Understanding PV Cell Modeling: Single vs Double Diode

[willDavidson]

TL;DR

I an trying to understand the PV cell diode and double diode model

I am looking at modeling a PV cell and I'm trying to understand the real difference between the single diode and double diode mode. I now realize that I don't fully understand the purpose of the diode in the model in the first place. I've just learned that it was there and went with it. I understand that it's supposed to represent a PN junction but I'm not sure what that really means at the end of the day.

Any discussion on this topic would be helpful. Also if anyone has suggestions on when to use the single or double diode model that would be helpful too. I am currently reading on the topic too.

 

[Baluncore]

https://www.pveducation.org/
https://www.pveducation.org/pvcdrom/characterisation/double-diode-model

 

[willDavidson]

https://www.pveducation.org/
https://www.pveducation.org/pvcdrom/characterisation/double-diode-model

Thanks, PVEducation is a useful. One of the parts that's got me on all of the equations is they seem to use the current (or current density) that you're looking for in the equation. Here I see J defined as the current density. There's also J01 and J02. I understand that I'm looking for J and J01 and J02 are a parameter for diodes 1 and 2 respectively. How do you solve the equation for J and J is part of the equation in the exponential?

Other equations I've found use current I but either term make sense to me.

 

[Baluncore]

How do you solve the equation for J and J is part of the equation in the exponential?

The equations requiring solution will depend on what type of model you are contemplating.
What is the purpose of the model?

 

[willDavidson]

I would like to find the current at a given voltage.

 

[anorlunda]

I would like to find the current at a given voltage.

Do you mean this curve?

 

[willDavidson]

Do you mean this curve?
View attachment 280165

Yes, basically I would like to find a value along that curve. Looking at the equations for the single and double diode model, The equation for I has I wrapped up in the exponential as well. I'm not sure how to solve that or if I in the exponentials are a different I than the output current.

 

[Baluncore]

I would like to find the current at a given voltage.

It is probably rational to model the PV cell performance parameters at a specified fixed illumination. The operating point may be dynamic, determined by small variations of the external loading. If the load is defined as a voltage with a series resistance, then a load line can be plotted that intersects the VI curve. That would model a battery or capacitor being charged through a series resistance. The changing load voltage and resistance may be determined by a controller searching in real time for the maximum power point.
The model will be determined by why you need to model the PV cell ?
What software system will use the model ?

 

[willDavidson]

If the load is defined as a voltage with a series resistance, then a load line can be plotted that intersects the VI curve. That would model a battery or capacitor being charged through a series resistance. The changing load voltage and resistance may be determined by a controller searching in real time for the maximum power point.
The model will be determined by why you need to model the PV cell ?
What software system will use the model ?

I was hoping to model a PV cell to look at the transient performance due to changes in irradiance due to issues like rapid shading since the response time of a PV panel is pretty much instant. I'll be using Matlab for this part which is why I'm interested in solving the equation referenced above. I know that I can use the solve function in Matlab and it will do its thing to solve it, but that still leaves me lost about the general equation. Breaking apart each piece of the equation it seems to make sense except having J (or I) on on both sides. Trying to solve for J by hand, I either have J in an exponential or J ln(J). Is it only possible to solve this using a iterative or numerical methods?

 

[Baluncore]

Is it only possible to solve this using a iterative or numerical methods?

Probably.
At some point you must connect the PV cell to a load.
When you do that you may find that the system is constrained and the equation becomes more tractable.

 

[willDavidson]

Ok thanks. I think my question from here may be more math related so I'll take continue the math topic there. I'm not sure how to link the thread in case anyone else is interested, but I'm really curious how to solve that thing. Even if I make some highly inaccurate assumptions to simplify it as much as possible, I get something like J*exp(J)=[constant]. I'm still lost on how to solve for J in the very simplest form.

That is letting J01=1, q/kt=1, Rs=1, Rshunt=infinity, V=0

 

[willDavidson]

Ok so the solution to this is the Lambert function.

https://www.physicsforums.com/threads/solving-y-exp-y-constant.1001440/