If power outages are a very frequent thing then you need to get power that is not tied to your grid. eg solar, wind, small scale hydro etc.
If outages are common but not a regular thing then one has to ask how stable is the power when it is on? Miners MUST have a stable incoming voltage typically between 208-240VAC. Prolonged operation below or above that range will quickly kill the miners.
The solution is not far from this advice, I will liken the power outage to my nation where national grid collapsed unpredictable and everything the electricity distribution company don't quarnatee you of light even when the grid is without collapsed, mining in sere of such electric or power issue need external power as listed by Notfuzzywarm, out side from such the mining can't work.
One need weigh and calculate the outage of the power to know the best alternative if solar, hydro or any other sources of power can be suitable why considering the cost of running external power outside from the national grid.