The Nuclear Regulatory Commission voted 4 to 1 on Friday to approve a plan to build two reactors at a power plant in South Carolina, the second nuclear plant construction permit to be in granted less than two months after a 34-year hiatus. The Scana Corporation plans to build the reactors at the Virgil C. Summer plant northwest of Columbia. The company plans to cover 55 percent of the project’s estimated $10.2 billion cost, with Santee Cooper, South Carolina’s largest power producer, paying the remainder. Based in Cayce, S.C., Scana, which submitted its application to the Nuclear Regulatory Commission in March 2008, said its first unit would not begin operating until 2017, about a year behind schedule, because of delays in the commission’s licensing process. The second is expected to start running in 2018.