How to define PV module IV curve using given parameters

[sodoyle]

TL;DR Summary

I would like to form an equation for a PV module using data provided on the datasheet. I'm not sure how to use this from the diode model.

I am looking at a solar panel and would like to be able to plot the IV curve for it. I have Isc, Voc, Imp, and Vmp from the datasheet so I can get the fill factor. I know each cells dimension and the number of cells too so I can find the current density if required. Is there a way to use the parameters given on a typical datasheet to form an analytical equation that I can use to plot the IV curve?

Here is a link to a PV module that I found with those parameters.

https://www.mitsubishielectricsolar.com/images/uploads/documents/specs/MLE_260Wp_Spec_Sheet_Feb2013_lr.pdf

 

[Baluncore]

At the bottom of page 2, on the LHS there is a diagram of I and W against V for different levels of illumination. Is that what you want to generate?

 

[sodoyle]

At the bottom of page 2, on the LHS there is a diagram of I and W against V for different levels of illumination. Is that what you want to generate?

Yes, that is what I want to generate. For that, my thought is that I would use the single diode equation which includes series resistance (Rs) and parallel resistance (Rp). I'm not sure how to determine Rs and Rp though.

 

[Baluncore]

I'm not sure how to determine Rs and Rp though.

Cell resistance is typically; Rs = 0.0001 ohm; Typical Rp = 1k ohm;
Run the model and compare the simulation results with the manufacturers data.
Adjust Rs and Rp until they agree.

The equations come in a few different forms.
The way you are going to use the equations will decide the form you need.
Do you want an SPICE PV array module, or a software function ?

 

[sodoyle]

I found a paper that provides an equation to estimate Rs and Rp based on Voc, Isc, Vmp, and Imp. I try using the values they provide for these parameters in a table but I do not get the same results. That means I'm interpreting the equations wrong, but I'm not sure how. A link to the article and what I'm doing is below.

Rs = -(dV)/(dI) evaluated for the section of the IV curve from Vmp to Voc
Rs = -(Voc-Vmp)/(Ioc-Imp) = - (0.58-0.44)/(0-1.93)
Rs = 72.5 mOhm
Their solution: Rs = 37.2 mOhm


They use Rsh instead of Rp, so for consistency with the paper I've used their nomenclature here.
Rsh = -(dV/dI) evaluated for the section of the IV curve from Isc to Imp.
Rsh = - (Vmp-Vsc)/(Imp-Isc) = - (0.44-0)/(1.93-2.2)
Rsh = 1.63 Ohm
Their solution: Rsh = 9.94 Ohm

Am I using these equations correctly?

Looking at it now I see that those were their actual measurements. They didn't provide the values for their calculations but they did plot the results and it was a close match. Based on my calculations, the series resistance is smaller and shunt resistance is higher than their measured. This would lead to a steeper falloff at the knee which is exactly where the largest mismatch was between their model and simulation. Unfortunately, this region is where maximum power is extracted which is the region we're typically the most interested in. This method is the best that I've found so far given the parameters I have available but maybe someone knows a method that provides a closer match?
https://iopscience.iop.org/article/10.1088/1742-6596/1144/1/012012/pdf

 

[sodoyle]

Do you want an SPICE PV array module, or a software function ?

I want a software function. I can start with some guestimates and iterate in Spice until I get a close enough fit. I as just hoping to find a more analytical approach to obtaining a good fit. Any ideas on how to obtain I₀? That's just property of the cell material itself isn't it?

 

[Baluncore]

We must specify more than half a dozen module parameters, then solve for the related V and I. Solar irradiation and operating temperature will be the two critical input variables.

I expect the solution for Io will end up looking something like;
Io = Irs * ( Top/Tref )^3 * Exp( ( q*Eg / ( n*k ) ) * ( 1/Top - 1/Tref ) )
But I find differences across papers in the definitions of the common symbols.

There are different depths of model accuracy available.
Models tend to be approximations that are more rigid than reality.
Or they are too complex and need too many unspecified module parameters.
It will take me time to come up with a reliable and realistic set of equations.

 

[anorlunda]

Unfortunately, this region is where maximum power is extracted which is the region we're typically the most interested in.

If your purpose is to build a MPPT controller, I suggest you search the literature for MPPT strategies. There are several successful strategies that don't necessarily need the kind of model your are seeking.

 

[sodoyle]

We must specify more than half a dozen module parameters, then solve for the related V and I. Solar irradiation and operating temperature will be the two critical input variables.There are different depths of model accuracy available.
Models tend to be approximations that are more rigid than reality.
Or they are too complex and need too many unspecified module parameters.
It will take me time to come up with a reliable and realistic set of equations.

Yes, at the end of the day I would like to vary irradiation and temperature of the module while operating to analyze the systems performance.

The method used in this paper may be good enough. I didn't see where they calculated the ideality factor which would effect the roll off so maybe they used a constant value found for 1000 W/m^2 since its a really close fit at the knee under their 994 W/m^2 test condition.

I didn't expect to see Rsh in the single digit Ohm range. None the less, my calculation was about double their measured for Rs and about 600% smaller Rs than their measured. Based on the previous calculations I showed, am I using the method they showed for estimating it correctly?

 

[sodoyle]

If your purpose is to build a MPPT controller, I suggest you search the literature for MPPT strategies. There are several successful strategies that don't necessarily need the kind of model your are seeking.

I will be using MPPT in the future, but for this I need to these equations to estimate the power available in the system under various conditions. I plan to use Perturb & Observe for the MPPT I think should be fairly straight forward. It won't need to differentiate between local and global maximums.