More than 40,000 homes lost electricity early yesterday after storm-force winds brought down power lines.
Over 100 ESB emergency crews were called into service.
Although they were hampered by the strong winds, they managed to restore power to three-quarters of affected homes by yesterday evening.
A spokesman for ESB said there would still be "pockets of customers" in remote, rural areas who would be without power last night. However, he said, emergency crews would be out at first light this morning to restore services.
By 6 p.m. yesterday, he said, power had been restored to all but about 7,000 homes. He said the ESB hoped this number would be down to a few hundred by nightfall.
"There is no point in sending out crews during the night. To inspect a line in the dark is impossible," he said.
The east coast was worst affected, with 10,000 to 15,000 homes losing electricity in Co Dublin alone.
The city area was not badly hit as electricity lines there run underground. However, the county area, north of Portmarnock and south of Dún Laoghaire, close to the Wicklow border, was severely affected, the spokesman said.
"The main damage was timber damage where trees and branches fell on lines. It was difficult for us because the eye of the storm passed over Dublin at about 7 a.m. or 8 a.m., hampering the repair teams."
Counties Wicklow and Carlow were also badly hit, with Arklow and Carlow town both losing power for a time.
"In Wicklow we were limited to dealing with emergencies. We also prioritised restoring power to areas of higher population. As a result, there may be pockets of three or four houses together in rural areas which will be without power overnight."
Up to 250 ESB staff took part in the repair works, including an emergency crew which travelled from the west to help restore power in the midlands.
The spokesman noted the storm was unusual for this time of year. A national timber-cutting programme, which took place each year to prevent damage caused by storms over the winter period, had yet to begin in earnest. "We would not normally expect a storm like this until December, January or February," he added.
