Energy Yield for Silicon Solar Cell

Using non-spectral data from NREL

This example shows how to model the performance of a single junction silicon solar cell. It uses irradiance data from the NSRDB providded by NREL. The irradiance data is part of the meta data of the sepctral on demand data product but can also be obtained from NSRDB as a seperate data product. For the absorptances of the cell it is assumed that the cell produces 39 mA/cm² short-circuit current density.

First, we load the required libraries and the preprocessed meta-data from spectral data for temperature and non-spectral irradiance data

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from pv_tandem.solarcell_models import OneDiodeModel
import pvlib

plt.rcParams['figure.dpi'] = 140

meta_ts = pd.read_csv(
    "../data/meta_ts_dallas_2020.csv", index_col=0, parse_dates=True
)

Next, we calculate the draction of DNI radiating on the tilted module plane (with tilt angle 20 deg) and a fixed fraction of the DHI of 80 %

# Convert angles from degrees to radians
solar_zenith = np.radians(meta_ts['Solar Zenith Angle'])
solar_azimuth = np.radians(meta_ts['Solar Azimuth Angle'])
tilt = np.radians(20)
plane_azimuth = np.radians(180)

# Calculate the cosine of the angle of incidence
cos_theta_i = np.cos(solar_zenith) * np.cos(tilt) + np.sin(solar_zenith) * np.sin(tilt) * np.cos(solar_azimuth - plane_azimuth)

# Calculate the DNI absorbed
dni_plane = meta_ts['DNI'] * cos_theta_i

# Make sure the absorbed DNI is not negative (i.e., the sun is behind the plane)
dni_plane[dni_plane < 0] = 0

# assuming 80% of the DHI are reaching the 20° tilted module plane

irrad_plane = dni_plane + meta_ts['DHI'] * 0.8

Next, we define the one-diode model of the solar cell and estiamte the cell temperature with the ross model of pvlib

one_diode = OneDiodeModel(
    tcJsc=0.0003, tcVoc=-0.004, R_shunt=3000, R_series=1.5, n=1, j0=1e-12
)

cell_temp = pvlib.temperature.ross(poa_global = irrad_plane,
                                         temp_air = meta_ts['Temperature'],
                                         noct=45
                                         )

Finally, the power output of the cell is calculated, assuming a linear relationship between irradaince and short circuit density, with Jsc of 39 mA/cm² for 1000 Watts irradiance

Jsc = irrad_plane/1000*39

iv_paras = one_diode.calc_iv_params(Jsc=Jsc, cell_temp = cell_temp)

power_max = iv_paras['Pmax']

# Converting from W/cm² to kW/m²

power_max = power_max * 10 / 1000

ax = power_max.groupby(power_max.index.dayofyear).sum().plot()
ax.set_xlabel('Day of year')
ax.set_ylabel('Daily yield (kWh/m2)')

print(f"Yearly yield: {(power_max).sum():.1f} kWh/m2")

Yearly yield: 394.4 kWh/m2

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