Why is your arbitrary choosing of X1 as a reference point any less arbitrary than choosing X23?
It isn't, but if any reference other than neutral is chosen, you have said, the 2-phase no longer exists. So why must the neutral point be the reference in order to determine the number of phases?
I just remembered something else you did not address:Why do you think the same current would flow in both sides of the transformer?
I was discussing the single current on the primary side of the transformer creating a corresponding current 'direction' in a single center tapped secondary winding.
A two-phase load would be a perfect example of where the currents are not the same. That would make the neutral conductor a grounded conductor, not just a connection to a neutral point. By your own rules, it would then be included when counting.
I did not say that a grounded conductor
must be counted, only that it
may be. It is you who is putting requirements on which conductors must be used. I am looking for a definition that does not change based on which reference is used.
So we at least these un-revoled issues:
1) The issue with four L-L voltages in the 5-wire 90 degree system.
There are two pairs of two L-L voltages. L1-L2 and L1'-L2'. L1-L1' and L2-L2' were never considered as valid connections (similar to the high leg in a 240/120 connection). This is why I refer to this as 2-phase 5-wire.
2) Ignoring the grounded conductor in the 3-wire wye.
With your logic, the presence or absence of a center tapped neutral changes the number of phases, but for some reason it doesn't affect a wye connection. With my logic it makes no difference.
3) Arbitrary selection of an X1 reference.
Not all grounded connections use a neutral, not all 'non-end point' taps are neutrals. For example, there is a standard control power connection of 24/120V (x1-X23= 24V, and X1-X4=120V).
4) Claiming a single L-L current through a coil with a neutral
I believe I have said there is a single current
direction, created by a single magnetic field direction, such as X1->X23->X4. But through the magic of math, X1->X23 and X23->X1 can be interchanged, by following proper 'signing' rules, giving the
appearance of two currents.
Do you say a high-leg 4-wire delta (one winding is center tapped) has these 3-phases: 2@180?, and 1@90? while ignoring the 3@120?? If you mention them all is this a 6-phase transformer?