EE/Battery max current question

[JHZR2]

Hi,

Trying to figure out an electrical question pertaining to batteries.

One might say that a battery's maximum "power", or discharge current in reality is based upon what provides a practical value of the equation:

Vt=Voc-IR where Vt is the terminal voltage, Voc is the terminal open circuit voltage, and IR is current times internal resistance.

So for, say, a 30mOhm internal resistance in a 1600mAh Li-ion 3.7V cell, one would notionally be able to discharge at up to 23A, since 23*.03=0.69, and one would not want to discharge a Li-ion cell past 3.0V.

Yet at the same time, manufacturers generally only rate their cells at up to 3C or 10C in some power designs, which corresponds to 6-16A for a typical small Li-ion cell. Is that purely being conservative, or am I missing something on the load side?

As I understand it, maximum power is obtained when load and source impedances match. I suppose then you could say that:

P = V^2 / (2R) where the R is the internal resistance of the battery, but matched identically to the load.

Then, one would say that for that cell: Vt=Voc-2IR, right?

So then for the max 0.7V drop, max current would be 11A roughly.

Does this make sense from a basic electrical perspective, and am I missing something in terms of how a max rating for a small cell is created?

Hope this is clear enough in explanation and my thought process.

Thanks!

 

[mahansm]

You are correct in your calculation of the maximum power obtainable from the battery. However, at this discharge level the battery will overheat fairly quickly. Also, the battery is not a pure voltage source, as the current is the result of a chemical reaction that occurs at a finite rate.

The manufacturer will generally give ratings for discharge rates the cell can sustain without damage. You will note that the higher the discharge rate the lower the energy you can obtain from the cell. The total current in amp-hours will also decline at higher discharge rates.

Battery engineers can optimize a number of different parameters in cell construction but, as always, there are tradeoffs. A large active area and robust current conductors will support high discharge rates but will lower the total capacity. It's always a tradeoff between discharge rate, charge rate, max energy capacity, cycle life, safety, and other parameters.

Steve Mahan
MSEE

 

[mechtech2]

In street cars, I always recommend as big of a battery as will fit.
For everything else, it is what it is.

 

[mechtech2]

Whew! Well, he DID warn us it is wordy and redundant!

Basically: If your oil gets real hot, use a thicker oil.