Cynical About Peukert's Equation

[thunderhead]

Still working on the kitcar, but I've also been thinking about Peukert's Equation.  I don't believe Peukert's Equation makes sense in the light of Faraday's Law of Electrolysis.

After analysis of the manufacturer's data for my batteries, I have an alternative model.

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[maker of toys]

. . . have you had a look at what this guy has to say?

http://www.smartgauge.co.uk/peukert.html

he does a really good job (IMHO) of explaining the rate dependance of battery capacity.

not that it goes into the chemistry of it, but his math fits my experience somewhat better than the 'classic' explaination.

(and remember that reation products build up on the plates, not just in the electrolyte)

-Dan

[thunderhead]

I saw that: it suggests that there is a "theoretical" capacity of which the rated capacity (often the "ten hour rate") is a fraction.

I'd already included that, by working out the Peukert number from the ratio between 10-hour rate and so adjusting the rated capacity to get a theoretical capacity.  This theoretical capacity came out almost exactly the same as the theoretical capacity in my alternative model.

The thing that my model does is relate internal resistance to the depth of discharge: approximately, the internal resistance rises in inverse proportion to the square of the discharge depth.  That sort of inverse square law is what we'd expect if the plates were being coated in an insulator - which is exactly what is happening.

Using this adjusted internal resistance and the open circuit voltage for various depths of discharge gives a good agreement with the Peukert models  (and a better agreement with the manufacturer's data for discharge curves, which doesn't quite follow Peukert). It also explains why, for example, an EV which apparently has a flat battery can still be "nursed home" at slow speeds.  For many batteries, at motorway speeds the point where internal resistance brings the battery terminal voltage to endpoint has more than 50% of the charge remaining.

The other point about all this is that it may be a basis for better modelling of "fuel meters" in lead-acid EVs.  The endpoint doesn't come when the battery runs out of fuel, it comes when the battery internal resistance can no longer support a sensible road speed.

I haven't yet figured out what that means in terms of how the fuel meter should display, though.

[maker of toys]

My feeling is that you want at least these data when driving an EV:

Road speed

Battery temperature (you'll have this data anyway to calculate your battery capacity, might as well display it to warn the driver if bad things are trying to happen)

instantaneous power (watts/amps) consumption (for obvious reasons)

estimated maximum watts/amps available at existing charge state for "full and abrupt" control inputs (like merging into traffic)  This would enable you to choose routes and gaps better suited to your machine's current capabilities (pardon the pun)

estimated watthours/amphours remaining in bank.  . . . might take a leaf out of luxury car/aircraft  practice and give a 'guestimated range/endurance' number based on existing consumption rates verses estimated capacity remaining.

the items in bold might be useful for house banks, too. . . . especially for those of use who have shops/appliances with significant power requirements.

just me thinking out loud-- your milage may vary.

-Dan

[thunderhead]

Although I'd want all these indications on my own car (and probably more: battery internal resistance would be an example), one of my interests in EVs is in getting them accepted by the general population.

My wife would probably manage -- she figured out why her brake lights didn't work last week, and ordered and fitted the new switch without any assistance -- but my mother would not.  A production EV that my mother couldn't drive would be a failure: in the early days, EVs were favoured by grannies because they were reliable.

Most drivers would want an EV to have a single transmission control (probably labelled "P-R-N-D-L" or somesuch), and accelerator and brake.  A temperature gauge could be provided (although most drivers would not look at it) and a fuel gauge is essential.  But a fuel gauge needs to give some kind of abstracted notion of how far the car will go before it needs recharging, not something measured in Ah or kWh.  The petrol gauge on a dinosaur-powered car doesn't read in gallons or litres: it reads "E" and "F", and places in between.

That also means that as the batteries wear, the needle should stop reaching 'F' at the end of a charge.  When the driver looks at the needle and realises that it is closer to the 'E' than the distance it would normally move in a commute, then they know it is time to replace the batteries.

Re-wiring the rev-counter to read power is the other thing I'd do - but again, I'd not expect most drivers to look at it.

The final detail is something to tell the driver that if they press the accelerator the car will go.  Since an EV would naturally be silent, that could lead to surprises.  A green light with the word "GO!" on it might be a good plan - or maybe something that makes a noise at idle.