The Eversource power company has released estimated completion times for the towns in its coverage area.
The company said it hopes to have the vast majority of towns back up and running by Sunday night.
Eversource classified "vast majority" as less than 1 percent of a community being without power.
As of 6 p.m. on Thursday, Eversource reported 51,000 powerless customers.
The company posted the complete estimated restoration list here.
"The safe restoration of all customers is our priority," Eversource said on its website. "Customers without power in communities where your neighbors have power are asked to report your outage online or call our Customer Service Team at 800-286-2000."
Three EF1 tornadoes touched down in Connecticut on Tuesday night and caused widespread damage in a number of communities.
The president of Connecticut operations for Eversource said the 110 mile per hour winds tore up the western part of the state on Tuesday.
"It’s been a lot different usually you don’t see the devastation with the trees like this storm. When you look at the streets in the communities you just can’t get around. It’s impacting us. I know it’s impacting the communities as well," said Craig Hallstrom, Eversource president for Regional Electric Operations in CT & MA.
An estimated 750 utility poles were damaged, and in the worst hit areas, workers need to do much more than just reconnect lines.
"Instead of in a repair mode, like we are in most winter storms, we’re in a rebuild mode," Hallstrom said.
That's why Eversource is asking for patience.
As crews continue going from location to location to get power restored for everyone, if you happen to come across debris, do not touch it do not go near it. Instead, give Eversource a call.
Stay with Channel 3 for continuing coverage of the storm aftermath.
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