Four-wire delta, phasors, and Kirchoff:

[rattus]

You can"t do that!

You can"t do that!

The thing about phasors and vectors, is that no matter what order you place them, the answer is still the same. It doesn't matter if you walk 20 feet north, 20 feet west and 20 feet east, versus walking 20 feet west, 20 feet north, and 20 feet east--you still end up at the same place. This shouldn't be news to anyone that has spent any time with phasors or vectors.

So to put this into perspective, I have redrawn "Yuck" and "Yumm", only I changed their order. As you can see, when you place "Yuck" tip-to-tail in standard phasor/vector addition, the result is suddenly a 240 volt gap. When "Yumm" is rearranged, it looks like an hourglass, but still closes back to the original point.

To reiterate what I said in the previous thread, I don't care whether or not someone wants to call the two halves of the transformer out of phase or not. That is a matter of semantics that I do not need or want to argue. My issue was on the use of "phasors" as a justification for making the argument.

New Edit I apologize for this, and I do try to avoid editing a posting that has been posted for over an hour now, but since it is so late at night, I don't think this edit should screw anyone up. The reason for my edit was because I scrolled back up to the top of this thread and read the original posting, as follows:I added the Bold emphasis. This is directly applicable to the diagram I drew above, and is why I edited this posting to restate the original topic. The diagram I drew represents proper phasor/vector summation.

Can't do that Rick. You have changed the reference on Vcg so it adds instead of subtracts. This is absolutely wrong! Both 120V phasors must be drawn tail to tail! In other words, you screwed up my perfectly good diagram.

 

[rattus]

Negative Magnitude?

Negative Magnitude?

1. Why do you continue to use the term, "negative magnitude", when "magnitude" is defined to be the absolute value? The magnitude of a phasor can be found by taking the POSITIVE square root of the sum of the squares of the real and imaginary components.

The real and imaginary parts of the phasor may be negative, but never the magnitude.

2. I have demonstrated that Vcg is 120 @ 180. Now, you are telling me I can't draw my phasor that way?

3. KVL states that the ALGEBRAIC sum of the voltages around the loop must be zero. Then, some negative values must be present.

4. You must provide some references to prove I am wrong. So far, I hear only your own notions.

 

[iwire]

Just a friendly reminder, keep this discussion on the subject.

No more 'I am better then you' or 'Your not a real engineer' type comments.

 

[LarryFine]

Just a friendly reminder, keep this discussion on the subject.

No more 'I am better then you' or 'Your not a real engineer' type comments.

You're not a real moderator! :grin:

 

[winnie]

I am siding with those noting that this discussion is far more about terminology and convention then about the physics of the situation.

First, to answer Carl in his request that we use _standard_ language to discuss these issues: "The great thing about standards is that there are so many to choose from." Where the math or the physics offers reasonably equivalent choices about a representation, you are bound to find that different parties (standards organizations, text book publishers, teachers, etc) choose different representations.

As examples: think about which side of the road is the correct one to drive on, where you find the origin and the first quadrant in a computer display, which direction +y is on a milling machine, what is the direction of a positive rotation, etc. I agree that we here should select an already common representation rather than inventing our own, however it is almost certain that we are speaking from different conventions.

On rattus' diagrams, I see either as correct and equivalent. However the diagrams make an implicit statement about the representation of 'vector' that rattus is applying. As rattus is representing them, it is permissible to connect vectors head to head or tail to tail, however when vectors are connected head to head you are required to use a _different_ addition rule (perhaps called subtraction).

Rick, you seem to be saying that vectors must be connected head to tail. I argue that this is a convention of the vector representation that you are using, not a requirement of the basic math. I endorse this as a more common convention, and often a _clearer_ convention. But I do not see this as an absolute requirement. Under this convention, when you come to a 'head to head' situation, you are required to replace one of the vectors with a vector of the same magnitude but opposite direction, making a 'head to tail' situation. Under this convention, rattus' first diagram is 'incorrect'.

rattus, I don't see Rick as anywhere saying that 'negative magnitude' is being used. Both you and he have stated that negative magnitudes are incorrect. I see this aspect of things as a convention; vectors work just fine if you permit the use of negative magnitudes, but I accept the convention that the magnitude of a vector must be positive. Note: a very intuitive interpretation of vectors connected 'head to head' is that the second vector has a negative magnitude, so perhaps your use of 'head to head' vectors is being seen as a use of negative magnitudes for vectors.

-Jon

 

[iwire]

You're not a real moderator! :grin:

LOL,

I just play one on the Internet.

 

[Rick Christopherson]

Can't do that Rick. You have changed the reference on Vcg so it adds instead of subtracts. This is absolutely wrong! Both 120V phasors must be drawn tail to tail! In other words, you screwed up my perfectly good diagram.

Please be careful rattus. I am trying to keep this civil, but it sounds like you are losing your temper already.

As I stated in the preface to this diagram, I have rearranged your phasor diagram using the proper rules of vector analysis to demonstrate more clearly how your phasor diagram violates Kirchoff's Voltage Law.

Rick, you seem to be saying that vectors must be connected head to tail. I argue that this is a convention of the vector representation that you are using, not a requirement of the basic math.
...................
it is permissible to connect vectors head to head or tail to tail, however when vectors are connected head to head you are required to use a _different_ addition rule (perhaps called subtraction).

I do not say that you cannot subtract phasors. However, the only way to make rattus' diagram work is if you use subtraction, and that is where it violates Kirchoff's Law for the "Summation" of voltages.

KVL is still applicable to phasor diagrams, and that is what my drawing is supposed to represent. It shows that the application of KVL reveals that rattus has interjected a negative sign (or more accurately, forgot to have a negative of a negative).

 

[rattus]

Kirchoff rules:

Kirchoff rules:

Please open the attached diagram which discusses voltage rises and drops around a loop. Basic stuff.

 

[iwire]

Statements like this.....

This is so basic it baffles me why anyone would argue the point.

....are not helpful.



However they do raise the threads temperature and will lead to another closed thread.

 

[Rick Christopherson]

Please open the attached diagram which discusses voltage rises and drops around a loop. Basic stuff.

Can you draw the circuit that this phasor diagram is supposed to represent?

 

[rattus]

Oxymorons:

Oxymorons:

Winnie,

The term "negative magnitude" is an oxymoron and should never, ever be used. It just can't be! Only the x & y components carry signs.

True, the convention is head to tail in a delta phasor diagram, but one can define the phasors backwards so to speak, and Kirchoff still works. Also, the diagram should reflect the transformer connections--not shuffled around.

I have shown that Vcg = 120V @ 180 which some still deny. This is true with the yumm diagram as well because Vgc = -Vcg. That is all there is to it--subtracting instead of adding.

Now let's talk wye. Define the voltages as follows:

Van = 120 @ 0
Vbn = 120 @ -120

Now compute Vab by summing the phasors from B to A.

-Vbn + Van = Vab = 208V @ 30

Can anyone argue with that?

 

[rattus]

Can you draw the circuit that this phasor diagram is supposed to represent?

The point is that it could represent a number of things, for example,

Two out of phase generators in series which provide the voltage, Vab.

One generator, Vab, driving series reactive loads with different voltage drops. The exact circuit is not that important, although it could be an RL or RC circuit.

Think DC, say a battery driving a lamp. Summing the voltages around the loop, we see a voltage rise and a voltage drop. One is positive, one is negative, therefore we have to subtract.

 

[Rick Christopherson]

The exact circuit is not that important, although it could be an RL or RC circuit.

Actually, it is important. I wouldn't expect you to resolve the two reactive loads. You can leave these two items as black boxes, but just provide the complex expressions for which they represent (i.e. real and imaginary).

 

[mivey]

However they do raise the threads temperature and will lead to another closed thread.

Ya'll behave. Mama says I can't come out and play right now and I don't want the game to end before I'm free to play. I'm sneaking a peak right now.

 

[rattus]

Proper rules?

Proper rules?

Rick,

How about a reference of the "proper rules of vector analysis"?

By your rearrangement, you have made Vcg a rise instead of a drop. If you had stuck it on the head of Vag, it would be mathematically correct, but not indicative of the transformer connections.

You just can't do that!

I have asked for references, and until you provide them, I cannot accept your arguments.

 

[Rick Christopherson]

I have taken your original “Yuck” and "Yumm” phasor drawing, and converted each phasor back into rectangular coordinates. These rectangular coordinates represent exactly what you drew with your phasor diagram, including the appropriate minus signs, as per your drawing.

According to Kirchoff’s Law, you should be able to add up all of the rectangular coordinates around a closed path, and their sum must be zero.

Oh, I used colors to make it easier to track where each number in the summation is coming from.

Edited to correct the reference from polar to rectangular. Sorry about that.

 

[winnie]

Winnie,

The term "negative magnitude" is an oxymoron and should never, ever be used. It just can't be! Only the x & y components carry signs.

Why not? The math works just fine. The only _problem_ with negative magnitude is that it violates _convention_. The magnitude of a vector is _by definition_ positive, so a negative magnitude is a problem with the words.

True, the convention is head to tail in a delta phasor diagram, but one can define the phasors backwards so to speak, and Kirchoff still works. Also, the diagram should reflect the transformer connections--not shuffled around.

As I said, it is quite easy to work with 'head to head' vectors. IMHO such are mathematically consistent yet violate convention almost as much as vectors with negative magnitude.

Van = 120 @ 0
Vbn = 120 @ -120

Now compute Vab by summing the phasors from B to A.

-Vbn + Van = Vab = 208V @ 30

The above is exactly the reason that I _prefer_ viewing a single phase center tapped system as Van = 120 @ 0, Vbn = 120 @ -180. I simply prefer to think of the vectors from neutral to line rather than some line to neutral and others neutral to line.

-Jon

 

[rattus]

Still waiting:

Still waiting:

I have taken your original ?Yuck? and "Yumm? phasor drawing, and converted each phasor back into polar coordinates. These polar coordinates represent exactly what you drew with your phasor diagram, including the appropriate minus signs, as per your drawing.

According to Kirchoff?s Law, you should be able to add up all of the polar coordinates around a closed path, and their sum must be zero.

Oh, I used colors to make it easier to track where each number in the summation is coming from.

Three of these phasors are rises. One is a drop. You must subtract the drop -(-120) = +120.

I await your references which prove subtraction is not allowed.

 

[winnie]

Rick,

Do you have a copy of Kirchoff's paper spelling out the law? The phrasing in Wikipedia (which for this is _not_ a rigorous reference in that the quote is not attributed and may be an interpretation) is "The directed sum of the electrical potential differences around a closed circuit must be zero."

Directed sum does not mean 'add'. Directed sum means 'add while cognizant of direction". Clearly the reverse pointed vector in the loop of the "Yuck" diagram must be added in a different fashion. You are not using rattus' representation in an internally self consistent fashion, getting a clearly incorrect result, and then calling the representation itself incorrect.

-Jon

 

[Rick Christopherson]

Three of these phasors are rises. One is a drop. You must subtract the drop -(-120) = +120.

Which 3 are rises? The Blue, Violet, and Red polar coordinates all have the same Real component, but you are suggesting that only the Red should be subtracted?

I put these into polar coordinates so it becomes straight mathematics--no vectors anymore. If you can't add them up as Kirchoff states, that means that one of them is improperly defined.

Kirchoff doesn't say that you can selectively subtract when you get to a voltage source that doesn't fit his law. If you need to subtract, then it means that the polarity of the voltage source is wrong.

Kirchoff states that you sum the voltages as you go around a closed loop:
G to A, A to B, B to C, C to G

You are trying to jump from C to G and then go back to C:
G to A, A to B, B to C, G to C

That's not a closed path. You are ending at C instead of G, where you started.