"""
The ``mismatch`` module provides functions for spectral mismatch calculations.
"""
import pvlib
import numpy as np
import pandas as pd
from scipy.interpolate import interp1d
import os
[docs]def get_example_spectral_response(wavelength=None):
'''
Generate a generic smooth spectral response (SR) for tests and experiments.
Parameters
----------
wavelength: 1-D sequence of numeric, optional
Wavelengths at which spectral response values are generated.
By default ``wavelength`` is from 280 to 1200 in 5 nm intervals. [nm]
Returns
-------
spectral_response : pandas.Series
The relative spectral response indexed by ``wavelength`` in nm. [-]
Notes
-----
This spectral response is based on measurements taken on a c-Si cell.
A small number of points near the measured curve are used to define
a cubic spline having no undue oscillations, as shown in [1]_. The spline
can be interpolated at arbitrary wavelengths to produce a continuous,
smooth curve , which makes it suitable for experimenting with spectral
data of different resolutions.
References
----------
.. [1] Driesse, Anton, and Stein, Joshua. "Global Normal Spectral
Irradiance in Albuquerque: a One-Year Open Dataset for PV Research".
United States 2020. :doi:`10.2172/1814068`.
'''
# Contributed by Anton Driesse (@adriesse), PV Performance Labs. Aug. 2022
SR_DATA = np.array([[ 290, 0.00],
[ 350, 0.27],
[ 400, 0.37],
[ 500, 0.52],
[ 650, 0.71],
[ 800, 0.88],
[ 900, 0.97],
[ 950, 1.00],
[1000, 0.93],
[1050, 0.58],
[1100, 0.21],
[1150, 0.05],
[1190, 0.00]]).transpose()
if wavelength is None:
resolution = 5.0
wavelength = np.arange(280, 1200 + resolution, resolution)
interpolator = interp1d(SR_DATA[0], SR_DATA[1],
kind='cubic',
bounds_error=False,
fill_value=0.0,
copy=False,
assume_sorted=True)
sr = pd.Series(data=interpolator(wavelength), index=wavelength)
sr.index.name = 'wavelength'
sr.name = 'spectral_response'
return sr
[docs]def get_am15g(wavelength=None):
'''
Read the ASTM G173-03 AM1.5 global spectrum on a 37-degree tilted surface,
optionally interpolated to the specified wavelength(s).
Global (tilted) irradiance includes direct and diffuse irradiance from sky
and ground reflections, and is more formally called hemispherical
irradiance (on a tilted surface). In the context of photovoltaic systems
the irradiance on a flat receiver is frequently called plane-of-array (POA)
irradiance.
Parameters
----------
wavelength: 1-D sequence of numeric, optional
Wavelengths at which the spectrum is interpolated.
By default the 2002 wavelengths of the standard are returned. [nm]
Returns
-------
am15g: pandas.Series
The AM1.5g standard spectrum indexed by ``wavelength``. [(W/m^2)/nm]
Notes
-----
If ``wavelength`` is specified this function uses linear interpolation.
If the values in ``wavelength`` are too widely spaced, the integral of the
spectrum may deviate from the standard value of 1000.37 W/m^2.
The values in the data file provided with pvlib-python are copied from an
Excel file distributed by NREL, which is found here:
https://www.nrel.gov/grid/solar-resource/assets/data/astmg173.xls
More information about reference spectra is found here:
https://www.nrel.gov/grid/solar-resource/spectra-am1.5.html
References
----------
.. [1] ASTM "G173-03 Standard Tables for Reference Solar Spectral
Irradiances: Direct Normal and Hemispherical on 37° Tilted Surface."
'''
# Contributed by Anton Driesse (@adriesse), PV Performance Labs. Aug. 2022
pvlib_path = pvlib.__path__[0]
filepath = os.path.join(pvlib_path, 'data', 'astm_g173_am15g.csv')
am15g = pd.read_csv(filepath, index_col=0).squeeze()
if wavelength is not None:
interpolator = interp1d(am15g.index, am15g,
kind='linear',
bounds_error=False,
fill_value=0.0,
copy=False,
assume_sorted=True)
am15g = pd.Series(data=interpolator(wavelength), index=wavelength)
am15g.index.name = 'wavelength'
am15g.name = 'am15g'
return am15g
[docs]def calc_spectral_mismatch_field(sr, e_sun, e_ref=None):
"""
Calculate spectral mismatch between a test device and broadband reference
device under specified solar spectral irradiance conditions.
Parameters
----------
sr: pandas.Series
The relative spectral response of one (photovoltaic) test device.
The index of the Series must contain wavelength values in nm. [-]
e_sun: pandas.DataFrame or pandas.Series
One or more measured solar irradiance spectra in a pandas.DataFrame
having wavelength in nm as column index. A single spectrum may be
be given as a pandas.Series having wavelength in nm as index.
[(W/m^2)/nm]
e_ref: pandas.Series, optional
The reference spectrum to use for the mismatch calculation.
The index of the Series must contain wavelength values in nm.
The default is the ASTM G173-03 global tilted spectrum. [(W/m^2)/nm]
Returns
-------
smm: pandas.Series or float if a single measured spectrum is provided. [-]
Notes
-----
Measured solar spectral irradiance usually covers a wavelength range
that is smaller than the range considered as broadband irradiance.
The infrared limit for the former typically lies around 1100 or 1600 nm,
whereas the latter extends to around 2800 or 4000 nm. To avoid imbalance
between the magnitudes of the integrated spectra (the broadband values)
this function truncates the reference spectrum to the same range as the
measured (or simulated) field spectra. The assumption implicit in this
truncation is that the energy in the unmeasured wavelength range
is the same fraction of the broadband energy for both the measured
spectra and the reference spectrum.
If the default reference spectrum is used it is linearly interpolated
to the wavelengths of the measured spectrum, but if a reference spectrum
is provided via the parameter ``e_ref`` it is used without change. This
makes it possible to avoid interpolation, or to use a different method of
interpolation, or to avoid truncation.
The spectral response is linearly interpolated to the wavelengths of each
spectrum with which is it multiplied internally (``e_sun`` and ``e_ref``).
If the wavelengths of the spectral response already match one or both
of these spectra interpolation has no effect; therefore, another type of
interpolation could be used to process ``sr`` before calling this function.
The standards describing mismatch calculations focus on indoor laboratory
applications, but are applicable to outdoor performance as well.
The 2016 version of ASTM E973 [1]_ is somewhat more difficult to
read than the 2010 version [2]_ because it includes adjustments for
the temperature dependency of spectral response, which led to a
formulation using quantum efficiency (QE).
IEC 60904-7 is clearer and also discusses the use of a broadband
reference device. [3]_
References
----------
.. [1] ASTM "E973-16 Standard Test Method for Determination of the
Spectral Mismatch Parameter Between a Photovoltaic Device and a
Photovoltaic Reference Cell" :doi:`10.1520/E0973-16R20`
.. [2] ASTM "E973-10 Standard Test Method for Determination of the
Spectral Mismatch Parameter Between a Photovoltaic Device and a
Photovoltaic Reference Cell" :doi:`10.1520/E0973-10`
.. [3] IEC 60904-7 "Computation of the spectral mismatch correction
for measurements of photovoltaic devices"
"""
# Contributed by Anton Driesse (@adriesse), PV Performance Labs. Aug. 2022
# get the reference spectrum at wavelengths matching the measured spectra
if e_ref is None:
e_ref = get_am15g(wavelength=e_sun.T.index)
# interpolate the sr at the wavelengths of the spectra
# reference spectrum wavelengths may differ if e_ref is from caller
sr_sun = np.interp(e_sun.T.index, sr.index, sr, left=0.0, right=0.0)
sr_ref = np.interp(e_ref.T.index, sr.index, sr, left=0.0, right=0.0)
# a helper function to make usable fraction calculations more readable
def integrate(e):
return np.trapz(e, x=e.T.index, axis=-1)
# calculate usable fractions
uf_sun = integrate(e_sun * sr_sun) / integrate(e_sun)
uf_ref = integrate(e_ref * sr_ref) / integrate(e_ref)
# mismatch is the ratio or quotient of the usable fractions
smm = uf_sun / uf_ref
if isinstance(e_sun, pd.DataFrame):
smm = pd.Series(smm, index=e_sun.index)
return smm