Attaching the Inverter directly to the battery, It's up to the Inverter to decide when generating 220V ac and when not.

My Green Cell 500W 12V pure sinewave decides to generate power when the battery voltage reaches around 12V and stops when the voltage goes below 10.5V. 

These two parameters are fixed, while I wanted some more flexibility and extending the range to 13.5V,

So I'm designing a voltage comparator, which you'll see soon in the Details section.

Bye Bye!