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I am trying to determine a battery's internal resistance using the open circuit voltage, terminal voltage, and load current for each battery cycle.

As per my current understanding, these calculations must be conducted at a particular charge of the battery (Li-ion). Initially, I note the open circuit voltage of the battery at that charge and then connect a load, then determine the internal resistance and do the same calculations for each battery cycle at the same charge. So my question is, what is the correct battery charge to conduct these resistance calculations?

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    \$\begingroup\$ All of them. Then you can plot the resistance vs state of charge and see how it varies. Use the highest value above normal exhaustion if you need a single value. \$\endgroup\$
    – user16324
    Aug 23, 2022 at 11:09

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Depends on the chemistry.

For nickel-based batteries and alkaline batteries, the resistance changes with the charge level. Interestingly, some batteries show the lowest internal resistance when the charge level is almost half. Older lead acid batteries tend to show an increasing behaviour i.e. internal resistance increases during discharge and hits to its maximum when empty.

For modern lead acid batteries and lithium-ion batteries the internal resistance stays almost flat for the entire operating range. So it doesn't matter what charge level the measurements are taken at.

And also it's worth to mention that the temperature has a significant effect on internal resistance. And for some battery types the internal resistance is a great indication about the life i.e. the internal resistance tends to increase as the battery approaches to end of life. So, apart from charge level, the battery health and environmental conditions are also important.

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You perform the test at the state of charge that's appropriate for your use.

If you are a battery manufacturer and want a repeatable way to check cells, then you'll pick one state of charge. The most convenient and easiest to reproduce is fully charged. If you want to publish the figure to potential customers, then you'll probably want to push the best figure (if you're one type of manufacturer) or a worst case figure (if you're a responsible manufacturer), and you'll choose a SOC based on that. Different chemistries have different resistance to SOC curves, and they're all temperature dependent.

If you're using the battery, and want to see whether it will still drive your circuit adequately, then you need to measure the internal resistance at all SOC's down to the minimum the circuit will accept.

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If you want whatever's connected to the battery to operate right down to the last drop of battery charge, then you must consider its internal resistance when it's nearly discharged. That's when attached circuitry will receive the lowest battery terminal voltage.

Commonly we wish to determine which batteries would be suitable for a given application, where we are more interested in knowing at what charge state the battery's terminal voltage becomes too low. For example, a battery which is still 50% charged, but has too much internal resistance to supply the required current and terminal voltage, might not be considered suitable. Here we are more interested in defining some maximum acceptable internal resistance, and finding the charge state corresponding to that.

Vehicles with internal combustion engines keep their own batteries charged, and the battery is only really expected to provide sufficient engine cranking current while it's holding a significant charge. In this case, you might be interested in the internal resistance of a 50% charged battery, using this figure as "worst case".

Sometimes the type of battery is not debatable (perhaps due to size or weight constraints), and the attached circuitry has to be designed around it, not the other way around. In such cases it's more useful to have a graph of internal resistance at all charge states, and maybe even graphs relating internal resistance to battery age, or charge cycle count.

Some applications might require a battery to only ever be used when near-fully charged. I am reminded of questions from people who use "ignition fuses" to launch home made rockets. My response is always to consider the internal resistance of an 80% charged battery.

So the answer is, as usual, "it depends".

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I don't use any percentage of charge to do this test, because it is difficult to estimate.
So, only "full" charge should be a "repeatable" test. For my own uses, I check the internal resistance at a current like C/10 A or C/2, whatever the charge is.

Example: if capacity = 2000 mAh, I would test it at 0.2 A ... or 1 A.
But I could use also 2A (or more) under pulse conditions (in case of non-linear internal resistance).

Some batteries should be tested at bigger currents, whatever the charge is.
Example: if C=10 Ah and max current can be as high as 300 A (some more ...), I would test it at 300 A, always in pulse conditions ... because I don't have a precise resistor as needed for such test, and because it is specified until 300 A.
This kind of test can be done, using the battery with a dedicated circuit, and whatever battery is in use or not.

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