Around 2,500 homes and businesses remain without power after Storm Amy as of 8.30pm.
The ESB had warned that it could take until "early next week" for all customers to be reconnected.
At its peak, the storm caused a loss of supply to around 184,000 customers in the republic and 65,000 in the north.
The "vast majority" of properties without power in Northern Ireland will have it restored on Sunday, crews have advised.
There were 3,000 properties still without power this morning, as crews from NIE Networks continued their clean-up.
Alex Houston, NIE Networks operations manager, said his team was doing its "very best to get as many as possible reconnected today".
