The winds caused havoc on coastal roads
Northern Ireland Electricity said the main areas still affected are Coleraine, Ballyclare and Ballymena.
Approximately 35,000 customers were affected at various stages throughout Sunday night and Monday due to 80mph winds.
The company said engineers were working to repair the faults and hoped to have everyone back on-line by midnight.
Ferry services
Although the storms were widespread, mid-Ulster and Fermanagh were worst affected.
Hundreds of engineers have been working since the early hours of Monday morning to repair broken power lines.
However, NIE has warned that some faults may take time to fix because there are still fallen poles which need to be replaced.
All routine programme work had been postponed to allow staff to concentrate on getting remaining customers back on supply as soon as possible.
Traffic and travel services have also been affected by the strong winds although ferry sailings that were cancelled earlier on Monday have returned to normal.
Fallen trees and power cables blocked some road and it is understood some flights from Belfast International and the City Airports were affected.
Some flights from Londonderry have been cancelled due to high winds.
NIE has set up a fault helpline on 08457 643643.
High winds
Winds have been easing but the Met Office says they will remain fresh to strong throughout Monday evening.
Meanwhile, premises in the Republic of Ireland have also been affected.
In County Donegal, more than 1,000 homes lost power and more people have been cut off in the west of the country.
The Electricity Supply Board (ESB) said repair crews were battling against high winds to repair the cables.
Much of the work is being carried out in the Carrick-on-Shannon area of Leitrim, the Ballinrobe area of County Mayo and the Loughrea and Gort areas of County Galway, where services were worst hit.
An ESB spokesman said: "Since early morning ESB crews have been dispatched and are working on restoring power.
"We would also warn people if anyone notices fallen lines, to steer well clear of them and contact us immediately."