The push to bring the turbine to Brooklyn began in 2008, Mr. Outerbridge said, adding that he hoped the installation would give wind power and other forms of renewable energy more legitimacy in the city.

He said he first applied for a permit with the Buildings Department in 2010.

“The Buildings Department had a process set up for building-mounted turbines, but nothing for commercial-scale turbines,” he said. “It was bit of a learning curve for all of us.”

A spokesman for the department said it had developed a protocol for handling turbine permits in 2011.

While many wind turbine proposals attract opposition on aesthetic grounds, or because of their potential to cause damage to bird and bat habitats, Mr. Outerbridge said the Sunset Park project had received a positive response from the community as well as representatives of nearby Green-Wood Cemetery and the Audubon Society.

All told, the turbine cost $750,000 to build, and Mr. Outerbridge said he expected it to pay for itself within five years.

The New York State Energy Research and Development Authority, which awards grants for renewable energy projects, provided $130,000 toward the cost of the turbine. The agency has given out grants for 200 windmills in the state over the last eight years. So far, no other turbines are planned for New York City, said Mark Mayhew, a project manager for the agency.

Donna DeConstanzo, a lawyer with the Natural Resources Defense Council, said that, although her organization was not involved with the Sunset Park project, “wherever you have an opportunity to generate clean, renewable energy in New York City, that’s significant and exciting.”