A post on the Utility Workers Union of America Local 1-2's Facebook page said a tentative agreement is in place.
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More than 8,000 utility workers had threatened to walk off the job starting at midnight on Sunday.
Details of the agreement have not been released.
The union said Saturday that a long, hot summer would put major strain on the electrical grid and, with no deal in place, would be a disaster waiting to happen.
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Local 1-2 President James Shillitto said Con Ed paid no heed to the sacrifices by the more than 700 members sickened by COVID-19.
Shillitto said his Local 1-2 workers are first-responders in any emergency and vital to any recovery effort.
Con Ed has not responded publicly.