plot_agrivoltaics_ground_irradiance.py

"""
Agrivoltaic system modeling
===========================

Irradiance at crop level between rows
"""

# %%
# This example demonstrates how to calculate power output for a bifacial
# agriPV plant as well as calculating the irradiance at crop level
# using pvlib's infinite sheds model.
# For an overview of agrivPV concepts and performance, the reader
# is referred to :doi:`10.69766/XAEU5008`.
#
# This gallery example is based on an actual AgriPV plant, namely
# European Energy's `Flakkebjerg AgriPV site
# <https://europeanenergy.com/2023/12/20/using-the-same-land-twice-at-european-\
# energys-flakkebjerg-solar-park/>`_.
#
# The first steps are to define the plant location and to calculate solar
# position and clearsky irradiance for a single day as an example.
#
# .. figure:: ../../_images/agrivoltaics_system.jpg
#    :align: center
#    :width: 75%
#    :alt: Photo of an agriPV system
#
#    Photo of an agriPV system.
#    *Source: Adam R. Jensen*

import pvlib
import pandas as pd
from pvlib.tools import cosd
import matplotlib.pyplot as plt

# sphinx_gallery_thumbnail_path = '_images/agrivoltaics_system.jpg'

location = pvlib.location.Location(latitude=55, longitude=10)

times = pd.date_range('2020-06-28', periods=24*60, freq='1min', tz='UTC')

solpos = location.get_solarposition(times)

clearsky = location.get_clearsky(times, model='ineichen')

# %%
# Next, we need to define the plant layout:

height = 2.6  # [m] height of torque above ground
pitch = 12  # [m] row spacing
row_width = 2 * 2.384  # [m] two modules in portrait, each 2 m long
gcr = row_width / pitch  # ground coverage ratio [unitless]
axis_azimuth = 0  # [degrees] north-south tracking axis
max_angle = 55  # [degrees] maximum rotation angle

# %%
# Before running the infinite sheds model, we need to know the orientation
# of the trackers. For a single-axis tracker, this can be calculated as:

tracking_orientations = pvlib.tracking.singleaxis(
    apparent_zenith=solpos['apparent_zenith'],
    apparent_azimuth=solpos['azimuth'],
    axis_azimuth=axis_azimuth,
    max_angle=max_angle,
    backtrack=True,
    gcr=gcr,
)

# %%
# For agrivPV systems, the local albedo is dependent on crop growth and thus
# changes throughout the seasons. In this example, we only simulate one
# day and thus use a constant value. Similarly, we will assume a constant
# air temperature to avoid getting external data. Both albedo and air
# temperature could be defined as Series with the same index as used for the
# solar position calculations.

albedo = 0.20  # [unitless]
temp_air = 18  # [degrees C]

# %%
# Now, we are ready to calculate the front and rear-side irradiance using
# the pvlib infinite sheds model.

dni_extra = pvlib.irradiance.get_extra_radiation(times)

irradiance = pvlib.bifacial.infinite_sheds.get_irradiance(
    surface_tilt=tracking_orientations['surface_tilt'],
    surface_azimuth=tracking_orientations['surface_azimuth'],
    solar_zenith=solpos['apparent_zenith'],
    solar_azimuth=solpos['azimuth'],
    gcr=gcr,
    height=height,
    pitch=pitch,
    ghi=clearsky['ghi'],
    dhi=clearsky['dhi'],
    dni=clearsky['dni'],
    albedo=albedo,
    model='haydavies',
    dni_extra=dni_extra,
    bifaciality=0.7,  # [unitless] rear-side power relative to front-side
)

# %%
# Once the in-plane irradiance is known, we can estimate the PV array power.
# For simplicity, we use the PVWatts model:

N_modules = 1512  # [unitless] Number of modules
pdc0_per_module = 660  # [W] STC rating
pdc0 = pdc0_per_module * N_modules

gamma_pdc = -0.004  # [1/degrees C]

temp_cell = pvlib.temperature.faiman(
    poa_global=irradiance['poa_global'],
    temp_air=temp_air,
)

power_dc = pvlib.pvsystem.pvwatts_dc(
    g_poa_effective=irradiance['poa_global'],
    temp_cell=temp_cell,
    pdc0=pdc0,
    gamma_pdc=gamma_pdc)

power_dc.divide(1000).plot()
plt.ylabel('DC power [kW]')
plt.show()

# %%
# In addition to the power output of the PV array, we are also interested
# in how much irradiance reaches the crops under the array. In this case
# we calculate the average irradiance on the ground between two rows, using
# the infinite sheds utility functions.
#
# This consists of two parts. First we determine the diffuse irradiance on
# ground and second we calculate the fraction of the ground that is unshaded
# (i.e., receives DNI).

vf_ground_sky = pvlib.bifacial.utils.vf_ground_sky_2d_integ(
    surface_tilt=tracking_orientations['surface_tilt'],
    gcr=gcr,
    height=height,
    pitch=pitch,
)

unshaded_ground_fraction = pvlib.bifacial.utils._unshaded_ground_fraction(
    surface_tilt=tracking_orientations['surface_tilt'],
    surface_azimuth=tracking_orientations['surface_azimuth'],
    solar_zenith=solpos['apparent_zenith'],
    solar_azimuth=solpos['azimuth'],
    gcr=gcr,
)

crop_avg_irradiance = (unshaded_ground_fraction * clearsky['dni']
                       * cosd(solpos['apparent_zenith'])
                       + vf_ground_sky * clearsky['dhi'])

fig, ax = plt.subplots()
clearsky['ghi'].plot(ax=ax, label='Horizontal irradiance above panels')
crop_avg_irradiance.plot(ax=ax, label='Horizontal irradiance at crop level')
ax.legend(loc='upper center')
ax.set_ylabel('Irradiance [W/m$^2$]')
ax.set_ylim(-10, 1050)
plt.show()