The Appeals Court ruling, issued in June, said the Public Service Commission's process for considering such permits has been flawed. If upheld, the ruling would require the plant to start that process over.
SWEPCO said it was pleased the high court was to review the case.
"This is an important case — both for the Turk Plant and for the process used to approve major utility projects in Arkansas for more than 30 years," said Paul Chodak, SWEPCO's president and chief operating officer. "We believe the record in the case will show that the approval process was correct and that the Turk Plant approval should stand."
SWEPCO said that as of September 30, about $830 million had been spent on the Turk project.
Opponents have argued that the plant would violate the federal Clean Air Act.
"The SWEPCO power plant would spew millions of tons of pollutants and poisons into our air, water, and bodies every year for the next 40 to 50 years," said Glen Hooks, regional director for the Sierra Club's Beyond Coal Campaign. "More than 100 proposed coal-fired power plants across the country have been stopped or abandoned in the last few years. They are a clear danger for our state and nation, and we look forward to the court closely examining the issue."
SWEPCO said the plant will use "ultra-supercritical" advanced coal combustion technology that will use less coal and produce fewer emissions, compared with traditional pulverized coal plants.
"It will be one of the cleanest, most efficient coal-fueled plants in the United States," Chodak said.
The Arkansas Supreme Court has not yet said how it will proceed in the case and whether it will accept briefs or hold oral arguments.
SWEPCO is a subsidiary of Columbus, Ohio-based American Electric Power, among the largest electric utilities in the country.