Even the golf club is part of the program: Members carry hand weeders on the links and pry up errant plants, reducing the need for herbicides, and sheep graze to keep tall grasses in check. Since the members can also arrange to buy the meat, said Jesper Roug Kristensen, a golf club member who works at the energy academy, “you can eat the golf course.”

It has taken $80 million in investment, about 20 percent from government subsidies, to turn the island into a renewable-energy community, Mr. Hermansen estimates. But in the end, the island’s accomplishments seem to stem not so much from government policies and subsidies as from Mr. Hermansen’s ability to show people how the changes could benefit them. The wind turbines, for instance, faced opposition from residents who said the modern machines would ruin the charm of their villages. So the planners moved some turbines from the most sensitive areas, but also added to their appeal by allowing locals to buy shares in the projects.

Ole Kaempe, a teacher who can see the turbine he and his wife invested in from between the rows of wine grapes near his farmhouse, said that the income made the low mechanical hum sound better. “Otherwise it would be noise,” he said, “but now, it’s beautiful music.”

An Imperfect Model

Samso’s energy independence suggests that Denmark’s aggressive goal of becoming fossil-fuel free by 2050 is feasible, said Mr. Petersen, the energy minister. “We need front-runners,” he said, “and they are just that.” The country as a whole is well on its way: Last year, Denmark drew almost 40 percent of its electricity from wind, up from 33 percent the year before. Over 60 percent of Danish houses get their heat from central sources, like Samso’s, that are already using renewables or can be easily converted, Mr. Petersen said. The hardest challenge, he said, is ridding its transport system of fossil fuels, so he is looking to Samso for ideas. “I hope that they can crack that nut first.”

To that end, the island is promoting the use of electric vehicles and plans to test using gas from decomposing waste as fuel for a new ferry set to arrive next month. Yet while the national government is expecting useful results from Samso’s efforts, there are signs that its consensus and momentum could flag. Mr. Hermansen, who says he is on the road about 100 days a year promoting the island’s story, is beginning to talk of doing other things. The academy is working with islands in Europe and Japan that are adapting Samso’s approaches, and he mused that he might shift more of his time to creating partnerships like those.

And although many residents express pride in the island’s green image, others point to shortcomings. It still relies on fossil fuels when the wind does not blow or the heating plants break down. Only 10 to 15 percent of the population has invested in the wind farm production, and electricity bills have stayed high, in part because of Danish tax and energy policies.