891. National Renewable
+    Energy Lab.(NREL), Golden, CO (United States), 2013.
     """
     lon = deg2rad(ds["lon"])
     lat = deg2rad(ds["lat"])
@@ -112,16 +115,73 @@ def SurfaceOrientation(ds, solar_position, orientation, tracking=None):
         cosincidence = sin(surface_slope) * cos(sun_altitude) * cos(
             surface_azimuth - sun_azimuth
         ) + cos(surface_slope) * sin(sun_altitude)
+
+    elif tracking == "horizontal":  # horizontal tracking with horizontal axis
+        axis_azimuth = orientation[
+            "azimuth"
+        ]  # here orientation['azimuth'] refers to the azimuth of the tracker axis.
+        rotation = np.arctan(
+            (cos(sun_altitude) / sin(sun_altitude)) * sin(sun_azimuth - axis_azimuth)
+        )
+        surface_slope = abs(rotation)
+        surface_azimuth = axis_azimuth + np.arcsin(
+            sin(rotation / sin(surface_slope))
+        )  # the 2nd part yields +/-1 and determines if the panel is facing east or west
+        cosincidence = cos(surface_slope) * sin(sun_altitude) + sin(
+            surface_slope
+        ) * cos(sun_altitude) * cos(sun_azimuth - surface_azimuth)
+
+    elif tracking == "tilted_horizontal":  # horizontal tracking with tilted axis'
+        axis_tilt = orientation[
+            "slope"
+        ]  # here orientation['slope'] refers to the tilt of the tracker axis.
+
+        rotation = np.arctan(
+            (cos(sun_altitude) * sin(sun_azimuth - surface_azimuth))
+            / (
+                cos(sun_altitude) * cos(sun_azimuth - surface_azimuth) * sin(axis_tilt)
+                + sin(sun_altitude) * cos(axis_tilt)
+            )
+        )
+
+        surface_slope = np.arccos(cos(rotation) * cos(axis_tilt))
+
+        azimuth_difference = sun_azimuth - surface_azimuth
+        azimuth_difference = np.where(
+            azimuth_difference > pi, 2 * pi - azimuth_difference, azimuth_difference
+        )
+        azimuth_difference = np.where(
+            azimuth_difference < -pi, 2 * pi + azimuth_difference, azimuth_difference
+        )
+        rotation = np.where(
+            np.logical_and(rotation < 0, azimuth_difference > 0),
+            rotation + pi,
+            rotation,
+        )
+        rotation = np.where(
+            np.logical_and(rotation > 0, azimuth_difference < 0),
+            rotation - pi,
+            rotation,
+        )
+
+        cosincidence = cos(rotation) * (
+            sin(axis_tilt) * cos(sun_altitude) * cos(sun_azimuth - surface_azimuth)
+            + cos(axis_tilt) * sin(sun_altitude)
+        ) + sin(rotation) * cos(sun_altitude) * sin(sun_azimuth - surface_azimuth)
+
     elif tracking == "vertical":  # vertical tracking, surface azimuth = sun_azimuth
         cosincidence = sin(surface_slope) * cos(sun_altitude) + cos(
             surface_slope
         ) * sin(sun_altitude)
-    elif tracking == "vh":  # both vertical and horizontal tracking
+    elif tracking == "dual":  # both vertical and horizontal tracking
         cosincidence = np.float64(1.0)
     else:
-        assert (
-            False
-        ), "Values describing tracking system must be None for no tracking, 'vertical' for 1-axis vertical tracking, or 'vh' for 2-axis tracking"
+        assert False, (
+            "Values describing tracking system must be None for no tracking,"
+            + "'horizontal' for 1-axis horizontal tracking,"
+            + "tilted_horizontal' for 1-axis horizontal tracking of tilted panle,"
+            + "vertical' for 1-axis vertical tracking, or 'dual' for 2-axis tracking"
+        )
 
     # fixup incidence angle: if the panel is badly oriented and the sun shines
     # on the back of the panel (incidence angle > 90degree), the irradiation

doc/index.rst

@@ -111,6 +111,8 @@ If you would like to cite the Atlite software, please refer to `this paper <http
    examples/using_gebco_heightmap.ipynb
    examples/plotting_with_atlite.ipynb
    examples/logfiles_and_messages.ipynb
+   examples/solarpv_tracking_options.ipynb
+   examples/working-with-csp.ipynb
    examples/more_examples.rst
 
 .. toctree::