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"""
Calculating a module's IV curves
================================
Examples of modeling IV curves using a single-diode circuit equivalent model.
"""
# %%
# Calculating a module IV curve for certain operating conditions is a two-step
# process. Multiple methods exist for both parts of the process. Here we use
# the De Soto model [1]_ to calculate the electrical parameters for an IV
# curve at a certain irradiance and temperature using the module's
# base characteristics at reference conditions. Those parameters are then used
# to calculate the module's IV curve by solving the single-diode equation using
# the Lambert W method.
#
# The single-diode equation is a circuit-equivalent model of a PV
# cell and has five electrical parameters that depend on the operating
# conditions. For more details on the single-diode equation and the five
# parameters, see the `PVPMC single diode page
# <https://pvpmc.sandia.gov/modeling-steps/2-dc-module-iv/diode-equivalent-circuit-models/>`_.
#
# References
# ----------
# .. [1] W. De Soto et al., "Improvement and validation of a model for
# photovoltaic array performance", Solar Energy, vol 80, pp. 78-88, 2006.
#
# Calculating IV Curves
# -----------------------
# This example uses :py:meth:`pvlib.pvsystem.calcparams_desoto` to calculate
# the 5 electrical parameters needed to solve the single-diode equation.
# :py:meth:`pvlib.pvsystem.singlediode` is then used to generate the IV curves.
from pvlib import pvsystem
import pandas as pd
import matplotlib.pyplot as plt
# Example module parameters for the Canadian Solar CS5P-220M:
parameters = {
'Name': 'Canadian Solar CS5P-220M',
'BIPV': 'N',
'Date': '10/5/2009',
'T_NOCT': 42.4,
'A_c': 1.7,
'N_s': 96,
'I_sc_ref': 5.1,
'V_oc_ref': 59.4,
'I_mp_ref': 4.69,
'V_mp_ref': 46.9,
'alpha_sc': 0.004539,
'beta_oc': -0.22216,
'a_ref': 2.6373,
'I_L_ref': 5.114,
'I_o_ref': 8.196e-10,
'R_s': 1.065,
'R_sh_ref': 381.68,
'Adjust': 8.7,
'gamma_r': -0.476,
'Version': 'MM106',
'PTC': 200.1,
'Technology': 'Mono-c-Si',
}
cases = [
(1000, 55),
(800, 55),
(600, 55),
(400, 25),
(400, 40),
(400, 55)
]
conditions = pd.DataFrame(cases, columns=['Geff', 'Tcell'])
# adjust the reference parameters according to the operating
# conditions using the De Soto model:
IL, I0, Rs, Rsh, nNsVth = pvsystem.calcparams_desoto(
conditions['Geff'],
conditions['Tcell'],
alpha_sc=parameters['alpha_sc'],
a_ref=parameters['a_ref'],
I_L_ref=parameters['I_L_ref'],
I_o_ref=parameters['I_o_ref'],
R_sh_ref=parameters['R_sh_ref'],
R_s=parameters['R_s'],
EgRef=1.121,
dEgdT=-0.0002677
)
# plug the parameters into the SDE and solve for IV curves:
curve_info = pvsystem.singlediode(
photocurrent=IL,
saturation_current=I0,
resistance_series=Rs,
resistance_shunt=Rsh,
nNsVth=nNsVth,
ivcurve_pnts=100,
method='lambertw'
)
# plot the calculated curves:
plt.figure()
for i, case in conditions.iterrows():
label = (
"$G_{eff}$ " + f"{case['Geff']} $W/m^2$\n"
"$T_{cell}$ " + f"{case['Tcell']} $C$"
)
plt.plot(curve_info['v'][i], curve_info['i'][i], label=label)
v_mp = curve_info['v_mp'][i]
i_mp = curve_info['i_mp'][i]
# mark the MPP
plt.plot([v_mp], [i_mp], ls='', marker='o', c='k')
plt.legend(loc=(1.0, 0))
plt.xlabel('Module voltage [V]')
plt.ylabel('Module current [A]')
plt.title(parameters['Name'])
plt.show()
plt.gcf().set_tight_layout(True)
# draw trend arrows
def draw_arrow(ax, label, x0, y0, rotation, size, direction):
style = direction + 'arrow'
bbox_props = dict(boxstyle=style, fc=(0.8, 0.9, 0.9), ec="b", lw=1)
t = ax.text(x0, y0, label, ha="left", va="bottom", rotation=rotation,
size=size, bbox=bbox_props, zorder=-1)
bb = t.get_bbox_patch()
bb.set_boxstyle(style, pad=0.6)
ax = plt.gca()
draw_arrow(ax, 'Irradiance', 20, 2.5, 90, 15, 'r')
draw_arrow(ax, 'Temperature', 35, 1, 0, 15, 'l')
print(pd.DataFrame({
'i_sc': curve_info['i_sc'],
'v_oc': curve_info['v_oc'],
'i_mp': curve_info['i_mp'],
'v_mp': curve_info['v_mp'],
'p_mp': curve_info['p_mp'],
}))