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?

Because of the way the system is defined. Don't get the idea that I am saying that voltages 'disappear'. What I am saying is that the voltage will not fit in the particular system phase-counting bucket. You have to pick a reference in order to define a voltage. There is no universal designation for picking a reference point. Neither is there a universal designation to say which voltage has the angle from which all other angles will be measured.

There are several systems we can define using the transformer terminals. The transformer can supply any of these different systems. If the transformer is capable of supplying more than one order of system, I am saying the transformer is a supply of the highest order.

There are several type loads we can serve. Single-phase loads use only one pressure wave. Two-phase loads use two different pressure waves. Three-phase loads... you get the idea. Whether the voltages to these loads will all fit into a single phase-counting system bucket has to be determined.

Let's use the 240/480 volt transformer with the X1, X23, X4 terminals for example so we can put in some real numbers for some example systems:

System 1: A 240 volt single-phase system

System 2: A 480 volt single-phase system

System 3: A 240 volt two-phase system

Now pick a voltage reference and let's see what possible systems we can have:

X1 (or X4) Reference: We can have two single-phase systems, each with one voltage (one at 240 volts and one at 480 volts). Both voltages are present, but they are classified into two different systems.

X23 Reference: We can have two single-phase systems with one voltage each. One single-phase system is 240@0 and the other single-phase system is 240@180. This system can serve two independent loads from separate sides of the winding.

We can also have one two-phase system with two voltages. This type system serves loads that use both voltages and one voltage is 240@0 and the other voltage is 240@180.

Whether we have two systems with one voltage each or one system with two voltages, both voltages are used.

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.

Un-equal loads can cause the "neutral" to be different from the natural neutral point. With these loads, the neutral is just a grounded conductor. It is forcing the common connection point away from a point of natural equilibrium. Regardless of the direction you pick to be positive, there are times when the current in one side of the coil is positive and the current in the other side of the coil is negative. They are actually flowing in two different directions. Even when in the same direction, the flux can be different because of a magnitude difference.

Looking at the primary current is not representative of what is going on in the secondary because the net current in the primary is going to be based on the net flux of two different secondary currents. By looking at the primary current, the real secondary currents are hidden from you because you can't see the original individual fluxes.

Without the neutral, the currents would stabilize such that the voltage balance point was located inside the load away from the common connection point. In that case, there is no unbalanced current and the current in both sides of the secondary coil would be exactly the same. At that point, you would just have one single-phase load, one flux, etc.

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.

I have given you a method but you haven't been able to see it yet. It is a general definition that can apply to more than one type system. The formula to determine the available system types and which voltages you can put into each system bucket for counting phases does not change.

How you configure the source can restrict the number of available systems. Saying you don't want the neutral to make a change is like saying you are okay with saying we have a 480 volt source, but don't want to recognize that you can also get 240 volts if you use the center-tap. The neutral gives you an option you did not have without it.

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.

The high-leg is a valid connection but since its voltage is higher than the others, it is put in a system phase-counting bucket by itself. The only unique voltage in that bucket is one 208 volt high-leg so it becomes a single-phase 208 volt source. The four L-L voltages in the 5-wire are just as legitimate as any other voltage. They are real voltages. Whether or not we can find a practical use for them is immaterial.

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.

Then I think you are misunderstanding something I have said. A 120/208 wye source with no possible connection to the neutral can only supply a single-phase 208 system. If we can use the neutral, the transformer can supply the following:

1) one single-phase system with one 208 voltage

2) two single-phase systems with one voltage each (one at 0 deg and one at 120 deg)

3) one two-phase system with two voltages (one at 0 deg and one at 120 deg)

FWIW, the utility industry considers the open-wye distribution system to be two-phase. The load of the system as a whole appears as a two-phase load. If an open-wye is labeled "single-phase" it would be because of the nature of the loads. As I have said before, the load types have been used as part of the labeling. If it is serving single-phase loads, it can get labeled as a single-phase supply. That does not mean it is no longer a valid source for two-phase loads.

If you consider two voltages and how you are going to classify systems for them to be counted in, there is a difference between two single-phase systems and one two-phase system.

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).

I know that. And not all "neutrals" are true neutral points.

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.

Pick any direction you want, but the currents will not always flow in the same direction or have the same magnitude. It is a physical reality, not math magic.

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?

No. To be included in a system phase count, the voltage must have the same magnitude and a different angle from another counted voltage. All of those phases are not classified in the same system as each system phase-counting bucket has its own voltage level. Here are examples of some of the systems a 120/240 high-leg transformer could supply:

1) Three 240 volt single-phase systems with one voltage each.

2) One 208 volt single-phase system with one voltage.

3) One 120 volt single-phase system with one voltage.

4) One 120 volt two-phase system with two voltages.

5) One 240 single-phase system with one voltage.

Each system has one voltage magnitude to use for counting voltages..