NIE Networks says power has been restored to nearly all of its customers following the storm.
It said 15 customers still require more complex repairs but that “generators have been provided to ensure they have power until permanent repairs are completed”.
Around 95,000 homes were without power in Northern Ireland at the height of the storm at the weekend due to strong winds.
Several community assistance centers were opened on Monday to help those still without power.
Around 15,000 homes, farms and businesses remained without power in the Republic of Ireland on Tuesday morning.
A team of 60 technicians from French electricity supplier Enedis has arrived in the Republic of Ireland to help repair power outages following the storm.
ESB Networks regional manager Brian Tapley told Irish broadcaster RTÉ that most of its affected customers would have power restored on Tuesday, but some would remain without power for the rest of the week.
Many of the customers without power are in more remote areas, but not all, Mr Tapley said.
Stena Line and Irish Ferries canceled several ferry crossings between Dublin and Holyhead on Monday and Tuesday.
A spokesman for Holyhead Port said there was an “incident at Holyhead Port which caused damage to port infrastructure” on Saturday morning during the storm.
“As a result, Holyhead Port is currently closed to marine traffic and, at this time, the port is expected to remain closed until 18:00 on Tuesday morning, while a full assessment is carried out,” the spokesperson added.