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I'd also thought of this independently in the past, presumably lots of people have. As for decelerating, I have no idea if any modern trains do this, but you could in theory charge a battery with the kinetic energy from decelerating the train and use that for acceleration. Naturally it wouldn't be a perfect energy transfer, but I presume much of it could be captured.

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It's quite common. Except that there are no batteries (battery won't do, you can't charge it fast enough), you just need to have another train in the same section to consume it (or whole network, if your converter substations are ready for that). Energy savings estimates were like 10 to 20 percent (don't have any link for this, it was some British study I remember, sorry).

http://en.wikipedia.org/wiki/Regenerative_brake

Seems like it's everywhere these days. Even in urban metro lines where you've got like 1km between stations. HK subway trains have been doing this since the 90s. Wikipedia sez Delhi Metro has it too.

It's most useful in such cases (and trams and so on), with very frequent braking and starts and a lot of trains. There is always some other train accelerating. And you have majority (if not all) axles powered, so you can have regenerative brake on all of them, allowing you to brake effectively only with the regenerative brake to almost zero. It's even much more silent than a mechanical brake, also an advantage in urban environment :-)

(And even if you don't give the energy back to the network and just burn it in the resistors in locomotive, it gives you more effective braking. Locomotives from 1960's already had that.)

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