Why is residential wiring known as single phase?

[rbalex]

To you or to me?

Hopefully to you - you said you couldn't read the original.

I provided expressions for all six voltages.

Yes - So? Are you saying that three of the "phases" cannot be written in terms of their inverse as I gave in the example? That is, assuming a common t₀, three of your "phases" will have the same period, inital phase angle or equivalent inverse and thus phase as three others.

What genuinely makes it hexaphase is that there are six phases.

Only if you include line-to-line voltages; not if you only consider line-to-neutral voltages - then there are only three phases.

 

[rbalex]

Homework Problem:

Plot the functions, sin(wt) and -sin(wt) and determine the phase of each.

Solution:

The plots are inverses of each other, so I would think that do not carry the same phase.

Certainly wt is the phase of the first, but am not so sure of the second.

Flash of genius: Apply a trig identity to get the answer I want even if it may be wrong.

-sin(wt) = sin(wt + PI)

The answers are: wt and (wt + PI)

But that looks right not wrong to me. Phases differ by PI the difference in phases? Just like the plots, separated by PI?

Naw, couldn't be! Too easy.

BTW, I couldn't find anything to support this move, just made it up myself.

I guess you just can?t help misapplications, can you. You cannot to swap the application of definitions any more indiscriminately as you have been doing pulling arguments in and out of the Sine functions.

I originally introduced the concept that the phase of a function was ωt + φ₀ in post 132. It was in that context I introduced trig identities where they are appropriate and valid.

When you proposed ?phase is the fractional part of a period through which time or the associated time angle wt has advanced from an arbitrary reference," identities were no longer necessary assuming a common t₀ and period.

In either case, used correctly, both definitions lead to the same conclusion: All valid voltage functions of a single-phase system can be written in terms of one identical phase.

KEEP your applications straight.

 

[__dan]

Well, I thought you were familiar with complex numbers and phasors. You are finding the DIFFERENCE between two voltages, therefore you subtract.

How do you obtain 208V from any two legs of a 120V wye? Try it with 120V @ 0 and 120V @ -120; what do you get?

No. In the OP's 120 0 120 transformer, I am adding windings in series that are wound in the same direction end to end, to add the voltage. I add the physical reality and the sum is what I get when I measure line to line at the output. The measurements you provide sum to zero, which is not what is found by observation. Your premise fails the test of usefulness (or accuracy).

If I saw the winding in half and stick my head in the middle of the winding, then rotate my head 180deg to look at one winding then the other, the windings will appear to be wound clockwise on one side and counterclockwise on the other. This is the applicable analogue and equal to what your measuring protocol delivers for results. Then you say "subtract them". I say "you first, be my guest". I will help you, use my saw.

Going to a Y source, you are pointing to a different animal in your menagerie, going from a horse to a zebra, and saying 'explain the stripes'.

The Y source example has two iron cores, two phase displaced primary voltage sources, and resulting secondary phi0 = x constant differences. For the OP's example, all solutions reside in a one dimensional coordinate system, linearly along the same line. In the substitution you propose, the solutions reside in a two dimensional coordiate system. You have changed "a" for "b" and wish to claim "a" resembles or is equivalent in some way to "b".

In fact "a" has material differences from "b".

 

[rattus]

I guess you just can’t help misapplications, can you. You cannot to swap the application of definitions any more indiscriminately as you have been doing pulling arguments in and out of the Sine functions.

I originally introduced the concept that the phase of a function was ωt + φ₀ in post 132. It was in that context I introduced trig identities where they are appropriate and valid.

When you proposed “phase is the fractional part of a period through which time or the associated time angle wt has advanced from an arbitrary reference," identities were no longer necessary assuming a common t₀ and period.

In either case, used correctly, both definitions lead to the same conclusion: All valid voltage functions of a single-phase system can be written in terms of one identical phase.

KEEP your applications straight.

Read further:

"In the case of a simple sinusoidal variation, the origin is usually taken as the last previous passage through zero from the negative to the positive function..............." In other words, time is measured from the zero crossing, not from the traditional origin, therefore the phase constant must be included in the expression for phase.

I used an identity to put the expression in a form where the phase could be easily extracted. Apples to apples you know. If you can do it, I can do it, only my equivalence makes sense.

 

[rattus]

No. In the OP's 120 0 120 transformer, I am adding windings in series that are wound in the same direction end to end, to add the voltage. I add the physical reality and the sum is what I get when I measure line to line at the output. The measurements you provide sum to zero, which is not what is found by observation. Your premise fails the test of usefulness (or accuracy).

If I saw the winding in half and stick my head in the middle of the winding, then rotate my head 180deg to look at one winding then the other, the windings will appear to be wound clockwise on one side and counterclockwise on the other. This is the applicable analogue and equal to what your measuring protocol delivers for results. Then you say "subtract them". I say "you first, be my guest". I will help you, use my saw.

Going to a Y source, you are pointing to a different animal in your menagerie, going from a horse to a zebra, and saying 'explain the stripes'.

The Y source example has two iron cores, two phase displaced primary voltage sources, and resulting secondary phi0 = x constant differences. For the OP's example, all solutions reside in a one dimensional coordinate system, linearly along the same line. In the substitution you propose, the solutions reside in a two dimensional coordiate system. You have changed "a" for "b" and wish to claim "a" resembles or is equivalent in some way to "b".

In fact "a" has material differences from "b".

dan, you are weighting yourself down with transformers. Just think phasors, one pointing right, the other left. They oppose each other. You want the potential difference between V1 and V2. You subtract one from the other to get the difference.

You could draw both phasors in the same direction, then you would add, but we lose our common reference that way.

 

[rattus]

rbalex,

Since you introduced the concept that phase is expressed by,

(wt + phi0), where phi0 is the phase constant which is different for each waveform.

How do you justify dumping phi0 through trig identities?

None of us have ever seen this done, you included.

Clearly, the phases of a sinusoid and its inverse are different. Your claim makes no sense!

True, the identity is valid, but your application of it is not.

 

[rbalex]

rbalex,

Since you introduced the concept that phase is expressed by,

(wt + phi0), where phi0 is the phase constant which is different for each waveform. WOW is that out of left field

How do you justify dumping phi0 through trig identities? It isn't "dumped" and it doesn't disappear; it is adjusted into an equivalent argument. I wanted to say "integrated into an equivalent argument, but that would have set off a new tangent for those that don't read for comprehension.)

None of us have ever seen this done, you included. YOU may never have seen it before, but several others have recognized it as valid.

Clearly, the phases of a sinusoid and its inverse are different. Your claim makes no sense! Which definition are you using? I said you can't keep pulling the arguments in and out.
True, the identity is valid, but your application of it is not. If it isn't valid for me it isn't valid for you.

Keep your applications straight!!!!

 

[mivey]

Do you understand what I mean now?

No I do not.

Well that's unfortunate. I've tried to be very plain in explaining what I mean. I have given examples that I felt would clearly demonstrate what I mean. At the moment, I can't think of a plainer way to put it.

If two people can't have a clear understanding between them about what the other person means, then there is little chance at debating each other's position. If I can think of another way to explain what I mean, then perhaps we can continue. At this point, I'll just have to let it go because we have reached a communications impasse and I see no way around it.

For now, I have a report to finish and I am out of spare time.

 

[rattus]

Keep your applications straight!!!!

The quantity φ is called the phase constant. It is determined by the initial conditions of the motion. If at t = 0 the object has its maximum displacement in the positive x-direction, then φ = 0, if it has its maximum displacement in the negative x-direction, then φ = π. If at t = 0 the particle is moving through its equilibrium position with maximum velocity in the negative x-direction then φ = π/2. The quantity ωt + φ is called the phase.

Already posted. It is clear that φ in this case is different for each wave.

Now just who supports your position? None of the text books do. None of the reference books do.

 

[rattus]

FWIW, I have seen mention of four phase, six phase, and hexaphase in textbooks. All involved center tapped transformers. Apparently the old heads believed an inversion created a phase, with its own unique phase constant.

 

[rattus]

Consider a 3-phase wye, and let the voltages be:

V1n = 120Vrms[(cos(wt +0) + jsin(wt + 0)]
V2n = 120Vrms[(cos(wt -120) + jsin(wt -120)]
V3n = 120Vrms[(cos(wt -240) + jsin(wt -240)]

Clearly, phi0 is set to 0, -120, and -240. It determines the starting points of each wave. Each wave clearly carries its own phase constant and that is phi0, or perhaps we should say, phi1, phi2, and phi3.

There is no point in setting phi0 to a constant value throughout the system. It is unique to its own wave.

 

[jim dungar]

FWIW, I have seen mention of four phase, six phase, and hexaphase in textbooks. All involved center tapped transformers. Apparently the old heads believed an inversion created a phase, with its own unique phase constant.

How many primary 'phases' are used to create a six-phase system?
Does the unique connection of multiple center-tapped transformer secondaries have anything to do with the hexaphase system?
How many loads are routinely connected Line-Line in these poly-phase systems?

This is why I have tried to stay out of the rabbit hole of polyphase sysems, except in a glancing touch.

 

[__dan]

FWIW, I have seen mention of four phase, six phase, and hexaphase in textbooks. All involved center tapped transformers. Apparently the old heads believed an inversion created a phase, with its own unique phase constant.

You are of course making the leap from 'it's named as an extra phase' to 'there is an extra phase'. Naming conventions have the uses, certainly. But spreading fear, uncertainty, and doubt is not one of the intended uses.

When the car rolls forward, do the front tires revolve in different directions or the same direction ? What if I am between the tires and rotate my head 180 deg (adding 180 to wt) to look at one tire then the other. Does this change the answer from the first question to the second. Is it valid to claim that a phase difference exists or that a phase difference has been created as an artifact of the measuring protocol.

Is the phase difference present in and created by the transformer or created by how the load is connected to the transformer or created by the choice of reference point?

 

[rattus]

How many primary 'phases' are used to create a six-phase system?
Does the unique connection of multiple center-tapped transformer secondaries have anything to do with the hexaphase system?
How many loads are routinely connected Line-Line in these poly-phase systems?

This is why I have tried to stay out of the rabbit hole of polyphase sysems, except in a glancing touch.

Point is Jim, that someone saw fit to label these systems with the number of phases that they saw. Others make the claim that phase is the same for all voltages in an ideal system although the phase constants are clearly different.

 

[rattus]

You are of course making the leap from 'it's named as an extra phase' to 'there is an extra phase'. Naming conventions have the uses, certainly. But spreading fear, uncertainty, and doubt is not one of the intended uses.

When the car rolls forward, do the front tires revolve in different directions or the same direction ? What if I am between the tires and rotate my head 180 deg (adding 180 to wt) to look at one tire then the other. Does this change the answer from the first question to the second. Is it valid to claim that a phase difference exists or that a phase difference has been created as an artifact of the measuring protocol.

Is the phase difference present in and created by the transformer or created by how the load is connected to the transformer or created by the choice of reference point?

I don't think it matters. According to the definition of phase, we have two phases in the single phase residential system, four in a four phase system, six in a six phase system.

 

[pfalcon]

120306-1712 EST

A classic way of defining simple harmonic motion is to use a disk of radius R and rotated at a uniform angular velocity. Pick a point on the radius of the disk and project the motion of that point to the Y axis. The result is a sinusoidal variation with angular rotation of the disk.

Add a second point on the radius displaced by some non-zero or non N*2*Pi angle, and a second, but separated simple harmonic motion is generated.

These two motions have identical shapes when plotted vs the angle of the shaft, but are displaced from each other by a "phase difference". That "phase difference" exists at zero velocity as well. Time does not have to be part of the phase difference definition.

Or, take the first point on the radius and drill a hole clear through. Chart the point on the Y axis from the front, then from the back. The two charts will have a 180 degree phase difference which will exist at zero velocity as well.

A different question for each of the responders.
Do you favor RPN calculators like HP, or so called algebraic like TI?

TI (Automatic Operating System? AOS). The option to type an equation exactly as written. The option to reduce keystrokes as low as RPN should I desire.

 

[pfalcon]

I don't think it matters. According to the definition of phase, we have two phases in the single phase residential system, four in a four phase system, six in a six phase system.

There are multiple definitions of phase in play.

Point is Jim, that someone saw fit to label these systems with the number of phases that they saw. Others make the claim that phase is the same for all voltages in an ideal system although the phase constants are clearly different.

Measurable phase constants are different therefore by (2) there are multiple phases. Where others are addressing definition (1).

Phase 1: The phase generated by the induction field that gives single-phase it's name.
Phase 2: The individual voltage readings that can be measured.
Phase 3: The individual current readings that can be measured.

Phase is an overloaded word just as the word duck is (duck beneath, also the water fowl). Therefore depending on which usage the poster is discussing may generate 1, 2, 4, 6, or infinite phases. All are legitimate answers depending on the usage in play. But only one usage gives the system it's name.

Follow my post back for more details but simply stated: Single phase has only one phase (1) but several measurable phases (2,3). The word is overloaded and the number of phases present is definitely defined by it's immediate use.

 

[rbalex]

Consider a 3-phase wye, and let the voltages be:

V1n = 120Vrms[(cos(wt +0) + jsin(wt + 0)]
V2n = 120Vrms[(cos(wt -120) + jsin(wt -120)]
V3n = 120Vrms[(cos(wt -240) + jsin(wt -240)]

Clearly, phi0 is set to 0, -120, and -240. It determines the starting points of each wave. Each wave clearly carries its own phase constant and that is phi0, or perhaps we should say, phi1, phi2, and phi3.

There is no point in setting phi0 to a constant value throughout the system. It is unique to its own wave.

Yes - So?

 

[rbalex]

I don't think it matters. According to the definition of phase, we have two phases in the single phase residential system, four in a four phase system, six in a six phase system.

Which definition was that? The "shell game - switch thing around indiscriminately " version or the "Just cause rattus sez so." version?

 

[rattus]

Phase and In-Phase

Phase and In-Phase

To be in phase, waves must meet these criteria:

They must of course be of the same frequency.

They must start at the same time. That is their phase constants must be equal providing that both waves are expressed as sines (or cosines)

If their phase constants are equal, the phases of both waves are equal.

If the waves are NOT in phase, their phase constants differ, therefore their phases are NOT equal.

Then it follows that out of phase waves cannot carry equal phases.

Then a wave and its inverse cannot be of the same phase.

Specifically V1n and V2n CANNOT carry the same phase.

Therefore it is UNTRUE that all waveforms in an ideal split phase system carry the same phase.