“This fits into his M.O. of doing these big, grandstanding things to get attention for the company and the technology that he’s building,” said Ashlee Vance, the author of a 2015 biography of Mr. Musk. “Tesla’s at this really critical stage where they’re trying to be both a car company and an energy company at the same time.”

Australia is a fitting target for Mr. Musk. The country is the world’s largest exporter of coal. By most measures, it is the sunniest continent on earth. It has abundant wind and hydroelectric power capabilities. And yet the cost of electricity in Australia increased 20 percent from 2012 to 2016, and Australians this year paid between 50 and 100 percent more for their power than Americans, according to experts.

South Australia has the highest electricity prices in the world. This imbalance of supply and demand has resulted in regular blackouts and astronomical bills for the state’s 1.7 million residents.

The high-capacity Tesla battery does not create energy, it just stores it. The state already invests in wind and solar energy. The battery would give it a bank of saved energy, which could ease pressure during periods of high demand and help better manage the electrical grid.

“More than 40 percent of South Australia’s electricity is coming from wind, which is good,” said Tony Wood, an energy director at the Grattan Institute, a think tank. “But the consideration of how to integrate it — and manage that intermittency — wasn’t so good.”

The day after Mr. Weatherill was roused from his couch in March, he and Mr. Musk spoke on the phone about the proposal. The Australian, knowing the tech mogul’s ability to stir the news media, had one demand: If Tesla were to win the contract, Mr. Musk would appear in South Australia to announce it to the world.

“He usually doesn’t come for announcements of winning a tender,” Mr. Weatherill said, “but he said he’d come.”