In the extended version of the film, Elwood parks the Bluesmobile in an electric substation that was used to power Chicago's elevated trains.
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In the documentary "Stories Behind the Making of the Blues Brothers", Dan Aykroyd (Elwood) stated that the Bluesmobile would get charged from the substation, which would explain how it would be able to do impressive stunts.
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In the original theatrical release, director John Landis had cut that scene to shorten the length of the film and said there was no need to explain the car's powers.