again because we did not depend on the presence of a neutral to define our systems.
And I would say it would be better to count the number of equal magnitude but phase-displaced waveforms. I admit when I first heard you say it, it sounded good as I had not given the labeling a whole lot of thought. I have since found out that there are holes in your methodology. Refer to the graphic that follows and let's go through the results of the configurations depicted:
Using the graphic below (problems noted in parenthesis):
#1: center-tapped winding = single phase
#2: grounded wye = three phase
#3: ungrounded delta = three phase
#4: historic 2-phase = two phase
#5: grounded open-wye = single phase
#6: 5-wire historic 2-phase = four phase (does not agree with your previous assertion)
#7: 3-wire historic 2-phase = single phase (does not agree with your previous assertion)
#8: corner grounded delta = single phase (obviously does not work)
What attempts could you make to fix the problems?
To fix #6 you will have to say that a center-tapped winding does indeed double the number of phases and that it is indeed four phases, not two. That would create issues with #1 because it would become two-phase.
To fix #7 to get back to two-phase, you will have to concede that the common point is actually a point where you connect a phase conductor. When you make that concession, you also have to make the same concession for #5 and then you have created another issue because #5 becomes two-phase.
To fix #8, you will have to concede that a common point can indeed be a point where you would connect a phase conductor. Same issues as #7.
The problem is that you are trying to mix configurations, different systems, and load types. The methodology is flawed.
Let's try a more generalized method that will work for any case:
Now let's look at the general methodology and how we derive the labels we use. I will state the method again: The # of phases equals the number of equal magnitude and equal frequency waveforms that have a different phase angle and where waveforms of opposite polarity (180? phase angle difference) are counted as separate phases. Waveforms are taken from any two points as long as the set of points is only used once.
This identifies what systems of voltages are available, not necessarily how many are used or how they are used. That means that one bank of transformers can deliver multiple system configurations. We might also deliver multiple system types to loads. A lot of times the label we use is based on the type loads we have.
Let's look at a 3-phase wye for an example:
There are 4 types of systems delivered: #1) three L-L voltages, #2) three L-N voltages, #3) two L-N voltages #4) one L-N voltage. Let's look at some examples of what we have and what we could use for each type of system:
#1A) 3 phases available, 3 phases used per load, label = 3-phase
#1B) 3 phases available, 1 phase used per load, label = 3-phase. Note: Here is where the labeling has to be clear. We have a three phase system delivered but we are actually using it as a combination of three single-phase systems. As long as you understand it, it is OK.
#1C) 3 phases available, 2 phases used per load, label = 2-phase. Note: Loads that might use two phase could be an power supply, phase converter, or something else that requires two voltages with a phase displacement.
#2A) 3 phases available, 1 phase used per load, label = 3-phase. (See 1B note)
#2B) 3 phases available, 2 phases used per load, label = 2-phase. (see 1C note)
#3A) 2 phases available, 1 phase used per load, label = network or single-phase
#3B) 2 phases available, 2 phases used per load, label = 2-phase
#4) 1 phase available, 1 phase used per load, label = 1-phase
What have we discovered?
So you can see that although a system may actually be a higher order (the # of phases available), traditional labeling methods may use the load to pick a label with a lower order. The problem that shows up is that people try to use this load-determined label to label the system in general.
What gets lost in the translation is why the system was labeled the way it was. If you remove the restrictions placed by the load, the system may have a higher order than the label would indicate.
Two-phase example:
As another example, lets consider the 5-wire system with 90 degree displacements. There are four phases available so it is a 4-phase system. You can just use two phases and label it two-phase.
You can also deliver from one to four single phase voltages. As long as you understand the general system, you will have no trouble transitioning from one to the other. If you try to restrict yourself to one type configuration, you have turned a blind eye to what is really happening and you will have trouble trying to apply that restricted label method to other configurations and systems.
Finally:
You can refer to my previous post and graphic for some examples of how systems can combine and be reconfigured.
If you use the general method, the number of phases will agree with the historic accounting of poly-phase systems as well as the system orders used in analysis by symmetrical components. You will also be able to see how the different labels apply and what caveats go along with their use.
Graphic dealing with your methodology: