1080 ti's have a minimum recommended power supply of 600 Watts
Depends on the loads and your actual power delivery.
Through voltage conversation the PSU delivery is actually = ~0.85xGivenWattageValue.
Normally a basic system (depends on how old an which specturm, obviously HEDT takes more) needs ~100-150Watts to run + graphics card power connection.
PCIe = 75 Watts max (if not OCed), 6 Pin = 75Watts, 8Pin = 150 Watts.
Lets say 2x8 pins + PCIe = 375Watts at max load GPU.
Would be around 525Watts needed which should be around 600-650Wattage PSU needed at full load, which is like Crypto mining and CPU rendering at the same time to reach its' peak.
Normally if the power delivery isn't enough it should just turn the PC down.
It sounds like something on your system is unstable.
Did you activate some kind of automatic software overdrive or did you move into your BIOS/UEFI settings and activated some kind of "automatic tweaking"?