ESB crews are hoping to restore power to most of the 60,000 homes and businesses who've lost supply by the end of today.
The strong winds from Storm Barra have eased in many areas - but a status orange alert remains in place for Donegal.
There's a status yellow warning for 16 counties - mainly in the northern half of the country.
Power outages are still affecting 2,500 customers across Cork - 2,000 of those customers are in the county with the remainder in the city.
The ESB says full construction crews have been responding to the faults since 6am .
Speaking to RedFM News Jim Hernan of ESB Networks Cork say they expect to have power restored to all customers across the day.
"Outside of the city it's predominantly to the west, but we have some in Mitchelstown, some in Garryvoe, Bantry, Dunmanway and we have an outage in Castletownbere as well.
"The larger of those faults we've had construction crews on site working on them shortly after 6am this morning.
"We had emergency crews and response crews out all night.
"For the larger of those faults we're very optimistic we would have those restored today."
