Total energy required to heat is same irrespective of what voltage you give. For 220V input, you will heat it faster than 110V, but there is no saving in your electricity bill. Energy consumed will remain the same. Power is Energy/time.
I am using a 1KVA inverter with 220V output, this was resetting the inverter. So I connected to a step down transformer 220V to 110V ac to the inverter. This 110V ac I am giving to the A1. Your step down transformer should support minimum 6 amp at the secondary side.
Maximum power consumption of A1 is 1300W at 220V ac. If your inverter can really give 1800W power, then this should suffice, but I feel its on the border line and you may experience sudden reset of inverter sometimes.
I am using ,my setup for the last 8 to 10 months with no problem.