Please check my math

[off-grid-geeks]

I'm trying to explain battery bank size to my wife, and want to make sure I've got the math in the correct ballpark. Precision is not the goal, just not way off in left field.

Our solar panel array produces 4,000 watt/hours in an average day.
We typically use 50 watts per hour on average throughout the day = 1,200 watt/hours

4,000 - 1,200 = 2,800 watt/hours excess to put in the battery bank.

Our battery bank consists of 12 volts at 208 amp/hours.
Converted to watt hours results in 12 * 208 = 2,500 watt hours.
So our 2,800 available watt/hours would be enough to fill this bank if it was empty.

Please use generalities, I know that the battery bank is not exactly 12 volts, I know that there is battery charging inefficiency, etc. etc.
I'm just trying to convey the idea.

Thanks!

[TomW]

It all looks fine to me on this lazy and steamy hot Sunday afternoon, without messing with (in)efficiencies or the pesky detail that you cannot actuallyextract the full capacity from most battery banks.

You are wise to convert everything to watt hours up front to avoid conversion  confusion later on.

You will not have much reserve for low sun days but your numbers are certainly not out of left field.

Good luck with your project.

Tom

[dgd]

Ogg,

The numbers seem good except the battery capacity. As Tomw indicated you can never use the full capacity of the battery bank, it depends on the battery chemistry.
For lead acid types, either flooded or SLA types then a normal absolute max depth of discharge is probably about 30%. Most manufacturers quote the battery life in cycles of charge/discharge with 20% DOD being usual for a reasonable battery life
So using your figures for lead acid then to extract that 2.5wHr overnight you may need a 700 to 800aH 12v bank (or 400ah 24v, 200ah 48v bank).

With LiFePO4 cells they can be safely used within 20% to 95% SOC so a 12v 300Ah would cover your needs.

dgd

[off-grid-geeks]

Dgd, thanks, got it. 

That's why I said in my question:

Please use generalities, I know that the battery bank is not exactly 12 volts, I know that there is battery charging inefficiency, etc. etc.
I'm just trying to convey the idea.