Floating PV gallery example

docs/examples/floating-pv/README.rst

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+Floating PV Systems Modelling
+-----------------------------

docs/examples/floating-pv/plot_floating_pv_cell_temperature.py

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+r"""
+Calculating the cell temperature for floating PV
+================================================
+
+This example demonstrates how to calculate the cell temperature for
+floating photovoltaic (FPV) systems using the PVSyst temperature model.
+
+One of the primary benefits attributed to FPV systems
+is lower operating temperatures, which are expected to increase the
+operating efficiency. In general, the temperature at which a photovoltaic
+module operates is influenced by various factors including solar radiation,
+ambient temperature, wind speed and direction, and the characteristics of the
+cell and module materials, as well as the mounting structure. Both radiative
+and convective heat transfers play roles in determining the module's
+temperature.
+
+A popular model for calculating the PV cell temperature is the
+empirical heat loss factor model suggested by Faiman. A modified version of
+this model is implemented in PVSyst
+(:py:func:`~pvlib.temperature.pvsyst_cell`). The PVSyst model for cell
+temperature :math:`T_{C}` is given by
+
+.. math::
+ :label: pvsyst
+
+ T_{C} = T_{a} + \frac{\alpha \cdot E \cdot (1 - \eta_{m})}{U_{c} + U_{v} \cdot WS}
+
+Where :math:`E` is the plane-of-array irradiance, :math:`T_{a}` is the
+ambient air temperature, :math:`WS` is the wind speed, :math:`\alpha` is the
+absorbed fraction of the incident irradiance, :math:`\eta_{m}` is the
+electrical efficiency of the module, :math:`U_{c}` is the wind-idependent heat
+loss coefficient, and :math:`U_{v}` is the wind-dependent heat loss coefficient.
+
+However, the default heat loss coefficient values of this model were
+specified for land-based PV systems and are not necessarily representative
+for FPV systems.
+
+In FPV systems, variations in heat loss coefficients are considerable, not
+only due to differences in design but also because of geographic factors.
+Systems with extensive water surfaces, closely packed modules, and restricted
+airflow behind the modules generally exhibit lower heat loss coefficients
+compared to those with smaller water surfaces and better airflow behind the
+modules.
+
+For FPV systems installed over water without direct contact, the module's
+operating temperature, much like in land-based systems, is mainly influenced
+by the mounting structure (which significantly affects the U-value), wind,
+and air temperature. Thus, factors that help reduce operating temperatures in
+such systems include lower air temperatures and changes in air flow beneath
+the modules (wind/convection). In some designs where the modules are in
+direct thermal contact with water, cooling effectiveness is largely dictated
+by the water temperature.
+
+The table below gives heat loss coefficients derrived for different systems
+and locations as found in the literature. In this example, the FPV cell
+temperature will be calculated using some of the coefficients below.
+
++-------------------------+-------------+--------------------------------+----------------------------------------+-----------+
+| System | Location |:math:`U_{c}` | :math:`U_{v}` | Reference |
+| | |:math:`[\frac{W}{m^2 \cdot K}]` | :math:`[\frac{W}{m^3 \cdot K \cdot s}]`| |
++=========================+=============+================================+========================================+===========+
+| Monofacial module, | Netherlands | 24.4 | 6.5 | [1]_ |
+| open structure, | | | | |
+| two-axis tracking, | | | | |
+| small water footprint | | | | |
++-------------------------+-------------+--------------------------------+----------------------------------------+-----------+
+| Monofacial module, | Netherlands | 25.2 | 3.7 | [1]_ |
+| closed structure, | | | | |
+| large water footprint | | | | |
++-------------------------+-------------+--------------------------------+----------------------------------------+-----------+
+| Monofacial module, | Singapore | 34.8 | 0.8 | [1]_ |
+| closed structure, | | | | |
+| large water footprint | | | | |
++-------------------------+-------------+--------------------------------+----------------------------------------+-----------+
+| Monofacial module, | Singapore | 18.9 | 8.9 | [1]_ |
+| closed stucuture, | | | | |
+| medium water footprint | | | | |
++-------------------------+-------------+--------------------------------+----------------------------------------+-----------+
+| Monofacial module, | Singapore | 35.3 | 8.9 | [1]_ |
+| open strucuture, | | | | |
+| free-standing | | | | |
++-------------------------+-------------+--------------------------------+----------------------------------------+-----------+
+| Monofacial module, | Norway | 86.5 | 0 | [2]_ |
+| in contact with | | | | |
+| water | | | | |
++-------------------------+-------------+--------------------------------+----------------------------------------+-----------+
+| Monofacial module, | South Italy | 31.9 | 1.5 | [3]_ |
+| open structure, | | | | |
+| free-standing | | | | |
++-------------------------+-------------+--------------------------------+----------------------------------------+-----------+
+| Bifacial module, | South Italy | 35.2 | 1.5 | [3]_ |
+| open structure, | | | | |
+| free-standing | | | | |
++-------------------------+-------------+--------------------------------+----------------------------------------+-----------+
+
+References
+----------
+.. [1] Dörenkämper M., Wahed A., Kumar A., de Jong M., Kroon J., Reindl T.
+ (2021), 'The cooling effect of floating PV in two different climate zones:
+ A comparison of field test data from the Netherlands and Singapore'
+ Solar Energy, vol. 214, pp. 239-247, :doi:`10.1016/j.solener.2020.11.029`.
+
+.. [2] Kjeldstad T., Lindholm D., Marstein E., Selj J. (2021), 'Cooling of
+ floating photovoltaics and the importance of water temperature', Solar
+ Energy, vol. 218, pp. 544-551, :doi:`10.1016/j.solener.2021.03.022`.
+
+.. [3] Tina G.M., Scavo F.B., Merlo L., Bizzarri F. (2021), 'Comparative
+ analysis of monofacial and bifacial photovoltaic modules for floating
+ power plants', Applied Energy, vol 281, pp. 116084,
+ :doi:`10.1016/j.apenergy.2020.116084`.
+""" # noqa: E501
+
+# %%
+# Read example weather data
+# ^^^^^^^^^^^^^^^^^^^^^^^^^
+# Read weather data from a TMY3 file and calculate the solar position and
+# the plane-of-array irradiance.
+
+import pvlib
+import matplotlib.pyplot as plt
+from pathlib import Path
+
+# Assume a FPV system on a lake with the following specifications
+tilt = 30 # degrees
+azimuth = 180 # south-facing
+
+# Datafile found in the pvlib distribution
+data_file = Path(pvlib.__path__[0]).joinpath('data', '723170TYA.CSV')
+
+tmy, metadata = pvlib.iotools.read_tmy3(
+ data_file, coerce_year=2002, map_variables=True
+)
+tmy = tmy.filter(
+ ['ghi', 'dni', 'dni_extra', 'dhi', 'temp_air', 'wind_speed', 'pressure']
+) # remaining columns are not needed
+tmy = tmy['2002-06-06 00:00':'2002-06-06 23:59'] # select period
+
+solar_position = pvlib.solarposition.get_solarposition(
+ # TMY timestamp is at end of hour, so shift to center of interval
+ tmy.index.shift(freq='-30T'),
+ latitude=metadata['latitude'],
+ longitude=metadata['longitude'],
+ altitude=metadata['altitude'],
+ pressure=tmy['pressure'] * 100, # convert from millibar to Pa
+ temperature=tmy['temp_air'],
+)
+solar_position.index = tmy.index # reset index to end of the hour
+
+# Albedo calculation for inland water bodies
+albedo = pvlib.albedo.inland_water_dvoracek(
+ solar_elevation=solar_position['elevation'],
+ surface_condition='clear_water_no_waves'
+)
+
+# Use transposition model to find plane-of-array irradiance
+irradiance = pvlib.irradiance.get_total_irradiance(
+ surface_tilt=tilt,
+ surface_azimuth=azimuth,
+ solar_zenith=solar_position['apparent_zenith'],
+ solar_azimuth=solar_position['azimuth'],
+ dni=tmy['dni'],
+ dni_extra=tmy['dni_extra'],
+ ghi=tmy['ghi'],
+ dhi=tmy['dhi'],
+ albedo=albedo,
+ model='haydavies'
+)
+
+# %%
+# Calculate and plot cell temperature
+# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+# The temperature of the PV cell is calculated for lake-based floating PV
+# systems:
+
+# Make a dictionary containing all the sets of coefficients presented in the
+# above table.
+heat_loss_coeffs = {
+ 'open_structure_small_footprint_tracking_NL': [24.4, 6.5],
+ 'closed_structure_large_footprint_NL': [25.2, 3.7],
+ 'closed_structure_large_footprint_SG': [34.8, 0.8],
+ 'closed_structure_medium_footprint_SG': [18.9, 8.9],
+ 'open_structure_free_standing_SG': [35.3, 8.9],
+ 'in_contact_with_water_NO': [86.5, 0],
+ 'open_strucutre_free_standing_IT': [31.9, 1.5],
+ 'open_strucutre_free_standing_bifacial_IT': [35.2, 1.5],
+ 'default_PVSyst_coeffs_for_land_systems': [29.0, 0]
+}
+
+# Plot the cell temperature for each set of the above heat loss coefficients
+for coeffs in heat_loss_coeffs:
+ T_cell = pvlib.temperature.pvsyst_cell(
+ poa_global=irradiance['poa_global'],
+ temp_air=tmy['temp_air'],
+ wind_speed=tmy['wind_speed'],
+ u_c=heat_loss_coeffs[coeffs][0],
+ u_v=heat_loss_coeffs[coeffs][1]
+ )
+ # Convert Dataframe Indexes to Hour format to make plotting easier
+ T_cell.index = T_cell.index.strftime("%H")
+ plt.plot(T_cell, label=coeffs)
+
+plt.xlabel('Hour')
+plt.ylabel('PV cell temperature\n$[°C]$')
+plt.ylim(20, 45)
+plt.xlim('06', '20')
+plt.grid()
+plt.legend(loc='upper left', frameon=False, ncols=2, fontsize='x-small',
+ bbox_to_anchor=(0, -0.2))
+plt.tight_layout()
+plt.show()
+
+# %%
+# The above figure illustrates the necessity of choosing appropriate heat loss
+# coefficients when using the PVSyst model for calculating the cell temperature
+# for floating PV systems. A difference of up to 11.5 °C was obtained when
+# using the default PVSyst coefficients and the coefficients when the panels
+# are in contact with water.