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LiFePo4 or NMC discharge heatup calculation?

550 Views 11 Replies 4 Participants Last post by  serious_sam
I would like to determine the heat generated by a battery under load.
You can calculate heat generated over time, if you know the internal resistance.
Internal resistance is often specified (in a range). However that doesn't tell the whole story.
Because I am sure the internal resistance in discharge varies over time, because of different power output (higher and lower C rating)
as well as temperature.
What I would like to know is how I determine that. And that in a theoretical way, because I don't have the batteries to do any testing.
This is also because I still need to make the choice which batteries I use.

So for example, we take a typical LiFePo4 cell of around 300Ah (could be EVE or CATL). It is at ambient temperature of 10 degrees Celcius.
Then put a 2C load on it, so 600A. Lets assume the internal resistance is 0.25mOhm because that is often listed.
P = I^2 * R so 600A^2 * 0.00025Ohm = 90W dissipation in the cell right?

Lets say the cell weighs 5.5 kilogram.
And specific heat of LiFePo4 is listed at 1130 J/kg.K (but this number varies over temperature right?)

For 1 minute load of 600A means 90W for 60 seconds is 1.5 Watthour = 5400 Joules

Then heat capacity of LiFePo4 at 1130 J/kg.K
5.5 kg * 1130 J/kg.K means that it needs 6215 Joules for the cell to heat up 1 degree. Right?
So at 60 seconds it will have almost raised 1 degree, actually 0.87 degrees to be exact.

Does the above sound about right or did I make big errors?
I expect the internal resistance to change based on temperature and amount of current drawn.
The same goes for the specific heat, but it might not have a huge impact on the calculations.
And it seems that internal resistance will also become larger as the state of charge drops.

Of course, it leaves out any heat up of busbars and other connections, or inverter/motor etc. It is just about the batteries.

Background: I am checking if I should use LiFePo4, which I could keep at atleast 10 degrees Celcius (which is better when you draw some current)
in an insulated box. Of course, under load (2C will be maximum motor power draw) it will heat up, and due to the isolation not so easy to lose that heat.
However, if the rise in heat is acceptable, than I think it would be a great setup. Skipping a battery cooling system for simplicity.
But in general I am trying to understand the theory, to later verify it in practical test.

Edit: For some NMC EV cells you can find a bit more info, like discharge internal resistance for several conditions.
See the example below of a Samsung SDI 94Ah cell (as used in BMW i3).
At 94Ah you need three in parallel to be comparable in energy density (ok NMC has higher voltage but just for simplicity)
So internal resistance of 0.7mOhm becomes 0.23mOhm and thus very comparable to LFP heat up profiles?
Only specific heat is a bit less per C/kg.K so they heat up slightly faster?
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5,383 Posts
Everybody and his dog measures battery temperature and turtles the vehicle if even one cell gets high in temperature from high discharge.

If predictive models were accurate enough, the industry could save tens of millions of dollars by eliminating the components and related assembly costs with measuring cell temperatures.

Since they are not using predictive modeling, anything you do in this space falls under academia...of no practical use, but some suckers might grant you a PhD if you BS it well enough in a thesis or paper.

So, no, it's not done, doesn't exist, and is so variable over time and per cell it is totally pointless. But you can wow them at a conference 馃槀

5,383 Posts
We should smack some batteries together with a motor, put the pedal to the metal, and see whatever burns down first.
We use a BMS to manage our batteries, which uses precise voltage measurement, temperature measurement, and coulomb counting. We set limits on inverter operating parameters.

This is feedback-based control. Nothing burns down when you floor it, but it will go turtle on you when the BMS gets fed up with your childish driving or craptastic vehicle architectural design.

What you want to do is feedforward control based on predictive multidimensional models that don't comprehend reality.

Mathturbation, in other words. Some people can't let go of, or get past, theory - the fundamental difference between science and engineering (which is applied science). Science can't design a car until it has an equation for it.
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