Problem 3.10

Fundamentals of Solar Cells and Photovoltaic Systems Engineering

Solutions Manual - Chapter 3

Problem 3.10

A company is developing a new solar cell. The quantum efficiency (QE) is assumed to be equal to 0.9 for wavelengths between 350 and 900 nm and zero elsewhere.

(a) Calculate the photocurrent for the solar cell under Standard Test Conditions (STC). Let’s consider that the solar cell has an area of 12.5x12.5 cm\(^2\) and that the solar spectrum under STC \(G_{STC}\) can be approximated by the equation \(G_{STC}(\lambda)=3-0.0023 \cdot \lambda\) Wm\(^{-2}\)nm\(^{-1}\), where \(\lambda\) is the photon wavelength

(b) Calculate the photocurrent for the solar cell in an hour where the spectral distribution of solar radiation is different from the standard and can be approximated by \(G(\lambda)=2-0.001 \cdot \lambda\) Wm\(^{-2}\)nm\(^{-1}\).

We will use the package scipy for function integration and matplotlib.pyplot to plot the results

import pandas as pd
import numpy as np
from scipy.integrate import quad
import matplotlib.pyplot as plt

We define the spectral response as a function of the QE

h=6.63*10**(-34) # J·s Planck constant
e=1.60*10**(-19) #C electron charge
c =299792458 #m/s Speed of light

def SR(wl):
    return 0.9*1e-9*wl*e/(h*c)

We define the solar spectrum as function of the wavelength

def G1(wl): #wl in nm
    return 3-0.0023*wl

The photocurrent density is calculated using Eq. 3.5

\(J = \int SR(\lambda) \cdot \ G(\lambda) \ d\lambda\)

The photocurrent is the product of the photocurrent density and the cell’s area

\(I = J \cdot A\)

pc_dens=quad(lambda wl: G1(wl) * SR(wl), 350, 900)[0] #mA/m2
print ('The photocurrent density is ' + str(round(pc_dens*1e3/1e4, 2)) + ' mA/cm2') #mA-->A, m2-->cm2
area = 12.5*12.5 #cm2
print ("The photocurrent is " + str(round(pc_dens*area/1e4, 2)) + ' A') #cm2-->m2

The photocurrent density is 36.6 mA/cm2
The photocurrent is 5.72 A

(b) Calculate the photocurrent for the solar cell in an hour where the spectral distribution of solar radiation is different from the standard and can be approximated by \(G(\lambda)=2-0.001 \cdot \lambda\) Wm\(^{-2}\)nm\(^{-1}\).

We redefine the solar spectrum

def G2(wl): #x in nm
    return 2-0.001*wl

We recalculate the photocurrent with the new spectrum

pc_dens=quad(lambda wl: G2(wl)*SR(wl), 350, 900)[0] #mA/m2
print ('The photocurrrent density is ' + str(round(pc_dens/10, 2)) + ' mA/cm2') #mA-->A, m2-->cm2
area = 12.5*12.5 #cm2
print ("The photocurrrent is " + str(round(pc_dens/1e4*area, 2)) + ' A') #cm2-->m2

The photocurrrent density is 33.24 mA/cm2
The photocurrrent is 5.19 A