Split phase service--one or two?

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rattus

Senior Member
Of course I know that mathematically they are equivalent. I know that if you invert a pure sine wave or if you shift it by an odd multiple of pi it looks the same. Duh. :p But phase shifting only works for the special case of a pure sine wave while inverting the waveform works for the general case. Any waveform, any frequency or combination of frequencies. The math as you present it is a simplistic model that predicts what the waveforms look like, and it breaks down if you feed it anything more complex than a simple sine wave. Yeah, I know, all you want to talk about is a simple sine wave and for that restricted case it works. That's OK by me. No skin off my nose.

But I don't think that there is any doubt in anyone's mind that what is physically happening in our all too familiar center tapped transformer is an inversion, not a time based phase shift (i.e., delay). I use this same type of transformer (though much smaller, of course) all the time in my audio work to generate a balanced (complementary) signal from an unbalanced one. If you look at those waveforms you will see that no amount of phase shift will produce the complement of a complex waveform. Still, in audio many folks who should know better erroneously refer to an inversion of an audio signal as generating a signal which is "180 degrees out of phase". Whatcha gonna do? We all know what it means even if it is technically incorrect. But I digress... :p

I know that mathematically it makes no difference whatsoever whether you use -sin(wt) or sin(wt+PI) (or sin(wt+3PI) or sin(wt+(10^31+1)PI), for that matter) to represent the complementary waveform in the case of a pure sine wave, but -sin(wt) describes more accurately what is physically happening in the transformer.

I know of no definition of phase shift that stipulates a time delay. Anyway, we are discussing ideal transformers and ideal waveforms. There are no complex waveforms, one cannot tell the difference between a delay of PI and an inversion. There is no noise. To add fine points such as this to the discussion is just a side issue which has no real bearing on the question.

Plus the term is commonly used interchangeably with phase difference.

Perhaps that subtlety is important in audio, but this is not audio.

And, that raises the question: Which voltage is the inverse? Is it V1n? Or is it Vbn?
 

gar

Senior Member
Location
Ann Arbor, Michigan
Occupation
EE
120404-1251 EDT

Rick:

What is the connection between electrons and two waveforms on paper?

If I draw two waveforms on paper what is the relationship between those waveforms and electrons? My only guess is that the carbon from the pencil contains electrons in the carbon atoms. But how does that relate to the phase relationship of the waveforms on the paper?

.
 

Rick Christopherson

Senior Member
...one cannot tell the difference between a delay of PI and an inversion. There is no noise. To add fine points such as this to the discussion is just a side issue which has no real bearing on the question.
Yup!!! And we can't tell the difference whether the earth is orbiting about our galaxy versus the rest of the universe orbiting about our Earth. The mathematics are sound for both cases.
 

rattus

Senior Member
120404-1251 EDT

Rick:

What is the connection between electrons and two waveforms on paper?

If I draw two waveforms on paper what is the relationship between those waveforms and electrons? My only guess is that the carbon from the pencil contains electrons in the carbon atoms. But how does that relate to the phase relationship of the waveforms on the paper?

.

gar,

I see absolutely no connection, but my eyesight is not so good either.
 

rattus

Senior Member
Mathematics! The understanding that what you model on paper is not necessarily what occurs in real life.

Well, our mathematical models had better reflect what happens in real life. Otherwise, there would be no point.

Whatever, the equations describing the voltages in question are quite sufficient for the purposes of this discussion.

Furthermore, I don't see that any of this helps answer the question.
 

ggunn

PE (Electrical), NABCEP certified
Location
Austin, TX, USA
Occupation
Electrical Engineer - Photovoltaic Systems
I know of no definition of phase shift that stipulates a time delay. Anyway, we are discussing ideal transformers and ideal waveforms. There are no complex waveforms, one cannot tell the difference between a delay of PI and an inversion. There is no noise. To add fine points such as this to the discussion is just a side issue which has no real bearing on the question.
Exactly what is the question, anyway? To my observation there is nothing to this discussion but fine points.

Plus the term is commonly used interchangeably with phase difference.
As I pointed out, many in audio commonly use "180 degrees out of phase" to describe a signal inversion, as well. Although we all know what they mean by it, that doesn't make it correct.

Perhaps that subtlety is important in audio, but this is not audio.
It's an AC waveform moving through a transformer whether it's power or audio. Your way of looking at it works only for a simple ideal sinusoid that doesn't even exist in the real world. "Mine" works for all cases, including your very narrow example. It's not at all a subtlety, it's the way that it physically works.

And, that raises the question: Which voltage is the inverse? Is it V1n? Or is it Vbn?
No, it doesn't. It doesn't matter. Pick one; the other is the inverse.
 

gar

Senior Member
Location
Ann Arbor, Michigan
Occupation
EE
120404-1432 EDT

Rick:

The title of this thread includes the word phase. Thus, to carry on this discussion it is necessary to have a definition(s) for phase. rbalex in the other long thread referenced the IEEE definition. That definition is useful and in a post in the long thread I analyzed what I thought the IEEE definition means.

Phase is a non-dimensional measurement between two points of a periodic phenomenon measured as the fractional part of the ratio of the difference between the two points along the independent variable axis divided by the period of the periodic phenomenon. Or (x1-x0)/P where x is the independent variable, and P is the period of the independent variable.

So I can draw a periodic curve on a sheet of paper and make a phase measurement between any two desired points on the curve. No connection to electrons.

Phase is a measuring tool based on the period of the waveform.

.
 

rattus

Senior Member
120404-1432 EDT

Rick:

The title of this thread includes the word phase. Thus, to carry on this discussion it is necessary to have a definition(s) for phase. rbalex in the other long thread referenced the IEEE definition. That definition is useful and in a post in the long thread I analyzed what I thought the IEEE definition means.

Phase is a non-dimensional measurement between two points of a periodic phenomenon measured as the fractional part of the ratio of the difference between the two points along the independent variable axis divided by the period of the periodic phenomenon. Or (x1-x0)/P where x is the independent variable, and P is the period of the independent variable.

So I can draw a periodic curve on a sheet of paper and make a phase measurement between any two desired points on the curve. No connection to electrons.

Phase is a measuring tool based on the period of the waveform.

.

And I shall continue treating an inversion as a phase shift of PI radians or maybe -PI radians. Can't really tell the difference on a scope (realism) or on paper (idealism).

No connection to the phase of the moon either.
 

ggunn

PE (Electrical), NABCEP certified
Location
Austin, TX, USA
Occupation
Electrical Engineer - Photovoltaic Systems
And I shall continue treating an inversion as a phase shift of PI radians or maybe -PI radians. Can't really tell the difference on a scope (realism) or on paper (idealism).
Why not ((10^89) +1)PI radians? Never mind that at 60Hz it represents a time lag out past the heat death of the universe, it's still indistinguishable from an inversion in an infinite series. I don't see how you can separate phase shift from a time lag. Your scope plots the wave in the time domain; at 60Hz, a sine wave is 16.7msec from peak to peak, half that from Van peak to Vbn peak. A PI radian phase shift at 60Hz is 8.3msec, but voltage change on the primary of a transformer is reflected virtually simultaneously onto all terminals of the secondary. Mathematical phase shift may be time independent, but physical phase shift is not.

You may continue treating it however you wish but it does not change the way a transformer works. That the way you model it mimics reality as long as you stay in the box is irrelevant.
 
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Rick Christopherson

Senior Member
And I shall continue treating an inversion as a phase shift of PI radians or maybe -PI radians. Can't really tell the difference on a scope (realism) or on paper (idealism).

No connection to the phase of the moon either.
You keep bringing the topic up, but then you run away when it gets challenged. The difference will be seen on a scope, and that is where the noise example or sawtooth example come into play. Those examples reveal when your "idealism" model doesn't match the "Realism" of the system. You're the one that keeps making the statements, so why are you unwilling to discuss the ramifications of those statements?
 

rattus

Senior Member
KISS==Keep It Simple Sam

KISS==Keep It Simple Sam

There is a precept in engineering which says simply, ?Keep It Simple?. Applied to a design, it means no Rube Goldberg contraptions, no extra bells and whistles. Applied to modeling, it means that the model should be lean and clean. That is, we do not model events which are unlikely to happen or don?t really matter..

In this case, the difference between a time delay and inversion is unimportant. Even if a noise spike occurs, the phase of the fundamental frequency is unaffected and that is what we are trying to model. So we choose to model the transformer secondary as two ideal voltage sources with opposing phases, because that is basically how transformers work. Neither do we model current because we are only interested in the phase of the voltages. It would be useless to include winding resistance and leakage reactance in our model with no current.

Now, since the 3-phase wye consists of three sources, with a common neutral, separated by 120 degrees, why not say that the two sources of a split phase system provide two phases?
 

Rick Christopherson

Senior Member
Different models are needed for different purposes. There is no one-size-fits-all. Not everyone analyzes the system in the same manner or for the same reasons. However, what you have been saying all along is that the system "becomes" what your model represents, even though you admit to utilizing a stripped-down model.

The model doesn't define the system. The system defines the model(s).

Those previous examples were presented to reveal when your model doesn't match the system, which exemplifies why it is improper to try to define the system based on your limited model.
 

jim dungar

Moderator
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Location
Wisconsin
Occupation
PE (Retired) - Power Systems
...we choose to model the transformer secondary as two ideal voltage sources with opposing phases, because that is basically how transformers work. ...
A single winding 'cut in half' is not the same physical thing as two independent sources.

Following the KISS principal, saying 120V+120V=240V is hard to beat. It is single phase there is no basic reason need to include angles.
 

rattus

Senior Member
A single winding 'cut in half' is not the same physical thing as two independent sources.

Does not need to be the same physical thing. The two sources model the output of the transformer secondary quite well. The same waveforms are provided by the sources as provided by the transformer windings.

Just how would you model a CT transformer?

Following the KISS principal, saying 120V+120V=240V is hard to beat. It is single phase there is no basic reason need to include angles.

You can't talk about phase without specifying phase angles which is the point of this discussion.
 
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jim dungar

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Location
Wisconsin
Occupation
PE (Retired) - Power Systems
Does not need to be the same physical thing. The two sources model the output of the transformer secondary quite well. The same waveforms are provided by the sources as provided by the transformer windings.

Just how would you model a CT transformer?



You can't talk about phase without specifying phase angles which is the point of this discussion.

You can do whateveryou want to with models, just admit that they are what they are and not what they are not. In my opinion, a model that can be used to represent (2) independent sources and also (2) dependent sources should have a clarifying note when it is used. Assuming the intention of a 'out of context' item can lead to wrong conclusions.

CT = center tap? I have told you more than once, (2) identical voltages (magnitude and angle) connected in additive series.
CT = current transformer? Single phase single winding.

What part of 'single' is giving you a problem? It is one phase angle, which can be anything you want.
 

rattus

Senior Member
So how many phases are there in a 120/208/240 high leg open delta?

Well, depending how one treats the split phase transformer, one can count 5 phasors with 5 phase angles. Technically that is 5 phases. Even if one of the transformers is omitted, its L-L voltage is still present. We still call it a three phase service though.
 

mivey

Senior Member
Swapping the position of a generator shaft is a physical change, swapping reference points is not.

Physically changing reference points requires a physical change. The difference was demonstrated by Besoeker showing the difference in a dimmer circuit vs. a rectifier circuit.

It was also demonstrated in my open-wye example where physically taking voltages in the 1->2->3->4 direction produced no phase shift but physically taking them in the 2->1 and 3->4 opposed direction produced the phase shift needed to create the missing third phase. Both cases use the same center-tap transformer with terminals 2 & 3 tied together but physically taking voltages in different directions produces physical results that are the results of a physical change.

Given any two points X & Y, there is a single voltage difference between them (i.e. V).
You may arbitrarily assign a direction to this single voltage, giving you a single magnitude and a reference direction (i.e. Vyx), but you still only have the single voltage, V.

You may also assign a mathematical equivalency such as Vxy = -Vyx, but you still only have a single voltage V

You can also arbitrarily assign an angle to this single voltage creating a reference phasor (i.e. V@0?), but you still only have a single voltage, V.
You can take the conjugate (colloquially referred to as the inverse) of the phasor (i.e. V@180?), but you still only have a single voltage, V.

With a center-tap transformer we have more than two terminals thus more than two voltages.

You can also arbitrarily assign your phasor angle to your reference direction (i.e. V@180?=Vxy=Vxy@180?), you now have two directions but you still only have a single voltage, V.

If you relate your direction to the angle then, reversing (inverting) the reference direction is different than conjugating (inverting) the angle, but you still only have a single voltage, V.
Vxy@180? invert (opposite) direction yields -Vxy@180?=Vyx@180?
Vxy@180? invert (conjugate) angle yields Vxy@0?
Vxy@180? invert direction and invert angle yields Vyx@0?

You are not using correct notation. By sticking an angle on the end of the name, you are mixing the name and value. It is like saying the "direction from x to y in the north direction is in the north direction".

Also, while a pair of conjugate angles adds to 360?, mathematical conjugation is something completely different.

For one, the series interconnection versus the parallel interconnection of a single phase reconnectable transformer output.
Given terminals X1-X2 and X3-X4, does it make sense to say the (2) 120V voltages are 'out-of-phase' when connected in series but they 'in-phase' when connected in parallel?

V12 is out of phase with V43 whether the connections are in series or parallel. V21 is in phase with V43 whether the connections are in series or parallel.

As for whether it makes sense to say V43 is phase-opposed to V12 when the windings are in series: Yes it does make sense when the voltages are used that way. My open-wye example shows exactly that. For "in-phase" voltages, we have V21 and V43. But we use the V12 voltage that is "out-of-phase" with V43 in order to create the missing third phase of the three-phase supply.
 
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