While we talking about storing energy. The law of conservation of energy states energy cannot be created or destroyed only changed in form. So what you are considering is changing kinetic energy to potential energy. With regards to electricity that would be electrons.
AC current and voltage changes their polarity 50 times a second (for 50Hz system). When connected to an AC supply, the energy storage device charges during positive half cycle and discharges during the negative half cycle so the net current is zero in a complete cycle and there is no storage of energy in batteries due to AC supply. If you can invent a storage device to store ac energy for later or emergency use then you will be remembered for ever. Flywheels that have been stated earlier store kinetic energy on a short time basis to bridge the gap between the interruption of the mains power and connection of emergency generator and are not considered real storage of energy.
In a DC circuit electrons flow in one direction and in an AC circuit they flow in two directions (within the confines of a wire). Power P = VI voltage (or potential) times current (flow). Consider the flow. If we connect a capacitor to a DC source, electrons will flow off of one plate and onto the other plate of the capacitor until the voltage rises to the DC buss voltage (kinetic energy).
The flow stops when the capacitor reaches buss voltage and the difference in potential between them is zero and the capacitor now stores energy as potential energy. Connect a load to the capacitor and the electrons will flow back out.
An AC current flows in ne direction then the other but the principle is still the same except the electrons are only stored for 1/2 cycle then reversed and stored at the opposite potential for the second half cycle. AC is DC that flows in one direction then the other.
You could conceivably use two capacitors and rectifiers or switches to store each half cycle then using switching return the electrons to the system at a later point. The issue for engineers and scientists is to be able to find a practical container to store the electrons and an efficient cost effective means to control them.
Batteries store them in a chemical reaction. Flywheels store them as mechanical energy. Fuel cells and electrolysis stores them in another type of chemical reaction compressors store them as pressure. Even ocean tides are captured and stored as mechanical potential.
So as you can see AC storage is possible but it is a question of which method will yield the highest efficiency at the lowest cost. The lowest cost means the least amount of energy and materials to make it. After all a great storage medium for AC is no good if it take more energy to build it then it could possibly store over its lifetime.