Problem 2.16

Fundamentals of Solar Cells and Photovoltaic Systems Engineering

Solutions Manual - Chapter 2

Problem 2.16

Estimate the global irradiance G(α,β) reaching the plane of array (POA) of a north-facing, 20° tilted generator over grass (reflectivity \(ρ_{alb}\) =0.2) located at a PV plant in Antananarivo, Madagascar (18° 56′ 0″ S, 47° 31′ 0″ E) at midday (true solar time) on May 12, 2022.

Solve the problem using pvlib-python and selecting the same day from the typical meteorological year (TMY) obtained from PVGIS.

We will use the packages pvlib, pandas and matplotlib.pyplot to plot the results.

import pvlib
import pandas as pd
import matplotlib.pyplot as plt

We start by defining the location, date and time. We will implement the calculation for every hour on May 12, 2022.

# Antananarivo, Madagascar
lat, lon = 18.93, 47.52
tz = 'Indian/Antananarivo' #existing timezones can be checked using pytz.all_timezones[::20]

date = '2022-05-12'

# surface angles beta, alpha
tilt, orientation = 20, 0 # pvlib sets orientation origin at North -> North=0

# location
location = pvlib.location.Location(lat, lon, tz=tz)

# albedo
albedo = 0.20 # grass reflectivity

# datetimes
times = pd.date_range(start=date, freq='h', periods=24, tz=tz)

Retrieve typical meteorological year (TMY) data from PVGIS.

tmy, _, _, _ = pvlib.iotools.get_pvgis_tmy(latitude=lat, longitude=lon, map_variables=True)
tmy.index = [ts.replace(year=2022) for ts in tmy.index] # homogenizes year to 2022

tmy.index = tmy.index.tz_convert(tz) # use local time

# select the hourly values corresponding to the day=May 12
tmy_day = tmy.loc[date]

We calculate the Sun’s coordinates and calculate the irradiance on the plane of array (POA)

# calculates Sun's coordinates
solar_position_tmy = location.get_solarposition(times=tmy_day.index)

poa_fixed_tmy_irradiance = pvlib.irradiance.get_total_irradiance(
    surface_tilt=tilt,
    surface_azimuth=orientation,
    dni=tmy_day['dni'],
    ghi=tmy_day['ghi'],
    dhi=tmy_day['dhi'],
    solar_zenith=solar_position_tmy['apparent_zenith'],
    solar_azimuth=solar_position_tmy['azimuth'])

We can plot the daily evolution of direct, diffuse, and global irradiance

poa_fixed_tmy_irradiance.plot()
plt.ylabel('Irradiance [$W/m^2$]')

Text(0, 0.5, 'Irradiance [$W/m^2$]')

And obtain the value at midday.

poa_fixed_tmy_irradiance.loc[poa_fixed_tmy_irradiance.index[12]]

poa_global            1012.632016
poa_direct             759.224942
poa_diffuse            253.407075
poa_sky_diffuse        245.371117
poa_ground_diffuse       8.035958
Name: 2022-05-12 12:00:00+03:00, dtype: float64

We can also obtain the values at any other time step.

poa_fixed_tmy_irradiance

	poa_global	poa_direct	poa_diffuse	poa_sky_diffuse	poa_ground_diffuse
2022-05-12 00:00:00+03:00	0.000000	0.000000	0.000000	0.000000	0.000000
2022-05-12 01:00:00+03:00	0.000000	0.000000	0.000000	0.000000	0.000000
2022-05-12 02:00:00+03:00	0.000000	0.000000	0.000000	0.000000	0.000000
2022-05-12 03:00:00+03:00	0.000000	0.000000	0.000000	0.000000	0.000000
2022-05-12 04:00:00+03:00	0.000000	0.000000	0.000000	0.000000	0.000000
2022-05-12 05:00:00+03:00	0.000000	0.000000	0.000000	0.000000	0.000000
2022-05-12 06:00:00+03:00	10.751232	0.000000	10.751232	10.668309	0.082923
2022-05-12 07:00:00+03:00	189.640070	20.431896	169.208174	167.783412	1.424762
2022-05-12 08:00:00+03:00	566.935107	318.432935	248.502172	244.401270	4.100902
2022-05-12 09:00:00+03:00	794.877004	548.407304	246.469700	240.521885	5.947815
2022-05-12 10:00:00+03:00	943.291771	694.540539	248.751232	241.491731	7.259501
2022-05-12 11:00:00+03:00	1014.898647	762.536803	252.361844	244.401270	7.960574
2022-05-12 12:00:00+03:00	1012.632016	759.224942	253.407075	245.371117	8.035958
2022-05-12 13:00:00+03:00	942.827059	695.751674	247.075384	239.552039	7.523346
2022-05-12 14:00:00+03:00	803.094325	563.931090	239.163235	232.763114	6.400121
2022-05-12 15:00:00+03:00	632.953091	430.098931	202.854160	197.848647	5.005512
2022-05-12 16:00:00+03:00	412.459845	249.238913	163.220932	160.024641	3.196291
2022-05-12 17:00:00+03:00	182.034432	85.632577	96.401854	95.044938	1.356916
2022-05-12 18:00:00+03:00	0.000000	0.000000	0.000000	0.000000	0.000000
2022-05-12 19:00:00+03:00	0.000000	0.000000	0.000000	0.000000	0.000000
2022-05-12 20:00:00+03:00	0.000000	0.000000	0.000000	0.000000	0.000000
2022-05-12 21:00:00+03:00	0.000000	0.000000	0.000000	0.000000	0.000000
2022-05-12 22:00:00+03:00	0.000000	0.000000	0.000000	0.000000	0.000000
2022-05-12 23:00:00+03:00	0.000000	0.000000	0.000000	0.000000	0.000000