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Relative to the original post I will describe the normal US residential arrangement as a "single phase system" as a way of giving it a name, and I can accept calling it "single phase" for a shorter name. The argument for using this name is that at the input side of the distribution transformer there are only two terminals thru which power is supplied and thus at this point it is single phase.
I choose to describe the output from the center tapped secondary as two phases and I usually would call them phase A and phase B. Others disagree with this concept. But I suspect that many electricians will describe the two hot lines as different phases so that they have a convenient name to apply to the wires.
The DOT notation on a schematic is very important as a unique means of identification of transformer phasing. K8MHZ I have never seen an electrical engineering drawing where transformer phasing was defined by the direction of the swirls of the schematic drawing of a transformer.
Whether a center tapped secondary is fabricated as one single coil with a center tap wire soldered to the mid-point of the coil, or is made from two identical coils makes no difference.
Thus, consider the two coil secondary approach.
Label one coil X1 - X2 with the dot adjacent to X2, and
label coil two X3 - X4 with its dot adjacent to X4.
Note, when talking about phase it is only relevant to a sine wave. The assumption is that the sine wave is continuous from -infinity to +infinity in time. Practically it does not have to exist for that long of a time.
Connect X1 to X3, but do not connect X2 to X4.
What is the voltage difference between X2 and X4?
Very near zero because the two voltages are in phase. Virtually no phase difference.
Connect X2 to X3, but do not connect X1 to X4.
What is the voltage difference between X1 and X4?
Very near 2 times either X1 - X2 or X3 - X4 because the two voltages are 180 degrees out of phase. Big sparks fly if X1 is connected to X4. This is one reason an electrician must understand the phase relationship.
Next get a phase sensitive voltmeter like what I use with an LVDT. Get your phase reference from the primary of the transformer. Now measure the voltage from X2 to X1 and assume it is +120 V. Do the same from X4 to X3 and the result will also be +120 V. Measure from X3 to X4 and the result is -120 V.
Use an ordinary non-phase sensitive voltmeter and the above readings are all just 120 V.
You can put any names you want on the above voltages and use some other name for phase, but the measured results will be the same.
To confuse things more in a three phase system with a delta primary, only 3 phases at the input, without center tapped secondary windings from each phase, and a Y secondary I really have 6 phases available. These are VAN, VBN, VCN, VAB, VBC, VCA. Is this real useful, probably not, but they are 60 deg apart, and none are the same phase.
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