Electricity pole fallen beside trees at Rushall Road in Ardmore
NIE Networks says power has been restored to nearly all of its customers following Storm Darragh.
It said 15 customers still require more complex repairs but that "generators have been provided to ensure they have electricity until permanent fixes are completed".
About 95,000 homes in Northern Ireland were without power at the height of the storm over the weekend due to the strong winds.
Several community assistance centres opened on Monday to help those still without power.
In the Republic of Ireland, about 15,000 homes, farms and businesses remain without electricity on Tuesday morning.
A team of 60 technicians from French power provider Enedis has arrived in the Republic of Ireland to assist in the repair of power outages following Storm Darragh.
ESB Networks told Irish broadcaster RTÉ that some customers could be without supply for "approximately a week" because of the scale and severity of the damage in places.
Its delivery manager Cormac Collins said Storm Darragh was "one of the most severe storms we have received in the last number of years".
He said crews and contractors are "really into the difficult stage of the storm restoration now".
Stena Line and Irish Ferries cancelled several ferry crossings between Dublin and Holyhead on Monday and Tuesday.
A spokesperson for Holyhead port said that on Saturday morning during Storm Darragh, "an incident occurred at Holyhead Port causing damage to port infrastructure".
"As a result, Holyhead Port is currently closed to marine traffic and, at this time, it is expected that the port will remain closed until 18:00 Tuesday at the earliest, while a thorough assessment is conducted," the spokesperson added.
Road closures
In Northern Ireland some road closures are still in place on Tuesday morning due to fallen trees and electricity poles:
In Carrickfergus, West Street was closed after the fire service declared a derelict building unsafe
Traffic signals on the New Forge Road in Magheralin and the Bank Road in Larne are not working due to power cuts, and motorists are advised to approach with caution
Shanco Road in Clogher, County Tyrone, closed due to fallen power lines
Shrigley Road in Killyleagh closed as a tree brought down electricity cables
Several road closures in Antrim including Old Staffordstown Road, Rough Lane, Holestone Road, Kingscourt and Bridge End Road
See here for further updates on road closures.
Related topics
Northern Ireland
Severe weather