Why isn't the optimal surface_azimuth for energy production in pvlib at or around 180° in the Northern hemisphere?

Question

I'm building a model using the open-source pvlib software (and CEC Modules) to estimate yearly photovoltaic energy output. I have encountered some inconsistencies in the model and would appreciate any troubleshooting the community can offer.

My main problem is this: the model tells me that the ideal Northern hemisphere surface_azimuth for energy production (ie. surface_azimuth with the highest energy output) is around 76° (just North of due-East) while the worst surface_azimuth for energy production is around 270° (due West). However, I understand that the ideal surface_azimuth in the Northern hemisphere should be about180° (due South) with the worst surface_azimuth at 0° (due North).

I've included this graph to help visualize the variation in energy production based on surface_azimuth This is also generated at the end of the code attached.

Can anyone help me rectify this issue or correct my understanding?

Code copied below for reference

import os
import pandas as pd
import numpy as np
import os
import os.path
import matplotlib.pyplot as plt
import pvlib
from geopy.exc import GeocoderTimedOut 
from geopy.geocoders import Nominatim 
from IPython.display import Image


## GET THE LATITUDE & LONGITUDE OF A GIVEN CITY
geolocator = Nominatim(user_agent="____'s app") 
geo = geolocator.geocode("Berkeley") 
## CHECK THAT CITY IS CORRECT (by Country, State, etc.)
print(geo.address)
# CHECK THE LAT, LON order
print(geo.latitude, geo.longitude)


## SELECT THE YEAR & TIMES YOU'D LIKE TO MODEL OFF
YEAR = 2019
STARTDATE = '%d-01-01T00:00:00' % YEAR
ENDDATE = '%d-12-31T23:59:59' % YEAR
TIMES = pd.date_range(start=STARTDATE, end=ENDDATE, freq='H')

## ACCESS THE NREL API TO EXTRACT WEATHER DATA
NREL_API_KEY = os.getenv('NREL_API_KEY', 'DEMO_KEY')
## FILL IN THE BLANK WITH YOUR EMAIL ADRRESS
EMAIL = os.getenv('EMAIL', '_______.com')

##NEED TO COMMENT OUT THIS LINE BELOW -- if you call it too many times within an hour, it will break your code
header, data = pvlib.iotools.get_psm3(LATITUDE, LONGITUDE, NREL_API_KEY, EMAIL)


## SELECT THE PVLIB PANEL & INTERVTER YOU'D LIKE TO USE
## CAN ALSO CHOOSE FROM SANDIA LABS' DATASET OF PANELS & INVERTERS (check out the function)
## WE CHOSE THE CECMods because they highlighted the ones that were BIPV
INVERTERS = pvlib.pvsystem.retrieve_sam('CECInverter')
INVERTER_10K = INVERTERS['SMA_America__SB10000TL_US__240V_']
CECMODS = pvlib.pvsystem.retrieve_sam('CECMod')

## SELECT THE PANEL YOU'D LIKE TO USE (NOTE: THE PEVAFERSA MODEL IS A BIPV PANEL)
CECMOD_MONO = CECMODS['Pevafersa_America_IP_235_GG']


## CREATING AN ARRAY TO ITERATE THROUGH IN ORDER TO TEST DIFFERENT SURFACE_AZIMUTHS
heading_array = np.arange(0, 361, 2)
heading_array

heading_DF = pd.DataFrame(heading_array).rename(columns = {0: "Heading"})
heading_DF.head()


# geo IS AN OBJECT (the given city) CREATED ABOVE
LATITUDE, LONGITUDE = geo.latitude, geo.longitude

# data IS AN OBJECT (the weather patterns) CREATED ABOVE
# TIMES IS ALSO CREATED ABOVE, AND REPRESENTS TIME
data.index = TIMES
dni = data.DNI.values
ghi = data.GHI.values
dhi = data.DHI.values
surface_albedo = data['Surface Albedo'].values
temp_air = data.Temperature.values
dni_extra = pvlib.irradiance.get_extra_radiation(TIMES).values

# GET SOLAR POSITION
sp = pvlib.solarposition.get_solarposition(TIMES, LATITUDE, LONGITUDE)
solar_zenith = sp.apparent_zenith.values
solar_azimuth = sp.azimuth.values


# CREATING THE ARRY TO STORE THE DAILY ENERGY OUTPUT BY SOLAR AZIMUTH
e_by_az = []


# IDEAL surface_tilt ANGLE IN NORTHERN HEMISPHERE IS ~25
surface_tilt = 25

# ITERATING THROUGH DIFFERENT SURFACE_AZIMUTH VALUES
for heading in heading_DF["Heading"]:
    
 
    surface_azimuth = heading

    poa_sky_diffuse = pvlib.irradiance.get_sky_diffuse(
        surface_tilt, surface_azimuth, solar_zenith, solar_azimuth,
        dni, ghi, dhi, dni_extra=dni_extra, model='haydavies')

    # calculate the angle of incidence using the surface_azimuth and (hardcoded) surface_tilt
    aoi = pvlib.irradiance.aoi(
        surface_tilt, surface_azimuth, solar_zenith, solar_azimuth)
    # https://pvlib-python.readthedocs.io/en/stable/generated/pvlib.irradiance.aoi.html
    # https://pvlib-python.readthedocs.io/en/stable/generated/pvlib.pvsystem.PVSystem.html

    poa_ground_diffuse = pvlib.irradiance.get_ground_diffuse(
        surface_tilt, ghi, albedo=surface_albedo)
    poa = pvlib.irradiance.poa_components(
        aoi, dni, poa_sky_diffuse, poa_ground_diffuse)
    poa_direct = poa['poa_direct']
    poa_diffuse = poa['poa_diffuse']
    poa_global = poa['poa_global']
    iam = pvlib.iam.ashrae(aoi)
    effective_irradiance = poa_direct*iam + poa_diffuse
    temp_cell = pvlib.temperature.pvsyst_cell(poa_global, temp_air)

    # THIS IS THE MAGIC
    cecparams = pvlib.pvsystem.calcparams_cec(
        effective_irradiance, temp_cell,
        CECMOD_MONO.alpha_sc, CECMOD_MONO.a_ref,
        CECMOD_MONO.I_L_ref, CECMOD_MONO.I_o_ref,
        CECMOD_MONO.R_sh_ref, CECMOD_MONO.R_s, CECMOD_MONO.Adjust)
    # mpp is the list of energy output by hour for the whole year using a single panel
    mpp = pvlib.pvsystem.max_power_point(*cecparams, method='newton')
    mpp = pd.DataFrame(mpp, index=TIMES)
    first48 = mpp[:48]
    Edaily = mpp.p_mp.resample('D').sum()
    # Edaily is the list of energy output by day for the whole year using a single panel

    Eyearly = sum(Edaily)
    
    e_by_az.append(Eyearly)


## LINKING THE Heading (ie. surface_azimuth) AND THE Eyearly (ie. yearly energy output) IN A DF
heading_DF["Eyearly"] = e_by_az
heading_DF.head()


## VISUALIZE ENERGY OUTPUT BY SURFACE_AZIMUTH
plt.plot(heading_DF["Heading"], heading_DF["Eyearly"])
plt.xlabel("Surface_Azimuth Angle")
plt.ylabel("Yearly Energy Output with tilt @ " + str(surface_tilt))
plt.title("Yearly Energy Output by Solar_Azimuth Angle using surface_tilt = " + str(surface_tilt) + " in Berkeley, CA");

# FIND SURFACE_AZIMUTH THAT YIELDS THE MAX ENERGY OUTPUT
heading_DF[heading_DF["Eyearly"] == max(heading_DF["Eyearly"])]

# FIND SURFACE_AZIMUTH THAT YIELDS THE MIN ENERGY OUTPUT
heading_DF[heading_DF["Eyearly"] == min(heading_DF["Eyearly"])]

Answer 1

Thanks to [email protected] for helping me out in the pvlib-python Google Group. He pointed out that my "TIMES variable is not timezone-aware and so the solar position calculation is assuming UTC".

To fix that, he suggested that I initialize TIMES with tz='Etc/GMT+8' (ie. PST in the US).

In his words, "the code [I] originally posted is modeling a hypothetical system where solar position and irradiance are timeshifted with respect to each other. That's a big departure from reality, and so real-life expectations don't apply to your model".

Thanks to Kevin and hopefully this helps anyone else having a similar issue.