The most common configuration turbo kit for cars is a simple compressor that works off of exhaust fumes from the engine. It's a semi practical use of otherwise mostly useless exhaust. This approach does cause some problems since you have to wait for the fumes to propagate out of the engine and into the impeller as well the volatile corrosive nature of the fumes themselves which leads to turbo failure.
The idea is that an electric turbo with a compressor would be much faster and lag free as the turbo can spin up as the RPM increases. Our first prototype will be in a 2004 Nissan 350Z.
The eventual idea is to build a prototype and then develop a kit that can be applied to a variety of cars.
As of time of writing, there has not been a single production car to include a electric turbo though Audi reportedly has one in the works for 2016-ish. I don't know of any other electric turbo kits so this will be one of a kind.
The thing that makes turbos efficient is the exhaust gas. That makes the turbo power "free" because it doesn't cost much to run. When you move to a belt driven or electric drive you lose that efficiency because now it "costs" you to spin the turbo. If you need more than a car battery to run your electric turbo, you probably also need a bigger alternator to charge that bigger battery bank, right? The bigger alternator then requires more power from the engine...
The F1 racing teams are moving to hybrid electric turbos, which can put power into or take power out of the spinning compressor wheel. You're doing something right by adding the motor but don't rule out the importance of the exhaust gases to do the bulk of the work.