NIE Networks are still working to restore electricity to about 1,500 customers following Storm Darragh.
About 95,000 homes in Northern Ireland were without power at some point over the weekend due to the strong winds.
Several community assistance centres will be opened on Monday afternoon and evening to help those still without power.
Desi Houston, a farmer in Lisburn, has been using a generator to keep his farm running since Saturday.
The assistance centres are due to open between 12:00 GMT and 14:00 and then again between 17:00 and 19:00.
NIE Networks estimates that the vast majority of customers will be restored by Monday evening, though small pockets could remain off supply into Tuesday.
Contractors from Scotland are due to arrive in Northern Ireland on Monday afternoon to help with the restoration works.
The Energy Networks Association, which represents energy networks in the UK, said as of 08:00 GMT on Monday about 66,000 customers were without power.
In the Republic of Ireland, 35,000 homes and businesses remained without power on Monday morning.
Desi Houston, who owns a farm on the Ballinderry Road, has been without power over the weekend.
He said he saw a “flash of light” when trees fell on an electricity pole shortly after 01:00GMT on Saturday.
He has been using a generator to keep the freezers, which are full of Christmas food, running and to put on lights to feed the cattle.
He said he was hopeful that power would be restored on Monday.
Ferries cancelled
Stena Line and Irish Ferries have 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.
In a statement to BBC News NI Ger Hyland, President of the Irish Road Haulage Association said that businesses were having to “twist and turn to make it work” in the face of weather-related delays.
“Issues like these tend to leave us three to four days behind, we end up having to play catch up,” he added.
In Northern Ireland some road closures are also still in place on Monday 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 to due power cuts, and motorists are advised to approach with caution
- Shanco Road in Clogher, County Tyrone, closed due to fallen power lines
- Warren Road in Donaghadee closed between the New Road and Stockbridge Road due to a faulty electrical pole
- Several road closures in Antrim including Old Staffordstown Road, Rough Lane, Holestone Road, Kingscourt and Bridge End Road
‘Gesture of goodwill’
Six Irish Premiership football matches were cancelled on Saturday due to the storm.
Northern Ireland Football League chief executive Gerard Lawlor apologised to fans for the short-notice announcements.
Mr Lawlor told Good Morning Ulster: “If people are out of pocket as supporters clubs, we will look as seeing can we help in some way as a gesture of goodwill.”
Communities Minister Gordon Lyons told BBC’s Good Morning Ulster programme on Monday: “The frustration comes from the fact that many people felt with the weather the way it was, there was an inevitability to all this happening and it could have been done earlier.
“It’s especially important that there was a recognition that there was a financial cost to fans and to clubs.”