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.

enter image description here

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?

  • \$\begingroup\$ I do not totally get what you mean, however you should take the non linear behavior of solar cells in consideration. The current-to-voltage relation is similar to a diode. \$\endgroup\$ – auoa Feb 27 '17 at 19:12

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? enter image description here

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