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what will be happen if we put asynchronous generator in vacuum chamber & run it above its synchronous speed. After reaching its over synchronous speed we will cut off electrical supply. Can it run continuously? Can we generate electricity from it?

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Can it run continously? No.

If you put it in a vacuum environment you will reduce losses due to the friction with air, but there are still other losses that will slow it down. For example friction in the bearings and eddy current losses.

It is possible though to store electricity in this way by converting it to rotational energy. Something similar is already done for uninterruptable power supplies, cars and other applications by using a flywheel. This system can be made quite efficient to store energy but it is technologically challenging as you need a rotor at really high speed (think of a rotating steel disk with up to 50000 rpm)

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