Close to 1,700 homes across the Shannonside Northern Sound region are still without power.
It follows black-outs caused by Storm Amy, which made landfall on Friday.
The situation is looking optimistic for Co. Longford, with 66 ESB customers expecting their power to be restored by 10am this morning.
While 443 ESB customers in Co. Leitrim are out of power -- their electricity is estimated to be restored by 7pm this evening.
A similar outlook for Co. Roscommon, where 633 are currently without electricity.
However, 95 customers in Boyle and 10 in Arigna will only see their power restored as late as Tuesday evening.
In the Northern Sound region, 525 homes are still without power, only 152 customers in Carrickmacross can expect their electricity back today.
While power for 283 homes across Cavan Town, Clones and Castleblayney in Co. Monaghan is estimated to be restored by tomorrow evening.
The remaining customers will see power restored by 7pm on Tuesday evening.
