Problem 9.13

Fundamentals of Solar Cells and Photovoltaic Systems Engineering

Solutions Manual - Chapter 9

Problem 9.13

Assume a PV system is installed on the rooftop of a dwelling in Dakar, Senegal (14.7166\(^{\circ}\)N, 17.4676\(^{\circ}\)W). The system includes one PV panel LG290N1C (oriented towards the south) and one microinverter ABB-MICRO-0.25. For the cell temperature estimation, assume that the PV module is glass-glass, and mounted on the rooftop surface (close mount). Use pvlib and the Typical Meteorological Year (TYM) to:

(a) find the optimum inclination for the PV generator that maximizes the reference yield \(Y_R\)

(b) find the optimum inclination for the PV generator that maximizes the final yield \(Y_F\)

Discuss the results.

We will use the packages pvlib, pandas and matplotlib.pyplot to plot the results. We will also use the package pytz to determine the time zone of Egypt.

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

We start by defining the location, date, and time.

# Dakar, Senegal
lat, lon =  14.7166, -17.4676
altitude = 22

tz = pytz.country_timezones('SN')[0] # timezone corresponding to country 'EG' (Egypt)

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

orientation = 180 # pvlib sets orientation origin at North -> South=180

We retrieve typical meteorological year (TMY) data from PVGIS.

tmy, _, _, _ = pvlib.iotools.get_pvgis_tmy(latitude=lat, longitude=lon, map_variables=True)

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

We retrieve the PV modules and inverter specifications from the database at the NREL SAM (System Advisory Monitoring).

sandia_modules = pvlib.pvsystem.retrieve_sam('SandiaMod')

sapm_inverters = pvlib.pvsystem.retrieve_sam('cecinverter')

module = sandia_modules['LG_LG290N1C_G3__2013_'] # module LG290N1C

inverter = sapm_inverters['ABB__MICRO_0_25_I_OUTD_US_208__208V_']

For the temperature parameters, we assume a close mount glass-glass configuration.

temperature_model_parameters = pvlib.temperature.TEMPERATURE_MODEL_PARAMETERS['sapm'] ['close_mount_glass_glass']

We calculate the Sun’s coordinates

# calculate Sun's coordinates
solar_position = location.get_solarposition(times=tmy.index)

We calculate the reference and final yields for different tilt angles.

#list of potential tilt angle
tilts=range(0,90,1)

Y_F = pd.Series(index=tilts, dtype=float)
Y_R = pd.Series(index=tilts, dtype=float)

for tilt in tilts: 
    # calculate irradiante at the plane of the array (poa)
    poa_irradiance = pvlib.irradiance.get_total_irradiance(surface_tilt=tilt,
                                                           surface_azimuth=orientation,
                                                           dni=tmy['dni'],
                                                           ghi=tmy['ghi'],
                                                           dhi=tmy['dhi'],
                                                           solar_zenith=solar_position['apparent_zenith'],
                                                           solar_azimuth=solar_position['azimuth'])
    
    #save reference yield
    Y_R[tilt]=0.001*poa_irradiance['poa_global'].sum()

    #calculate airmass 
    airmass = pvlib.atmosphere.get_relative_airmass(solar_position['apparent_zenith'])
    pressure = pvlib.atmosphere.alt2pres(altitude)
    am_abs = pvlib.atmosphere.get_absolute_airmass(airmass, pressure)
    
    #calculate the angle of incidence (aoi)
    aoi = pvlib.irradiance.aoi(surface_tilt=tilt,
                               surface_azimuth=orientation,
                               solar_zenith=solar_position['apparent_zenith'],
                               solar_azimuth=solar_position['azimuth'])

    #calculate the effective irradiance
    effective_irradiance = pvlib.pvsystem.sapm_effective_irradiance(poa_irradiance['poa_direct'],
                                                                    poa_irradiance['poa_diffuse'],
                                                                    am_abs,
                                                                    aoi,
                                                                    module)
    #calculate the cell temperature
    cell_temperature = pvlib.temperature.sapm_cell(poa_irradiance['poa_global'],
                                                   tmy["temp_air"],
                                                   tmy["wind_speed"],
                                                   **temperature_model_parameters,)
    
    #calculate the DC and AC energy generation in every hour
    dc_power = pvlib.pvsystem.sapm(effective_irradiance, cell_temperature, module)

    ac_power = pvlib.inverter.sandia(dc_power['v_mp'], dc_power['p_mp'], inverter)

    #save the final yield
    P_STC=module['Impo']*module['Vmpo']

    Y_F[tilt] = ac_power.sum()/P_STC 

We can plot the reference yield and the final yield as a function of the tilt angle.

Y_R.plot(label="reference yield, $Y_R$", color='dodgerblue')
Y_F.plot(label="final yield, $Y_F$", color='firebrick')
plt.ylabel('Yield (kWh)')
plt.xlabel('Tilt angle')
plt.legend()

<matplotlib.legend.Legend at 0x7fa878a3d350>

Both, the reference and final yields are maximized for a tilt angle of 14 degrees.

Y_R.idxmax()

14

Y_F.idxmax()

14