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            967.400908
poa_direct            690.117058
poa_diffuse           277.283850
poa_sky_diffuse       269.617274
poa_ground_diffuse      7.666576
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	206.758018	30.647844	176.110174	174.572336	1.537838
2022-05-12 08:00:00+03:00	426.573387	127.589048	298.984339	295.803125	3.181214
2022-05-12 09:00:00+03:00	740.955832	454.137046	286.818786	281.255430	5.563356
2022-05-12 10:00:00+03:00	899.108129	627.419815	271.688315	264.768043	6.920272
2022-05-12 11:00:00+03:00	973.182885	705.635191	267.547695	259.918811	7.628883
2022-05-12 12:00:00+03:00	967.400908	690.117058	277.283850	269.617274	7.666576
2022-05-12 13:00:00+03:00	910.400388	657.769770	252.630617	245.371117	7.259501
2022-05-12 14:00:00+03:00	780.907612	537.076067	243.831545	237.612346	6.219198
2022-05-12 15:00:00+03:00	610.576463	401.114302	209.462162	204.637571	4.824590
2022-05-12 16:00:00+03:00	402.771171	238.655777	164.115394	160.994488	3.120907
2022-05-12 17:00:00+03:00	184.360920	90.853528	93.507392	92.135399	1.371993
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