ESB Networks have restored power to 540,000 customers impacted by Storm Éowyn since last Friday.
Efforts to reconnect the remaining 228,000 homes, farms and businesses are continuing.
The ESB are warning that it could be next week before power in some areas is restored.
They have also received reports of potentially life-threatening incidents where people are unknowingly approaching fallen wires.
The public are being reminded to be extra cautious.
ESB Networks are seeking help from crews in the UK and Europe due to the scale of the power outages.