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Determination of the model parameters

Thus for a given temperature and irradiance, we have a model based on 5 unknown parameters (Rs, Rsh, Iph, Io ref and Gamma,).

The value of the shunt resistance Rsh, representing the inverse of the slope of the plateau  I(V) for low V, will be independently treated (that is, fixed in the equations). As it is not possible to deduce it from the manufacturer's data sheet, PVsyst has to choose a default value for processing the Database.

In order to determine the 4 remaining parameters, we can write the 4 equations below, for the specified reference conditions Gref    and   Tc ref  :

-        I(V) at  point   V=0   (short circuit),

-        I(V) at  point    I=0   (open circuit),

-        I(V) at any other point, close to the maximum power point.

-        The derivative muVco  =  dVco / dTc.

These equations are based on the following parameters (manufacturer's or measured data):

ISCref        =        Short-circuit current at reference conditions.

Vco ref        =        Open circuit voltage at reference conditions.

Impref, Vmpref        =        Current / Voltage at any point (close to the MPP).

muIsc        =        temperature coefficient of the short-circuit current.

muVco        =        temperature coefficient of the open circuit voltage.

Unfortunately, the resolution of this system sometimes leads to a solution whose values  (Iph, IoRef, Gamma, Rs)  do not have a coherent physical meaning (Rs negative, Gamma out of its physical validity domain between 1 and 2, ...).
 

Model parameters in PVsyst

This is the reason why we preferred, in the program PVsyst, to use only the first 3 equations and to propose to give the user, with the help of a graphical representation of various solutions, the explicit choice of the resistance Rs, which will completely fix the solution.

The last equation gives an explicit value for  muVco. So, if he knows the value of muVco (often specified by the manufacturer), the user may chose the Rs value  suitable for obtaining this required value  (if possible…).

But for the automatic generation of the model (used for the whole database), we found more reliable to set the Gamma value at a reasonable level (i.e. Gamma = 1.35 for Si-crystalline), which determines the Rs and all other values.
 

NB:  Model parameters with measured I/V characteristics

If the complete I/V curve is known (which is normally not the case in PVsyst), the model parameters can be determined without ambiguity: Rsh is simply fitted on the data around V=0, while Rs is determined by minimizing the errors between the measured and the modeled values (one only free parameter).
 

Reverse part of the Characteristics

Some tools in PVsyst - namely in the study of Shading or Mismatch in arrays - require the knowledge of the reverse characteristics, when a negative voltage is applied to the module  (region V < 0).

This model is not as well determined in PVsyst as the direct characteristics (see Reverse characteristics modeling), but this description is sufficient for understanding the behavior figures in the involved tools. It is not used in the hourly simulation process.