Which is why using the construction of the transformer (bank) is a perfectly valid reference
Do you think I have said it is not a valid reference? I have continually said that both references are valid.
which provides consistency even when the arrangement does not contain a true neutral point for each winding connection (i.e with a zig-zag).
If there is no neutral connection, then we have a different set of circumstances. Additional voltages are available when we add a neutral connection.
Their waveforms must start at the same point in time: t0. A simple inversion does not create a time delay, Vbn 'is created' at the exact same time as is Vnb.
That is correct. But it is just not that the inversion does not create a time delay; neither do any of the other transformer configurations that create a phase shift because they are all the result of physical manipulations of the voltages.
Your PI is not a direct part of the phase constant: rather it is simply a modifier to it.
Vbn has not been modified; it is the same as when it was created. The phase constant for Vbn includes PI, the phase constant for Vnb does not.
But a mathematically inverted wave is not a different wave.
It will certainly produce different results. But before we digress, we are talking about voltages from different sets of terminals anyway: Van and Vbn are certainly different waves and they can have different fluxes.
We don't really generate a negative voltage, we simply take a positive increasing voltage and then swap our reference terminals, the result is -Vab = Vba.
That is what keeps baffling me about your position. The way you wrote your post reads as if you think only one voltage is "the real voltage". In this case it reads like you have said that only the "positive increasing" voltage is real. Vab is no more real than Vba but your wording makes it look like you think one is more real than the other. I know you also say both are real, so what do you mean by "We don't really generate a negative voltage"?
Also, "positive increasing" is a relative term. There is nothing that says both windings must be taken as "positive increasing" in the same direction. You can take both to be positive in the same linear direction or both positive relative to their common point and either way is valid. Both are really generated voltages.
Given two identical transformer windings;
They are not clones in every manner because they can have different fluxes.
V12=V34:two phasors pointed in the same direction, this is the actual physical connection of the transformer
The positive direction is not dictated by polarity marks so we also have two phasors pointed in opposite directions created at the same time.
Vn4=-V4n: two phasors, where one equals the opposite of a phasor that has been rotated. NOTE: two opposing actions occur in this equation.
Why do you think in order to get V4n that we have to rotate Vn4? The truth of the matter is that V4n is created at the same time that Vn4 is created. Both exist.
V14=V1n+(-V4n)=V1n-V4n: two phasors connected same end-to-same end, this is a mathematical model of the connection of the transformer (we know if the one winding was actually physically rotated the result would be V12-V43=V13=0).
The fact that you sum V1n plus Vn4 does not mean that V4n is not there. The V4n voltage exists also.
If the truth be known, you are basing your premise on a voltage that was rotated from its real physical relationship to the primary anyway because the transformer has a 180? phase shift. Do you not see the peculiarity in trying to represent the physical inversion that negates the 180? phase shift as the "really generated" voltage?
The only problem I have with the neutral as a reference, is when the analyst does not acknowledge that for the equality of Vxn=-Vnx, two opposing actions have occurred. First there is the action of the 'rotation' of the subscripts and second the inversion of the first action.
First, the voltages Van and Vbn and Vnb and Vna all exist. We do not "rotate" one of them to "create" the other as they are all created at the same time. The voltages are there. We do not "rotate" the voltages because they were there before we connect to them and they will be there after we connect to them.
Second, we can take a potential difference. That does not mean we have to invert one of the voltages and then add them together. It is not (A) + (-B) but rather (A) - (B). We do not have to "invert" B to take the potential difference between points A & B.