I often run out of energy when using Psionic storms and I then proceed to get decimated. Does it just come back on its own? Can anything hasten the process of how fast energy is accumulated?
Energy regenerates on its own for all units. The standard regeneration rate for the vast majority of units is 0.5625 per game second. The only exception to this rate is the point defense drone which regenerates at 1 energy per game second. You cannot hasten the energy regeneration rate.
Time. That's it.
If you want more storms more often, make more HT so you have more generators.