Why is residential wiring known as single phase?

[rbalex]

...Care to discuss Fibonacci expansion and retracement?
...

PLEASE don't start them off on that tangent!!!!

 

[rbalex]

Yes, sin(0) = 0 = sin(n*PI), but is that true for the general case? That is:

Is sin(wt) = sin(wt + phi0) where phi0 can be any value between 0 and 2PI?

Nope never said that either. But then, that wouldn't apply to a conventional 120/240V system - would it? As I said, keep your applications straight.

 

[rattus]

Math is loaded with periodic twisted functions and this does fascinate me. Can you be more specific? Care to discuss Fibonacci expansion and retracement?

wt is the period and phi0 is the phase constant. The sum (wt + phi0) is the phase, which is a time dependent function.

The sin function is the ratio of the opposite side of a triangle to the hypotenuse. For all values of y, when h != 0, the ratio y/h solves to a range of -1 to +1, or 0 to 360 deg, or 0 to 2pi radians. The phase is the instantaneous value of the ratio as a function of time, so this value naturally includes the period and the fixed phase constant.

Phase = wt for the case where phi0 = 0. Phi0 is a constant that is fixed and determined or provided to you by the system that you are observing. It can also be any fixed, arbitrary, reference point. If you reverse the polarity of your test leads, this has the effect of adding pi radians or 180 deg to the phase constant phi0. Note that this change to phi0 was caused by you and not by a change to the system under observation.

Similarly, as proposed by your partners, multiple and arbitrary changes to the system under observation can cause changes to the phase constant phi0. When you stop making arbitrary changes to the system under test, stop changing the parameters and definitions, phi0 will stop changing.

So, yes, I can also twist the parameters of the system under test, by either reversing the test leads of the instrument, or by other arbitrary means proposed, to change the phase constant of the resulting measurement, so that phi0 can be made to be any number that I choose.

I think you said the phase of sin(wt) is (wt) and the phase of sin(wt + phi0) is (wt + phi0), that is the arguments of the sine functions. In general the phases are not equal, right? Even if I let phi0 = PI? Right?

 

[rattus]

Nope never said that either. But then, that wouldn't apply to a conventional 120/240V system - would it? As I said, keep your applications straight.

Then the phases of sin(wt) and sin(wt + PI) are not equal, right?

 

[rbalex]

Then the phases of sin(wt) and sin(wt + PI) are not equal, right?

The expressions aren't equal, but by your defintion the, the phases are; i.e.,: "phase is the fractional part of a period through which time or the associated time angle wt has advanced from an arbitrary reference." If t₀ is the same and the period is the same, the phase is the same. (Edit add) as it applies to conventional 120/240V systems. You cannot keep indiscriminately pulling (wt + Phi0) in and out of the argument (or the definition). Time is the only relevant independent variable with respect to definiton of phase in a periodic function.

 

[mivey]

I don't understand what it is you are calling a physical shift. Nothing is physically moved, so this does not seem to be an appropriate term. I've never heard the term before, so I don't think I could agree that it is industry standard.

Appropriate or not, it is what is known as a phase shift in a transformer. It happens as I noted here:

Whether it is a 180? phase shift by inversion we use on the very front end to negate the 180? primary to secondary phase shift, or a phase shift due to taking voltages between different terminals and in different directions...

In fact, in the metering world, we use these physical phase shifts in the voltages taken from different points on the transformer windings. While these physical shifts do not produce time shifts, they are still known as phase-shifting transformers. These are being replaced in modern meters by electronic methods of shifting phases.

But more importantly, I am not levying an argument about naming conventions, because they are just that, conventions. I don't have a problem representing an inversion with a phase shift. That is quite common. What I take issue with is the distinction between a real phase shift and an apparent phase shift. Your own discussion even suggests when and why these are different. A real phase shift shifts the signal in time, but an apparent phase shift does not. This lack of a time shift is evident in the graphics that we both have now shown.

I agree there is no time shift. The phase shift is a result of a physical action like taking voltages between different terminals and in different directions. Even the polarity marks are based on inversions themselves for many transformers because we actually reverse the polarity to compensate for the 180? shift from the primary side to the secondary side.

 

[Rick Christopherson]

What is the phase of said function? Is it (wt + phi0)? Can you twist the math around to make the phase equal to (wt)? If you say you can, please justify your answer.

The reason why I keep pointing this out as "the pot calling the kettle black" is because you originally transformed (aka "twisted" to use your words) the original expression to introduce the phase constant, but then demand others provide some sort of reference to "untwist" your original transformation.

In other words, your argument is that it is OK for you to do it, but for someone else to either undo it, or never do it in the first place, then they must provide a reference to support the operation. That's a double-sided argument.

If you can perform this operation without reference, then others can undo it without reference. If you do it with reference, then the same reference permits it to be undone too.

 

[__dan]

I think you said the phase of sin(wt) is (wt) and the phase of sin(wt + phi0) is (wt + phi0), that is the arguments of the sine functions. In general the phases are not equal, right? Even if I let phi0 = PI? Right?

Recall your instructing me to subtract when I add, so if I follow the algorithm provided by you, I have a hard time remembering how many negative signs to throw into the equation, is it one, or two, or ..

sin(wt) = -sin(wt + PI). The phases are equal if we recall reversing the polarity of the leads relative to the winding turn directon when taking the second measurement. Adding the phase constant PI is a special case of multiplication by (-1).

 

[Rick Christopherson]

Appropriate or not, it is what is known as a phase shift in a transformer.

Let's take a moment and pause to discuss what is contended and what is not. I do not mean for this to sound snarky, but I couldn't care less what our industry considers to be "common usage". We all know that our industry has common usage that is known to be in error--current direction versus electron direction to be the most obvious. I am not arguing conventions or names. I am arguing the technical specifics because this is a technical discussion.

As an industry, we all agree that current flows from positive to negative by convention. This is all fine and well, unless someone states that this means electrons flow from positive to negative relative voltages. This may be considered an inappropriate use of the term "apparent", but the apparent current flows from positive to negative, but the real current flows from negative to positive.

Our industry (or at least part of it, because we know it is not universal) may call these inversions phase-shifts, but that does not automatically mean that convention is correct. Regardless what it is called, an inversion does not result in a time shift, but a real phase shift does result in a time shift.

---

Please don't take this comment as though it was harping, but I am still unclear about why you refer to these as "physical phase shifts". I have never heard it expressed that way, so I am unsure why this is considered "physical". From my perspective, nothing "physical" has changed, so I am unclear why this word appears in the description.

Forgive me. I spent the whole morning writing a lengthy status email to a client, so I have very few brain cells left at this point. If I misstated something above, please give me the benefit of doubt.

 

[rattus]

The expressions aren't equal, but by your defintion the, the phases are; i.e.,: "phase is the fractional part of a period through which time or the associated time angle wt has advanced from an arbitrary reference." If t₀ is the same and the period is the same, the phase is the same. (Edit add) as it applies to conventional 120/240V systems. You cannot keep indiscriminately pulling (wt + Phi0) in and out of the argument (or the definition). Time is the only relevant independent variable with respect to definiton of phase in a periodic function.

Yes, one could interpret it that way, but if one looks at the examples, ti becomes clear that phi0 is included. And, phase is commonly described as the argument of the sinusoid describing the wave. Consider now this excerpt from an article from the Net.

"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.'

http://electron9.phys.utk.edu/phys135d/modules/m9/oscillations.htm

The article is about simple harmonic motion, but the math is the same. Then given that phase is described as (wt + phi0), only when phi0 = 0 are the phases of the two functions equal.

 

[rbalex]

Yes, one could interpret it that way, ...

Which is the clearest and correct way.

 

[rattus]

Recall your instructing me to subtract when I add, so if I follow the algorithm provided by you, I have a hard time remembering how many negative signs to throw into the equation, is it one, or two, or ..

sin(wt) = -sin(wt + PI). The phases are equal if we recall reversing the polarity of the leads relative to the winding turn direction when taking the second measurement. Adding the phase constant PI is a special case of multiplication by (-1).

dan, forget the transformers. This is a trig identity which holds for all sine functions, whatever the application. This identity shows that the inverse of sin(wt + PI) is -sin(wt)--that's all.

BTW, I have put together a spreadsheet for adding and subtracting phasors. If you wish, I can provide it for you.

 

[rbalex]

Yes, one could interpret it that way, but if one looks at the examples, ti becomes clear that phi0 is included. And, phase is commonly described as the argument of the sinusoid describing the wave. Consider now this excerpt from an article from the Net.

"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.'

http://electron9.phys.utk.edu/phys135d/modules/m9/oscillations.htm

The article is about simple harmonic motion, but the math is the same. Then given that phase is described as (wt + phi0), only when phi0 = 0 are the phases of the two functions equal.

BTW you don't get to replace the definition indiscriminately either.

 

[rattus]

Which is the clearest and correct way.

Perhaps you would be kind enough to quote my ENTIRE statement.

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.

The statement in red clearly describes phase. Please don't ignore it or we will think you are playing dirty pool.

 

[rbalex]

Perhaps you would be kind enough to quote my ENTIRE statement.

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.

The statement in red clearly describes phase. Please don't ignore it or we will think you are playing dirty pool.

OK I did above. And if you want to commit to that then, as I've said time and again: Every valid voltage function in a conventional 120/240V system can be written in terms of the same ωt + φ or it's equivalent inverse BUT NOT BOTH.

 

[Besoeker]

Bes I apologize for not responding earlier.

No apology required.

Basically as I explained to Gar in 1740, if you limit your described system to the voltages you indicated, assuming a common t₀, all six voltage functions may still be written validly in terms reduced to ([ωt + φ₀]), ([ωt + φ₀]+ 120?) and ([ωt + φ₀]+ 240?) or (not both) their equivalent inverses; i.e., it is still a simple three-phase system if you don't introduce EVERY equivalent inverse into the argument mix. What genuinely creates "hexiphase" is the secondary delta connections (line to line) that are also valid; whether you use them or not. Depending on the secondary connection, (DyN1 or DyN11) the additional three phases would be ([ωt + φ₀]+30?), ([ωt + φ₀]+ 150?) and ([ωt + φ₀]+ 270?) or (not both) ([ωt + φ₀]-30?), ([ωt + φ₀]+ 90?) and ([ωt + φ₀]+ 210?) or their equivalent inverses. Need I say you don't get to use them indiscriminately either.

All the tags in there that show up when composing a response make that very difficult to read in plain English. So I've just picked out one point.

What genuinely creates "hexiphase" is the secondary delta connections (line to line)

There is no secondary delta connection. I should have thought that perfectly evident.
The arrangement shows six voltages. i have given the expression for each. All different.
That's why it's hexaphase.

 

[rattus]

OK I did above. And if you want to commit to that then, as I've said time and again: Every valid voltage function in a conventional 120/240V system can be written in terms of the same ωt + φ or it's equivalent inverse BUT NOT BOTH.

Then I choose to express V1n and V2n as:

V1n = 120Vrms(sin(wt) + 0)
V2n = 120Vrms(sin(wt) +/- PI)

These expressions describe a sine wave starting at 0, phi0 = 0
and its inverse, starting at PI, phi0 = PI.

We have two separate expressions starting at different points. Since phi0 determines the starting points of the sine waves, phi0 must be 0 in the first case and PI in the second. Therefore the phases are not equal. You cannot ignore PI in the second expression.

 

[rbalex]

No apology required.

All the tags in there that show up when composing a response make that very difficult to read in plain English. So I've just picked out one point.

There is no secondary delta connection. I should have thought that perfectly evident.
The arrangement shows six voltages. i have given the expression for each. All different.
That's why it's hexaphase.

I didn't say there were delta connections; in fact, I said whether you used them or not. But it requires both line-to-neutral and line-to-line (usually delta, but could be any line-to-line) voltage functions to require six phases to be identified.

If only the star connections are considered then only three phases are needed to be identified, assuming a common t₀; e.g., using your terms V_M Sin(ωt+5π√3) and -V_M Sin(ωt+5π√3) are a legitimate set written in terms of a single phase, [ωt+5π√3] since -Sin(ωt+5π√3) and Sin(ωt+2π√3) are trigonometric equivalents.

Not a biggie, but did you happen to check Post 132?

 

[rbalex]

Then I choose to express V1n and V2n as:

V1n = 120Vrms(sin(wt) + 0)
V2n = 120Vrms(sin(wt) +/- PI)

These expressions describe a sine wave starting at 0, phi0 = 0
and its inverse, starting at PI, phi0 = PI.

We have two separate expressions starting at different points. Since phi0 determines the starting points of the sine waves, phi0 must be 0 in the first case and PI in the second. Therefore the phases are not equal. You cannot ignore PI in the second expression.

However, V2n = -120Vrms(sin(wt)) is a legitimate substitution and both functions are in terms of "wt."

 

[Besoeker]

I didn't say there were delta connections;

What genuinely creates "hexiphase" is the secondary delta connections

That kinda sounds like you are saying there are delta secondary connections.
There aren't.