Duke Energy Corp. plans to build a $250 million facility in North Carolina to stockpile heating fuel for the coldest days of the year.

The 685-acre liquefied natural gas production and storage plant in Robeson County will include a tank to hoard the equivalent of 1 billion cubic feet of heating fuel, enough for 100,000 homes on a frigid day, said Frank Yoho, president of Duke’s natural gas business. The project, slated to start up in the...