Around 67,000 homes and businesses are without power following Storm Ali.
The storm battered much of the country since early this morning.
However all weather warnings associated with the storm have been cancelled.
ESB Networks say fallen trees on overhead lines are responsible for most of the damage to the network.
Its 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.
STORM ALI UPDATE: 8pm: We have restored power to 119K customers, 67K customers are still without power. Estimated restoration times on https://t.co/cwxXH3X4kM. We will work late into the night to restore supply before resuming at first light tomorrow. https://t.co/98bzds4OQZ pic.twitter.com/H3tuBFO9AK
— ESB Networks (@ESBNetworks) September 19, 2018
"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 says.
But based on experience of previous storms, it estimates it'll 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.
Meanwhile, an extra day has been added to this year's National Ploughing Championships to make up for today's cancellation.
Tens of thousands of people had headed to the site in Screggan in Co Offaly - before the decision was made to call it off because of Storm Ali.
— National Ploughing (@NPAIE) September 19, 2018
Tents and hoarding have been damaged and portaloos were blown over because of the high winds.
Additional reporting: Jack Quann