Simulink: Thermal conductance in a PV system

Dear community,

I am trying to simulate the heat transfer in a PV system. There, I am struggeling a bit with the thermal conduction. I try to explain as good as I can what I try to achieve and what I did so far, so bear with me reading this short text :).

So far, I have implemented:

• Heat transfer by sun irradiation (on solar cell level)
• Heat transfer with atmosphere by radiation & convection (on solar cell level)

To complete my simulation for now, I miss the heat transfer with atmosphere by conduction (on solar cell level)

I looked into several examples (Photovoltaic Generator, House Heating System, Motor Thermal Circuit) to get an idea of how the thermal conduction between different bodies may be simulated. In my understanding, I would need to use a thermal resistance between the two bodies. Another alternative suggested by literature is the one in the image below: putting the conductive heat transfer element in series with heat transfer by radiation/convection, where the "Conductive Heat transfer" elements are filled with the area & thermal conductivity of the cell. But here, I am struggeling with the thickness I should enter.

Which would be your implementation?

I hope my questions are clear. A consent would already be enough, although I prefer a more detailed explanation to understand Simulink/Simscape better and enjoy the software even more!

Thank you all in advance.

[Philipp Wälchli]

Dear community

Anybody able to help me here? Would welcome any comment, even short notices if a similar question was already asked.

Thank you in advance!

Answer 1

[Chuan Liu]

Hi Philipp,

My knowledge of heat transfer are strongly based on electrical machines on a very practical level, which might be different to what you are studying, which means that I might be completely wrong about this.

As far as I know, for such scenarios, the heat transfer between the solid and the fluid is normally doninated by convection, since the thermal conductivity of the air is very low and the process is in open space. Furthermore, in practice the conduction is often included in convection, becasue it is usually impossible to seperate the two with normal measurement techniques. However, in some circumstances the two methods of heat transfer can be and will be seperated due to research interests, e.g., boiling water in a kettle.

For your case here, I believe you could model the air and the sun as two individual nodes, and connect them to your PV cell with convection and radiation respectively.

[Philipp Wälchli]

Hi Chuan

Thank you for your contribution!

I partially agree with you. My model has two separate thermal contributions: One is the interaction of sun with the solar cell, i.e. heating up the cell by irradiation. The second part is the atmosphere, which influences the temperature of the cell. Both convection and radiation play a key role there, as the solar cell radiates to the cooler atmosphere while convection takes place simultaneously.

But I agree with you that the conduction can be neglected, as it is a minor contribution. Nevertheless, I have to model the thermal conduction between the cell and the atmosphere. It is a part of my work and I am unfortunately not able to neglect it.

[Chuan Liu]

Well in that case I suppose you can try to add a conduction element in parallel with the conduction element. May I ask what technique do you use to measure or calculate the conduction to air?

[Philipp Wälchli]

Hi Chuan

Alright - and which parameters would you use in the conduction element? The ones from the metal or from the air? I am not actually measuring the conduction-to-air; so far I am still in the simulation stage. We are calculating it the equaiton which is also listed here: https://www.khanacademy.org/science/physics/thermodynamics/specific-heat-and-heat-transfer/a/what-is-thermal-conductivity

[Chuan Liu]

Hi Philipp,

From what I understand, what you are trying to do is to separate the diffusion (conduction) component and the advection component from the convection. Is that correct?

If that's the case, it might be more convenient to use thermal resistance cell for both the conduction and convection components, since none of them can be easily calculated by the parameters involved in those cells if you intend to separate the two. You might need to do some calculation by hand to determine the resistances, which would require some additional knowledge beyond what's presented in the weblink.

Again, I'm not an expert on this matter, there might be some better way to do this, and I may be completely wrong (especially if your device is intended to be used in extreme environment, such as zero-g, extreme temperature/pressure, exotic atmosphere, etc.). I suppose you could start by finding a proper empirical correlation for Nusselt number (you can find them in many heat and mass transfer textbooks), so that you can determine the HTC in your case. After that, you could calculate the overall thermal resistance between your PV cell and the atmosphere. Then, you will need to calculate the Rayleigh number based on the parameters of your application. Since Rayleigh number is the ratio of the time scales of diffusion and convection, you may separate them by using this ratio and the overall thermal resistance you calculated earlier.

This could be wrong, but I couldn’t think of any other ways to do this. I’m really curious about your application. In general, such separations are not necessary in most thermal modelling intended for large scale (comparing to molecular level) applications. I think it is more concerned in fluid mechanics and chemical engineering. May I ask what you are trying to achieve by the thermal modelling in this case?

[Philipp Wälchli]

Hi Chuan

Thank you very much for your input, which reallly helps a lot! I think I have now an idea of how I can deal with my problem. The recommended separation sounds promising and I will give a try with that.

I am simply trying to do a very detailed thermal analysis as it is very critical for my project. The exact application I am not allowed to tell, but it has nothing to do with extreme environmental situations. :)

Answer 2

[Hytham Emam]

Dear Philipp and Chuan,

This thread was very useful for me. I wonder if you can help me or point me to the right direction as I want to simulate the heat transfer (mainly through convection) from solar panels on ambient air temperature/density at different heights (10m - 100m) above the the solar PV panels, is this posible?

I'm quite new to using MATLAB apps/tools but I'm trying to educate myself more now so any guidance from you will help me a lot :)

Thanks,

[Chuan Liu]

Hi Hytham,

I would suggest to try to build a lump parameter thermal network for your case on a piece of paper first. Try to identify all the parameters you need and determine the effect of altitude on the convection. After that, you can build the model in Simscape.

This looks like something helpful for your case:

https://www.mdpi.com/2076-3417/7/11/1107/pdf

https://dspace.mit.edu/bitstream/handle/1721.1/39011/20404614-MIT.pdf

Cheers,

Chuan