Duke Energy Corp., the third-biggest U.S. coal consumer, has won state approval to begin construction of only one coal-burning power plant in North Carolina, not the two it had requested.

Duke may add one 800-megawatt generator at its existing Cliffside station northeast of Charlotte, the North Carolina Utilities Commission said yesterday in a notice posted on its Web site. Duke failed to prove a sister unit is necessary, the panel said. The decision means Duke can add the cost of the plant to utility bills.

Duke pushed for approval this month, insisting it needs to lock in construction costs that soared 43 percent from September to November amid a surge in plans for new power plants. It had estimated cost of the two units at $3 billion.

“This could spell the end of the project because Duke Energy insisted that it would be too costly to build a single unit based on economies of scale,” said Jim Warren, executive director of the North Carolina Waste Awareness & Reduction Network, a plant opponent.