The free electrical power is just one example of the power authority’s complex and paradoxical role in the economy here. On Tuesday, Mr. Bhatia will begin hearings to determine who and what are to blame for the authority’s larger problems, especially its ancient and inefficient power plants, among the last in North America to burn oil. Culprits are expected to include the authority’s secretive purchasing managers, elected officials who wasted money on natural gas pipelines that were scrapped and an institutional hostility to wind and solar power that is hard to fathom on a breezy island where the sun shines most days.

“This is the great mystery that we have to unravel in the coming months,” Mr. Bhatia said in an interview.

Meanwhile, though, the free electricity offers a window into the workings of the island’s sole power provider and demonstrates how complex the solutions to the larger debt troubles are likely to be.

“It’s symbolic of a lot of things here in Puerto Rico,” said Miguel Soto-Class, the president of the Center for a New Economy, which has been urging changes at Prepa for the last 10 years. “Every time we start to get into this, they always come back and say: ‘Well, there’s nothing we can do. We’ve got to keep the lights on.’ ”