IV discharge curves for a working Prius 12V battery?

Anybody have a link to a table or plot of I vs. V for a healthy Prius 12V battery at various SOCs? The AGM battery Toyota sells, not a generic AGM plot.

The 12V battery in my car tested "good" at the auto parts store today (not sure what model tester but it was big and brick shaped and had a small fan blowing to carry off heat), and also with the little Harbor Freight battery tester:

12V Digital Battery and System Tester

However, if it is 12.51V with the car off (~20mA load), it falls to 12.31V with ~1A load (car to READY, then off, fob left plugged into dash), and 12.15V with 2.22A (ACC mode). Current measured with a UT210 ammeter clamp on the ground strap, and voltage on the battery posts, in all 3 cases. The spec for the battery is 320 CCA, which is about 45 Ah. 1/45 = .022C and 2.2/45 = .049C. Looking at the first table "Open Circuit Voltage of AGM Battery" and second table "AGM Battery Voltage under Discharge Condition 0.1C" here:

https://sunonbattery.com/agm-battery-voltage-capacity/

we see that the battery was initially about 70% charged. From the second table, at 0.1C (4.5A) that should be a voltage of around 12.15V (extrapolating between 60% and 80%). So .36V drop due to the current, if this was the reference battery. Measured on the battery in my car though it is 12.15V at .049C. That is, it acts like it has twice the internal resistance of the battery in that link, if all of the voltage drop is assigned to that factor. An IV curve or table for the same type battery would tell me if they are all like this.

The HF tester says the battery has internal resistance of 8.3 to 8.6 mOhms, which is higher than the 2 mOhms usually cited for an AGM battery. It was also 3 times the internal resistance measured on an old conventional 12V truck battery.

All discharge tests show the battery capacity (in CCA or Ah) is close to that on the label. Yet the battery charges to "full" from 12.5V (no load) in less than 5h15m on a Battery Tender Junior, which is nominally 0.75A. .3 * 45 = 13.5A, but .75 * 5.25h =~ 4Ah. In other words by charging rate it seems to have less than 1/3 of the capacity. It has done this twice now, with slightly different times, probably because the temperature was different.

So by some measures this battery is good, but on others (like charge time) it is way below capacity. Something odd is going on. This unit is still within 2 years from when it was purchased, but I'm pretty sure if I show up at the dealer they will just slap it on a tester like the one at the auto store and declare it not only good to go, but as good as new! (I started looking at this because MPG had fallen to around 40. When in use it seems to be dropping voltage much too fast. The car isn't being driven much, but charge all the way and reinstall and it falls down to 12.2V on the MFD in ACC in a couple of days. The MFD shows 14.1V in READY mode.)

I also looked high and low for a parasitic load that might have damaged it or be dragging it down. Couldn't find one. Once the car settles down it goes to 20 mA, which is normal. I cannot rule out that it wakes up in the middle of the night and runs something, but there is no evidence that it does so. The only consistently weird thing I see now is that when checking the voltage in ACC mode there is always a glitch briefly (one reading) up above 13 volts a minute or two minutes after starting to look. Today it was reading 12.0V and jumped to 13.4V, then back down again. That one I really don't get - either there is some other stored energy briefly brought into play, or the MFD consistently misreads or misdisplays one value around that time point.

 

Nice theory. The problem is that observations don't agree with it. It is a common observation that MPG decreases as the 12V battery declines. The last time I had a 12V battery die exactly the same thing happened - the MPG became progressively worse, and it jumped right back up into the 47-49 range when the new battery was installed. This time I noticed the MPG dropping and subsequent testing of the 12V showed that it was indeed on the way out. I think the fault in your logic is exactly that it is being charged, and charged, and charged, and that must not be very efficient, because it shows up in the MPG.

I ended up driving the car over to a dealer today to see if they could/would test it. Before doing so two different people on the phone insisted that the battery must be in the car for them to consider warranty, and it has to go to service. When I get there, of course, service said exactly the opposite: it has to be out, and go to the parts department. They kindly offered to test it, with the caveat that they would bill $190 to reinstall it (or the replacement). I did eventually get the service manager to confirm that the "test" was indeed just plugging it into a conventional 12V battery tester. I knew it would not fail that, as I had already tested it that way. By my calculations the battery has a capacity of about 12.5Ah (roughly1/4 of a healthy battery), but that sort of test only takes 1 to 3 Ah out, so it would certainly not collapse the voltage enough to fail. A Prius 12V would need to get down to 5Ah or less to fail that test. So I left.

For future reference, here is how to figure out the capacity (if no external load is available). Unhook the battery from the car. Charge the battery to max, let it sit overnight. On this battery it was 12.74V. Reattach it. Put the car in IG-ON with all lights off, all doors shut, AC off, cabin fan at 3rd highest setting (one above the middle). On my car that resulted in nearly exactly 20A current coming out of the 12V battery. Drain for 15 minutes. Turn car off and wait 20 minutes or so for the voltage to recover (all doors closed, car locked). That was 12.22V. Look up those voltages on an AGM SOC table. Top one is 90% SOC, bottom one is 50% SOC, and 5Ah out. So divide 5 by .4 and get a capacity of 12.5 Ah (roughly, not sure how big the error bars are.) This would probably be close on any Gen 2.

Maybe worth putting this thing on a modern 4A charger and see if the high frequency mode improves capacity any. I have a HF 4A charger

4 Amp Fully Automatic Microprocessor Controlled Battery Charger/Maintainer

but it isn't clear that it goes into any sort of special restoration mode unless the battery is very low. As is typical of their documentation, it is pretty vague about exactly what it is doing. CTEK makes better chargers, but their 4A model is actually 4.3A, and supposedly this Prius battery should not be charged at over 4A. I had the HF charger on for a couple of minutes, just to test, and it was only putting in 3.8A, so below that limit.

 

Isolating the battery from the car while charging and resting avoids the possibility of any intermittent parasitic load changing the "full" voltage. It is also 100% safe - a charger cannot blow up delicate and expensive Prius electronics. This is more of a concern for larger currents. When trickle charging an already mostly charged battery I wouldn't worry as much, since the trickle charger is designed to run in that mode. That said, I once tried to charge a different battery through the open hatch, which worked poorly, since it was only a .75A charger and "door open" causes a .5A drain even though no lights were on. Had the battery been disconnected, it would have worked as intended.

No safety reason to disconnect the battery when testing as long as the car is well and truly off.

IV is current vs. voltage. It is a common plot for things like diodes or transistors. For a given SOC V will go down as I goes up. Made up numbers for 100% SOC might be
0A 7.8V
1A 7.7V
2A 7.5V
and so on. This information is usually plotted as V vs. SOC for constant I, as in this plot

https://www.researchgate.net/figure/Li-ion-cells-voltage-curve-at-different-discharge-rates-at-25-o-C_fig8_4185795

I thought it might be one way to determine the SOC from the ACC voltage value, as current in that mode had been previously measured.