|
| 1 | +""" |
| 2 | +Agrivoltaic system modeling |
| 3 | +=========================== |
| 4 | +
|
| 5 | +Irradiance at crop level between rows |
| 6 | +""" |
| 7 | + |
| 8 | +# %% |
| 9 | +# This example demonstrates how to calculate power output for a bifacial |
| 10 | +# agriPV plant as well as calculating the irradiance at crop level |
| 11 | +# using pvlib's infinite sheds model. |
| 12 | +# For an overview of agrivPV concepts and performance, the reader |
| 13 | +# is referred to :doi:`10.69766/XAEU5008`. |
| 14 | +# |
| 15 | +# This gallery example is based on an actual AgriPV plant, namely |
| 16 | +# European Energy's `Flakkebjerg AgriPV site |
| 17 | +# <https://europeanenergy.com/2023/12/20/using-the-same-land-twice-at-european-\ |
| 18 | +# energys-flakkebjerg-solar-park/>`_. |
| 19 | +# |
| 20 | +# The first steps are to define the plant location and to calculate solar |
| 21 | +# position and clearsky irradiance for a single day as an example. |
| 22 | +# |
| 23 | +# .. figure:: ../../_images/agrivoltaics_system.jpg |
| 24 | +# :align: center |
| 25 | +# :width: 75% |
| 26 | +# :alt: Photo of an agriPV system |
| 27 | +# |
| 28 | +# Photo of an agriPV system. |
| 29 | +# *Source: Adam R. Jensen* |
| 30 | + |
| 31 | +import pvlib |
| 32 | +import pandas as pd |
| 33 | +from pvlib.tools import cosd |
| 34 | +import matplotlib.pyplot as plt |
| 35 | + |
| 36 | +# sphinx_gallery_thumbnail_path = '_images/agrivoltaics_system.jpg' |
| 37 | + |
| 38 | +location = pvlib.location.Location(latitude=55, longitude=10) |
| 39 | + |
| 40 | +times = pd.date_range('2020-06-28', periods=24*60, freq='1min', tz='UTC') |
| 41 | + |
| 42 | +solpos = location.get_solarposition(times) |
| 43 | + |
| 44 | +clearsky = location.get_clearsky(times, model='ineichen') |
| 45 | + |
| 46 | +# %% |
| 47 | +# Next, we need to define the plant layout: |
| 48 | + |
| 49 | +height = 2.6 # [m] height of torque above ground |
| 50 | +pitch = 12 # [m] row spacing |
| 51 | +row_width = 2 * 2.384 # [m] two modules in portrait, each 2 m long |
| 52 | +gcr = row_width / pitch # ground coverage ratio [unitless] |
| 53 | +axis_azimuth = 0 # [degrees] north-south tracking axis |
| 54 | +max_angle = 55 # [degrees] maximum rotation angle |
| 55 | + |
| 56 | +# %% |
| 57 | +# Before running the infinite sheds model, we need to know the orientation |
| 58 | +# of the trackers. For a single-axis tracker, this can be calculated as: |
| 59 | + |
| 60 | +tracking_orientations = pvlib.tracking.singleaxis( |
| 61 | + apparent_zenith=solpos['apparent_zenith'], |
| 62 | + solar_azimuth=solpos['azimuth'], |
| 63 | + axis_azimuth=axis_azimuth, |
| 64 | + max_angle=max_angle, |
| 65 | + backtrack=True, |
| 66 | + gcr=gcr, |
| 67 | +) |
| 68 | + |
| 69 | +# %% |
| 70 | +# For agrivPV systems, the local albedo is dependent on crop growth and thus |
| 71 | +# changes throughout the seasons. In this example, we only simulate one |
| 72 | +# day and thus use a constant value. Similarly, we will assume a constant |
| 73 | +# air temperature to avoid getting external data. Both albedo and air |
| 74 | +# temperature could be defined as Series with the same index as used for the |
| 75 | +# solar position calculations. |
| 76 | + |
| 77 | +albedo = 0.20 # [unitless] |
| 78 | +temp_air = 18 # [degrees C] |
| 79 | + |
| 80 | +# %% |
| 81 | +# Now, we are ready to calculate the front and rear-side irradiance using |
| 82 | +# the pvlib infinite sheds model. |
| 83 | + |
| 84 | +dni_extra = pvlib.irradiance.get_extra_radiation(times) |
| 85 | + |
| 86 | +irradiance = pvlib.bifacial.infinite_sheds.get_irradiance( |
| 87 | + surface_tilt=tracking_orientations['surface_tilt'], |
| 88 | + surface_azimuth=tracking_orientations['surface_azimuth'], |
| 89 | + solar_zenith=solpos['apparent_zenith'], |
| 90 | + solar_azimuth=solpos['azimuth'], |
| 91 | + gcr=gcr, |
| 92 | + height=height, |
| 93 | + pitch=pitch, |
| 94 | + ghi=clearsky['ghi'], |
| 95 | + dhi=clearsky['dhi'], |
| 96 | + dni=clearsky['dni'], |
| 97 | + albedo=albedo, |
| 98 | + model='haydavies', |
| 99 | + dni_extra=dni_extra, |
| 100 | + bifaciality=0.7, # [unitless] rear-side power relative to front-side |
| 101 | +) |
| 102 | + |
| 103 | +# %% |
| 104 | +# Once the in-plane irradiance is known, we can estimate the PV array power. |
| 105 | +# For simplicity, we use the PVWatts model: |
| 106 | + |
| 107 | +N_modules = 1512 # [unitless] Number of modules |
| 108 | +pdc0_per_module = 660 # [W] STC rating |
| 109 | +pdc0 = pdc0_per_module * N_modules |
| 110 | + |
| 111 | +gamma_pdc = -0.004 # [1/degrees C] |
| 112 | + |
| 113 | +temp_cell = pvlib.temperature.faiman( |
| 114 | + poa_global=irradiance['poa_global'], |
| 115 | + temp_air=temp_air, |
| 116 | +) |
| 117 | + |
| 118 | +power_dc = pvlib.pvsystem.pvwatts_dc( |
| 119 | + effective_irradiance=irradiance['poa_global'], |
| 120 | + temp_cell=temp_cell, |
| 121 | + pdc0=pdc0, |
| 122 | + gamma_pdc=gamma_pdc) |
| 123 | + |
| 124 | +power_dc.divide(1000).plot() |
| 125 | +plt.ylabel('DC power [kW]') |
| 126 | +plt.show() |
| 127 | + |
| 128 | +# %% |
| 129 | +# In addition to the power output of the PV array, we are also interested |
| 130 | +# in how much irradiance reaches the crops under the array. In this case |
| 131 | +# we calculate the average irradiance on the ground between two rows, using |
| 132 | +# the infinite sheds utility functions. |
| 133 | +# |
| 134 | +# This consists of two parts. First we determine the diffuse irradiance on |
| 135 | +# ground and second we calculate the fraction of the ground that is unshaded |
| 136 | +# (i.e., receives DNI). |
| 137 | + |
| 138 | +vf_ground_sky = pvlib.bifacial.utils.vf_ground_sky_2d_integ( |
| 139 | + surface_tilt=tracking_orientations['surface_tilt'], |
| 140 | + gcr=gcr, |
| 141 | + height=height, |
| 142 | + pitch=pitch, |
| 143 | +) |
| 144 | + |
| 145 | +unshaded_ground_fraction = pvlib.bifacial.utils._unshaded_ground_fraction( |
| 146 | + surface_tilt=tracking_orientations['surface_tilt'], |
| 147 | + surface_azimuth=tracking_orientations['surface_azimuth'], |
| 148 | + solar_zenith=solpos['apparent_zenith'], |
| 149 | + solar_azimuth=solpos['azimuth'], |
| 150 | + gcr=gcr, |
| 151 | +) |
| 152 | + |
| 153 | +crop_avg_irradiance = (unshaded_ground_fraction * clearsky['dni'] |
| 154 | + * cosd(solpos['apparent_zenith']) |
| 155 | + + vf_ground_sky * clearsky['dhi']) |
| 156 | + |
| 157 | +fig, ax = plt.subplots() |
| 158 | +clearsky['ghi'].plot(ax=ax, label='Horizontal irradiance above panels') |
| 159 | +crop_avg_irradiance.plot(ax=ax, label='Horizontal irradiance at crop level') |
| 160 | +ax.legend(loc='upper center') |
| 161 | +ax.set_ylabel('Irradiance [W/m$^2$]') |
| 162 | +ax.set_ylim(-10, 1050) |
| 163 | +plt.show() |
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