About 2,000 households in Carrigaline, Co. Cork, were blacked out overnight, but the ESB have confirmed power has been restored to these homes.
Areas of counties Galway and Limerick were also badly affected, with about 500 homes left dark.
Winds of up to 60km/h and gusts of up to 110km/h lashed the north and west coasts last night. The forecast is for more wet and windy weather over the next few days.