At least 500 incidents have been reported in the region, Northern Powergrid said.
The service has restored power to 88,000 homes and businesses but 112,000 are still without power.
Northern Powergrid tweeted an updated: "#StormArwen is continuing to batter our region and causing ongoing damage to our network.
"We have restored power to 88,000 homes and businesses.
"We currently have 112,000 customers without power and we have more than 550 instances of damage on our network."
More to follow.