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How to calculate Voc(temp) using one-diode model I=0 ?


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I have got a batch of CIS modules of which some of them suffer PID. Before sorting the modules on Isc I'd wish to sort the modules on the amount of PID degradation. As an example Voc=30V instead of 72,8V at STC.

The idea is to measure Voc outdoors, as well as G and T. From G and T the expected Voc(G,temp) minus a percentage is displayed. Let's say -3,4% for bin 1 lowest value, -9,8%, -15,8%, and -21,3%. The exact voltages change real-time with outdoor irradiance and temperature. Resulting in 4 sorting bins + 1 trash bin.

Now I wish to calculate Voc (G,temp) according to the post at https://forum.pvsyst.com/viewtopic.php?f=23&t=3764&p=9161&hilit=one+diode+Voc#p9161

That post suggest to set I to 0 to calculate Voc.

I=0 results in Iph = Io · (exp(something) -1) + V/Rsh. Thus V = Rsh · (Iph - Io·(exp(something) -1)).

I manage to calculate: Gamma(temp), Rsh(G), Iph(G,temp), Io(temp).

Now I am stuck at exp(something). Because "something" = q · V/ ( Ncs·Gamma·k·Tc), that is that it contains voltage again, and that voltage is within the exponential.

How to calculate Voc according to the one-diode model, with G and Temperature as input parameters?

What will the to be expected differences in Voc values look like between calculated using that formula and the PVsyst Voc results (for temperatures between 5 and 30ºC and irradiances between 100 and 1000 Watt/m2)?

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Without a clue how to manually check / calculate the one-diode model its Voc, I ended up with exporting the data of the module graphs at different irradiation's (100-1000W/m2) and temperatures (5-45ºC). With that data

a.) a 5th grade polynomial regression was determined, resulting in 99,99954851% fit at 25ºC, and

b.) applying a 2nd grade polynomial regression for the temperature correction muVoc (100% fit).

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