Can capacitors store AC power?
Capacitors store charge or energy, not power. the charge and the energy are neither ac nor dc. the amount of charge or energy stored in a capacitor can vary from moment to moment. in a DC circuit, each instant is identical, so that the load is constant, like DC.
If you connect a capacitor to an AC power source, the load will vary from instant to instant, such as alternating current. if you disconnect the capacitor, it simply retains the charge it had when you disconnected it.
So, it can save energy from an AC power source, but once you have disconnected it, the load stays constant, like continuous. The capacitor stores energy only when there is a voltage difference between its terminals, corresponding to this voltage.
in an alternating circuit, the terminal voltage varies constantly and the polarity of the terminals changes at each half-cycle. Current conducts the voltage of 90 degrees. So, whatever the power absorbed in the first cycle, we went back to supplying the next cycle. so that energy is accepted in one quarter and returned to the next cycle. there is no question of storing energy in a capacitor fed with alternating current.
a capacitor can only store a DC voltage.
However, a special type of circuit called tank circuit, consisting of a capacitor and an inductor, is capable of storing AC power for a short time. the energy comes and goes between the two components, like water coming and going in a bathtub. soon thereafter, the resistance of the wiring and the components themselves absorb all this energy until there is no more.
Therefore, there is no long-term effective way of storing AC power as such.
However, you can rectify the AC current in DC so you can store it in a big capacitor or a chemical battery. you can then use an inverter to transform the stored energy of the capacitor / battery into alternating current.