[RE-wrenches] Help me do the math: amortized cost per amp-hour

[R Ray Walters]

 Mick, 

To calculate the lifetime amp-hrs, as you wanted, you first have to have the Cycle Life vs. DOD (depth of discharge) info for your battery, then multiply the cycles at your proposed DOD, by the amp hrs rating of the battery by the DOD% (cycle # x battery AMpHr x DOD%) 
One thing I can tell you, is that a battery that is being discharged at less than about 15% each cycle is not getting the full use out of the battery. Once you run a few calculations at various DODs, you'll see that an under utilized battery (as in your case) doesn't give you as much extra life as you paid for. Basically from about 20% to 80% DOD you have an almost linear relationship. (ie 1000 cycles at 30% DOD = 2000 cycles at 60%DOD) 
So this means 2 things:  1) don't grossly oversize or undersize your battery, and 2) in your case you can add loads without significantly reducing the life of the battery.
This all makes sense, if you think about it: a battery in float charge that is barely cycled if at all will still NOT last forever,  and a battery that is cycled regularly more than 80% will die a quick death.
Now for the exclusion clause:  I'm basing these conclusions on HUP, Trojan L16 and golf cart battery data, so your battery may differ some. I'd love for some others to look at this again for some other battery brands & types.


R. Walters
ray at solarray.com
Solar Engineer




On Jun 10, 2010, at 10:02 AM, Mick Abraham wrote:

> Greetings, fellow Energy Techs~
> 
> A client has a nice new set of 2v Concorde AGM sealed batteries: 915 amp hours in one 24 volt string. His cabin is often unoccupied with only the refrigerator running. During those "idle" days the battery is called upon to deliver an average of 90 amp hours every night...about 10% discharge.
> 
> The client wishes to rev up some more loads to run during these idle times. Coincidentally, those loads would also require an additional 10% discharge from the battery each night. The added loads surely have a cost in terms of decreased battery lifetime. I wish to do the math to amortize the battery cost and arrive at a "dollar value per month" for the additional loads.
> 
> The pack plus installation cost about $4,700. I don't know the number of "lifetime amp-hours" which could be expected from these batts, but I hope one of you can help me get that number. Could we then divide $4,700 by the lifetime amp-hours to get the cost per amp hour? If so...I could do the rest of the math from there.
> 
> *************************************************************
> 
> Side note: I realize that various factors such as shallow cycling, repeated overdischarge, repeated overcharge, etc. can affect the number of amp hours which any battery can deliver. In this case, let's assume the following:
> 
> * No repeat overcharge because I'm strictly following Concorde recommendations and I've even calibrated the Outback charge devices
> 
> * No repeat overdischarge because I >finally< have the generator automation dialed in and reliable (fingers crossed)
> 
> * Prompt recharge after discharge...because there's an OK sized solar array, many sunny days plus the genset backup
> 
> * Electronic sulfate dissolver is installed on the battery string
> 
> * Average cycle depth of 50% discharge. I'm using this value to factor in the times when the cabin is occupied and therefore cycling harder on the battery
> 
> * Limited heat stress on the battery. The cells are in a crawl space in alpine terrain so they will range from cold to cool, never warm
> 
> 
> **************************************************************
>  
> Thanks in advance for your assistance. The Wrench List is the bomb!
> 
> Mick Abraham, Proprietor
> www.abrahamsolar.com
> 
> Voice: 970-731-4675
> _______________________________________________
> List sponsored by Home Power magazine
> 
> List Address: RE-wrenches at lists.re-wrenches.org
> 
> Options & settings:
> http://lists.re-wrenches.org/options.cgi/re-wrenches-re-wrenches.org
> 
> List-Archive: http://lists.re-wrenches.org/pipermail/re-wrenches-re-wrenches.org
> 
> List rules & etiquette:
> www.re-wrenches.org/etiquette.htm
> 
> Check out participant bios:
> www.members.re-wrenches.org
> 

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.re-wrenches.org/pipermail/re-wrenches-re-wrenches.org/attachments/20100610/85540cf5/attachment-0004.html>