More than 65,000 Eversource customers are without power across the state.
The company has posted a list of estimated times of restoration on its website.
In a tweet on Wednesday night, Eversource said repairs in Brookfield, Danbury, Monroe and Newtown, where storm damage is most significant, are expected to be completed by Sunday at noon.
3,261 United Illuminating customers were still without power as of 5:09 a.m. on Thursday morning. Most of them are in Hamden, where 2,408 customers are without power.