MYSTIC, Conn.—Energy independence is still only a hypothetical goal for the U.S., but the owner of a tiny island off the coast of Connecticut says he has already achieved that feat and is offering his work as a model.

Dean Kamen, inventor of the Segway and numerous medical devices, jokingly refers to his North Dumpling Island as an independent nation and himself as Lord Dumpling. Kamen claims to have his own currency and offers visas to visitors to the tiny island a few miles from Mystic, where he is the only resident.

But Kamen, who bought the three-acre island in the ...

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