Energy Stored in a Battery

[jack11]

What is the energy stored in a 12V, 100Ah battery, when fully charged: 600 Wh or 1200 Wh?
I've seen it explained both ways.

In other words, what is the energy stored in a battery (disregarding all losses for now): 1/2*Q*V or Q*V, and why?

Critical to know this to see how much energy you can pull out of your system at night, etc.

[DamonHD]

Theoretically 1200Wh, but if you discharge a lead-acid battery below about 50% you will damage or destroy it.

I have 4x99Ah 12V batteries paralleled in my setup and treat the maximum available stored energy as 2kWh (2000Wh).

Rgds

Damon

[ChrisOlson]

.......but if you discharge a lead-acid battery below about 50% you will damage or destroy it

That is simply not true.  True deep cycles are designed to be discharged to 80% DoD for 1,500 cycles or more.  Some heavy duty deep cycles like Surrette 5000-series are rated in excess of 2000 cycles @ 80% DoD, and have specific recommendations for batteries that are shallow cycled to be fully discharged at least once a month.  Other manufacturers like GB Industrial do not recommend even recharging their batteries unless it has been discharged to 80% DoD.

The total efficiency of your battery is better when it is deeply discharged (>50% DoD) vs shallow discharged.  The most efficient part of the battery's charging curve is the bulk stage.  Absorb is least efficient.  That is why true deep cycles, aka Surrette 5000's et al, are more efficient for off-grid energy storage than light duty deep cycles like the standard GC-2 golf cart batteries.

To answer the OP's question, how much usable energy a battery has depends not only on the amp-hour capacity, but also Peukert Effect at discharge rates exceeding 20 hours from 100% SOC to 100% DoD.  So telling you how much energy your 12V 100ah battery stores is impossible to know based on just amp-hour capacity alone.  The common "rule of thumb" is to multiply voltage x amps x hours and come up with watt-hours.  However, this is not how top-end battery meters do their calculations to display SOC of a battery.

[jack11]

ok, let's be more specific.

Let's say this battery is specified to be 12V and 100Ah at 20hr discharge rate, and it's being charged/discharged at exactly that rate as specified - this should take care of the Peukert Effect.

I am still interested in the theoretical fully-charged energy capacity in Wh. For now I disregard all losses, the fact that you should not discharge a battery excessively, and I've taken care of the Peukert Effect.

The problem with the straight formula that gives 1200 Wh is that it does not seem to fit what we are trying to calculate. The units certainly add up, but the scaling may or may not be correct.

It is for calculating energy stored in the existing electric field as you move a charge Q in that field through a potential difference V. It's like the potential energy in the gravitational field, and you take the whole Q * V (that's how Damon got 1200 Wh).

For charging a battery, some people claim you should take ½ of that to calculate the theoretical capacity. I've seen them explain that the charge you put in battery distributes evenly: ½ positive and ½ negative. I've seen this applied to the electric vehicles, I guess they want to be conservative and not leave anyone stranded.

Also, if you start with another energy-storage device - capacitor, the energy stored in it's electric field is E = ½ * C * V^2.
But, C = Q / V, so E = ½ * Q * V (note the scaling by ½ here).
So, as far as the final result, how different is a capacitor from a battery, both accumulate charge Q, and both create a potential difference V? And, in calculating the stored energy the battery is typically scaled by 1, the capacitor by ½

This makes a big difference, like can you drive your electric car on a full charge 100 miles, or just 50 miles.

[ChrisOlson]

The realities come into play on how fast the battery is discharged.  The "rule of thumb" 600 watt-hours many times ends up being about 480 watt-hours of usable stored energy on a 50% cycle.  That type of battery is usually horribly inefficient as it would be an off-the-shelf "marine" type deep cycle, which is really a hybrid battery.

Spend the extra money on the same 100ah @ 12V in a Surrette 5000-series and then you get 820 watt-hours to the lowest usable voltage input to an inverter, and 1.0 kWh usable to a DC load.  That is why real deep-cycle batteries cost more money and a single human cannot move one without mechanical lifting equipment.  Amp-hour capacity is the same, but usable capacity is way different.

[jack11]

ok, I guess what needs to be done is to look into a data sheet for one of these (small) battery charger ICs, to see how they calculate the energy (Watt-hours) while "coulomb counting" (time-integrating the current that flows into the battery).

I'll try to get a hold of a data sheet like this, or maybe someone else can check it and post quicker, if they already have one handy.

[ChrisOlson]

ok, I guess what needs to be done is to look into a data sheet for one of these (small) battery charger ICs, to see how they calculate the energy (Watt-hours) while "coulomb counting" (time-integrating the current that flows into the battery).

Those chargers do no such thing.  They are simple voltage-based chargers.

[birdhouse]

i think if you told us the end term goal with said battery, it may be easier to figure out what is feasible for your application. 

it sounds like you potentially have a charging source that is smaller than your output needs, and are hoping to use a battery to buffer this imbalance for a certain duration of time. 

am i close?

adam

[Flux]

Strictly you can't use the Ah figures to work out energy stored.

The voltage will be falling throughout the discharge cycle so you need to take that into account as well as the current to get capacity.

Ah efficiency is really quite high for lead acid but the Wh efficiency is not so spectacular when you end with a discharged voltage around 11 and need to get to 14.4 at full charge.

I thought you were looking at the capacity of a fully charged battery, if you include the charging process then you atre probably looking at less than 50%.

As Chris said most battery chargers work on volts. If you use an Ah counter even if corrected for Peukert it will not stay in step with the battery for long, you have to reset it regularly at the only known point ( full charge).

Flux

[ChrisOlson]

The most important consideration is the type of battery.  Some batteries have high internal resistance with thin plates and are suitable for high amp delivery service as well as moderate cycling (hybrid "marine" starting/deep cycle).  Others have low internal resistance and very thick plates (forklift, etc) and are designed for deep cycling with maximum amp draw not to exceed C/8 and maximum charging rate of C/10.

The first type are very inefficient but very common.  They include so-called golf cart (GC-2 series) batteries.  The second type, the type of plates, separators and electrolyte used imposes limits on how fast the chemical reactions can take place inside the battery during both charging and discharge.  So the second type will experience huge voltage "sag" at amp loads that that the hybrid type can easily handle with less voltage "sag".

So there is no generic formula that can be applied to this because it depends not only on what type of battery it is, it depends on the discharge rate.  The best place to check is with your battery manufacturer.  Many manufacturers of hybrid batteries provide a RC (Reserve Capacity) test rating for them.  The Reserve Capacity is the amount of time the battery can deliver 25A from fully charged to 1.75VPC under load.  It is a much more useful yardstick to determine how much energy a battery can store than amp-hours.

[Bruce S]

To add an extra layer of thought to this thread.
There's the chemistry of the battery itself, that needs to be considered.
Lead based batteries, have a specific charge/discharge.
BUT if you are lucky enough to find/afford NiCd/NiMH based batteries, then even the discharge based rates of voltage of a normal Lead based battery, should not be applied, as the NiCd/NiMH based batteries will hold their voltage until 99% DoD.

[ChrisOlson]

Bruce, for off-grid applications I don't know that I'd necessarily consider cadmium or metal hydride batteries to be "lucky".  They have their problems too.  And even lithium batteries require specialized BMA's.  I think FLA is still the best for off-grid as far as "bang for the buck" and the longevity and reliability standpoint.  FLA's can be made to last 15+ years and thousands of cycles on off-grid duty, but these would be forklift type with the tubular grids, or Surrette 5000's with their legendary .260" CS grids.  These true heavy duty deep cycle batteries will withstand incredible abuse and cycling without failure.  But if you've ever priced a 6V Surrette 5000 the $1,200 per battery "sticker shock" to actually buy a bank of them will leave you in need of a defibrillator.

I think forklift batteries are still the best buy for off-grid energy storage.  Forklift batteries don't have quite as heavy duty plates as the Surrette 5000's, and you need overhead lifting equipment to handle a 2 ton forklift battery to get it into your utility or battery room.  But if you can handle one, the price is about 65% of what Surrette's cost.

[ChrisOlson]

Speaking of forklift batteries used in off-grid applications, one of our off-grid neighbors bought a rebuilt 24V forklift battery for $1,500 bucks for their off-grid system on their small farm in 1986.  I was not living in these parts at the time, but was home for the summer on my folks' place and helped get that battery into their battery room.  It came on a truck and we had a 544 International tractor with a loader on it and it would not pick the battery up off the deck on the semi trailer.

So we put some wood blocks on the ground and drove the rear tires of the tractor up on the blocks with the loader over the battery.  Then put the chains on the battery and lifted it with all the hydraulic power the tractor had, then put the tractor in gear and spun the blocks out from under the rear tires.  Then about 5 or 6 dudes jumped on the drawbar on the tractor to get the rear tires on the ground, which lifted the battery about 3" off the deck.  The truck drove out from under it and then we lowered it to the ground with the loader.

With all the dudes on the drawbar the tractor would barely move it by dragging it on the ground but that got it up to the utility room door.  With the help of pieces of pipe to roll it on the concrete floor, 6 dudes with prybars, two cable come-alongs, and a bunch of blocks of wood we got that battery into place where we could hook up the wires to it to their inverter.

It is now 2014 and that battery is still powering their place, although it is down to about 50% of its original capacity left.  28 years and that battery is still in service, although we have better equipment to move it now when it needs to be replaced   

[Bruce S]

With apologies to the OP 
ChrisO, that last post sounds like trying to build the Pyramids !!
BTW: Y'all can stop sending these cools spells down to the tropics of St Louis!! 

Back on track.
I tend to agree with the FLA statement. However when given real NiCds "meaning NOT the Bruce-packs" NTL, Norm, Wooferhound and several others re-purposed. BUT the ones that must be laid on their sides so the fluids can keep the plates covered can be just as useable.
I believe TomW was able to grab a small bank of them, small only weighing in at 4500lbs  .
Last we spoke he was still using them once the refurbish and inter-connections were made.

For me? the Lithium based batteries need more history before I go any further than portable and back-pack sized units.
 

[ChrisOlson]

That was just fair warning to anybody that orders a forklift battery for their off-grid power system.  These distributors normally ship them free of charge with their own trucks.  But when it arrives if you don't have the equipment to handle it about all you can do is sit on an upside down milk crate under the shade tree with a beer and look at it and go, "that sure is a nice battery......"

With the record the more exotic metal batteries have in laptops et al, I don't trust them for off-grid power.  We bought an electric lawnmower because we got tired of having to run into town after gas for the old one all the time.  I specifically looked for one with lead-acid 24V battery in it because when the battery goes bad I can replace it for less than $100 bucks.  They make them with NiCads too but the replacement battery pack costs more than mower is worth.  Same with cordless tools.  You can buy a new freaking drill for less money than it costs for a new 18V battery for it.  For a power system where you have to count on it day in and day out and it can't fail, I can't see it.

FLA batteries are simple and cheap device.  You can "fix" most of them because what primarily kills them is improper charging and sulfation of the negative plates.  Apply high enough voltage to them, and providing a separator hasn't failed or it has a dead short in it, you can bring most of them back to life and make them work again - even totally dead ones with the plates hard-scummed over I've been able to revive.  The flooded lead-acid battery is better than 150 year old design and to this day there is no technology that can match it in cost/kWh with the same reliability.

[jack11]

Adam/birdhuse, this is more of a theoretical probing, no specific application I am dealing with now. But, of course this has very large (up to a factor of two) impact on any practical use of batteries: electric vehicles, night-time use, etc.

And Chris, I can almost swear that I have seen the "coulomb counting" function in some data sheets for these smart battery charger/manager IC's. If they are counting coulombs, then it's only a step away from calculating the energy as in K*Q*V, where K is a scale factor, and the voltage is also a function of time as Flux had mentioned. BTW, this varying voltage may be a reason for the fractional scale factor.

Measuring this thing to verify what the scale factor is should be easy in principle. However in practice not so easy, as you'd have to count coulombs yourself in a charge or discharge cycle, discharge the battery completely or if not then deal with an inaccurate SOC estimators, etc.

Let me do some more digging and I should post something next week. Or maybe someone else can check Maxim Semiconductor, Linear Technology?, etc. anyone that makes these battery management chips.