Around 1,500 homes were still without power on Sunday after damage caused at the start of the weekend by Storm Amy.
Staff from NI Networks and Department for Infrastructure (DfI) have worked throughout the weekend to restore power to thousands of homes after damage caused by high winds and rain.
As many as 65,000 were without power at the height of the storm, and 1,457 incidents were reported to the DfI, including cases of fallen trees and flooding.
The impact of the storm also affected public transport, with speed limits in place on the railways following disrupted services.
In an update on Sunday, NIE networks said that around 1,500 properties were still without power following storm damage.
Alex Houston, NIE Networks Operations Manager, said; "Our teams are continuing their efforts today and we're now into the repairs which affect small numbers of customers but are equally as resource intensive.
"We've been able to bolster the teams in those areas and are doing our very best to have the most of these customers back on by the morning.
"At this stage we would encourage anyone who has not yet reported their power cut to contact the customer centre on 03457 643 643 so we can ensure all faults are reported and in the restoration process.
"We would also remind people to report any damaged equipment and to assume all electricity equipment is still live, even if it is broken, and to stay well clear."
The Infrastructure minister Liz Kimmins thanked the staff who had been working to restore power to homes, as well as deal with the rest of the aftermath of storm Amy over the weekend.
"My sincere thanks go to teams right across DfI who worked tirelessly in response to Storm Amy.
"The damage caused by the severe winds and heavy rain was significant with many roads, including the M1, M2 and M22, impacted by fallen trees and associated debris.
"The fact that 1457 incidents, including 1018 obstructions such as fallen trees and over 350 flooding incidents have been reported across the North paints a picture of the scale of what was being dealt with.
"I pay tribute to DfI colleagues and all multi agency partners who were out on the front line during these very dangerous and challenging times.
"They have been working hard to clear the affected parts of our road network, to mitigate the effects of flooding through proactive measures, maintaining critical drainage infrastructure as well as restoring power and water to homes and getting the public transport network back to normal.
"This is the work that so often goes unseen but is essential in reconnecting our communities and making our road network safe."
Storm Amy was itself partly caused by Hurricane Humerto, with Met Office metrologist Becky Mitchell saying the remnants of that weather system were "swept up into the jet stream" towards the islands of Ireland and Great Britain.
Looking ahead to the weather this week, Mrs Mitchell expects a "quite cloudy" start to Monday, "perhaps with some drizzly outbreaks."
"It does look to turn drier and brighter for most places by mid afternoon, so some good sunny spells developing," the meteorologist added.
"Coastal areas still look quite cloudy generally, but inland we look to have some brightness. It should be largely dry and a slight breeze inland, but coastal areas, where it's cloudy, will be quite blustery.
"We're in quite a warm air mass tomorrow, so temperatures reach 17 C or 18 C across Northern Ireland, above average for the time of year.
"Tuesday, we've got a weather front moving in, so it will be cloudy at first with outbreaks of light rain across the whole of Northern Ireland.
"The rain will gradually be clearing through the day, so hopefully by the mid-afternoon we should have some good spells of sunshine and light winds.
"It will be quite cool, so maximum temperatures on Tuesday will be a bit lower; we're looking at about 15 C."
For the week following Tuesday, Mrs Mitchell said "high pressure looks to take charge" in NI, leading to "settled conditions, but not necessarily dry all the time.
"We're not expecting any strong winds through the rest of next week, but there will be rain and cloud at times, possibly some mist and fog as well."
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Ms Mitchell confirmed that Northern Ireland has had an "Otctober-record-breaking gust at Magill again", and that climate change means that more powerful storms with occur with greater regularity going forwards.
"Generally speaking, climate change does mean we're going to expect more frequent and stronger storms across the UK. We generally see higher wind gusts and records being broken each storm season."
Looking ahead, Ms Mitchell emphasised that, while each individual storm season is difficult to predict, but on a "general basis, our longer term outlook is that we will expect more frequent and stronger storms in the UK for the next 10 to 20 years."