Why is residential wiring known as single phase?

[pfalcon]

Maybe you would like to show us the correct way to draw the diagram??

----------->----------->

 

[rattus]

The correct answer cannot be determined until after the subtraction operation has occurred.
Technically all phasors should always have a positive magnitude with their angles being 'inverted' as needed, after all a line cannot truly have a negative length.
Mathematically it makes no difference, so this convention is usually reserved until the final step.

Actually, the magnitude is ALWAYS positive.

This is why I have said we do not really 'generate' a negative AC voltage, so if we calculate one, we have simply assigned it the wrong direction.
Van=Vnb=-Vna=-Vbn for a single center-tapped winding.

If

Van = -Vbn, then

Van = Vbn + PI

Van and Vbn are out of phase by PI radians

Van and Vbn cannot be in phase or of the same phase

sin(wt) and [-sin(wt)] cannot in phase or of the same phase

 

[rattus]

----------->----------->

Which node is which? And, how come I get the right result by doing it wrong?

 

[Rick Christopherson]

Actually, the magnitude is ALWAYS positive.

This is true only for vectors. For any other analysis method, (including phasor math) a negative magnitude is perfectly acceptable. And as you pointed out last night, you don't use graphical representations.

Choosing between a negative sign and a 180 degree phase angle is also just a matter of personal preference. Personally speaking, unless I am using graphical vectors, I prefer to not add an extra phase angle that isn't necessary.

 

[ggunn]

For the life of me I cannot figure out why this is worth 240+ pages of bickering. Yes, the waveforms are 180 degrees out of phase, but it's an inversion, not a phase shift. It only looks like a phase shift because of the symmetry of the wave. Why is it more complicated than that? Pardon me for saying this but it just looks like an ego struggle to me. "I won't let you up until you say 'uncle'".

The terminology "split phase" is accurate and sufficiently describes a 240/120 system, and it neatly sidesteps this non-issue. I never call it "single phase" because it hopelessly confuses some folks.

Pass the popcorn.

 

[david luchini]

I did. Jim overlooked something. Tail-to-tail occurs when one is a resultant phasor. That would be the 240 phasor which cannot exist for rattus.

I'm afraid I don't understand your point. The two phasors are not "resultant" of anything. They are a model for the two windings of the transformer. They both use the neutral point as a common starting point. So, If Vna=120<180 and Vnb=120<0, Rattus' phasor diagram is correct. The resultant phasor from combining the two phasors would have a magnitude of 240. The angle of the resultant phasor would be dependent on which phasor was subtracted (tail-to-tail) from which.

Vab=Vnb-Vna = 120<0 - 120<180 = 240<0
Vba=Vna-Vnb = 120<180 - 120<0 = 240<180

So as you see, the resultant phasor is 240V for Rattus' phasor diagram. It also properly models the transformer. The resultant phasor for a connection between A and B would be 240V<0 and the resultant phasor for a connection between B and A would be 240V<180. This is correct.

The diagram is not correct for a basic phasor diagram. Rattus has drawn an origin shifted diagram. The flaw is evident because there's no origin tailed resultant.

The origin hasn't "shifted" anywhere. The origin for both phasor is the neutral point. There is no need for there to be a origin tailed resultant. The resultant 240V phasor is measured from head to head of the two base phasor. This is fine under basic vector math. There is no need to force the diagram into a head-to-tail arrangement.

Maybe you would like to show us the correct way to draw the diagram??

----------->----------->

That would be the correct phasor diagram for Van=120<0 and Vnb=120<0. It would be incorrect for Vna=120<180 and nb=120<0.

The correct diagram for Vna=120<180 and Vnb=120<0 would be: <-----------.----------->

Both of these phasor diagrams are correct for their base phasors, and both provide the same (and correct) resultant phasor when combined.

 

[rattus]

I did. Jim overlooked something. Tail-to-tail occurs when one is a resultant phasor. That would be the 240 phasor which cannot exist for rattus.


The diagram is not correct for a basic phasor diagram. Rattus has drawn an origin shifted diagram. The flaw is evident because there's no origin tailed resultant.

A 240 resultant starting at the origin should appear somewhere. Either 120 phasor should be placed at the origin. Then the other phasor can be indicated by subtracting the 120 phasor from the resultant 240 phasor.
No 240 phasor from the origin means a misdrawn diagram.

And, just how would you correctly draw the phasors for a 120V wye?

 

[rattus]

This is true only for vectors. For any other analysis method, (including phasor math) a negative magnitude is perfectly acceptable. And as you pointed out last night, you don't use graphical representations.

Now just where did you get this gem of wisdom? A negative magnitude would play havoc with the real and imaginary components. My book says the magnitude is the absolute value. After all, a line cannot have a negative length!

 

[jim dungar]

And, just how would you correctly draw the phasors for a 120V wye?

Lets stay on topic.
Three wye connected transfromers, is not the same as a single center-tapped winding where we have already agreed (?) Van=Vnb=-Vna=-Vbn.

 

[Rick Christopherson]

For the life of me I cannot figure out why this is worth 240+ pages of bickering. Yes, the waveforms are 180 degrees out of phase, but it's an inversion, not a phase shift. It only looks like a phase shift because of the symmetry of the wave.

The reason why the discussion has gone on this long is because there are several posters here that can't distinguish "opinion" from "fact", and they present their "opinion" as though it is "fact". This raises the hackles of those people that don't subscribe to the same opinion. If the arguments were properly stated as being opinion-based, then this whole argument would vanish in minutes.

When a poster comes forward and states, "this circuit functions only when you view it or analyze using my methods," then that is going to draw the ire of those people that know better. Likewise, when a poster states that analyzing a circuit can only be performed using their methods, and all other methods are foolish and flat out wrong, that is going to draw the ire of those that do not subscribe to that methodology. It all boils down to deliberate misinformation, and how far a poster chooses to push that misinformation before stirring up a hornet's nest.

You're right. It is ego-based. You will notice that the proponents of one side are almost exclusively very, very long-time engineers that have been so set in their ways for so many decades that they cannot accept other people using methods contradictory to their own. It's a "my-way or the highway mentality" and that doesn't sit well for those of us that know better.

 

[rattus]

Lets stay on topic.
Three wye connected transfromers, is not the same as a single center-tapped winding where we have already agreed (?) Van=Vnb=-Vna=-Vbn.

True, but pfalcon insists on redrawing my phasor diagram, and the phasor diagrams are similar.

 

[Rick Christopherson]

After all, a line cannot have a negative length!

Yes, my dear brainchild. That is graphics, and you stated last night that you do not employ graphics in your solutions. So which is it? Are you basing your responses on a graphical representation, or not?

Your statement applies to graphics. It does not apply to any other form of mathematical manipulation. You repeatedly state that you wish this discussion to focus solely on ideal mathematical manipulations. Take responsibility for the words you choose.

 

[pfalcon]

Which node is which? And, how come I get the right result by doing it wrong?

Doesn't matter which node is which. At any instantaneous moment their polarities match. So:

A -----------> N
+
N -----------> B
=
A -----------+-----------> B

or

A <----------- N
+
N <----------- B
=
A <-----------+----------- B

Voltages in series are additive not subtractive.

I'm afraid I don't understand your point. The two phasors are not "resultant" of anything. They are a model for the two windings of the transformer. They both use the neutral point as a common starting point. So, If Vna=120<180 and Vnb=120<0, Rattus' phasor diagram is correct. The resultant phasor from combining the two phasors would have a magnitude of 240. The angle of the resultant phasor would be dependent on which phasor was subtracted (tail-to-tail) from which.

Again, whether you measure from the neutral or an endpoint, you have to draw your phasors based on instantaneous voltage. Rattus keeps discarding <180 by measuring each voltage source 1/2 cycle off.

Vab=Vnb-Vna = 120<0 - 120<180 = 240<0
Vba=Vna-Vnb = 120<180 - 120<0 = 240<180

Vab is the resultant phasor. Vnb and Vna are the component phasors. As voltages in series they are ADDITIVE not subtractive. You've discarded a 1/2 cycle to get Vna as 120<180 by neglecting the instantaneous voltage direction.

So as you see, the resultant phasor is 240V for Rattus' phasor diagram. It also properly models the transformer. The resultant phasor for a connection between A and B would be 240V<0 and the resultant phasor for a connection between B and A would be 240V<180. This is correct.

Not correct. As drawn the expression should be Vab = Vnb + Vna = 0<0; In series the graphic lines are placed stacked. You shifted 1/2 cycle by lifting your pencil and moving back to the origin before drawing the second phasor.

The origin hasn't "shifted" anywhere. The origin for both phasor is the neutral point. There is no need for there to be a origin tailed resultant. The resultant 240V phasor is measured from head to head of the two base phasor. This is fine under basic vector math. There is no need to force the diagram into a head-to-tail arrangement.

As stated above the origin has been shifted 1/2 cycle. The origin for a phasor diagram for a voltage series has no neutral point. It's not on the phasor diagram. Just an origin with phasors having magnitude and angle. The origin is NOT 0V and it's NOT the neutral. It's the beginning point of the diagram. The resultant is measured from the origin of the first phasor to the end point of the second phasor. Without the 1/2 cycle shift rattus's diagram would yield 0<?, with the shift it yields a resultant of 120<180 measured on the graph.

That would be the correct phasor diagram for Van=120<0 and Vnb=120<0. It would be incorrect for Vna=120<180 and nb=120<0.

The correct diagram for Vna=120<180 and Vnb=120<0 would be: <-----------.----------->

Both of these phasor diagrams are correct for their base phasors, and both provide the same (and correct) resultant phasor when combined.

nb=120<0, N=120 B=0. na=120<180, N=120 A=240. Hence
|Vnb|=120 with + at <0 (leftward N>B); |Vna|=120 with <0 (leftward A>N); therefore drawn ----------->-----------> ; no origin required, just a starting point for the diagram.

 

[mivey]

The reason why the discussion has gone on this long is because there are several posters here that can't distinguish "opinion" from "fact", and they present their "opinion" as though it is "fact".

Then let's talk about facts. With a transformer, one does not have to have a time shift to have a phase shift.

These are the facts:
1) Phase shift without a time shift is in accordance with standard technical definitions of phase shift.
2) Phase shift without a time shift does not match all definitions of phase shift nor does it have to since we have often mutiple definitions for a word or phrase.
3) Phase shift without a time shift is common usage and technical terminology for transformers and other circuitry.
4) The physical changes made by taking voltages from different transformer terminals and in different transformer winding directions can produce phase shifts of the non-time shift type.
5) The phase shifts made by taking voltages from different terminals and in different winding directions do not produce time shifts like you get with propagation delays, but are still commonly and technically known as phase shifts.
6) The non-time phase shifts are related to time shifts because of the resulting time difference between similar locations on the different waves.
7) Phase shifts produced by taking voltages from different terminals and in different winding directions is also commonly known as phase displacement and phase difference.
8) Taking voltages in different transformer winding directions is commonly recognized to produce a 180? phase shift/difference/displacement.
9) The signals taken from the center-tap winding halves can be taken as in-phase signals or phase-opposed signals.

I have posted many references that support all of these facts. I have also posted many examples that demonstrate all of these facts. Other members have also posted references and examples that support and demonstrate these facts. There are many more references and sources available that also support and demonstrate these facts.

It is perfectly fine to have a different preference for definition or for application, but to deny the facts above is illogical and displays denialism.

 

[iwire]

2400+ replies.

Really?

Is anyone any closer to agreement?

 

[mivey]

2400+ replies.

Really?

Not really the first time. Just the first time it has been pretty much contained within one thread instead of spawning more threads.

Is anyone any closer to agreement?

I think we all agree you were right at the beginning.

 

[rattus]

Again, whether you measure from the neutral or an endpoint, you have to draw your phasors based on instantaneous voltage. Rattus keeps discarding <180 by measuring each voltage source 1/2 cycle off.

Obviously you are unfamiliar with static phasors, e.g.,

Van = 120Vrms @ 0
Vbn = 120Vrms @ PI

These are steady state values. They are NOT functions of time! RMS voltages are NOT functions of time. These phasors are connected tail to tail at the neutral, just like the circuit. To get Vab you change signs and add--as in algebra. You just jumped the gun a bit. But the voltage on node B is still 120Vrms @ PI however you draw the phasors.

In fact, you would obtain Vab without drawing any phasors at all. Just do the subtraction,

Vab = Van - Vbn, phasorially that is.

Suggest you study up on static phasors.

 

[Rick Christopherson]

Doesn't matter which node is which. At any instantaneous moment their polarities match. So:

A -----------> N
+
N -----------> B
=
A -----------+-----------> B

or

A <----------- N
+
N <----------- B
=
A <-----------+----------- B

Voltages in series are additive not subtractive.

Forgive me. I did not read your whole response, but your diagram is useful. This is not necessarily directed at you.

What some respondents in this thread may not realize is that Rattus brought this particular aspect up many times in the past as it relates to summing KVL around a loop. When it was brought to his attention that his vectors did not conform to KVL, his response was that when he encountered tail-to-tail vectors that it meant subtraction. As was demonstrated last night, tail-to-tail is an inappropriate method for signifying subtraction because it is indeterminate.

He presents his position from a graphical perspective, but then denies ever using graphical methods. This is why so many of us keep pointing out his hidden minus sign that he doesn't want anyone else to notice.

 

[david luchini]

Doesn't matter which node is which. At any instantaneous moment their polarities match. So:

A -----------> N
+
N -----------> B
=
A -----------+-----------> B

or

A <----------- N
+
N <----------- B
=
A <-----------+----------- B

Voltages in series are additive not subtractive.

I'm afraid you are still not grasping phasor combination correctly, despite repeated attempts to describe it, and despite Jim's very clear description in post #1999. Phasor combination can be EITHER additive or subtractive depending on the relationship of the phasors to each other. Head-to-tail is additive, tail-to-tail is subtractive. BOTH of these conventions are correct. You are NOT bound by one or the other.

Again, whether you measure from the neutral or an endpoint, you have to draw your phasors based on instantaneous voltage. Rattus keeps discarding <180 by measuring each voltage source 1/2 cycle off.

There is no measuring of each voltage source 1/2 cycle off. You are injecting this idea yourself. The phasors are time-invariant. You draw your phasors based on the magnitude and angle notation of the phasor. If Vna=120<180 and Vnb=120<0, then both have a magnitude of 120 and one has an angle of 0, the other and angle of 180. The component phasors are represented as:

Vna: A<--------------N = 120<180
Vnb: N-------------->B = 120<0

The combined phasor would be:

A<--------------N-------------->B

The resultant phasor by combination Vab would be:

A------------------------------->B

A<--------------N-------------->B Vab=Vnb-Vna= 120<0 - 120<180 = 240<0. You can see that the resultant phasor has the proper magnitude and angle when properly combined using subtraction of the component phasors based on the tail-to-tail configuration.

Vab is the resultant phasor. Vnb and Vna are the component phasors. As voltages in series they are ADDITIVE not subtractive. You've discarded a 1/2 cycle to get Vna as 120<180 by neglecting the instantaneous voltage direction.

This is where you go wrong. In your diagram, Vab is the resultant phasor, with Vnb and Van being the component phasors. Take another look:

A -----------> N
+
N -----------> B
=
A -----------+-----------> B

You show "A to Neutral" added with "Neutral to B" to get the resultant phasor "A to B". Yet above you substituted Vna for Van. This is an error. If you added component phasors Vnb and Vna, the resultant phasor would be zero (120<0+120<180=0). This is clearly wrong.

Not correct. As drawn the expression should be Vab = Vnb + Vna = 0<0; In series the graphic lines are placed stacked. You shifted 1/2 cycle by lifting your pencil and moving back to the origin before drawing the second phasor.

I'm sorry, but you are not correct here. The two phasors in the example are Vna=120<180 and Vnb=120<0. The phasor diagram is:

A<--------------N-------------->B

The combined phasor is:

A------------------------------->B

A<--------------N-------------->B Vab=Vnb-Vna= 120<0 - 120<180 = 240<0.

There is no 1/2 cycle shift anywhere to be found. Vnb is 120<0 at the same "instantaneous moment" that Vna=120<180, and at the same "instantaneous moment" that Vbn=120<180, and at the same "instantaneous moment" that Van=120<0.

As stated above the origin has been shifted 1/2 cycle. The origin for a phasor diagram for a voltage series has no neutral point. It's not on the phasor diagram. Just an origin with phasors having magnitude and angle. The origin is NOT 0V and it's NOT the neutral. It's the beginning point of the diagram. The resultant is measured from the origin of the first phasor to the end point of the second phasor. Without the 1/2 cycle shift rattus's diagram would yield 0<?, with the shift it yields a resultant of 120<180 measured on the graph.

The origin of each phasor is what you chose it to be. Vna and Vnb both have an origin at N. Vab and Van both have an origin at A. Vba and Vbn both have an origin at B. There is no one point that is required to be the origin of the phasor diagram, nor is there any 1/2 cycle shift going on.

I can look at your first diagram (from A to B) and use B as my origin to determine what Vba is, or what Vbn is. I could use N as the origin to determine what Vna is, even though you've only given us Van, Vnb and Vab.

Don't get locked into thinking that phasors must be drawn in only one certain direction, or that there is some mystery 1/2 cycle shift in using Vna together with Vnb. It is not true. With your instance that the phasor must have their "polarities match" at any "instantaneous moment" you are going to find it very hard to analyze systems when more phases are added.

 

[rattus]

Forgive me. I did not read your whole response, but your diagram is useful. This is not necessarily directed at you.

What some respondents in this thread may not realize is that Rattus brought this particular aspect up many times in the past as it relates to summing KVL around a loop. When it was brought to his attention that his vectors did not conform to KVL, his response was that when he encountered tail-to-tail vectors that it meant subtraction. As was demonstrated last night, tail-to-tail is an inappropriate method for signifying subtraction because it is indeterminate.

Perhaps you didn't understand my example where I showed that Vab = 208Vrms @ PI/6 in a wye.
How is that indeterminate?

He presents his position from a graphical perspective, but then denies ever using graphical methods. This is why so many of us keep pointing out his hidden minus sign that he doesn't want anyone else to notice.

The phasor graphics are supported by the math. There would be no graphics without the math. I use sketches to help in the thought process, but I do not solve the problem graphically because that is a cumbersome process and is not as precise.

There is nothing hidden anywhere!