Need a quick refresher please - Battery bank sizing formula

Hairfarm
Hairfarm Solar Expert Posts: 225 ✭✭✭
in Off Grid Solar & Battery Systems #1
A question for math brains:

I need to calculate the amp hours that a 12V battery system needs to support an 1100 watt hour per day draw. Basically, I'm looking for a simple formula that I can use if I only know the watt hours and battery voltage. Also, it should calculate a 25% DOD, two days autonomy, with inverter losses and wiring loss built in to it.

This is the formula I use but I don't know if its ideal, or if its even calculated in the correct order/sequence.

1100wh (total per day) / 12v = 92 amps * 2 (days of autonomy) = 183 / .25(DOD) = 733 ah / .97 (wiring eff.) = 756 / .85 (inverter eff.) = 889Ah

This tells me that I need 889ah for my 12VDC battery system to draw 1100 watt hours. This formula seem ok to use? Is it too much amp hour overkill?

I know that there are some basic calculators on the internet for battery bank bank sizing. But it would be great to have a formula I can print out and keep manuals when I'm not near an internet connection. Just looking for a solid formula that I can print out and memorize.

thanks,
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  • Cariboocoot
    Cariboocoot Banned Posts: 17,615 ✭✭✭
    #2
    Re: Need a quick refresher please - Battery bank sizing formula

    Okay first of all you're switching from 1100 Watt hours on AC to DC power; the inverter providing the change will only be 'X' percent efficient (usually 90) and will consume some power for itself (which depends on the model). So right away 1100 Watt hours AC becomes (1100 / .90) 1222 Watt hours DC. The inverter may be a small one like Morningstar's 300 Watt unit which will consume 6 Watts. If it's on for 24 hours that's an additional 144 Watt hours DC. It may also be a large one like an Outback which will use 20 Watts and thus add 480 Watt hours DC.

    Then you have your total DC Watt hours which you can divide by nominal system Voltage to get an approximate Amp hours used: 1222 + 144 = 1366 / 12 = 113.8 Amp hours, call it 114.

    Days of autonomy is a misleading concept and I wish it would go away. If you plan on 25% DOD average you can go down to 50% before the battery is in trouble: there's two days use. So 114 * 4 = 456 Amp hours @ 12 Volts.

    Time for some fudge factors. If some of the power is used during daylight hours the batteries will not have to provide it and you could shrink that battery size to 450 which is a capacity you can get from four Trojan T105's. Otherwise it is better to round up to the nearest available size.

    If you do the processes "in the order in which they occur" (i.e. starting with AC consumption and working back to DC Amp hours) you get better results.
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  • AuricTech
    AuricTech Solar Expert Posts: 140 ✭✭
    #3
    Re: Need a quick refresher please - Battery bank sizing formula

    Keep in mind that sizing your battery bank using this formula will have ripple effects on the minimum PV array needed to charge the bank effectively. You also should get at least some production from your PV system, even on very cloudy days.
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  • BB.
    BB. Super Moderators, Administrators Posts: 33,613 admin
    #4
    Re: Need a quick refresher please - Battery bank sizing formula
    Hairfarm wrote: »
    1100wh (total per day) / 12v = 92 amps * 2 (days of autonomy) = 183 / .25(DOD) = 733 ah / .97 (wiring eff.) = 756 / .85 (inverter eff.) = 889Ah

    You sort of did a double derating here... The "optimal" battery sizing we do is 2 days of no-sun storage and 50% maximum discharge... That gives you a 25% DOD number--You did another 2x larger again for storage... So, the way I do it:

    1,100 WH * 1/0.85 AC inverter eff * 1/12 volt battery * 2 days of storage * 1/0.50 max discharge = 431 AH @ 12 volts (Nominal)

    You could add a " * 1/0.97 Wiring Eff" to the derating--But we are now just getting way more accurate than the battery bank ratings really are (+10-20% is typical variation of battery bank capacity over age/cycling/temperature/how fast you use the current... Adding 1/0.97=1.03 or 3% more capacity is sort of lost in the noise.

    Make more sense?

    -Bill
    Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
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  • Hairfarm
    Hairfarm Solar Expert Posts: 225 ✭✭✭
    #5
    Re: Need a quick refresher please - Battery bank sizing formula
    Cariboocoot - Days of autonomy is a misleading concept and I wish it would go away. If you plan on 25% DOD average you can go down to 50% before the battery is in trouble: there's two days use. So 114 * 4 = 456 Amp hours @ 12 Volts.

    What does the number 4 represent in your formula? I can't figure out what it means. I can see where I doubled up on the days of autonomy and DOD now. thanks!
    BB. - Make more sense?

    It does now. And it'll save me from having to purchase extra PV panels to support unnecessary Amp hours too!


    Here's the kicker - I got this formula from a Trojan Battery calculator:
    http://www.batterysizingcalculator.com/

    They didn't have an option to use a DOD of 25% so I just used their 20% figure. But all of their other calculations I copied exactly to get my formula of 889ah. I wonder why their results are so much higher. You think it's to up-sell their batteries? Or do they really believe their calculation algorithms are sound? You guys have clearly shown how I inadvertently doubled-up on my DOD and 2 days of autonomy, so why doesn't Trojan know that? They're the battery experts. What am I missing?

    My results:
    Attachment not found.

    According to their calculator I need 1111.78 amp hours for my 1100watt hours @ 12 volts with a 20% DOD and two days of autonomy. Well alrighty then! ;)

    thanks,
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  • Cariboocoot
    Cariboocoot Banned Posts: 17,615 ✭✭✭
    #6
    Re: Need a quick refresher please - Battery bank sizing formula
    Hairfarm wrote: »
    What does the number 4 represent in your formula? I can't figure out what it means. I can see where I doubled up on the days of autonomy and DOD now. thanks!

    114 Amp hours is how many you need to supply the required AC Watt hours.
    Since a battery should not be discharged below 50% you need to at least double that (X2).
    If you want the 114 Amp hours to be 25% DOD you multiple by four: 456 Amp hours (25% of which is 114).

    I have no idea what math went in to Trojan's calculator, but I don't agree with it.
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  • Hairfarm
    Hairfarm Solar Expert Posts: 225 ✭✭✭
    #7
    Re: Need a quick refresher please - Battery bank sizing formula
    Cariboocoot - 114 Amp hours is how many you need to supply the required AC Watt hours.
    Since a battery should not be discharged below 50% you need to at least double that (X2).
    If you want the 114 Amp hours to be 25% DOD you multiple by four: 456 Amp hours (25% of which is 114).

    Got it. Consider it copied and pasted into my ever growing solar "cheat sheet".

    Thanks for the advice. It probably saved me from having to spend extra $$ on unneeded batteries (and panels to keep them charged.) That said, I realize that the more power the better, but it's really out of budget. Especially since I don't have to have it right now.

    I think the Trojan calculator seems to redundant with its two features, Desired DOD and Days of Autonomy. They overlap and seem redundant to me, now that I'm actually aware of the redundancy. ;)
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  • BB.
    BB. Super Moderators, Administrators Posts: 33,613 admin
    #8
    Re: Need a quick refresher please - Battery bank sizing formula

    Yea, they first "block off" 50% of battery capacity, and then the DOD of 20% is based on the remaining 1/2 of battery capacity...

    Basically 5 days of autonomy * 1/0.50 max discharge = 10x your basic daily loads.

    I guess you should have set 50% DOD for two days of autonomy. Then it would have worked (4x daily loads for battery AH capacity).

    That is why I really don't like on-line calculators (and complicated spread sheets that "hide" the calculations).

    You have to first reverse engineer their assumptions/equations, then you can use their output once you understand their methodology.

    -Bill
    Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
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  • vtmaps
    vtmaps Solar Expert Posts: 3,741 ✭✭✭✭
    #9
    Re: Need a quick refresher please - Battery bank sizing formula
    Hairfarm wrote: »
    Here's the kicker - I got this formula from a Trojan Battery calculator:
    <snip>
    I wonder why their results are so much higher. You think it's to up-sell their batteries?

    I will take a guess: Peukert.

    You put in your load as 1100 watts for 1 hour. Try 100 watts for 11 hours. In the real world you would need a larger battery bank for the 1100 watt load... maybe their calculator accounts for that (I would certainly account for it in choosing a battery bank for that load).

    Of course, if you only run that 1100 watt load while the sun is shining, you could cut back a bit on the battery size.... I'm sure their calculator doesn't account for that.

    One more thought... try telling the calculator that you want to use AGM batteries with an 1100 watt load for an hour... the calculator should come up with a reduced ah capacity because AGMs have less Peukert effect than flooded batteries.

    Loads are a lot more than just 'kwh per day'. To choose a battery you need to also know peak loads, duration of peak loads, and the time of day/night of all loads.

    --vtMaps
    4 X 235watt Samsung, Midnite ePanel, Outback VFX3524 FM60 & mate, 4 Interstate L16, trimetric, Honda eu2000i
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