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A proposed wind farm that would be the biggest offshore one in the nation won approval from Texas state officials, the latest development in the fast-growing segment of the alternative-energy industry.

Texas General Land Office, which manages state lands and mineral rights, said that it reached an agreement granting Superior Renewable Energy LLC the rights to 39,900 acres of submerged lands in the Gulf of Mexico, just off the coast of Padre Island and south of Baffin Bay.

The big wind turbines, expected to number more than 100, will be erected as few as three and as many as eight miles offshore.

The Houston company, headed by the former executive of a small oil company, said it plans to build 500 megawatts of capacity, enough to power a small city, or about 125,000 homes. But the firm’s executive vice president and general counsel Michael Hansen said it will probably be about four years before construction begins.

Though starting from a low base, wind generation is growing rapidly. The installed capacity of the wind industry grew by 25 percent last year. The wind industry’s current capacity is 9,149 megawatts, providing enough electricity to serve more than 2.3 million average households.

But the industry has run into some opposition from environmental, tourism and other groups concerned about the unsightly turbines and potential harm to birds, many of which migrate to the Texas coast in winter. Hansen said the firm would study bird migration patterns before starting construction and would use blades that he said would be unlikely to harm birds.

“At a time when energy prices are spiking and the science on global warming is so clear, it’s really amazing to see what appears to be a visionary project for the Gulf,” said Chris Miller, a senior energy campaigner for the advocacy group Greenpeace. Miller added, however, that officials need to look at the farm’s potential impact on local birds and sea turtles.

“A lot of work needs to be done,” he said.

Touting what he called a “wind rush,” Jerry Patterson, commissioner of the Texas General Land Office, said in an interview that he is determined to make Texas the epicenter of the wind industry, whether in manufacturing turbines for wind projects or establishing the farms themselves. Texas has 2,000 megawatts of wind farms operating on land; this is the state’s second agreement for an offshore farm.

“We want to be the U.S. leader, if not the world leader, in the whole business,” Patterson said. “Oil and gas someday, whether it’s 50, 150 or 1,500 years, will go away. We need to diversify our portfolio to provide electricity to the citizens of the great state of Texas.”

State leases are important sources of state revenue. Under the lease, Superior Renewable Energy pays a modest $80,000 initial fee, then pays the state 4 percent of its revenue for the first 20 years of operation and 5 percent thereafter. The General Land Office estimates that the wind farm could provide $34 million to $100 million in royalty payments over the 30-year lease.

Because of a quirk of history, the project does not need approval from the Interior Department, unlike most proposed offshore wind projects. States control waters up to three miles from shore. But when Texas, previously an independent country, joined the United States in 1845, Sam Houston insisted that the state’s rights extend to three leagues, or 10.3 miles, offshore.

After oil and gas were discovered there, controversy over the rights led to a Supreme Court decision against the state, but the rights were restored in 1953 legislation signed by President Eisenhower.