Updated: 20.35
Around 67,000 homes, farms and businesses are without power following Storm Ali.
The storm battered much of the country since early Wednesday morning.
However all national weather warnings associated with the storm have been cancelled.
Two people have died as a result of the weather conditions.
ESB Networks crews worked throughout the day to restore power to 119,000 customers who lost supply.
At the height of the storm, 186,000 customers were impacted.
Fallen trees on overhead lines are responsible for most of the damage to the network, the utility says.
"All available resources from ESB Networks are deployed to carry out repairs to the network and restore power and will work late into the evening and will resume at first light tomorrow morning", it adds.
But based on experience of previous storms, it estimates that it will take up to three days to restore power to all those affected.
However, it expects the vast majority will have their power restored much earlier.
ESB Networks apologised for any inconvenience caused, adding it has "mobilised repair crews who are currently working in very difficult conditions to restore power as quickly as possible to affected customers, once it is safe to do so".
Dozens of flights arriving into and departing from Dublin Airport were also cancelled or delayed earlier.
There was also disruption at Cork and Shannon airports as a result of high winds.
About 75 flights have now been cancelled due to high winds & 10 flights have been diverted. Passengers are advised to check with their airline in relation to their specific flight. #StormAli pic.twitter.com/c9ODitkci1
— Dublin Airport (@DublinAirport) September 19, 2018
Aer Lingus say the effects of the storm will disrupt its schedule for the rest of Wednesday.
The effects of #StormAli will continue to cause disruption to the remainder of today's schedule. We apologise to all guests affected by this. Live flight information can be found at https://t.co/0NhKl9BCz7
— Aer Lingus (@AerLingus) September 19, 2018
Most Irish Rail routes are running, but there is still disruption with Enterprise services.
#WeatherWatch Update: Line has reopened between Dundalk and Newry. Bus transfer will remain in place for 19.00 Connolly to Belfast service. 20.50 Connolly to Belfast service will operate through to Belfast #StormAli https://t.co/DGVOeux8qz
— Iarnród Éireann (@IrishRail) September 19, 2018
In Dublin, the Luas Green Line is operating bwtween Broombridge to Dawson and Brides Glen to Balally only.
There is no service between Dawson and Balally due to significant and extensive damage to infrastructure.
#GreenLine service update. Luas Green Line is operating Broombridge to Dawson and Brides Glen to Balally only. Luas tickets valid on @dublinbusnews for the duration of the disruption. Please see https://t.co/GkL4FmFo1J .
— Luas (@Luas) September 19, 2018
It has also announced a full service will not be restored by Thursday morning.
An Post also said the storm had 'taken its toll' on services in the north and north west of the country.
The company said earlier: "Heavy winds and subsequent storm damage meant disruptions to service in more than 60 post offices while mail deliveries across a wide area of the north and north west were temporarily disrupted during the height of the storm.
"An Post is working to restore full services as soon as possible."
Workmen deal with a fallen tree on Finglass Road by Glasnevin Cemetary, Dublin | Image: Brian Lawless/PA Wire/PA Images
Additional reporting: Jack Quann