Power Cuts

I recommend to always have some type of backup power supply, mostly those UPS type of units so at worst you can run a heater or chiller for a long period and maybe flick the filter on and off to prevent the beneficial bacteria from dying off (maybe even a small battery operated air pump to mix the water surface to get a good gas exchange going as well).

Invest in a whole house generator or even a standalone generator is something to look into. Your tank wasn't cheap to buy or to fill so think of it as an investment. You want to keep that investment safe and you care for the lives of your fish. We have a whole house generator that automatically clicks on when we lose power. It's worth it.

I would never take the risk of leaving the heater or the chiller without power for as long as a power cut could last. I would be too worried that it would cause more harm than good. I would definitely try and invest in some kind of backup generator if you are able to and have that set to kick in if there ever was a power cut, that way you would have that peace of mind that they were still running even if your power was out.