add spectrum.average_photon_energy gallery example

docs/examples/spectrum/average_photon_energy.py

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+"""
+Average Photon Energy Calculation
+============================
+
+Calculation of the Average Photon Energy from SPECTRL2 output.
+"""
+
+# %%
+# Introduction
+# ------------
+# This example demonstrates how to use the
+# :py:func:`~pvlib.spectrum.average_photon_energy` function to calculate the
+# Average Photon Energy (APE, :math:`\overline{E_\gamma}`) of spectral
+# irradiance distributions simulated using :py:func:`~pvlib.spectrum.spectrl2`.
+# More information on the SPECTRL2 model can be found in [1]_.
+# The APE parameter is a useful indicator of the overall shape of the solar
+# spectrum [2]_. Higher (lower) APE values indicate a blue (red) shift in the
+# spectrum and is one of a variety of such characterisation methods that is
+# used in the PV performance literature [3]_.
+#
+# To demonstrate this functionality, first we need to simulate some spectra
+# using :py:func:`~pvlib.spectrum.spectrl2`. In this example, we will simulate
+# spectra following a similar method to that which is followed in the
+# `Modelling Spectral Irradiance
+# <https://pvlib-python.readthedocs.io/en/stable/gallery/spectrum/plot_spectrl2_fig51A.html>`_
+# example, which reproduces a figure from [4]_. The first step is to
+# import the required packages and define some basic system parameters and
+# and meteorological conditions.
+
+# %%
+import numpy as np
+import pandas as pd
+import matplotlib.pyplot as plt
+from scipy.integrate import trapezoid
+from pvlib import spectrum, solarposition, irradiance, atmosphere
+
+lat, lon = 39.742, -105.18  # NREL SRRL location
+tilt = 25
+azimuth = 180  # south-facing system
+pressure = 81190  # at 1828 metres AMSL, roughly
+water_vapor_content = 0.5  # cm
+tau500 = 0.1
+ozone = 0.31  # atm-cm
+albedo = 0.2
+
+times = pd.date_range('2023-01-01 08:00', freq='h', periods=9,
+                      tz='America/Denver')
+solpos = solarposition.get_solarposition(times, lat, lon)
+aoi = irradiance.aoi(tilt, azimuth, solpos.apparent_zenith, solpos.azimuth)
+
+relative_airmass = atmosphere.get_relative_airmass(solpos.apparent_zenith,
+                                                   model='kastenyoung1989')
+
+# %%
+# Spectral simulation
+# -------------------------
+# With all the necessary inputs now defined, we can model spectral irradiance
+# using :py:func:`pvlib.spectrum.spectrl2`. As we are calculating spectra for
+# more than one set of conditions, the function will return a dictionary
+# containing 2-D arrays for the spectral irradiance components and a 1-D array
+# of shape (122,) for wavelength. For each of the 2-D arrays, one dimension is
+# for wavelength in nm and one is for irradiance in Wm⁻²nm⁻¹.
+
+spectra_components = spectrum.spectrl2(
+    apparent_zenith=solpos.apparent_zenith,
+    aoi=aoi,
+    surface_tilt=tilt,
+    ground_albedo=albedo,
+    surface_pressure=pressure,
+    relative_airmass=relative_airmass,
+    precipitable_water=water_vapor_content,
+    ozone=ozone,
+    aerosol_turbidity_500nm=tau500,
+)
+
+# %%
+# Visualising the spectral data
+# -----------------------------
+# Let's take a look at the spectral irradiance data simulated on the hour for
+# eight hours on the first day of 2023.
+
+plt.figure()
+plt.plot(spectra_components['wavelength'], spectra_components['poa_global'])
+plt.xlim(200, 2700)
+plt.ylim(0, 1.8)
+plt.ylabel(r"Spectral irradiance (Wm⁻²nm⁻¹)")
+plt.xlabel(r"Wavelength (nm)")
+time_labels = times.strftime("%H:%M")
+labels = [
+    "{}, AM {:0.02f}".format(*vals)
+    for vals in zip(time_labels, relative_airmass)
+]
+plt.legend(labels)
+plt.show()
+
+# %%
+# Given the changing broadband irradiance throughout the day, it is not obvious
+# from inspection how the relative distribution of light changes as a function
+# of wavelength. We can normalise the spectral irradiance curves to visualise
+# this shift in the shape of the spectrum over the course of the day. In
+# this example, we normalise by dividing each spectral irradiance value by the
+# total broadband irradiance, which we calculate by integrating the entire
+# spectral irradiance distribution with respect to wavelength.
+
+poa_global = spectra_components['poa_global']
+wavelength = spectra_components['wavelength']
+
+broadband_irradiance = np.array([trapezoid(poa_global[:, i], wavelength)
+                                 for i in range(poa_global.shape[1])])
+
+poa_global_normalised = poa_global / broadband_irradiance
+
+# Plot the normalised spectra
+plt.figure()
+plt.plot(wavelength, poa_global_normalised)
+plt.xlim(200, 2700)
+plt.ylim(0, 0.0018)
+plt.ylabel(r"Normalised Irradiance (nm⁻¹)")
+plt.xlabel(r"Wavelength (nm)")
+time_labels = times.strftime("%H:%M")
+labels = [
+    "{}, AM {:0.02f}".format(*vals)
+    for vals in zip(time_labels, relative_airmass)
+]
+plt.legend(labels)
+plt.show()
+
+# %%
+# We can now see from the normalised irradiance curves that at the start and
+# end of the day, the spectrum is red shifted, meaning there is a greater
+# proportion of longer wavelength radiation. Meanwhile, during the middle of
+# the day, there is a greater prevalence of shorter wavelength radiation — a
+# blue shifted spectrum.
+#
+# How can we quantify this shift? This is where the average photon energy comes
+# into play.
+
+# %%
+# Calculating the average photon energy
+# -------------------------------------
+# To calculate the APE, first we must convert our output spectra from from the
+# simulation into a compatible input for
+# :py:func:`pvlib.spectrum.average_photon_energy`. Since we have more than one
+# spectral irradiance distribution, a :py:class:`pandas.DataFrame` is
+# appropriate. We also need to set the column headers as wavelength, so each
+# row is a single spectral irradiance distribution. It is important to remember
+# here that the resulting APE values depend on the integration limits, i.e.
+# the wavelength range of the spectral irradiance input. APE values are only
+# comparable if calculated between the same integration limits. In this case,
+# our APE values are calculated between 300nm and 4000nm.
+
+spectra = pd.DataFrame(poa_global).T  # convert to dataframe and transpose
+spectra.index = time_labels  # add time index
+spectra.columns = wavelength  # add wavelength column headers
+
+ape = spectrum.average_photon_energy(spectra)
+
+# %%
+# We can update the normalised spectral irradiance plot to include the APE
+# value of each spectral irradiance distribution in the legend. Note that the
+# units of the APE are electronvolts (eV).
+
+plt.figure()
+plt.plot(wavelength, poa_global_normalised)
+plt.xlim(200, 2700)
+plt.ylim(0, 0.0018)
+plt.ylabel(r"Normalised Irradiance (nm⁻¹)")
+plt.xlabel(r"Wavelength (nm)")
+time_labels = times.strftime("%H:%M")
+labels = [
+    "{}, APE {:0.02f}".format(*vals)
+    for vals in zip(time_labels, ape)
+]
+plt.legend(labels)
+plt.show()
+
+# %%
+# As expected, the morning and evening spectra have a lower APE while a higher
+# APE is observed closer to the middle of the day. For reference, AM1.5 between
+# 300 and 4000 nm is 1.4501 eV. This indicates that the simulated spectra are
+# slightly red shifted with respect to the AM1.5 standard reference spectrum.
+
+# %%
+# References
+# ----------
+# .. [1] Bird, R, and Riordan, C., 1984, "Simple solar spectral model for
+#        direct and diffuse irradiance on horizontal and tilted planes at the
+#        earth's surface for cloudless atmospheres", NREL Technical Report
+#        TR-215-2436 :doi:`10.2172/5986936`
+# .. [2] Jardine, C., et al., 2002, January. Influence of spectral effects on
+#        the performance of multijunction amorphous silicon cells. In Proc.
+#        Photovoltaic in Europe Conference (pp. 1756-1759)
+# .. [3] Daxini, R., and Wu, Y., 2023. "Review of methods to account
+#        for the solar spectral influence on photovoltaic device performance."
+#        Energy 286 :doi:`10.1016/j.energy.2023.129461`
+# .. [4] Bird Simple Spectral Model: spectrl2_2.c
+#        https://www.nrel.gov/grid/solar-resource/spectral.html
+#        (Last accessed: 18/09/2024)