If I say “personal electric vehicle,” you might think “Paul Blart: Mall Cop,” or maybe “exploding hoverboards.” You don’t think global transportation revolution.

But in the past few years, with the convergence of better battery technology, lighter materials and smaller, more powerful electric motors, entirely new kinds of transportation have bloomed. The electric powertrain, unlike that of the internal combustion engine, scales smoothly from tiny to huge, powering everything from 10-pound electric skateboards to 20-ton electric...