Computer draws more watts when electricity in house isn't stable?

I have an i7 5960x (8-core, 16 threads) and two GTX 970s that are all running at full load 24/7. The total system power usage is typically around 450-550 watts when everything is under load. It has a 1000 watt power supply and is plugged into a UPS with a battery backup that is rated for 810 watts. When the electricity in our house goes out or lights start flickering briefly (common in the spring/early summer), the UPS starts emitting a constant tone. However, rather than continuing to power the computer like I would expect, the computer still shuts off anyway, defeating the purpose of the bat

Question by EllipticalInitial on Super User, licensed CC BY-SA. We show a short excerpt and link to the original thread as credit.