Single Phase or Polyphase?

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gar

Senior Member
100321-1459 EST

jim:

There will be less circulating current than when you parallel separately wound secondaries because the two halves of the hairpin loop more nearly have exactly the same flux linkages.

If this concoction is two windings, then so is a normal center tapped secondary.

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jim dungar

Moderator
Staff member
100321-1459 EST

jim:

There will be less circulating current than when you parallel separately wound secondaries because the two halves of the hairpin loop more nearly have exactly the same flux linkages.

If this concoction is two windings, then so is a normal center tapped secondary.

I am having a hard time envisioning how this is not simply two parallel windings. A normal center tap winding is entirely parallel to the single primary winding, they could be unwound and laid along side of each other X1 next to H1 and X4 on the same end as H2. But your hairpin turn cannot be laid out with X1 and X4 on opposite ends of the unwound winding.

mivey

Senior Member
Two out of phase voltages from a single winding, is only possible if you use the neutral as your reference. What you are doing is a trick of math because it requires a very specific assumption and it does not occur if any other assumption is made. For you to have two truly independent voltage directions, you need two independent secondary windings. A single winding with a center tap simply creates two in-phase series connected voltages.
I can take two separate 180 degree displaced voltages and connect them in series such that I can combine the fluxes they can create. I can send these combined fluxes through a single-winding transformer. On the secondary side, I can then separate the voltages created by these two combined fluxes and get back my two phases on the other side of the transformer.

These are the same two voltages I would get if I used two separate cores. The only trick involved was orienting the phases so that the fluxes would combine instead of canceling each other because of the single core. The combined power from both phases traveled through the transformer.

Mechanics aside, the point is the type systems the secondary voltages can represent. These voltages can be single phase (X1 or X4 reference) OR two-phase (neutral reference) as in a 360/2 = 180 degree polyphase system.
Using almost gross simplifications.
Farady's Law says a magnetic flux creates a voltage, the direction of the flux dictates the direction of the voltage. Lenz's Law says that current flows to oppose the change in the flux. With a single winding primary there is a single magnetic flux. With a single magnetic flux there is a single voltage direction induced. With a single voltage direction, there is a single current direction. And yes, while the current can be 'out of phase' with its voltage by +/-90? its relative direction is due to the voltage that created it.

I was hoping to get past single winding transformers (several pages ago in fact) but, it looks like that is not going to be possible. I found my old reference books, that confirm the method I was taught, so I am at peace for the present time.
This obsession with the mechanics of where the voltages came from has been yours. You made some broad statements that aren't necessarily true for all cases, so maybe your clarification of the specifics of what you really meant was needed. But now that you have refreshed your memory on how a transformer works, maybe we can get past the transformer.

mivey

Senior Member
...By keeping one lead on the N (CT), you're flipping the measuring polarity...
There are no "flipping" shenanigans taking place. We have established a reference voltage. Just because the only other voltage has a 180 degree displacement does not mean we are playing a game with the polarity. If we measure the voltages for a wye, and we start with "A" phase at a zero angle, there is no "flipping" going during the measuring of the 120 deg & 240 deg voltages as we are just measuring relative to our "A" reference.

mivey

Senior Member
...Go back to my two oscillator discussion. Let waveform 1 be the reference. As I adjust the phase of waveform 2 toward 180 deg is there some special transformation that at exactly 180 degrees of phase shift makes this not a 180 deg phase shift? Should there be such a discontinuity at exactly 180 deg? I do not think so.
Great point. And mirrors one I made many posts ago. That type of thinking will always hit a wall with that final one degree change. It reveals the discontinuity in that type logic.

...Changing the reference point simply changes the math not the physics of the single winding transformer...
No one is trying to re-write the rules of transformation. I am looking at the voltages on the secondary side of the transformer. A physical connection is being made, not a math connection. Again, any voltage must have a defined reference point regardless of how many transformations, windings, configurations, etc were used to create final voltage. The center-tap winding can provide both in-phase and out-of-phase voltages.

But, if you really want to trace it all the way back to the source (even though it does not really matter), I have made it clear the original sources could easily have been two 180-degree displaced voltages.

mivey

Senior Member
I am having a hard time envisioning how this is not simply two parallel windings. A normal center tap winding is entirely parallel to the single primary winding, they could be unwound and laid along side of each other X1 next to H1 and X4 on the same end as H2. But your hairpin turn cannot be laid out with X1 and X4 on opposite ends of the unwound winding.
I guess it would depend on what you say constitues a winding. You could say that each winding uses one piece of common real estate on the core, which gar's example does (one coil of primary, two coils of secondary). But, he might get a technical foul called. :grin:

gar

Senior Member
100321-2233 EST

In defining whether two or more voltages have different phase angles really has nothing to do with their source, or how they are created.

Suppose we limit the discussion to the relationship of sine waves of identical frequency. This leaves out harmonics.

My definition of voltages that are in phase is --- sine waves of the same frequency that have identical zero crossing points, and the same slope direction at the zero crossings are in phase. Anything different results in a different phase. This allows for different amplitudes to be in phase. Obviously phase shifts of N*2*Pi are equal to 0*2*Pi for an infinite continuous sine wave.

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jim dungar

Moderator
Staff member
This obsession with the mechanics of where the voltages came from has been yours. You made some broad statements that aren't necessarily true for all cases, so maybe your clarification of the specifics of what you really meant was needed. But now that you have refreshed your memory on how a transformer works, maybe we can get past the transformer.

I feel the basics of a single winding transformer are fundamental to discussing the issue of the central tapped neutral point as a reference point. You state that some of my broad statements are not applicable to all cases, but that is the same point I am making about the arbitrary selection of the neutral.

Physically, a center tapped transformer is either a single winding with an actual center tap (as in a utility 3-bushing transformer) or it is two windings connected in series X1-X2 + X3-X4 (as in standard dry type units). As you have pointed out, both the dot convention and the IEEE/ANSI terminal designation standards provide us with a method for defining voltage rise and current directions of the secondary in relation to the primary. In particular, H1 on the primary is identified as having a specific relationship with secondary terminal X1 (and also X3 for a two winding transformer). Using the neutral as the reference point requires ignoring the standard convention for identifying transformer terminals.

This whole fixation on the construction of transformer came from the claim that simply by using the neutral, a single transformer winding becomes a two phase unit. I been trying to get agreement that the physics of the transformer does not change with or without a neutral point. What actually happens, with a neutral reference, is simply a manipulation of the math normally used in conjunction with the industry standard terminal identification conventions.

Not all single winding transformers have neutral points.
Not all multi-tap single winding transformers have neutral points.
Not all single winding center taps are used as neutral points.
Not all single windings transformers meet the industry "dot" convention.
My point has been the math should not need to be changed simply because a neutral point becomes available. The transformer secondary should be analyzed in relation to, not independent from, its primary.

mivey

Senior Member
I feel the basics of a single winding transformer are fundamental to discussing the issue of the central tapped neutral point as a reference point. You state that some of my broad statements are not applicable to all cases, but that is the same point I am making about the arbitrary selection of the neutral.
I do not think the mechanism used to create the voltages should tell use how to connect the voltages. The source could be a transformer, UPS, some type of electronic synthesis, etc. It really has no bearing on the voltages that are present. The voltages are there for our use as we see fit. The source does not dictate the connection we make, especially if there is more than one configuration option.
Physically, a center tapped transformer is either a single winding with an actual center tap (as in a utility 3-bushing transformer) or it is two windings connected in series X1-X2 + X3-X4 (as in standard dry type units). As you have pointed out, both the dot convention and the IEEE/ANSI terminal designation standards provide us with a method for defining voltage rise and current directions of the secondary in relation to the primary. In particular, H1 on the primary is identified as having a specific relationship with secondary terminal X1 (and also X3 for a two winding transformer). Using the neutral as the reference point requires ignoring the standard convention for identifying transformer terminals.
I'm not trying to re-identify any transformer terminals. I only care about the pressure waves. I have many options on how I can use these waves, regardless of what the terminals are named. That is why I have tried to get you to quit focusing on the mechanism. It is a black box that has delivered you some voltages.

The voltages define themselves and do not need you to trace them back to the source. What if you did not know they came from a single transformer, how would you treat them? At this point, we only care if the source can supply the voltages, not the specifics of how it gets the job done. If it has trouble delivering under certain conditions, then we might get interested in the source and maybe decide to use a different source.
This whole fixation on the construction of transformer came from the claim that simply by using the neutral, a single transformer winding becomes a two phase unit.
I'm only interested in the voltages I can get from that unit. As far as I am concerned, with a two-terminal primary, the transformer is a single-phase unit. However, the different pressure waves that I can get out of the secondary center-tapped side can be in phase or out of phase. It is a single-phase unit that is capable of supplying two voltages that are 180 degrees out of phase. Not just mathematically, but physically out of phase. Identical to the voltages you could get by using two separate windings. The center-tap gives you access to that common point so you can separate the voltages.

I can take a two-phase transformer configuration and create three-phase voltages. The secondary in that case is not limited to the primary configuration. No big deal. The voltages are what they are, regardless of the source.
I been trying to get agreement that the physics of the transformer does not change with or without a neutral point.
OK: The physics of the transformer do not change. What changes is how I use the output from the transformer.

As for the transformer physics and input options: The supply could be two different phases. I can invert one of the phases of a 180-degree displaced two-phase source, run both sources through the transformer, and invert one of the outputs to get back my two sources I had to start with. These are indeed two separate sources. Take one out and the secondary voltages are completely different. It is the physics in the transformer, not just a game of math. The transformer can supply both type outputs and the primary side of the transformer does not dictate which type output I use.
What actually happens, with a neutral reference, is simply a manipulation of the math normally used in conjunction with the industry standard terminal identification conventions.
There are actually two different pressure waves. It is a physical reality, not just math, even though the math agrees with the reality. We can use these waves separately and in more than one way.
Not all single winding transformers have neutral points.
Not all multi-tap single winding transformers have neutral points.
Not all single winding center taps are used as neutral points.
Not all single windings transformers meet the industry "dot" convention.
My point has been the math should not need to be changed simply because a neutral point becomes available. The transformer secondary should be analyzed in relation to, not independent from, its primary.
That is just not the reality of the situation. The reality is that with a neutral you have more than one option for the way you can use the secondary voltages. The primary does not dicate how we use the secondary. It does not define the voltage references on the secondary.

The simple fact is: Having a neutral gives you more voltage configuration options on the secondary. It does not mean you have to use all the options but you should at least recognize them. These are real physical connections and pressure waves, not just mathematical models.

winnie

Senior Member
I know that I am harping on the same point repeatedly, but we are talking about _different_ things.

The transformer core here is a single phase core. Adding a center tap to the secondary winding does not change this, and does not change the physics of the transformer core. There is only one flux path, only one flux waveform, and only one flux phase angle. We could invert the sense of our flux detector, and get an inversion, but this would not change the fact that there is only a single flux being described.

When describing the secondary winding and the secondary circuits, we are talking about different things than the transformer core. A center tapped secondary coil has _two_ separate current paths, and can have two entirely different output currents.

If you count 'transformer core flux phases', you get a different number than if you count 'transformer secondary current phases', and we should not get too stuck on trying to make these two numbers equal. They are related but different characteristics of the transformer.

Consider a 'T' connected transformer. This is a transformer with _two_ cores, and thus only _two_ phases of flux waveform. But this type of transformer can be used to convert between conventional 3 phase (120 degree phase separation) and classic 2 phase (9 degree phase separation). Or consider the ways that a '12 lead' generator can be connected to produce single phase output. The alternator core has multiple flux paths, but the coils are connected to produce a single phase output.

Up until Friday, I had been considering two sources, 180 degrees out of phase, to be equivalent. I was happy to call them separate phases (thus 'phase A and phase B of a single phase panel'), but this was my bias as a motor guy showing. For motors, a 180 degree phase difference in your supply legs is simply redundant; it doesn't give you anything that you don't already have from the winding of the motor. However on Friday Mivey posted a circuit which clearly depends upon having two supply legs that are 180 degrees out of phase. The '2 diode full wave rectifier' will only work correctly if you have 3 supply conductors, a 'neutral' and a pair of equal and opposite 'phase' conductors. The two circuit halves conduct on alternating half cycles. This circuit works correctly with a 120/240V 'single phase' service, but not with a 120/208V 'single phase' service.

Again (to keep beating the dead horse). We are counting different things:

This is a single phase transformer (one magnetic core with a _single_ flux waveform)

There is a single phase of voltage induced in the coils; any apparent inversion is simply changing the sense of your measurement.

For the purpose of developing a rotating magnetic field, then there is only a single phase present. This is true with or without a center tap.

For certain circuits which depend upon the relative inversion of the two supply legs relative to the neutral, I believe that it is reasonable to say that there are _two_ output phases.

A service fed by such a transformer is a _single phase_ service.

If, for a specific application, you say that there are two phases, this should be distinguished from 'classic' two phase service with a 90 degree phase displacement.

If, for a specific application, you say that there are two phases, I do not believe that this would meet the requirements of 'polyphase'. Even though poly simply means more than 1, I believe that a defining characteristic of polyphase is the ability to produce a rotating magnetic field.

-Jon

mivey

Senior Member
Given the following phasor diagram for two voltages that were measured across two different loads, would you say:

1) V1 & V2 are two equal magnitude voltages with a 180? phase angle difference.
2) I'm going to have to see if these voltages were taken from a single-phase transformer before I can tell if they actually have a 180? angular difference or if your meter is playing mathematical tricks on you.

.....,.V1
..../|\
.....|
.....|
.....|
.....o
.....|
.....|
.....|
....\|/
.....'.V2

Again, in considering a normal polyphase system of voltages, an "n"-phase system has "n" equal-magnitude voltages evenly displaced by phase angles 360?/"n". In an abnormal system of "n" equal-magnitude voltages, the voltages are not evenly displaced.

For a system of voltages, we are considering the voltages at hand, not how they were derived. Looking at the source, we can say whether or not it is capable of delivering a particular system of voltages. How it accomplishes that is immaterial.

mivey

Senior Member
I know that I am harping on the same point repeatedly, but we are talking about _different_ things.

The transformer core here is a single phase core. Adding a center tap to the secondary winding does not change this, and does not change the physics of the transformer core. There is only one flux path, only one flux waveform, and only one flux phase angle. We could invert the sense of our flux detector, and get an inversion, but this would not change the fact that there is only a single flux being described.

When describing the secondary winding and the secondary circuits, we are talking about different things than the transformer core. A center tapped secondary coil has _two_ separate current paths, and can have two entirely different output currents.

If you count 'transformer core flux phases', you get a different number than if you count 'transformer secondary current phases', and we should not get too stuck on trying to make these two numbers equal. They are related but different characteristics of the transformer.
I agree. There is only one net flux in the single-winding transformer. That is simply how it works. And the output is quite capable of producing two opposing fluxes.
If, for a specific application, you say that there are two phases, I do not believe that this would meet the requirements of 'polyphase'. Even though poly simply means more than 1, I believe that a defining characteristic of polyphase is the ability to produce a rotating magnetic field.
We could certainly stipulate that for specific purposes, but the original term for an n-phase system was as I stated in post #132 for any system of two or more phases.

jim dungar

Moderator
Staff member
For a system of voltages, we are considering the voltages at hand, not how they were derived. Looking at the source, we can say whether or not it is capable of delivering a particular system of voltages. How it accomplishes that is immaterial.
I have acknowledged, it is possible to analyze circuits by calling the source a black box. But, when dealing with power systems in their entirety the connection and interaction of transformer primaries and secondaries is not "immaterial".

You have stated the number of phases depends on the use of the neutral: no neutral = 1-phase, add a neutral and get 2-phases. I have said the use of the neutral as a reference point should be optional and not a requirement when defining the number of phases.

IEEE/ANSI standard convention for transformers is to identify the direction of the secondary current as out of X1 and X3. This means the voltage directions are X1->X2 and X3->X4, which series connect to X1->x23->x4. Instead, you say that the directions are actually X2->X1 and X3->X4 if the neutral is used.

You have now clearly stated that, in your opinion, sources are not important and should not be considered.
mivey said:
The voltages are there for our use as we see fit.

winnie

Senior Member
[...]the original term for an n-phase system was as I stated in post #132 for any system of two or more phases.

Could you point me to the reference that defines this usage?

It is clearly correct for n=odd, but doesn't jive with history for n=2 or n=4. 3 wire n=2 with one common conductor carrying sqrt(2) * line current, and a line-line voltage of sqrt(2) * line-common voltage was quite common. Additionally, I don't recall seeing systems with all 4 90 degree separated phases called '4 phase'; they all seemed to be called '2 phase'.

-Jon

LarryFine

Master Electrician Electric Contractor Richmond VA
You have stated the number of phases depends on the use of the neutral: no neutral = 1-phase, add a neutral and get 2-phases.
I agree with you, Jim. I'd call the latter above two polarities, but not two phases.

gar

Senior Member
100322-2039 EST

I pulled out a book by Hehre copyright 1942. Electrical Circuits and Machinery.

It does not provide a direct definition of n-phase or polyphase. It uses vector terminology instead of phasor. I think phasor came into use in the later 40s.

There are items that are actually three phase transformers. I often see people referring to three single phase transformers as a three-phase transformer. Note singular. Hehre uses the terminology Three-phase Transformation to cover both the use of three single phase transformers and a single three-phase transformer. This would also include two transformers in an open delta.

When Hehre describes systems he clearly qualifies specifically what is being discussed, rather than simply saying a polyphase system with the reader having to imagine what polyphase means. For example he says things like:
Vector Diagram for a Balanced Non-inductive, Three-phase, Y-connected System
Two-phase, Four-wire System
Two-phase, Three-wire System
Unbalanced Delta-connected Load with Unbalanced Line Voltages
etc.

There is a good deal of calculus in this book, but there are a lot of discussions that might be useful to an average electrician. For example one on transformer inrush current.

This book does not provide any real direct information for this thread, but by his use of modifiers it is clear he considered polyphase alone as a very general term.

.

mivey

Senior Member
I have said the use of the neutral as a reference point should be optional and not a requirement when defining the number of phases.
Resist it as much as you want, but the number of voltages is the number of voltages. The neutral gives you more voltages that you can take from the source. That is impossible to deny.

As for optional, I think you have the option of seeing that a set of voltages may be taken from the source to create a system of voltages that may not necessarily match the label of the source.
You have now clearly stated that, in your opinion, sources are not important and should not be considered.
And I have clearly stated that in the past as well. The voltages are what defines a system of voltages, not how they were derived or created.

I just want people to understand why things are labeled the way they are even though there are technicalities that could make them fit under a different label. If they understand why the labels have been applied as they have, they won't be confused by the inconsistencies in the labeling.

mivey

Senior Member
Could you point me to the reference that defines this usage?

It is clearly correct for n=odd, but doesn't jive with history for n=2 or n=4. 3 wire n=2 with one common conductor carrying sqrt(2) * line current, and a line-line voltage of sqrt(2) * line-common voltage was quite common. Additionally, I don't recall seeing systems with all 4 90 degree separated phases called '4 phase'; they all seemed to be called '2 phase'.

-Jon
Since you are a motor guy, how about the classic reference "Electric Machinery" by Fitzgerald & Kingsley from the 5th Edition, where they are discussing the classic two-phase system:
The five-wire, four-phase system (Fig. A-18) is sometimes used for low-voltage distribution...Half of the four-phase system--the part aob (Fig. A-18), for example--constitutes a two-phase system.

Also from "Electric Machinery":
Generation, transmission, and heavy-power utilization of ac electric energy almost invariably involve a type of system or circuit called a polyphase system or polyphase circuit. In such a system, each voltage source consists of a group of voltages having related magnitudes and phase angles. Thus, an n-phase system will employ voltage sources which conventionally consist of n voltages substantially equal in magnitude and successively displaced by a phase angle of 360?/n.
...
The three individual voltages of a three-phase source may each be connected to its own independent circuit. We would then have three separate single-phase systems.

From "Techniques of Circuit Analysis" by Carter/Richardson concerning forming polyphase sources from voltage sources separated by phase angle differences:
...two voltage phasors in opposition-that is, with a phase difference of 180 degrees; a single-phase transformer with a center-tapped secondary winding would be such a source.

mivey

Senior Member
I agree with you, Jim. I'd call the latter above two polarities, but not two phases.
So we have you down for camp #2: "I'm going to have to see if these voltages were taken from a single-phase transformer before I can tell if they actually have a 180? angular difference or if your meter is playing mathematical tricks on you." :grin:

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