In my area, due to frequent storms, there are frequently short mains power cuts lasting a second or two at most. While the shorter several-millisecond outages don't usually cause issues, the longer momentary outages frequently cause my computer to shut off, resulting in filesystem corruption and other issues.
I want some type of system capable of providing around 600 watts for 2-3 seconds, just enough to hold the system over until mains power resumes. Ideally, this device would be small enough to fit inside my computer case.
The various UPSes available online are all either (a) really expensive or (b) not capable of providing the wattage I need. Besides, I don't need the hours or minutes one of those provides, just a few seconds.
I have considered just putting some supercapacitors between the power rails, but I think that could cause problems when starting up (the PSU would have to charge the capacitors, so the voltage would take much longer to reach the required supply voltage), during these momentary outages (not sure I want to be backfeeding power to the PSU, but I don't want to have to connect every line coming out of it), when shutting down (since they would continue supplying voltage), and during service (since things could potentially still be energized even after the PSU is unplugged). I have some ideas for how to solve some of these issues, but not all of them at once, and I am not sure this is the best way to solve this problem.
What is the best way to solve this problem?