Will use a 220V electric motor to turn the alternator with regulated rpm
Not only is the extra gasoline used more expensive than the cost of the energy in the battery, the cost of a lead-acid battery which is good for a few hundred cycles if it's a deep-cycle type is vastly more expensive than wall power even IF you had a free source of energy to charge it.
1KWH=$0.10 in cheap parts of USA. Say it's $0.25 in Europe or somewhere.
Deep cycle battery=$120, 12v/50AH usable=0.6KWH. Say it lasts for 200 cycles (that's quite a lot for lead-acid). Can move 120KWH over its entire life.
=$1/KWH to move it through a battery!
Oh wait... that's 4x/10x more than the wall power would have cost, even if I can charge it for nothing at all.