So, you want to plug a battery charger, into a power inverter, to charge the batteries that the power inverter is running off of?
You think that because your inverter is producing more power than the battery charger uses, that you'll be able to pump more power into the batteries than the inverter is using off of the batteries?
You think you have it all figured out, huh?
Think again.
You can't. What you're talking about is perpetual motion. You can't create energy from absolutely nothing. Something is always using energy.
I created this handy little graphic to help you realize why this doesn't work.
I talk to a ton of you geniuses every day about this. Some of you even suggested I sign an NDA before you went any further to explain your grand idea.
Doesn't work.
The math doesn't lie. Inversion process is about 85-95% efficient depending on load. So you've got between a 5 and 15% Efficiency loss for your system just in the inverter process.
Battery chargers are anywhere between 60 and 90% efficient. So you've got 10-30% efficiency loss in that component.
Batteries have voltage/amperage loss over time and through temperature, voltage normalization across the cells and just in general DC resistances (much higher at lower voltages).
So for a 40A charger, to charge a 12V battery bank at 40A every hour, you're drawing off of the battery bank around 48-52Amps. While yes, you're putting about 40A back into the bank, your batteries are 8-14 amps lower than when you first started the process an hour before.
This doesn't include the amperage your power inverter is putting out for other electronics either.
So, if you think you've got this ingenious idea, where you can create FREE POWER! Then I suggest you re-evaluate yourself and learn a little math and a little physics.