Why Alternating Current cannot be stored in Batteries

Why Alternating Current cannot be stored  in Battery Banks ? 

When we connect a battery with AC Supply, then It will charge during positive half cycle and discharge during negative half cycle because the Positive (+ve) half cycle cancel the negative (-Ve) half cycle, so the average voltage or current in a complete cycle is Zero. So there is no chance to store AC in the Batteries.

Also, We cannot store Alternating Current in batteries because AC changes its polarity upto 50 (When frequency = 50 Hz) or 60 (When frequency = 60 Hz) times in a second. Therefore the battery terminals keep changing Positive (+ve) becomes Negative (-Ve) and vice versa, but the battery cannot change their terminals with the same speed so that’s why we can’t store AC| in Batteries.

Also when we connect a battery with AC Supply, then It will charge during positive half cycle and discharge during negative half cycle because the Positive (+ve) half cycle cancel the negative (-Ve) half cycle, so the average voltage or current in a complete cycle is Zero. So there is no chance to store AC in the Batteries.

Also note that Average Voltage x Average Current ≠ Average Power.