I'm not sure where Jim is at, and I see no point in waiting further if he & I can't agree on common termonology.
I don't want to assume anything so I will re-state what I think your position is and you can correct any errors:
#1) You agree that we can supply your example circuit with two voltages that have a common Earth connection and we will have a voltage from input terminal #1 (fed by one of the un-grounded source conductors) to the neutral point that is a real voltage, plus we will have a voltage from input terminal #2 (fed by one of the un-grounded source conductors) to the neutral point that is a real voltage, and these two voltages have a 180? displacement?
This isn't exactly my stance, but it is not highly objectionable either. The only objection is that I had to read it a couple of times to make sure it says what it says. I'll come back to this below.
#2) These voltages, even while being phase-opposed, still produce currents in the circuit that, if look at any instantaneous point in time, are flowing exactly the same way as the currents that would flow if we fed the circuit with a center-tapped transformer source?
#3) Your issue is not that the two-generator source has phase-opposed voltages that we joined together, but that we can't have real phase-opposed voltages in the secondary of a single center-tapped transformer?
Number 3 is correct. Number 1 and 2 have minor technical points.
Let's say we have a voltage source V
s that is a black box with 2 wires coming out of it, S
1 and S
2. It has feet on the bottom, so it is always oriented with S
1 at the bottom and S
2 at the top, and it can be stacked on top of another V
s supply. The voltage from S
1 to S
2 is defined to be V
s = V
m sin(ωt), or V
m<0?
Now we have this big rack or frame that we can bolt our power supplies into that comes pre-wired with 3 bus bars: A, N, B with A at the top, B at the bottom, and N in the middle. N is also connected to our chassis frame/ground. The power supplies bolt straight in without turning them upside down. On the lower supply, S
1 bolts to the B-bus and S
2 bolts to the N-bus. Similarly, on the upper supply, S
1 bolts to the N-bus and S
2 bolts to the A-bus.
Now that our supplies are bolted into their frame, we can put on some labels: V
AN = V
s and V
BN = -V
s or if we prefer no negative signs, V
AN = V
s<0 and V
BN = V
s<180. We now have our external voltage designations V
AN and V
BN that appear to be 180? out of phase, but we did not change the definition of V
s in the process. The two V
s supplies are equal in magnitude and in phase with each other, but our external references can be labeled as being 180? out of phase.
My issue has been that with the way some people have been wording their discussions, they are taking the lower V
s power supply and physically rotating it so the feet are pointing upward. I think I have been pretty careful in my discussion to not object to those discussions that designated V
an and V
bn (unless it was an oversight on my part). I
don't object to saying V
an and V
bn are 180? out of phase. I
do object to saying the two power supplies (transformer windings, etc.) are 180? out of phase.
This is an industry where precision in communication is critical. Saying one thing while meaning another can be very disastrous. Some of the posters may not have realized that their wording was or was not communicating what they really intended it to convey.
In the diagram below, I didn't feel like redrawing a power supply, so I extracted it from the Hayt/Kemmerly text book.