We laugh here whenever someone finds an electric supercharger on eBay and asks "do these work". But it seems the serious car manufacturers are working on something pretty much along those lines.
http://autospeed.drive.com.au/cms/A_108916/article.html
Horsepower for horsepower turbocharged small engines are more economical than normally-aspirated big engines, but turbocharged small engines can't produce much low-speed torque. Use a supercharger instead and you can, but they chew up power and petrol to drive them. VW has a car with both. The supercharger provides the boost at low revs, and the turbocharger takes over at higher revs. So its just like a bigger engine, and its more economical, but its complex and expensive. Toyota is looking at a petrol-electric hybrid, with its small-displacement petrol engine turbocharged, and the turbocharger connected to an electric motor/generator. At low revs when there wouldn't be enough exhaust gas for the turbo to generate much boost the electric motor/generator would run as a motor effectively turning the turbocharger into a supercharger. At high revs when the exhaust gas produced more boost than you could use you wouldn't just open a blow-off valve and waste it, you'd switch the electric motor/generator into generator mode to slow the turbo compressor down, and the electricity generated would go into the battery.
http://autospeed.drive.com.au/cms/A_108916/article.html
Horsepower for horsepower turbocharged small engines are more economical than normally-aspirated big engines, but turbocharged small engines can't produce much low-speed torque. Use a supercharger instead and you can, but they chew up power and petrol to drive them. VW has a car with both. The supercharger provides the boost at low revs, and the turbocharger takes over at higher revs. So its just like a bigger engine, and its more economical, but its complex and expensive. Toyota is looking at a petrol-electric hybrid, with its small-displacement petrol engine turbocharged, and the turbocharger connected to an electric motor/generator. At low revs when there wouldn't be enough exhaust gas for the turbo to generate much boost the electric motor/generator would run as a motor effectively turning the turbocharger into a supercharger. At high revs when the exhaust gas produced more boost than you could use you wouldn't just open a blow-off valve and waste it, you'd switch the electric motor/generator into generator mode to slow the turbo compressor down, and the electricity generated would go into the battery.