Gusts of up to 70mph which swept in from the Atlantic have left parts of the north, east and exposed rural areas facing major blackouts.
Meanwhile two people were killed in other parts of the UK due to the stormy conditions.
In Scotland a lorry driver died after his vehicle was blown on top of cars.
Elsewhere, another man was killed by a falling tree in Nottinghamshire.
Energy company NIE said the damage was caused by flying debris and high winds and its latest figures estimate that around 7,000 properties had been affected during the storm.
According to NIE, some 2,700 customers remain without power as of 4pm.
Julia Carson of NIE said the firm continued to work in order to reconnect power to the thousands still left without electricity.
"We had been monitoring the incoming weather and made arrangements to open our local incident centres and put additional emergency crews, engineers and call handlers on standby," she said.
"All programmed work on the overhead network has been cancelled. The damage has been significant with lines brought down and poles broken by the high winds. Some areas experienced gusts of up to 70mph.
"We have been working since early morning and we’ll continue to respond to reports of damage and put customers back on supply as quickly and safely as possible."
Specialist incident centres have been set up while additional emergency crews and engineers have been drafted in to resolve the 200 faults on the network.
In Portrush, a felled tree caused damage and street closures.
More than 15,000 homes had power supplies restored overnight.
Killard House School in Donaghadee was closed due to a power cut.
An NIE spokeswoman said: "Damage has been caused by flying debris and high winds, including broken electricity lines and damage to poles and other equipment.
"There may also be further faults which have not yet been reported to Northern Ireland Electricity and adverse weather conditions, which could cause additional faults, are due to continue for the next few hours."
Roads and rail
The adverse weather has brought trees down across Northern Ireland, shutting roads and obstructing railway lines.
The Crawfordsburn and Rathgael Roads in Bangor were closed because of fallen trees as were the Spa Road, Ballynahinch, Mearne Road, Downpatrick and Castleward Road, Downpatrick.
In Belfast, morning rush hour traffic faced further congestion because the Antrim Road was blocked by a fallen tree at Kincraig Park. The Ormeau Embankment in the south of the city was only passable with care.
In Londonderry, high winds forced the closure of the Foyle Bridge but it has since re-opened.
The main Coleraine to Limavady Road was also shut due to fallen trees while in Co Tyrone the Sweep Road in Cookstown was shut due to an unsafe roof on a building.
Latest road closures include:
A37 Dunhill Road, Coleraine (Coleraine to Limavady Mountain Road) at Springwell Forest - REOPENED
Tanaghmore Road - Randalstown - REOPENED
Circular Road, Whiteabbey - REOPENED
Main Street Portrush closed from Atlantic Avenue due to unsafe Buildings - Main Street will remain closed overnight
A42 Carnlough Road between Tullymore Road and Ballylig Road - REOPENED
Dunadry Rd and Alder Road in Antrim Council area - Closed
B7 Burren Road, (between Dromara and Ballynahich) Closed
Mill Road at Knockbracken, CAstlereagh - REOPENED
The A29 Moneymore Road dual carriageway, Cookstown - REOPENED
U2210 Letteran Rd, Churchtown - closed
U715 Ballynagilly Lane, Cookstown - closed
U5053 Craigadick, Maghera - closed
Stranmillis Road near Danesfort - Closed whilst tree clearance takes place
Fardross Road, Clogher, is closed due to fallen BT poles. ( The trees which brought down the BT wires have been removed.)
Police have advised motorists to drive with care.
Train services have been disrupted, due to debris on the line, between Belfast and Yorkgate, Carrickfergus, Larne Harbour, Larne Town, Whitehead and Seaview.
Translink has said all lines are subject to alterations and short notice delays of up to 30 minutes. NI Railways tickets can be used on Ulsterbus and Metro services where there is this disruption.
A number of ferry crossings were expected to be disrupted including the P&O Larne to Cairnryan service. The company has advised customers to check the helpline before setting off on their journey.
All sailings between Ballycastle and Rathlin off the Co Antrim coast were cancelled for the day.
There were also reports of flooding in Portstewart, Co Antrim after waves, some as big as 20ft battered the promenade.
A shop partially collapsed on Belfast's Grosvenor Road narrowly missing a bus shelter.
In the city centre, the Christmas market was temporarily closed because of the high winds while the Christmas tree at Stormont's Parliament Buildings was blown over.
Severe weather warnings have been issued across the UK. While Britain is under 'amber warning', Northern Ireland has a less severe 'yellow warning' in place - which means to be aware of potential disruption.
The Met Office says Northern Ireland will see a narrow band of heavy rain moving down from the north over the course of the day with gale-force westerly winds.
This will be strongest along the north coast, where huge waves have been reported. Winds could reach 70mph (115kph) as a storm, dubbed Xaver, moves in from the Atlantic.
But it will soon become brighter with easing winds and showers developing.
Send your storm pictures and videos to email@example.com
Customers still affected by the storm can contact NIE on 08457 643643