Just 120 homes were still without electricity on Wednesday after storm-force winds battered the country.
ESB said engineers have managed to return power to almost 15,000 homes, but small pockets remain cut off, with Scariff in Co Clare, Carndonagh and Buncrana in Co Donegal, and Bagenalstown in Co Carlow worst-affected. Elsewhere, Eircom is continuing to fix more than 5,000 faults reported on its telecommunications network.
ESB spokesman Brian Montayne warned that some households may experience short power disruptions throughout the day as crews work to repair some faults which were temporarily fixed on Tuesday.
"We are expecting more winds today but not like yesterday," he said. "It is important to get these repairs right so we ask customers to bear with us."
Met Eireann has forecast gales during the day, with strong gale- force winds in the north, while outbreaks of rain over the north-west will spread to other areas and turn heavy.
Motorists are also being warned to take extra care during high winds.
Harry Blaney Bridge in Fanad, Co Donegal, is open to cars but is expected to remain closed to high-sided vehicles, caravans and motorcycles until later on Wednesday, due to strong winds.
On Tuesday, near-record hurricane winds were recorded off the north as an Atlantic storm brought gales gusting to 91 knots, 165kph (102mph) at Malin - a speed only surpassed seven times in Ireland.
Met Eireann said winds were strongest in Connacht and Ulster, with violent storm force 11 battering coasts between Bloody Foreland in Donegal and Fair Head in Co Antrim.