As a Canadian, I would say "when the power is/was cut" (most commonly), or "when the power is/was cut off" - "when the electricity was cut (off)" is not uncommon.
Note that "when the power was cut ..." has the connotation of an event that happened as a direct result of the power being cut (a bit like passé composé in French) whereas "when the power was out ..." would describe more general things or how you got along after (a bit like imparfait in French)
If it was the result of a general failure over a neighbourhood (i.e., not someone cutting a line on your property or a worker in your house shutting off the mains before doing repairs), I would instead say "When/with the power out, ..." or "During the blackout ..." or "During the (power) outage ..."
I would use "when the power was restored" or "when the power came back on" for when the electricity worked again.