There is a AC synchronous servo motor which can work both as 3-phase and single-phase. Here is a general datasheet.
These can work both with 3-phase and single phase.
I couldn't find what would be the advantage to use it as 3-phase instead of single phase for an application.
I made some simulations to clarify my question. Here is what happens to the output DC link of the "same 3-phase rectifier" with 3, 2 and 1 phase inputs:
As you see above, the DC link's average and ripple changes at all of the above variants.
But the AC servo motor's driver can take all of these three combinations as input.
How can we interpret these results?