Gusts of up to 70mph hit parts of the Province overnight from Thursday to Friday said Northern Ireland Electricity, causing damage to powerlines.
It said power was cut to around 17,500 customers across Northern Ireland, but that by about 10am, 13,000 of these had been restored.
The worst affected areas are across counties Tyrone, Londonderry and Antrim.
There are also some smaller faults in exposed rural and coastal locations in Counties Down and Antrim.
NIE emergency crews are replacing broken poles, clear trees and branches and replacing and reconnecting overhead powerlines as part of a widespread effort to restore power
Meanwhile the Saintfield Road into Belfast from Castlereagh direction was shut at about 9.40am to enable work to be done on overhead powerlines.
Bad weather is expected througout the weekend.
NI Electricity said: “We would like to remind customers that if they do lose electricity supplies they should report the fault online at nienetworks.co.uk or call our Customer Helpline on 03457 643 643.
“Put safety first and if you do see any trees down across powerlines or broken electricity poles, keep away and call NIE Networks immediately.”