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 PV systems using the PVSyst temperature model.
+
+One of the primary benefits attributed to floating photovoltaic (FPV) systems
+is their 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.
+
+One of the most common models for calculating the PV cell temperature is the
+empirical heat loss factor model suggested by Faiman and 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 cell temperature
+# ^^^^^^^^^^^^^^^^^^^^^^^^^^
+# The temperature of the PV cell is calculated for a floating PV system located
+# on a lake:
+
+# Monnofacial floating module open strucuture
+T_cell_floating = pvlib.temperature.pvsyst_cell(
+    poa_global=irradiance['poa_global'],
+    temp_air=tmy['temp_air'],
+    wind_speed=tmy['wind_speed'],
+    u_c=35.3,
+    u_v=8.9
+)
+
+# In order to idetify the effect of the heat loss coefficinets on the cell
+# temperature, the PV cell temperature for the same system is calculated
+# using the default coefficients of the equation. It should be noted that the
+# default coefficeints were derrived for land-based systems.
+T_cell_land = pvlib.temperature.pvsyst_cell(
+    poa_global=irradiance['poa_global'],
+    temp_air=tmy['temp_air'],
+    wind_speed=tmy['wind_speed']
+)
+
+# %%
+# Plot the results
+# ^^^^^^^^^^^^^^^^
+
+# Convert Dataframe Indexes to Hour format to make plotting easier
+T_cell_floating.index = T_cell_floating.index.strftime("%H")
+T_cell_land.index = T_cell_land.index.strftime("%H")
+
+fig, axes = plt.subplots()
+axes.set(
+    xlabel="Hour",
+    ylabel="Temperature $[°C]$",
+    title="PV cell temperature for floating and land-based system"
+)
+
+axes.plot(
+    T_cell_floating,
+    label='Floating PV coeff.'
+)
+
+axes.plot(
+    T_cell_land,
+    label='Land-based PV coeff.'
+)
+
+axes.set_ylim(20, 45)
+axes.set_xlim('06', '20')
+axes.grid()
+axes.legend(loc="upper left")
+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 10 °C was obtained for the two
+# sets of coefficients.