Northern Ireland Electricity said there was widespread damage, especially in Omagh, Enniskillen, Dungannon, Londonderry, Coleraine and Ballymena.
Roads have also been affected, with the Glenshane Pass closed for snow ploughing.
The road has been closed since the early evening and Roads Service said their work has been hampered by snow, lying up to 50cms in some areas.
The Met office is predicting heavy rain and snow with biting gales.
The police have said driving conditions across Northern Ireland are “treacherous” and have advised motorists to slow down.
The Glenshane Pass is said to be “particularly difficult”. Snow ploughs and gritters are working to clear the road.
Winds have brought down electricity lines and poles and caused 250 individual faults.
An NIE spokesperson said its engineers were working on faults as quickly as it was “safe to do so” and that an additional 250 staff have been called in.
Contractors from the Irish Republic will be called in to help on Wednesday morning.
“At present, around 30,000 customers are without electricity,” an NIE spokesperson said.
“This number is constantly changing – as faults are repaired in one area, customers are losing power in another.
“Poor visibility, high winds and worsening weather have meant that crews will stand down from midnight.
“Customers should be aware that if they are still off supply at midnight, their power will be off overnight.”