The number of homes, businesses and farms still without power in the Northern Sound region now stands at 9,000 as of 4pm.
The figure is down from 12,750 this time yesterday evening and a drop of 42,000 from the height of the storm when outages were 55,000 last Friday.
In a statement from ESB Networks this evening, they say during this current stage of restoration, teams are energising large sections of the rural network in order to restore supply to each individual customer in counties Cavan and Monaghan.
They say they are urging customers to never approach fallen wires or damaged ESB Networks infrastructure as it is LIVE and extremely dangerous. Please report any damage to electricity infrastructure by calling 1800 372 999.
The statement this evening says that the work required is of a scale that local crews have never experienced before following the unprecedented damage that the storm caused. ESB Networks, partner contractors and international crews supporting the post-Storm Éowyn restoration effort are doing everything they can to restore supply to all impacted customers as soon as possible.