TALLAHASSEE — A federal appeals court Wednesday backed Florida Power & Light and Duke Energy Florida in a class-action lawsuit that sought to recover money paid by utility customers under a controversial 2006 nuclear-power law.

A three-judge panel of the 11th U.S. Circuit Court of Appeals upheld a decision by a federal district judge to dismiss the lawsuit, which alleged “unjust enrichment” and contended that the law is unconstitutional. Attorneys for the plaintiffs sought to recover $2 billion that they said the utilities had collected from customers.

The law, approved by the Legislature and then-Gov. Jeb Bush, was intended to spur development of more nuclear energy in Florida. But it has been highly controversial, as it allowed utilities to collect money for nuclear projects that might never be built.

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FPL used a portion of the money it has collected to upgrade already-existing nuclear plants. But, for example, Duke in 2013 shelved plans to build two reactors in Levy County after billing customers for early stages of the project.

The lawsuit alleged that the law was unconstitutional under the Commerce Clause of the U.S. Constitution and that it is “preempted” under a federal law known as the Atomic Energy Act. The plaintiffs contended that, under the Atomic Energy Act, Congress did not intend for states to have a role in financing and promoting nuclear projects.

But in rejecting the Atomic Energy Act argument, the Atlanta-based appeals court pointed to a 1983 U.S. Supreme Court decision in a California nuclear-power case. It said the Supreme Court concluded “there was an economic (and non-safety) rationale for the California law, and this was enough to save it from preemption.”

“The (Florida law) is based on an economic rationale — whether flawed or not — that utilities like Duke Energy Florida and Florida Power & Light should be able to recoup from their customers the costs associated with a project for the construction of a nuclear power plant, and that they should not have to return the funds received even if the project is not completed,” said Wednesday’s 14-page ruling, written by Judge Gerald Tjoflat and joined by judges Adalberto Jordan and John Steele. “Plaintiffs point to no cases holding (nor authorities suggesting) that state laws promoting investment in new nuclear plants, or shifting the costs of nuclear plant construction, are preempted by the Atomic Energy Act.”

The Commerce Clause issue stemmed from a contention by the plaintiffs that the 2006 law discriminated against interstate commerce, at least in part because out-of-state wholesale energy providers would not be able to compete.

But the appeals court said such legal issues, involving what is known as the “dormant” Commerce Clause, are focused on out-of-state people or entities being harmed by other states’ actions.

“This is far from the case here,” the ruling said. “Plaintiffs are Florida electric utility customers. (The) utilities are Florida companies. Utilities are not ‘states’ such that their actions could give rise to (dormant Commerce Clause) claims from an out-of-state person or entity. Plaintiffs’ interests are well beyond the zone the (dormant Commerce Clause) is meant to protect.”

The lawsuit, which included one Duke customer and one FPL customer as named plaintiffs, is part of years of legal and legislative wrangling about the 2006 law. The Florida Supreme Court in 2013 rejected a challenge that was based on alleged violations of the Florida Constitution.