Battery capacity

Brilliant forum especially for those of us eagerly awaiting delivery. Can someone explain why the battery capacity is quoted so differently by different people? Using Kwh it appears variously as 18, 18.8, 19, 20 and 22. I assume the problem is the difference between Kw and kwh although we also have kw/h. Can somebody please explain for me in simple language?

Battery capacity is measured in kilowatt hours, that is the power it can deliver times the time for it can provide it. You will often see confusion on this forum and elsewhere between the power (kilowatts) and the energy (kilowatts x time). The proper symbol is kWh where k is a multiplier (1000), W is power in watts and h is the time in hours.

The i3 battery has a total capacity of 22 kWh of which only 18.8 is used allowing a margin at the low and high ends. 18, 19 and 20 may be approximations or errors.

Thanks Brian - very clear.

21.6 appears to be the exact number. 22 is the rounded number. Most other bevs use 1 decimal, so to be consistent and precise, 21.6 should be used

Ron

To put a finer point on some of this, battery capacity is usually at a fixed discharge rate for a period of time, the product of which is the rated capacity. So if a 100v battery could deliver 10a for 1hr, it would be a 1kWh battery. Or a 400v battery that could deliver 10a for 5hrs would be a 20kWh battery.

I have no idea what the standard (if there is one) is for rating EV batteries. Further confusing the issue (and the guess-o-meter) is Peukert's equation which basically says that the slower you discharge than the rated capacity, the larger the battery becomes (and vice versus). Though this effect is smaller in lithium ion batteries than lead acid.

On my boat I had a bank of 2v batteries (12 to yield 24v) that would deliver 100a for 10hrs = 24,000kWh, but discharged at a miserly 10a/hr they yielded quite a bit more capacity.

Batteries are chemistry, not digital electronics, hence the difficulty in accurately predicting remaining range.

On my boat I had a bank of 2v batteries (12 to yield 24v) that would deliver 100a for 10hrs = 24,000kWh

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You wish! It's actually 24kWh.
Other contributors to this thread have been getting confused between rates of discharge and capacity.
A battery - any battery - has a capacity. It may be measured in milli-Ampere-hours (mAh) for small batteries, and Ampere-hours (Ah) for bigger ones. It's a measure of how much electrical energy can be stored (or delivered by) it.
Lead-acid batteries in particular are almost always specified at a rate of discharge of either a 10-hour or 20-hour rate. If 10-hour rate, the stated capacity will be delivered if it is discharged at 1/10 of the Ah capacity. And so a 20 hour rate 100Ah battery would deliver 100/20 = 5Amps for 20 hours before it was discharged. They can deliver more current if needed (hundreds of Amps for engine starting, for example), but the amount of charge available at high rates is limited.
Lithium-ion batteries suffer much less from rate limitations than Lead-acid batteries and a discharge rate is not normally specified. It's feasible to discharge them quickly if needed.
Turning to the rates of discharge issue, there is also confusion between power and current. In the i3, it's usual to discuss power - which is a rate of discharge. So, for example, cruising at a steady 70mph, you might be using perhaps 18kW continuously - and so you'd use all the available charge in an hour (18kW*1hr = 18kWh), and have travelled 70 miles doing so. There is no current measurement available in the car, but we can calculate that at full power (125kW) over 300Amps are being drawn from the 400Volt battery! (It's a good thing that you can't actually use 125kW for long, because if you could, the battery would be flat in less than ten minutes.)
BrianStanier is correct, but didn't make clear that the "headroom" in capacity between 22 and 18.8kWh is shared between the fully-charged state and the fully discharged ends of the battery's capacity. It's important to have a bit of headroom near full charge so there is somewhere to "put" regenerated energy if necessary, and at the bottom it's important not to fully discharge the battery to avoid damaging it.

FrancisJeffries said:

On my boat I had a bank of 2v batteries (12 to yield 24v) that would deliver 100a for 10hrs = 24,000kWh

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You wish! It's actually 24kWh.

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Of course, my mistake, 24,000 Wh or 24kWh.

Understanding Lithium Ion batteries, brings another important factor - called the “C” rating of the battery. For example: A 10C Li-Ion battery can ideally be discharged for a short period at a rate up to 10 times the battery capacity size. So a 5 Amp/hour battery rated at 10C would be able to produce up to 50 amps discharge for a short period of time, a 5Ah battery with a 25C rating would be able to produce 125 amps discharge (for a very very short period of time). Of course a battery rated at 25C pushed to maximum discharge would get very hot and long term reduce the life of the battery.

Putting the BMW i3 high voltage battery in perspective: (reading through the Sales literature specs)

If you converted the BMW i3 18.9 kWh usable batteries to amp hours
Volts x Amps = Watts therefore Watts / Volts = Amps
Sales literature shows 21.6 kWh or 21600 watt hour or 21600 / 360 volts total = 60 amp hour batteries
But the practical value to prevent over charging and discharging: (as published at 18.9 kWh)
18.9 kWh = 18900 watt hours or 18900 / 360 volts = 52.5 amp hour batteries

Therefore each i3 battery made by Samsung SDI (12 batteries per pack with 8 packs total of 96 batteries) wired in series.
(as viewed from watching the BMW i3 production YouTube videos)
360 volt total divided by 96 batteries = 3.75 vdc per battery rated at 60 amp/hours. Wow…
So each battery is 3.75 vdc x 60 amp hour = 225 watt hours
225 watt hours x 96 batteries = 21.6 kWh

Back to the original C rating discussion, assuming the batteries are C rated as 8C and the practical battery usable potential is 18.9 kWh would result in 18900 watts x 8C rating or 151200 watt hours or 151.2 kWh maximum discharge for a very short time. Of course charging the battery would be a much lower value to prevent overheating. I would assume that BMW has published for their repair groups the max discharge rate of close to 150 kWh max which would be over 400 amps at 360vdc. Nice...

For the battery "Guess-o-meter" to determine your available range probably uses the swing in the min and max battery voltage - so a full charge I assume would be over 4 volts per battery and low around 3 volts per battery. You do not want to let Lithium Ion batteries to swing well below 3 volts per cell - at least in other electronic devices. For guessing your range, it would be nice to know what you put in as far as charge (minus out some internal loss) and then monitoring your total discharge or miles per kilowatt hour.

According to page 72 of the High-voltage Components manual:

There are 96 battery cells in series, each 3.75 V and 60 Ah
Storable amount of energy is 21.8 kWh (gross) and 18.8 kWh (net)
Maximum power (discharge) 147 kW (short-term), at least 40 kW (continuous)

So the burst discharge nicely exceeds the 125 kW motor allowing other things to run simultaneously. That "at least 40 kW" is a little vague but I suppose it depends on the temperature.

Near the end of the manual it mentions there is a 10% buffer at the low end. So 0% charge for the user is 10% SOC absolute. It doesn't mention what that is in volts per cell, but it does say that the battery voltage range is 259 V - 396 V (360 V nominal).

LivingBetterThruEV:

...is 18.9 kWh would result in 18900 watts x 8C rating or 151200 watt hours or 151.2 kWh maximum discharge for a very short time. Of course charging the battery would be a much lower value to prevent overheating. I would assume that BMW has published for their repair groups the max discharge rate of close to 150 kWh max...

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You're getting mixed up between capacity and rate, as I discussed in an earlier post in this thread. Your numbers are right, but the unit's aren't. You meant to write:
...is 18.9 kWh would result in 18900 watts x 8C rating or 151200 watt hours or 151.2 kW maximum discharge rate for a very short time. Of course charging the battery would be a much lower value to prevent overheating. I would assume that BMW has published for their repair groups the max discharge rate of close to 150 kW max...

Thanks for the update and clarification. Yes kW discharge not kWh...
I should not type up things to late before throughly proofreading.

Oh - and where do you get the "High-voltage Components manual"? That sounds like it would have saved me time to just reference it. Does it provide a Samsung SDI part #? C rating on batteries? I assume large single cell units since Lithium Ion is typically 3 volt per cell technology?

Probably for another thread - but what is the deal with the Fog lights on the i3 ?

LivingBetterThurEV said:

Oh - and where do you get the "High-voltage Components manual"?

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See - http://www.bimmerfest.com/forums/showthread.php?t=787263