Consider the configuration in picture, where a solar cell is kept at fixed distance from a light source and the load resistance is changed among different values.
simulate this circuit – Schematic created using CircuitLab
What mathematical relation is there between current and voltage while Rv is changed?
Since the solar cell is at constant distance from source I expect constant open circuit voltage of the cell \$V_{op}\$, therefore it should be
$$IV=P_{load}=\frac{V_{op}^2}{(R_v+R_i)^2} R_v\tag{1}$$
But also, at the same time, $$I=\frac{V}{R_v}\tag{2}$$
So will the current-voltage curve be the intersection of these two curves?
I found on many sites that the current voltage characteristic of a cell is a curve like the one in picture.
Is the blue curve what I would find also in the situation I described? That is, are the blue curve points given by the intersections of \$(1)\$ and \$(2)\$ (for different values of \$R_v\$)?
Or is the blue curve in picture given by different mathematical relations? If so, what is this relation?
Best Answer
You assumptions on the impedance of the PV are incorrect but your understanding of the curve for P=VI is correct.
The PV is not a voltage source with a fixed Ri. From a short circuit it behaves like a constant current source( modulated by solar intensity) and from no load it behaves like a lossy voltage source with Ri.
MPT occurs where the the slope of P=0 or dP/dV=0 or dP/dI=0 where the ESR is the slope of the VI curve, ESR=ΔV/ΔI
Can you see how VI curve slope is actually source impedance which changes with V.
Do you think there is any relationship between Voc/Isc=Ra ( some value Ra) and ESR at MPT?