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rkalebbo1-Visitor
1-Visitor
August 22, 2016
Question

Mathcad 15 - Problem with Modelling I-V characteristic of Solar PV cell

  • August 22, 2016
  • 12 replies
  • 6007 views

Using the root function, I have plotted a graph to show the I-V characteristic of a PV cell which is characterised by the implicit equation:

I=Iph-Io [exp((q(V+IRs))/akT)-1]- (V+IRs)/Rsh

Varying any of the parameters within the equation is expected to affect the I-V characteristic in a particular way. The plotted graphs takes on the expected shape but when I try to change the value of temperature, the plot shifts in an unexpected direction. Increasing temperature should lead to a decrease in open-circuit voltage and thus decrease in output power, but the model I've plotted suggests the opposite i.e. an increase in temperature leads to an increase in open circuit voltage which contravenes PV theory. Short circuit current (current when V=0) has a (slight) positive temperature coefficient while open circuit voltage (voltage when I=0) has a negative temperature coefficient.

In contrast, when I vary other parameters like , Iph, Io , Rsh and Rs, the results are consistent with PV theory e.g. increase in Iph leads to an increase in short circuit current and an increase in output power as expected from PV theory.

Please advise on how I can correct the model to be fully consistent with PV theory. I'm relatively new to Mathcad and I urgently need to resolve this problem for a paper I'm working on.

Please see attached worksheet.

Mike Armstrong‌, Valery Ochkov‌, Richard Jackson‌, AlanStevens (I've tagged you because I've seen your posts all over the community pages... I hope you can help... that's not to deter any other contributors though! )

12 replies

A
AlvaroDíaz12-Amethyst
12-Amethyst
August 23, 2016

Hi.

Your model seems to be ok, but I guess that the problem is that you take Io, the diode saturation current, as constant, which isn't the case, and vary also with the temperature, which make it less efficient for increasing temperatures, where "it" actually isn't the "diode", it is the PV by itself. PV makers give parameters and models for the Isat or Io in your notation. For the others plots, Io is constant.

Best regards.

Alvaro.

plot.gif

R
rkalebbo1-VisitorAuthor
1-Visitor
August 23, 2016

AlvaroDíaz‌ thank you for your response; that does produce the desired shift in the curves. I would like to improve the model a bit by incorporating temperature dependency of Iph and Io . I think I may need to define Iph and Io as functions of temperature but so far my attempts have not been successful resulting in problematic curves as before; it seems only the initially set values of Iph and Io are used in evaluating "I" in the worksheet I've created. Can you advise on how to ammend it so that when the value of T is changed, Iph and Io are evaluated before solving for "I"?

R
rkalebbo1-VisitorAuthor
1-Visitor
August 23, 2016

AlvaroDíaz I forgot to attach the worksheet before! See attached

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-MFra-21-Topaz II
21-Topaz II
August 23, 2016

Hi ,

It happens that for the same (irradiation) power (note !!!), as the temperature increases (taken as a parameter), the power (and the current) curve (as a function of the voltage produced by the cell), has to move to the left. Your graphics, although they are accurate, however do not consider the same irradiation power for each of the three  values of temperatures (parameters), as the voltage varies.

Bye

FM

irradiance.jpg

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