Predicting a graph from 3 (6?) values?

[Roger Hayter]

Caveat is that battery voltage drops at high current due to reversible changes, so using an underlying open circuit fixed voltage for detecting a given discharge point is too conservative. But, as I say, the makers use a linear relation up to 93A so perhaps it is not outrageously wrong. In any case, unless they tell you how you can't allow for this accurately.

[Dave W]

Please state the type no. of the battery; if more than one how they are connected; what current range you will be using.

[T i m]

They are MK 8GU1H

_MK_r1.pdf

3, in parallel.

0 to 30A (typically

[T i m]

Correct. The reason is because the *time* will vary with load and the load will vary with the situation (this is an electric outboard motor on a boat and not some lights in a caravan etc). ;-)

Correct, as a formula I could apply to an Arduino based 'display / low voltage' alarm.

Ok ...

They are indeed. ;-)

Magic! ;-)

Ok, I follow most of that because it's 'fuzzy logic'. ;-)

Hmm, should it be though (as as you say) it wouldn't be in practice)?

Oh. ;-(

Understood. I can only reasonably expect any gauge to work when the load is reasonably continuous (even if not consistent).

Ok.

Ok, well all I'm interested in is how it would work up to 30A when spread across the 3 batteries in parallel Roger. ;-)

So, sorry, I think I must have missed the conclusion. ;-(

Cheers, T i m

[T i m]

Agreed, and should only be done after resting the battery for 24 hours or so (I read somewhere).

But how does that fit with what they say here?

Or are you also taking that into consideration?

Capacity at C/100 = 36 Ah Capacity at C/20 = 31.6 Ah Capacity at C/5 = 26.8 Ah

They are saying that between that range of currents there is a 10Ah capacity difference, that's over 30% of it's average capacity? Realistically I would only be interested to see how much the capacity changed between say 10 and 30A. *If* the capacity doesn't change much between those particular values then it may not be worth including.

*If*. ;-)

Ok, but if I understand the above info correctly the difference in capacity changes significantly within the range of currents I intend to use therefore (in my mind anyway) making it worth of inclusion in any gauge trying to display the cutoff voltage for a given depth of discharge? As you say, we need the 'how' and I was hoping we might be able to extrapolate that from the information we *have* been given?

Thanks very much for your feedback on this Roger. ;-)

Cheers, T i m

[Roger Hayter]

It depends whether you are trying to predict capacity at a given current, which is where your Peurkert equation comes in. Or just finding out when you have reached 50% capacity. The latter will be indicated by the voltage they mention, and the fact that it was reached proportionately sooner with a lower effective capacity at high current is irrelevant to the problem of detecting when it has been reached. The battery has *been* inefficient at high current and it is too late to do anything about it.

This phenomenon is separate from the *temporary* loss of capacity after a period of high current. The only way to deal with this is to stop discharging the battery well before 100% use of capacity, which is what you are being advised to do when you use 50% as an end point. This makes sense to me though it is a bit speculative.

[Roger Hayter]

50% discharge voltage

[T i m]

No, I wouldn't say I was trying to predict anything (at this point anyway ), but calculate it from the current characteristics?

Yeah, that's the badger. ;-)

(at the discharge rates they mention, so far ...)

Ok, so, let's say that the battery would reach 50% depth of discharge if we were going along on speed 1 (of 5) in 3 hours. The alarm beeps and I know I might damage the battery any further so stop (the device has done it's job).

Then I fit the second battery but it's starting to get dark so we want to get home quicker so I put it on speed 3 that will have the alarm going off in 50 minutes (again, the device has done it's job).

The point is that in each case the only information that will be used to determine the battery voltage but with a rider that is a function of the current current being drawn.

And this isn't me imagining anything or making things up, this is scientifically proven fact that is measured and well published.

Of course.

Quite.

And why I'm trying to apply *some* science to whatever I end up with?

If I set the low voltage threshold to a voltage that would represent

50% DOD when discharged at 5A the alarm *will* sound prematurely when running at a higher current. Now I could take that on the grounds that at least it wouldn't over-discharge the batteries but I wouldn't get the full capacity either. ;-(

I'm not asking or expecting any solution to be an accurate measure of the DOD, just that I think I should be able to better than using one set voltage over a range of currents when we *know* the voltage will vary as a function of the current drawn?

Cheers, T i m

[T i m]

50% is often given as the maximum depth of discharge (DOD) as it typically represents a reasonable output of energy whilst giving a reasonable battery life.

Cheers, T i m

[T i m]

Ok, they look like numbers O could see in an Arduino sketch. ;-)

I can (TAIAP), several times a second. But we aren't measuring Ah are we, we are (only needing to) measure the instantaneous voltage and compare that with the instantaneous current and from those two calculate the instantaneous low voltage thresholds (rinse / repeat)?

eg, It will (very predictably) cope with the (example) scenario of me going continuously at speed one (5A) for three hours before the alarm sounds. It will also / equally easily cope with me going along at speed 3 for 50 minutes (15A) or speed 5 for 20 minutes (30A).

So stage one is using the (non linear) runtime / 'voltage that equals

50% DOD' divisor (that operates increasingly as the current goes up ITRW) as a constant over the entire battery use. Stage two is to dynamically calculate that LVD voltage as a function of voltage current and do so once every second. Stage 3 might be to store and hold and average those values over say 60 seconds to protect against a few second burst of speed 5 tripping the alarm whilst generally going at speed 3.

See above?

Cheers, T i m

[T i m]

Now, as an aside, because we may only go electric outboarding 10 times a year, we may decide to push the battery to say 100% DOD (which is near 10.5V, *not* 0V etc) because, according to the chart, even at

100% DOD those batteries should offer 450 cycles which would mean 45 years use at that usage rate!

However, the closer you go to 100% DOD the greater chance of doing irreversible damage to the battery, something I'd prefer to avoid.

That said, once we have the potentially 'arbitrary' 50% DOD covered, it would only be a matter of changing a couple of numbers to allow any program / formula / calculation to adapt accordingly and take it to 60 or 70% DOD. Better run time at the expense or a lower cycle life.

Cheers, T i m

[Roger Hayter]

This is where I think you are slipping into a fallacy. Although the capacity has been less at the higher current, you have *lost* that capacity by using a higher current and you can't get it back. Even though 50% DoD has been reached proportionaliy sooner, it *has* been reached and you can't reclaim the loss of capacity, except by over-discharging the battery. This is why for battery management, as opposed to journey management, the reduction of capacity with higher current is irrelevant to you. You still want to stop at 50% DoD however soon you reach it.

[Roger Hayter]

Sounds good to me. The other thing I thought of was to calculate the inequality every 100milliseconds, and trip when it remained low every time for a 100 times in succession. Same answer as your method I should think.

[T i m]

Quite and I am ... except this is also a bit of a project in itself (electric propulsion).

Campervan or campervan battery? FWIW the 3 batteries cost nearly as much as one of the boats so in our case the batteries are a significant part of the cost of the whole package. And there is a difference between 'died' and 'death by neglect or abuse' (even if non intentional). It would be like you not ever bothering to check the engine oil and knowing it uses some.

No, but if we are stuck without power 2 hours away from the car, in an open dinghy, in the rain it *would* be a big PITA.

Cheers, T i m

[T i m]

Yep, I understand that.

No, it won't have been reached if the meter is using an arbitrary low voltage threshold though?

Of course (if that was the case).

*Agreed*. Now, what low voltage is *correct* for what current, as one voltage can't be correct for all currents can it (or they wouldn't publish a graph showing different voltage cutoff points for different currents presumably)?

Please don't get embroiled in the thoughts that I want to actually monitor the actual battery capacity because I don't ... I just want to do a bit more that use a single 'catch-all' values for what is already known to be a conditional range. ;-)

Cheers, T i m

p.s. I have various electronic measurement tools including a watt hour meter but it's no use as a form of protection tool and it doesn't compensate for the varying capacities at varying loads. It could give me a 'worse case' value though (30A x the voltage x the period measured as a percentage (50% say) of the potential at that rate).

[T i m]

Agreed ... as we are talking runtimes in the 'hours' etc. So, how to achieve that ... ;-)

We know two LV values in the current range I need, so what formula do we use to calculate the rest?

ITRW the current is never likely to drop below 5A (ignoring stop times when the battery voltage might recover and cannot be quantified) and shouldn't go above 30A unless the prop gets stalled or fouled etc.

So from that we know that at 50% DOD, is seen at 12.05V @ 18.2A and

12.10V @ 4.65A (so we could use that as our lower RW limit) and, not that I would ever use it, it would be 11.75V @ 93A (but that might help our graph / formula). Now, I'm not sure if you said that works out to be a straight line (then the figures are obviously bogus) and if not, do they fit in with the capacities stated at the various discharge rates: 36Ah at C/100 (so when discharged at 0.36A for 100 hours) 31.6Ah at C/20 (so when discharged at 1.58A for 20 hours) 26.8Ah at C/5 (so when discharged at 5.3A for 5 hours)

_MK_r1.pdf

Thought: Now, in my real world tests (across all three batteries (singularly)) I was able to see 5A for 4 hours down to 11.2V (that

*should* represent 50% DOD at that current).

It was done manually but worked out like this (measurements taken every 10 minutes or so):

12.90, 12.72, 12.64, 12.46, 12.38, 12.30, 12.24, 12.18, 12.13, 12.08, 12.04, 11.99, 11.95, 11.90, 11.85, 11.80, 11.74, 11.68, 11.62, 11.55, 11.48, 11.41, 11.30, 11.21V

Irrespective of any published information, if you could extrapolate that above log down to 0V, it might give us the shape of the graph (and therefore the calculations) to continue?

Can we extrapolate any information from the chart on the bottom half of P6 to help create our formula?

So the questions is, once we have worked out how to compute the values for that range, are they still significant enough to bother with? I can only decide that once I know what it is. ;-)

'You can manage (or at least go some way towards managing) what you can measure (for', in this case). ;-)

Cheers, T i m

[Roger Hayter]

The model of the battery as a voltage source in series with a resistance is quite a good one I think, and the on-load voltage plus predicted voltage drop is quite a good measure of what the off-load voltage has fallen to. Which just leaves the temporary loss of capacity at high load, which would recover if the battery was left off load. The latter might be a relatively small effect at the moderate current of about 10A per battery that you are using. But as you might guess I don't know any better than you.

An interesting experiment would be to run the battery down to the indicated 50% discharge depth, then, without charging, use it again the next day and see if you get a significant amount of use before it falls to the same voltage. If not, then your measurement system is doing quite an accurate job of protecting the battery without wasting capacity.

[T i m]

As an aside on that I understand gel batteries aren't quite as linear as some other LA types. ie, They are quite slow to produce power and hence why they aren't generally used for engine starting (compared with flooded or AGM etc).

Quite. ;-)

Ok, I could try that. My only reservation is that it's not 'good' to leave LA batteries in a low charge state if possible but I could certainly discharge it to a higher DOD (say 70%) and try it from there?

FWIW, when I have also been monitoring the charge voltage (to test the compatibility of chargers etc, gel once again being a bit 'odd' in it's charging requirements amongst LA batteries in general), I've discontinued the charge process say before going to bed and resumed it the next day and it returns to it's previous 'level' very quickly.

Ok Roger. I'll give that a go and let you know what I see (so thanks again for the input). ;-)

Cheers, T i m

[John Rumm]

I can see that working where your source data are following some kind of exponential change being driven by a single (or predominate) physical variable, but it can get rather complicated where you have multiple non linearities competing in the same data set that have different weightings at different times in the process. You may find you just end up setting yourself a task that is of equal or greater difficulty to the original question.

If you are starting with an empirically collected data set, then you may find that after manually fitting a line (flexi curve etc) you can identify sections that behave differently from others, and then attempt to model them separately. I remember having to do that once years back with digitised data from a RF power coupler, that was supposed to have a linear response. Yet clearly the accuracy of the readings varied quite noticeably over the range of powers it could sense (10s of Watts, to

10+kW). In the end someone had to sit there for a few hours manually stepping up in 100W increments and recording the readings. Once plotted it was clear that while there were some nice straight linear sections, there was also a pronounced curve in the middle. Taking three points on the curve and treating as a quadratic was accurate enough to get a good model of the actual transformation for that bit. One then just needed a little bit pre-scaling decision making in the software before deciding what conversion to apply based on what range the raw reading was in.

[Rob Morley]

The rowing would keep you warm, and you could sing that song ...