Keep in mind that trains expend a lot of their output power only during takeoff. Maintaining a constant velocity requires relatively little power, and with regenerative braking some energy may be recovered (the primary reason for the Li-Ion cells between the power source and the motor).

I don't have any numbers on this, high-power electronics was never my field. But I wouldn't at all be surprised if cruising power was less than 10% of max engine power.

Cruising power can be almost zero. Trains run on shallow gradients, and most of the power is used to climb them.

When the gradient is negative trains freewheel down the slope, and the power source is only used to keep the lights, heating, and electronics running.

>Trains run on shallow gradients

This is genius. But could anyone confirms this. I try to do some google search and nothing useful or related came up.

Does that mean Trains are constantly running downhill? Because that doesn't seems to be the case long distance rails.

It means an ascent or descent of less than 1.5% is normal for railways, and there's so little friction a train can coast downhill without power.

They obviously need power to maintain speed going uphill.

It sounds as if the train has a battery pack as well, so it will recover breaking energy. Trains are uniquely suitable to energy recovery since they have mostly predictable acceleration and deceleration curves.

Not unusual for trains to be at 50-75% throttle even at cruise. No getting around v^2

A lot of this is just due them being relatively underpowered since acceleration isn't usually a priority. For instance the BR Class 319 mentioned up thread has 1300hp to move over 120 tons - and the aerodynamics of a barn.