plot_rtranpose_year.py

"""
Reverse transposition using one year of hourly data
===================================================

With a brief look at accuracy and speed.

Author: Anton Driesse

"""
# %%
#
# Introduction
# ------------
# When irradiance is measured on a tilted plane, it is useful to be able to
# estimate the GHI that produces the POA irradiance.
# The estimation requires inverting a GHI-to-POA irradiance model,
# which involves two parts:
# a decomposition of GHI into direct and diffuse components,
# and a transposition model that calculates the direct and diffuse
# irradiance on the tilted plane.
# Recovering GHI from POA irradiance is termed "reverse transposition."
#
# In this example we start with a TMY file and calculate POA global irradiance.
# Then we use :py:meth:`pvlib.irradiance.ghi_from_poa_driesse_2024` to estimate
# the original GHI from POA global.  Details of the method found in [1]_.
#
# Another method for reverse tranposition called GTI-DIRINT is also
# available in pvlib python (:py:meth:`pvlib.irradiance.gti_dirint`).
# More information is available in [2]_.
#
# References
# ----------
# .. [1] Driesse, A., Jensen, A., Perez, R., 2024. A Continuous form of the
#     Perez diffuse sky model for forward and reverse transposition.
#     Solar Energy vol. 267. :doi:`10.1016/j.solener.2023.112093`
#
# .. [2] B. Marion, A model for deriving the direct normal and
#        diffuse horizontal irradiance from the global tilted
#        irradiance, Solar Energy 122, 1037-1046.
#        :doi:`10.1016/j.solener.2015.10.024`

import os
import time
import pandas as pd

import matplotlib.pyplot as plt

import pvlib
from pvlib import iotools, location
from pvlib.irradiance import (get_extra_radiation,
                              get_total_irradiance,
                              ghi_from_poa_driesse_2024,
                              aoi,
                              )

# %%
#
# Read a TMY3 file containing weather data and select needed columns.
#

PVLIB_DIR = pvlib.__path__[0]
DATA_FILE = os.path.join(PVLIB_DIR, 'data', '723170TYA.CSV')

tmy, metadata = iotools.read_tmy3(DATA_FILE, coerce_year=1990,
                                  map_variables=True)

df = pd.DataFrame({'ghi': tmy['ghi'], 'dhi': tmy['dhi'], 'dni': tmy['dni'],
                   'temp_air': tmy['temp_air'],
                   'wind_speed': tmy['wind_speed'],
                   })

# %%
#
# Shift the timestamps to the middle of the hour and calculate sun positions.
#

df.index = df.index - pd.Timedelta(minutes=30)

loc = location.Location.from_tmy(metadata)
solpos = loc.get_solarposition(df.index)

# %%
#
# Estimate global irradiance on a fixed-tilt array (forward transposition).
# The array is tilted 30 degrees and oriented 30 degrees east of south.
#

TILT = 30
ORIENT = 150

df['dni_extra'] = get_extra_radiation(df.index)

total_irrad = get_total_irradiance(TILT, ORIENT,
                                   solpos.apparent_zenith,
                                   solpos.azimuth,
                                   df.dni, df.ghi, df.dhi,
                                   dni_extra=df.dni_extra,
                                   model='perez-driesse')

df['poa_global'] = total_irrad.poa_global
df['aoi'] = aoi(TILT, ORIENT, solpos.apparent_zenith, solpos.azimuth)

# %%
#
# Now estimate ghi from poa_global using reverse transposition.
# The algorithm uses a simple bisection search, which is quite slow
# because scipy doesn't offer a vectorized version (yet).
# For this reason we'll process a random sample of 1000 timestamps
# rather than the whole year.
#

df = df[df.ghi > 0].sample(n=1000)
solpos = solpos.reindex(df.index)

start = time.process_time()

df['ghi_rev'] = ghi_from_poa_driesse_2024(TILT, ORIENT,
                                          solpos.apparent_zenith,
                                          solpos.azimuth,
                                          df.poa_global,
                                          dni_extra=df.dni_extra)
finish = time.process_time()

print('Elapsed time for reverse transposition: %.1f s' % (finish - start))

# %%
#
# This graph shows the reverse transposed values vs. the original values.
# The markers are color-coded by angle-of-incidence to show that
# errors occur primarily with incidence angle approaching 90° and beyond.
#
# Note that the results look particularly good because the POA values
# were calculated using the same models as used in reverse transposition.
# This isn't cheating though.  It's a way of ensuring that the errors
# we see are really due to the reverse transposition algorithm.
# Expect to see larger errors with real-word POA measurements
# because errors from forward and reverse transposition will both be present.
#

df = df.sort_values('aoi')

plt.figure()
plt.gca().grid(True, alpha=.5)
pc = plt.scatter(df['ghi'], df['ghi_rev'], c=df['aoi'], s=15,
                 cmap='jet', vmin=60, vmax=120)
plt.colorbar(label='AOI [°]')
pc.set_alpha(0.5)

plt.xlabel('GHI original [W/m²]')
plt.ylabel('GHI from POA [W/m²]')

plt.show()