analytical solution for non-ideal solar cell equation

analytical_sln_to_solar_cell_eqn.py

#!/usr/bin/env python3

"""
written by Grey Christoforo <first name [at] last name [not] net>
analytical solution for non-ideal solar cell equation
"""

import sympy

# make symbols
Iph, Rs, Rsh, n, I0, Vth, I, V = sympy.symbols('Iph Rs Rsh n I0 Vth I V')
"""
where
Iph is the photocurrent generated
Rs is the series resistance
Rsh is the shunt resistance
n is the diode's ideality factor
I0 is the diode's reverse saturation current
Vth is the thermal voltage (kT/q)
I is the current through the load
and
V is the voltage across the load
"""

# symbolic representation for solar cell equation:
lhs = I
rhs = Iph-((V+I*Rs)/Rsh)-I0*(sympy.exp((V+I*Rs)/(n*Vth))-1)
char_eqn = sympy.Eq(lhs, rhs)  # see https://en.wikipedia.org/wiki/Theory_of_solar_cells#Characteristic_equation

print("Solving. Please wait...")

# isolate current term in solar cell equation
current_alone = sympy.solve(char_eqn, I)[0]

print(current_alone)
# this prints: "(Rs*(I0*Rsh + Iph*Rsh - V) - Vth*n*(Rs + Rsh)*LambertW(Rs*exp((Rs*V + Rs*(I0*Rsh + Iph*Rsh - V) + Rsh*V + log((I0*Rsh)**(Vth*n*(Rs + Rsh))))/(Vth*n*(Rs + Rsh)))/(Vth*n*(Rs + Rsh))))/(Rs*(Rs + Rsh))"