Around 330,000 homes, farms and businesses remain without power after Storm Éowyn.
The National Emergency Coordination Group has met today and said electricity is back for 438,000 ESB Networks customers.
It said by Friday most people will have their supply restored, but around 100,000 will gradually have their power back over the following week.
The group also confirmed the country has activated the EU Civil Protection Mechanism and has made a request for high-capacity generators to support critical infrastructure operators.
Storm Herminia is bringing strong winds and heavy downpours across the country.

There is currently a status yellow wind and rain alert in place for most of Ireland until 6pm this evening.
However, it will remain in place for Cork, Kerry and Waterford until 9am tomorrow.
Around 94,000 homes and businesses are still without broadband this evening.
Eir said it has restored fixed and broadband services to 110,000 customers since Friday.
The northern half of the country is the most impacted by outages and faults, particularly in the Midlands, West and North West.
Service has been restored to more than 500 mobile sites in the same timeframe in the wake of Storm Éowyn.