By Joseph B. White

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BMW’s i3 electric concept car is among the models worth watching.

Los Angeles is a town where people like to get noticed for what they drive, and expect to be served the auto industry’s freshest ideas.

Which is why the Los Angeles Auto Show, which opened late last week, makes an excellent place for spotting trends. There, the newest approaches to electric cars are being spotlighted. And old notions of what makes high-performance luxury cars worth the money are being upended.

This year, auto makers used the L.A. show to unveil 24 cars for the first time anywhere, and 25 for the first time in the U.S. About a dozen of the premieres were from luxury brands, reflecting Southern California’s status as one of the biggest luxury- and performance-car markets in the country.

The models getting attention in L.A. are diverse in price and style. They reflect the demands of consumers who spend an inordinate amount of time on the road and want better fuel efficiency without compromising performance, seamless digital connectivity and at least the promise of a car that runs on electricity and is fun to drive.

Here are some cars from the L.A. show worth watching in 2013.

BMW i3 Concept

BMW.XE +0.62%What it is: An electric “city car” from BMW.

Why it’s important: It’s a high-end plug-in car that will test the market pioneered by boutique plug-in brand Tesla—with far more powerful global branding and sales oomph.

BMW’s i3 concept car (which company executives say is very close to the real i3 BMW intends to start selling next year) doesn’t look like a Bimmer—and that’s the point. The shell of the passenger compartment is formed of lightweight carbon fiber. The exterior body panels are plastic. The batteries are built into the floor.

Projected range? About 100 miles. The i3 coupe and its sibling i8 roadster are the most thorough effort yet by a major auto maker to design an ultralightweight, batterypowered car from scratch instead of repurposing a conventional car.

BMW plans to blanket its electric i3 and i8 cars in a cocoon of connectivity and services, ranging from customized home-charging setups to apps that locate local parking, public charging stations, even other modes of urban transportation such as bike rentals and BMW’s recently introduced car-sharing service.

The challenge: The very un-BMW looks of the i3 could be an obstacle for brand loyalists. Plus, the “green premium” could be significant. While BMW isn’t disclosing exact prices, company officials say cost for the compact i3 will be comparable to the much larger, conventional 5-series sedan, which starts at $48,395.

Read more in Eyes on the Road.

By Joseph B. White