Photovoltaic cell

WHAT YOU ARE LOOKING AT

A solar cell is a diode with a current source across it. Light generates I_ph; whatever the load does not take flows through the diode and sets the voltage. Rearranging the diode equation for that leftover current gives the one line the script is built on:

V_D = n·V_T·ln((I_ph − I_load)/I_S + 1)

Two limits fall straight out. Draw no current and all of I_ph goes through the diode, giving the open-circuit voltage — a logarithm, so it barely moves with light level. Draw all of it and the diode gets nothing, the voltage collapses to zero, and the short-circuit current is I_ph — linear in light level. Neither limit delivers any power; the useful point is the knee between them.

The left panels are the script's view, against load current: voltage, then power. The right panels are the same data plotted the way a solar data sheet does it, against voltage. The fill factor is the area of the maximum-power rectangle divided by V_OC·I_SC — how close the cell gets to the rectangle it would fill if it were an ideal source.

THINGS WORTH TRYING

Move I_ph over six decades — bright sun down to indoor light. I_SC follows it exactly, decade for decade. V_OC falls by only about 60 mV per decade, because it is a logarithm. A cell in a dim room still makes most of its voltage; what it loses is current. This is why energy harvesting is a current problem, not a voltage problem.
Drag the operating point across the knee. Slightly the wrong side of it and you lose a lot of power for very little voltage — which is the entire reason a harvester carries a maximum-power-point tracker instead of a fixed load.
Raise the temperature. V_OC drops a couple of millivolts per degree, exactly as in the diode example, because it is the same junction. A hot panel makes less power, and in this model I_S is held fixed so you are seeing only the kT/q part of that — a real cell is worse, because I_S climbs too.
Tick 4 cells in series. The voltage axis scales by four, the current does not, and the fill factor is unchanged. That is why panels are strings and why one shaded cell ruins the string.

THE PYTHON

i_load = np.linspace(1e-5,1e-3,200)
i_s  = 1e-12
i_ph = 1e-3
V_T = 1.38e-23*300/1.6e-19

V_D = V_T*np.log((i_ph - i_load)/(i_s) + 1)
P_load = V_D*i_load

Source: ex/pv.py (against current) and ex/pv_v.py (against voltage) — the same equation, plotted two ways. Neither models series or shunt resistance, so the knee here is sharper than a real cell's.