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Equation for Rshunt exponential behavior


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The help file for PVsyst 6 has the following expression for the Rsh dependence on irradiance:

Rsh = Rsh(Gref) + [ Rsh(0) - Rsh(Gref) ] · exp(-Rsh exp · (G / Gref))

As Rsh(Gref) is the Rsh value at the reference irradiance Gref, equating G to Gref should lead to Rsh = Rsh(Gref).

However, Rsh(G=Gref) = Rsh(Gref) + [Rsh(0) - Rsh(Gref)] * exp(-RshExp) = Rsh(Gref) * { 1 + [Rsh(0)/Rsh(Gref) - 1] * exp(-RshExp) } which is not equal to Rsh(Gref) unless Rsh(0) = Rsh(Gref).

For the generic module "Poly 285 Wp 72 cells", where Rsh(Gref) = 550 Ohm, Rsh(0) = 2000 Ohm, and RshExp = 5.5, the exponential expression as shown in the help file leads to Rsh(G = Gref) = 555.9 Ohm, about 1% higher than Rsh(Gref) value of 500 Ohm. Pmp-wise this is not a big effect (~0.1W), but still non-zero.

I wonder if the help file description is consistent with the actual Rsh calculation within PVsyst 6? To me it would be more plausible if a separate term "RshRef" was being used internally where

Rsh = RshRef + [Rsh(0) - RshRef] * exp(-RshExp * (G/Gref)) and

RshRef = [Rsh(Gref) - Rsh(0)*exp(-RshExp)] /[1 - exp(-RshExp)]

Then you actually get Rsh = Rsh(Gref) when G = Gref.

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