# 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.

## 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 `pvlib.pvsystem.calcparams_desoto()` to calculate the 5 electrical parameters needed to solve the single-diode equation. `pvlib.pvsystem.singlediode()` and `pvlib.pvsystem.i_from_v()` are used to generate the IV curves.

```from pvlib import pvsystem
import numpy as np
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,
'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:
SDE_params = {
'photocurrent': IL,
'saturation_current': I0,
'resistance_series': Rs,
'resistance_shunt': Rsh,
'nNsVth': nNsVth
}
curve_info = pvsystem.singlediode(method='lambertw', **SDE_params)
v = pd.DataFrame(np.linspace(0., curve_info['v_oc'], 100))
i = pd.DataFrame(pvsystem.i_from_v(voltage=v, method='lambertw', **SDE_params))

# plot the calculated curves:
plt.figure()
for idx, case in conditions.iterrows():
label = (
"\$G_{eff}\$ " + f"{case['Geff']} \$W/m^2\$\n"
"\$T_{cell}\$ " + f"{case['Tcell']} \$\\degree C\$"
)
plt.plot(v[idx], i[idx], label=label)
v_mp = curve_info['v_mp'][idx]
i_mp = curve_info['i_mp'][idx]
# 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.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()

ax = plt.gca()
draw_arrow(ax, 'Irradiance', 20, 2.5, 90, 15, 'r')
draw_arrow(ax, 'Temperature', 35, 1, 0, 15, 'l')
plt.show()

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'],
}))
```
```       i_sc       v_oc      i_mp       v_mp        p_mp
0  5.235561  52.129783  4.742475  39.614016  187.868473
1  4.190781  51.483033  3.805721  39.867812  151.725757
2  3.144837  50.649228  2.861983  39.956701  114.355380
3  2.043319  56.987478  1.886789  47.278408   89.204377
4  2.070523  53.238567  1.901044  43.490203   82.676791
5  2.097727  49.474044  1.912108  39.735026   75.977656
```

Total running time of the script: (0 minutes 0.306 seconds)

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