Martinez shading factor

docs/examples/shading/plot_martinez_shade_loss.py

@@ -0,0 +1,276 @@
+"""
+Modelling shading losses in modules with bypass diodes
+======================================================
+"""
+
+# %%
+# This example illustrates how to use the model proposed by Martinez et al.
+# [1]_. The model proposes a power output losses factor by adjusting
+# the incident direct and circumsolar beam irradiance fraction of a PV module
+# based on the number of shaded *blocks*. A *block* is defined as a group of
+# cells protected by a bypass diode. More information on *blocks* can be found
+# in the original paper [1]_ and in the
+# :py:func:`pvlib.shading.direct_martinez` documentation.
+#
+# The following key functions are used in this example:
+#
+# 1. :py:func:`pvlib.shading.direct_martinez` to calculate the power output
+#    losses fraction due to shading.
+# 2. :py:func:`pvlib.shading.shaded_fraction1d` to calculate the fraction of
+#    shaded surface and consequently the number of shaded *blocks* due to
+#    row-to-row shading.
+# 3. :py:func:`pvlib.tracking.singleaxis` to calculate the rotation angle of
+#    the trackers.
+#
+# .. sectionauthor:: Echedey Luis <echelual (at) gmail.com>
+#
+# Problem description
+# -------------------
+# Let's consider a PV system with the following characteristics:
+#
+# - Two north-south single-axis trackers, each one having 6 modules.
+# - The rows have the same true-tracking tilt angles. True tracking
+#   is chosen in this example, so shading is significant.
+# - Terrain slope is 7 degrees downward to the east.
+# - Rows' axes are horizontal.
+# - The modules are comprised of multiple cells. We will compare these cases:
+#    - modules with one bypass diode
+#    - modules with three bypass diodes
+#    - half-cut cell modules with three bypass diodes on portrait and landscape
+#
+# Setting up the system
+# ----------------------
+# Let's start by defining the system characteristics, location and the time
+# range for the analysis.
+
+import pvlib
+import pandas as pd
+import numpy as np
+import matplotlib.pyplot as plt
+from matplotlib.dates import ConciseDateFormatter
+
+pitch = 4  # meters
+width = 1.5  # meters
+gcr = width / pitch  # ground coverage ratio
+N_modules_per_row = 6
+axis_azimuth = 180  # N-S axis
+axis_tilt = 0  # flat because the axis is perpendicular to the slope
+cross_axis_tilt = -7  # 7 degrees downward to the east
+
+latitude, longitude = 40.2712, -3.7277
+locus = pvlib.location.Location(
+    latitude,
+    longitude,
+    tz="Europe/Madrid",
+    altitude=pvlib.location.lookup_altitude(latitude, longitude),
+)
+
+times = pd.date_range("2001-04-11T04", "2001-04-11T20", freq="10min")
+
+# %%
+# True-tracking algorithm and shaded fraction
+# -------------------------------------------
+# Since this model is about row-to-row shading, we will use the true-tracking
+# algorithm to calculate the trackers rotation. Back-tracking reduces the
+# shading between rows, but since this example is about shading, we will not
+# use it.
+#
+# Then, the next step is to calculate the fraction of shaded surface. This is
+# done using :py:func:`pvlib.shading.shaded_fraction1d`. Using this function is
+# straightforward with the variables we already have defined.
+# Then, we can calculate the number of shaded blocks by rounding up the shaded
+# fraction by the number of blocks along the shaded length.
+
+# Calculate solar position to get single-axis tracker rotation and irradiance
+solar_pos = locus.get_solarposition(times)
+solar_apparent_zenith, solar_azimuth = (
+    solar_pos["apparent_zenith"],
+    solar_pos["azimuth"],
+)  # unpack for better readability
+
+tracking_result = pvlib.tracking.singleaxis(
+    apparent_zenith=solar_apparent_zenith,
+    apparent_azimuth=solar_azimuth,
+    axis_tilt=axis_tilt,
+    axis_azimuth=axis_azimuth,
+    max_angle=(-90 + cross_axis_tilt, 90 + cross_axis_tilt),  # (min, max)
+    backtrack=False,
+    gcr=gcr,
+    cross_axis_tilt=cross_axis_tilt,
+)
+
+tracker_theta, aoi, surface_tilt, surface_azimuth = (
+    tracking_result["tracker_theta"],
+    tracking_result["aoi"],
+    tracking_result["surface_tilt"],
+    tracking_result["surface_azimuth"],
+)  # unpack for better readability
+
+# Calculate the shade fraction
+shaded_fraction = pvlib.shading.shaded_fraction1d(
+    solar_apparent_zenith,
+    solar_azimuth,
+    axis_azimuth,
+    axis_tilt=axis_tilt,
+    shaded_row_rotation=tracker_theta,
+    shading_row_rotation=tracker_theta,
+    collector_width=width,
+    pitch=pitch,
+    cross_axis_slope=cross_axis_tilt,
+)
+
+# %%
+# Number of shaded blocks
+# -----------------------
+# The number of shaded blocks depends on the module configuration and number
+# of bypass diodes. For example,
+# modules with one bypass diode will behave like one block.
+# On the other hand, modules with three bypass diodes will have three blocks,
+# except for the half-cut cell modules, which will have six blocks; 2x3 blocks
+# where the two rows are along the longest side of the module.
+# We can argue that the dimensions of the system change when you switch from
+# portrait to landscape, but for this example, we will consider it the same.
+#
+# The number of shaded blocks is calculated by rounding up the shaded fraction
+# by the number of blocks along the shaded length. So let's define the number
+# of blocks for each module configuration:
+#
+# - 1 bypass diode: 1 block
+# - 3 bypass diodes: 3 blocks in landscape; 1 in portrait
+# - 3 bypass diodes half-cut cells:
+#   - 2 blocks in portrait
+#   - 3 blocks in landscape
+#
+# .. figure:: ../../_images/PV_module_layout_cesardd.jpg
+#    :align: center
+#    :width: 75%
+#    :alt: Normal and half-cut cells module layouts
+#
+#    Left: common module layout. Right: half-cut cells module layout.
+#    Each module has three bypass diodes. On the left, they connect cell
+#    columns 1-2, 2-3 & 3-4. On the right, they connect cell columns 1-2, 3-4 &
+#    5-6.
+#    *Source: César Domínguez. CC BY-SA 4.0, Wikimedia Commons*
+#
+# In the image above, each orange U-shaped string section is a block.
+# By symmetry, the yellow inverted-U's of the subcircuit are also blocks.
+# For this reason, the half-cut cell modules have 6 blocks in total: two along
+# the longest side and three along the shortest side.
+
+blocks_per_module = {
+    "1 bypass diode": 1,
+    "3 bypass diodes": 3,
+    "3 bypass diodes half-cut, portrait": 2,
+    "3 bypass diodes half-cut, landscape": 3,
+}
+
+# Calculate the number of shaded blocks during the day
+shaded_blocks_per_module = {
+    k: np.ceil(blocks_N * shaded_fraction)
+    for k, blocks_N in blocks_per_module.items()
+}
+
+# %%
+# Plane of array irradiance example data
+# --------------------------------------
+# To calculate the power output losses due to shading, we need the plane of
+# array irradiance. For this example, we will use synthetic data:
+
+clearsky = locus.get_clearsky(
+    times, solar_position=solar_pos, model="ineichen"
+)
+dhi, dni = (
+    clearsky["dhi"],
+    clearsky["dni"],
+)
+dni_extra = pvlib.irradiance.get_extra_radiation(times)
+airmass = pvlib.atmosphere.get_relative_airmass(solar_apparent_zenith)
+sky_diffuse = pvlib.irradiance.perez_driesse(
+    surface_tilt, surface_azimuth, dhi, dni,
+    solar_apparent_zenith, solar_azimuth, dni_extra, airmass,
+)  # fmt: skip
+poa_components = pvlib.irradiance.poa_components(
+    aoi, dni, sky_diffuse, poa_ground_diffuse=0
+)  # ignore ground diffuse for brevity
+poa_global, poa_direct = (
+    poa_components["poa_global"],
+    poa_components["poa_direct"],
+)
+
+# %%
+# Results
+# -------
+# Now that we have the number of shaded blocks for each module configuration,
+# we can apply the model and estimate the power loss due to shading.
+#
+# Note that this model is not linear with the shaded blocks ratio, so there is
+# a difference between applying it to just a module or a whole row.
+
+shade_losses_per_module = {
+    k: pvlib.shading.direct_martinez(
+        poa_global=poa_global,
+        poa_direct=poa_direct,
+        shaded_fraction=shaded_fraction,
+        shaded_blocks=module_shaded_blocks,
+        total_blocks=blocks_per_module[k],
+    )
+    for k, module_shaded_blocks in shaded_blocks_per_module.items()
+}
+
+shade_losses_per_row = {
+    k: pvlib.shading.direct_martinez(
+        poa_global=poa_global,
+        poa_direct=poa_direct,
+        shaded_fraction=shaded_fraction,
+        shaded_blocks=module_shaded_blocks * N_modules_per_row,
+        total_blocks=blocks_per_module[k] * N_modules_per_row,
+    )
+    for k, module_shaded_blocks in shaded_blocks_per_module.items()
+}
+
+# %%
+# Plotting the results
+# ^^^^^^^^^^^^^^^^^^^^
+
+fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True)
+fig.suptitle("Martinez power losses due to shading")
+for k, shade_losses in shade_losses_per_module.items():
+    linestyle = "--" if k == "3 bypass diodes half-cut, landscape" else "-"
+    ax1.plot(times, shade_losses, label=k, linestyle=linestyle)
+ax1.legend(loc="upper center")
+ax1.grid()
+ax1.set_xlabel("Time")
+ax1.xaxis.set_major_formatter(
+    ConciseDateFormatter("%H:%M", tz="Europe/Madrid")
+)
+ax1.set_ylabel(r"$P_{out}$ losses")
+ax1.set_title("Per module")
+
+for k, shade_losses in shade_losses_per_row.items():
+    linestyle = "--" if k == "3 bypass diodes half-cut, landscape" else "-"
+    ax2.plot(times, shade_losses, label=k, linestyle=linestyle)
+ax2.legend(loc="upper center")
+ax2.grid()
+ax2.set_xlabel("Time")
+ax2.xaxis.set_major_formatter(
+    ConciseDateFormatter("%H:%M", tz="Europe/Madrid")
+)
+ax2.set_ylabel(r"$P_{out}$ losses")
+ax2.set_title("Per row")
+fig.tight_layout()
+fig.show()
+
+# %%
+# Note how the half-cut cell module in portrait performs better than the
+# normal module with three bypass diodes. This is because the number of shaded
+# blocks is less along the shaded length is higher in the half-cut module.
+# This is the reason why half-cut cell modules are preferred in portrait
+# orientation.
+
+# %%
+# References
+# ----------
+# .. [1] F. Martínez-Moreno, J. Muñoz, and E. Lorenzo, 'Experimental model
+#    to estimate shading losses on PV arrays', Solar Energy Materials and
+#    Solar Cells, vol. 94, no. 12, pp. 2298-2303, Dec. 2010,
+#    :doi:`10.1016/j.solmat.2010.07.029`.

docs/sphinx/source/reference/effects_on_pv_system_output/shading.rst

@@ -12,4 +12,4 @@ Shading
    shading.sky_diffuse_passias
    shading.projected_solar_zenith_angle
    shading.shaded_fraction1d
-
+   shading.direct_martinez

docs/sphinx/source/whatsnew/v0.11.0.rst

@@ -45,6 +45,9 @@ Enhancements
 * Added extraterrestrial and direct spectra of the ASTM G173-03 standard with
   the new function :py:func:`pvlib.spectrum.get_reference_spectra`.
   (:issue:`1963`, :pull:`2039`)
+* Added function :py:func:`pvlib.shading.direct_martinez` to calculate
+  shading losses by taking into account the amount of bypass diodes of a module.
+  (:issue:`2063`, :pull:`2070`)
 
 Bug fixes
 ~~~~~~~~~