These are for a power controller circuit for a Pi Compute Module, for an embedded controller system I designed. There are (6) 10F caps in series, connected through diodes to 12v, and a micocontroller that sequences the power to the Compute Module. The µC enables 3.3v when the caps are charged, and then sends a power-fail signal to the CM when input power falls. Once the CM shuts down, the µC turns off 3.3v, and waits for power to be restored (there are actually a few more states, but this is the basics). This solves the “SD card corruption” problem that many Raspberry Pi controllers have.
One of the factoids I discovered when designing this circuit is that electrolytic capacitor lifetime is strongly dependent on operating voltage. So, even though 5 caps in series (5 x 2.7v = 13.5v) would have been sufficient, I used 6, because it more than trippled the expected lifetime of the caps. Instead of some complicated balancing circuit, I used 20K precision resistors in a ladder to equalize the voltage on each cap.