The utility's website said heavy, wet snow and high winds have taken down wires and tree limbs, causing power outages across the state.
In Medfield, 49 percent (2,349 out of 4,772) of NSTAR customers are without power as of Sunday morning. Across the state, 114,000 customers remain without power. NSTAR said it has restored 70,000 customers as of Sunday morning.
"Most of the outages are concentrated in the company's Western service territory around the communities of Framingham, Waltham and Walpole, and in the south on Cape Cod," NSTAR said. "While many customers will have power restored within the next 24 hours; do to the difficult driving conditions, downed trees and severe damage experienced on the utility's system; NSTAR is anticipating its power restoration effort will last into the work week."
According to its website, NSTAR has activated its Emergency Response Plan - opening regional service centers as storm response headquarters, adding extra line crews and support staff in its service centers, and adding additional staffing to its customer call center.
The utility said it is prepared to address any damage and outages resulting from the storm and encourages customers whose electric service is affected to report it by using the "Report an Outage" tool or by calling (800) 592-2000. A list of customers without power by town is also available.
"We strongly urge people to stay away from all down wires and to report them to us and local emergency officials," NSTAR said.
This story will be updated.