>>12529109OK since way way back when I worked for a defense contractor, I did some research into things like this.
If you really want to use capacitors for energy storage, go look for companies that make multi-Farad capacity supercaps for transportation (read as: things like subway cars) use. You'll need several depending on how much storage capacity you want in the first place.
Charging them won't be fast or easy, you'll need to use a current-limited charging circuit, because the bank will be a *dead short* for a long time until they reach at least 60-70% full charge.
Next you'll need a discharge circuit that includes a buck-boost switching power supply, so you get a voltage- and current-regulated output for whatever you're powering, and to also protect the supercap bank from a catastropic discharge from something like a dead short or overcurrent load. The supercaps I described will have an *extremely* low ESR and if short-circuited might just cause a fire or explosion.
This is all do-able.
Now that being said: The energy density of ANY kind of capacitor energy storage system is INFERIOR to Li+ cells. You should be using that instead. 18650 cells are common and easy to get, and charge/discharge controllers for them are COTS (commercial off-the-shelf) assemblies. You'd have what you want in a fraction of the time and a fraction of the COST.
That is why we don't use massive supercap banks for long-term energy storage.