When you turn on a light or charge your phone, the electricity coming from the outlet may well have traveled hundreds of miles across the power grid that blankets most of North America — the world’s largest machine, and one of its most eccentric.

Your household power may have been generated by Niagara Falls, or by a natural-gas-fired plant on a barge floating off the Brooklyn shore. But the kilowatt-hour produced down the block probably costs more than the one produced at the Canadian border.

Moreover, a surprising portion of the system is idle except for the hottest days of the year, when already bottlenecked transmission lines into the New York City area reach their physical limit.