Yeah, well, F1 turbines aren't electrically powered. The turbos are used as generators. While the electric generator can be reversed to spin the turbo, this is used as an anti-lag measure, not a power-boosting measure... to keep the turbo "spooled" while off-throttle, so you don't have to wait for the boost to come back when you get on the gas again.
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An actual belt driven supercharger doesn't have lag issues. And on a street car, converting mechanical drive into electricity by connecting the alternator to the crank pulley, then back into mechanical drive, by sending electricity to the supercharger, is rather pointless, when you can simply connect the supercharger straight to the crank pulley, in the first place.
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A compound hybrid turbo as on F1 cars, on the other hand, makes more sense. You're still recovering waste heat and using that to spool the turbo, but you're also using excess exhaust energy to generate electricity. No need for a wastegate... the electric generator acts as a brake, slowing down the turbine and converting excess boost into electricity, instead. Then you use that electricity to prevent lag (not to generate steady boost, per se) and perhaps to power other accessories.
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