Add simple turbine clustering functionality to SciPy yaw optimization (…

…#261)

* Add function to cluster turbines and add a yaw optimization class that is a wrapper around the regular YawOptimization class in yaw.py which clusters turbines and then optimizes their yaw angles sequentially. In simple test cases with 10-20 turbines, this cuts down the computation time by about 50% while sometimes also increasing accuracy due to better convergence.

* Update docstring in yaw_clustered.py

* Add optimization classes for WindRose and WindRoseParallel that include the clustering algorithm

* Update class names and dependent in clustered and parallelized yaw optimization in scipy

floris/tools/optimization/scipy/cluster_turbines.py

@@ -0,0 +1,187 @@
+# Copyright 2021 NREL
+
+# Licensed under the Apache License, Version 2.0 (the "License"); you may not
+# use this file except in compliance with the License. You may obtain a copy of
+# the License at http://www.apache.org/licenses/LICENSE-2.0
+
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
+# WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
+# License for the specific language governing permissions and limitations under
+# the License.
+
+# See https://floris.readthedocs.io for documentation
+
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+def cluster_turbines(fi, wind_direction=None, wake_slope=0.30, plot_lines=False):
+    """Separate a wind farm into separate clusters in which the turbines in
+    each subcluster only affects the turbines in its cluster and has zero
+    interaction with turbines from other clusters, both ways (being waked,
+    generating wake), This allows the user to separate the control setpoint
+    optimization in several lower-dimensional optimization problems, for
+    example. This function assumes a very simplified wake function where the
+    wakes are assumed to have a linearly diverging profile. In comparisons
+    with the FLORIS GCH model, the wake_slope matches well with the FLORIS'
+    wake profiles for a value of wake_slope = 0.5 * turbulence_intensity, where
+    turbulence_intensity is an input to the FLORIS model at the default
+    GCH parameterization. Note that does not include wind direction variability.
+    To be conservative, the user is recommended to use the rule of thumb:
+    `wake_slope = turbulence_intensity`. Hence, the default value for
+    `wake_slope=0.30` should be conservative for turbulence intensities up to
+    0.30 and is likely to provide valid estimates of which turbines are
+    downstream until a turbulence intensity of 0.50. This simple model saves
+    time compared to FLORIS.
+
+    Args:
+        fi ([floris object]): FLORIS object of the farm of interest.
+        wind_direction (float): The wind direction in the FLORIS frame
+        of reference for which the downstream turbines are to be determined.
+        wake_slope (float, optional): linear slope of the wake (dy/dx)
+        plot_lines (bool, optional): Enable plotting wakes/turbines.
+        Defaults to False.
+
+    Returns:
+        clusters (iterable): A list in which each entry contains a list
+        of turbine numbers that together form a cluster which
+        exclusively interact with one another and have zero
+        interaction with turbines outside of this cluster.
+    """
+
+    if wind_direction is None:
+        wind_direction = np.mean(fi.floris.farm.wind_direction)
+
+    # Get farm layout
+    x = fi.layout_x
+    y = fi.layout_y
+    D = np.array([t.rotor_diameter for t in fi.floris.farm.turbines])
+    n_turbs = len(x)
+
+    # Rotate farm and determine freestream/waked turbines
+    is_downstream = [False for _ in range(n_turbs)]
+    x_rot = (
+        np.cos((wind_direction - 270.0) * np.pi / 180.0) * x
+        - np.sin((wind_direction - 270.0) * np.pi / 180.0) * y
+    )
+    y_rot = (
+        np.sin((wind_direction - 270.0) * np.pi / 180.0) * x
+        + np.cos((wind_direction - 270.0) * np.pi / 180.0) * y
+    )
+
+    if plot_lines:
+        fig, ax = plt.subplots()
+        for ii in range(n_turbs):
+            ax.plot(
+                x_rot[ii] * np.ones(2),
+                [y_rot[ii] - D[ii] / 2, y_rot[ii] + D[ii] / 2],
+                "k",
+            )
+        for ii in range(n_turbs):
+            ax.text(x_rot[ii], y_rot[ii], "T%03d" % ii)
+        ax.axis("equal")
+
+    srt = np.argsort(x_rot)
+    usrt = np.argsort(srt)
+    x_rot_srt = x_rot[srt]
+    y_rot_srt = y_rot[srt]
+    affected_by_turbs = np.tile(False, (n_turbs, n_turbs))
+    for ii in range(n_turbs):
+        x0 = x_rot_srt[ii]
+        y0 = y_rot_srt[ii]
+
+        def wake_profile_ub_turbii(x):
+            y = (y0 + D[ii]) + (x - x0) * wake_slope
+            if isinstance(y, (float, np.float64, np.float32)):
+                if x < (x0 + 0.01):
+                    y = -np.Inf
+            else:
+                y[x < x0 + 0.01] = -np.Inf
+            return y
+
+        def wake_profile_lb_turbii(x):
+            y = (y0 - D[ii]) - (x - x0) * wake_slope
+            if isinstance(y, (float, np.float64, np.float32)):
+                if x < (x0 + 0.01):
+                    y = -np.Inf
+            else:
+                y[x < x0 + 0.01] = -np.Inf
+            return y
+
+        def determine_if_in_wake(xt, yt):
+            return (yt < wake_profile_ub_turbii(xt)) & (yt > wake_profile_lb_turbii(xt))
+
+        # Get most downstream turbine
+        is_downstream[ii] = not any(
+            [
+                determine_if_in_wake(x_rot_srt[iii], y_rot_srt[iii])
+                for iii in range(n_turbs)
+            ]
+        )
+        # Determine which turbines are affected by this turbine ('ii')
+        affecting_following_turbs = [
+                determine_if_in_wake(x_rot_srt[iii], y_rot_srt[iii])
+                for iii in range(n_turbs)
+        ]
+
+        # Determine by which turbines this turbine ('ii') is affected
+        for aft in np.where(affecting_following_turbs)[0]:
+            affected_by_turbs[aft, ii] = True
+
+        if plot_lines:
+            x1 = np.max(x_rot_srt) + 500.0
+            ax.fill_between(
+                [x0, x1, x1, x0],
+                [
+                    wake_profile_ub_turbii(x0 + 0.02),
+                    wake_profile_ub_turbii(x1),
+                    wake_profile_lb_turbii(x1),
+                    wake_profile_lb_turbii(x0 + 0.02),
+                ],
+                alpha=0.1,
+                color="k",
+                edgecolor=None,
+            )
+
+    # Rearrange into initial frame of reference
+    affected_by_turbs = affected_by_turbs[:, usrt][usrt, :]
+    for ii in range(n_turbs):
+        affected_by_turbs[ii, ii] = True  # Add self to turb_list_affected
+    affected_by_turbs = [np.where(c)[0] for c in affected_by_turbs]
+
+    # List of downstream turbines
+    turbs_downstream = [is_downstream[i] for i in usrt]
+    turbs_downstream = list(np.where(turbs_downstream)[0])
+
+    # Initialize one cluster for each turbine and all the turbines its affected by
+    clusters = affected_by_turbs
+
+    # Iteratively merge clusters if any overlap between turbines
+    ci = 0
+    while ci < len(clusters):
+        # Compare current row to the ones to the right of it
+        cj = ci + 1
+        merged_column = False
+        while cj < len(clusters):
+            if any([y in clusters[ci] for y in clusters[cj]]):
+                # Merge
+                clusters[ci] = np.hstack([clusters[ci], clusters[cj]])
+                clusters[ci] = np.array(np.unique(clusters[ci]), dtype=int)
+                clusters.pop(cj)
+                merged_column = True
+            else:
+                cj = cj + 1
+        if not merged_column:
+            ci = ci + 1
+
+    if plot_lines:
+        ax.set_title("wind_direction = %.1f deg" % wind_direction)
+        ax.set_xlim([np.min(x_rot) - 500.0, x1])
+        ax.set_ylim([np.min(y_rot) - 500.0, np.max(y_rot) + 500.0])
+        for ci, cl in enumerate(clusters):
+            ax.plot(x_rot[cl], y_rot[cl], 'o', label='cluster %d' % ci)
+        ax.legend()
+
+    return clusters