Pvlib / Bird1984: North-facing element shows negative Irradiance

Question

When using pvlib (but also the spectrl2 implementation provided by NREL), I obtain negative Irradiance for a north-facing panel. Is this expected behaviour? Should the spectrum simply be cut at zero?

Added example code based on the tutorial below:

## Using PV Lib

from pvlib import spectrum, solarposition, irradiance, atmosphere
import pandas as pd
import matplotlib.pyplot as plt

# assumptions from the technical report:
lat = 49.88
lon = 8.63
tilt = 45
azimuth = 0 # North = 0
pressure = 101300  # sea level, roughly
water_vapor_content = 0.5  # cm
tau500 = 0.1
ozone = 0.31  # atm-cm
albedo = 0.2

times = pd.date_range('2021-11-30 8:00', freq='h', periods=6, tz="Europe/Berlin") # , tz='Etc/GMT+9'
solpos = solarposition.get_solarposition(times, lat, lon)
aoi = irradiance.aoi(tilt, azimuth, solpos.apparent_zenith, solpos.azimuth)

# The technical report uses the 'kasten1966' airmass model, but later
# versions of SPECTRL2 use 'kastenyoung1989'.  Here we use 'kasten1966'
# for consistency with the technical report.
relative_airmass = atmosphere.get_relative_airmass(solpos.apparent_zenith,
                                                   model='kasten1966')

spectra = 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,
)

plt.figure()
plt.plot(spectra['wavelength'], spectra['poa_global'])
plt.xlim(200, 2700)
# plt.ylim(0, 1.8)
plt.title(r"2021-11-30, Darmstadt, $\tau=0.1$, Wv=0.5 cm")
plt.ylabel(r"Irradiance ($W m^{-2} nm^{-1}$)")
plt.xlabel(r"Wavelength ($nm$)")
time_labels = times.strftime("%H:%M %p")
labels = [
    "AM {:0.02f}, Z{:0.02f}, {}".format(*vals)
    for vals in zip(relative_airmass, solpos.apparent_zenith, time_labels)
]
plt.legend(labels)
plt.show()

Answer 1

No, this is not expected behavior. I suspect the issue is caused by improper handling of angle-of-incidence values greater than 90 degrees, and essentially the same problem (for a different function) discussed here: https://github.com/pvlib/pvlib-python/issues/526

It's unfortunate that the reference implementation from NREL has the problem too (perhaps when the model was originally designed, nobody could conceive of a panel facing away from the sun,). but I think the pvlib implementation should be fixed regardless: I encourage you to file a bug report here: https://github.com/pvlib/pvlib-python/issues

In the meantime, I think you can resolve the issue in your own code by adding a line like aoi[aoi > 90] = 90 prior to passing it to spectrum.spectrl2 , although be careful about this if you end up using aoi for other purposes later in the script. I would be interested to hear if the resulting spectra are consistent with your expectations.