Why battery cannot store AC voltage:
Battery is a two terminal, static charge accumulator device. The batteries convert the chemical energy to electrical energy. Where the charge stored on the plates in form of chemical reaction is in static in nature. As a result, the power stored in the battery is static is nature that’s direct current (DC).
Must Refer: Why battery United in AH (Amps-Hour)
At that same time, we cannot store Alternating Current in batteries because AC changes its polarity periodically which means the conventional AC supply has upto 50Hz or 60Hz (50 to 60 times in a second).
To store Alternating current, the battery terminal should change which means during positive half cycle the battery’s positive terminal should connect with the AC source and during negative half cycle, the battery’s negative terminal should be connected with AC source. But in practical this condition highly impossible. 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.
Before connecting AC source, you must know about why AC has a negative half cycle:
Within a wire carrying direct current, electrons hop from atom to atom while moving in a single direction. Thus, a given electron that starts its trek at one end of the wire will eventually end up at the other end of the wire.
In alternating current, the electrons don’t move in only one direction. Instead, they hop from atom to atom in one direction for a while, and then turn around and hop from atom to atom in the opposite direction. Every so often, the electrons change direction. In alternating current, the electrons don’t move steadily forward. Instead, they just move back and forth.
When the electrons in alternating current switch direction, the direction of current and the voltage of the circuit reverses itself. In public power distribution systems in the United States, (including household current), the voltage reverses itself 60 times per second. In some countries, the voltage reverses itself 50 times per second.
Also when we connect a battery with AC source, then It will charge during positive half cycle and during negative half cycle it does not create any action. At the same time the negative cycle to be connected in negative terminal of the battery to charge but the terminal reverse cannot be done in practical case. The negative half cycle also will be in the positive terminal. Due to this periodic action Positive half cycle cancels the negative half cycle, so the average Stored voltage or current in a complete cycle is Zero. Hence the entire work will be wasted. That’s why we can’t store Energy from AC in Batteries.
Also, Average Voltage x Average Current ≠ Average Power.
Even if you charge a battery with low quality DC power (including ripple voltage), the battery takes more charging times, waste of energy, leads to weakening of the battery electrolytic materials etc..