ESB crews have restored power to more than 12,000 homes across the country.
Repair work to the network damaged by last night's storms is continuing in the west and north-west.
The ESB said all but a few hundred customers will have supplies restored by midnight. Work will continue tomorrow in a small number of inaccessible areas.
Near Westport in Co Mayo, a boat will be brought in tomorrow and used to reach a power line which has fallen into the sea at Clew Bay.
Repair crews were unable to reach it because of tidal conditions and adverse weather this afternoon.
All trees which fell on roads have now been removed.
Four cars were damaged in City West hotel car park in Dublin overnight when a tree fell in high winds.
Severe weather conditions also led to the today's racing at the Cheltenham Festival being abandoned.
Officials made the announcement after another morning of intense gusts at Prestbury Park.
All six races due to take place this afternoon will instead be staged on Thursday and Friday. Read more here