3 phase vs 1 phase generator

[Teachme]

So I have been trying to figure out the actual advantages that a 3 phase generator has over a 1 phase generator. I have been trying to find a mathimatical proof as to why 3 phase is more efficient. I have looked everywhere and have not been able to find an answer. I know how to prove that 3 phase is better than 1 phase transmission wise, but have not been able to show the internal advantages.

I have tried calculating the internal copper losses in the coils of a three phase and one phase generator, with the same number of coils, and I get the same copper loss for both types of generators... I am lost.
Can anyone give me mathematical proof that shows the difference in efficiency between a 3 phase and 1 phase generator?

Thanks

 

[sophiecentaur]

I guess the power output is more continuous (being the sum of the instantaneous VXI for all three phases). Would that not suggest that the peak current in a single winding would need to be more (√3 times as much,possibly)? That could be a reason for a difference in efficiency.
You certainly get a much better deal out of a three phase alternator when you want to rectify its output to produce DC. But I realize that's not a majority case.