I'm doing a model on battery ageing (mostly capacity fade and internal resistance increase).
Then, as I'm seeing around, the Arhenius function is used for calendar ageing (no current through). I've related it to SOC, as at higher SOC and T faster ageing is found.
But when referring to dynamics, I'm not sure if the T effect is simply multiplied to the other factors (C-rate and Voltage) or it should be considered as an additional factor to consider appart from temperature. Most of the models do it together, but I really doubt it.
The DOD, Is considered logaritmically. But is it also related to T in the same way?
Thank you very much
Lluc Canals Casals
Dear Lluc,
I work at the laboratory scale and I am not really familiar with SOC and DOD problems. The thing I can tell you is that C-rate has a dependency on T although it might not be that simple to modelize it.
You see, T decreases the viscosity of the electrolyte and at the same time increases the conductivity (ionic) of insulating electrodes such as LiFePO4 or (better) Li2FeSiO4. In this way, T can help you increase the C-rate for faster charge/discharge cycles.
On the other hand, the electrolytes are generally organic solvents which don't really like T (evaporation, accelerated decomposition, etc.)
Everybody does it calendar (no current) because it's the easiest way (less parameters to link) and because T increases the ageing rate (as you say at higher SOC and T there is faster ageing but this is general, also at lower SOC with T ageing is faster respect to the same SOC at 25°C).
So I guess I just messed your work up a little more.
Hope this helps.
Thanks to all.
It really is something a little bit complicated.
I think that the relation should be somethink like:
Storage + Cycling
(a·Arrhenius)·t^C + (b·Arrhenius)·I·SOC·log(DOD)·t
That's why I'm asking about the relations of T and C-rate, SOC and DOD, in order to put them together or if each one has an specific relation with T.
I'l look a little bit more about it and yet I hope to receive more interesting oppinions.
Lluc
Dear Lluc,
in my opinion this question depends strongly on the used materials and it will be difficult to introduce the dependency just by a mathematical model without describing the real processes behind it.
A nice paper on this topic is link.
Kind regards,
S. Wolter
http://www.sciencedirect.com/science/article/pii/S0378775314004352
Thank you!
True, I don't pretend to do it for all cells in the world, just for one type of cells. But each reaction has to be, in some way or another, related to a matematical explanation. The question is, how to introduce them all?
Dear Lluc Canals Casals,
note, please, that a battery is a very complicated device. We have to realize that there are many reactions j taking place in this "box", even at storage phase, with a specific Temperature evolution Rj(T). I propose to simplify the problem focusing on the cathode electrode (e.g. only ONE parameter). One good tool is the EIS. Then you may address the ageing factors related to Temperature via the electrical equivalent elements Ej of the model, e.g. Ej(T) evolution with Temperature.
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