# Battery Sizing Formula

I'm trying to calculate my loads for proper 48volt battery bank sizing and trying to find the correct method.

watts / volts = amps
amps * hours = amp hours

My question is which voltage to use for calculating the correct amp hours?
1. The voltage of the bulb in 120volt AC
2. The voltage of the battery in 48volt DC

Example: 100watt 120volt ac light blub for 4 hours

100watts / 120volts = .83amps
.83amps * 4hours = 3.33amp hours

OR

100watts / 48volts = 2.08amps
2.08amps * 4hours = 8.33amp hours

OR

I completely have the all the above messed up and need the proper formula.

Regards

Re: Battery Sizing Formula

2nd one is correct because you want the 48 volt battery ah calculation.

-Bill
Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
• Re: Battery Sizing Formula

If using the battery voltage then do I need to also add a xxx factor for converting the 100watts AC load to some other watts DC because of inverter efficiency?

IE.. inverter efficiency 90% (10% inverter loss)

100watts AC *110% = 110watts (10% inverter efficiency loss)
110watts / 48volts = 2.29amps
2.08amps * 4hours = 9.16amp hours

Regards
Re: Battery Sizing Formula

Yes, plus conversion and wiring losses

I use 1/0.85 but you can use 1/0.90 or whatever makes sense for your setup.

-Bill
Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
• Banned Posts: 17,615 ✭✭
Re: Battery Sizing Formula
reefbum wrote: »
If using the battery voltage then do I need to also add a xxx factor for converting the 100watts AC load to some other watts DC because of inverter efficiency?

Yes. Also inverter consumption needs to be included.

For example:

100 Watts for 4 hours = 400 Watt hours (AC side).
Inverter efficiency 90% means that is ~444 Watt hours (DC side).
Inverter uses 20 Watts (DC) over the 4 hours itself: add 80 Watt hours.
Total DC Watt hours: 524

On 12 Volts that is approximately 44 Amp hours used. On 24 Volts it is approximately 22 Amp hours and on 48 Volts approximately 11 Amp hours.

Amp hour used must be factored against desired maximum DOD (usually not exceeding 50%) to get battery capacity. So that would be 88 Amp hours @ 12 Volts utilizing 50% DOD.

Approximations all. It is best to round things up to make sure you have a margin for error and understand that capacity goes down over time no matter what.