Why is residential wiring known as single phase?

[rattus]

Unprofessional!

Unprofessional!

No the argument of [-sin(wt)] is wt - by your own definition. Sin(wt) is -sin(wt + PI) by identity.

Then -sin(wt) = sin(wt + PI); which clearly shows the argument to be wt + PI

You ignored the negative sign! Again! No fair! Dirty pool! Unprofessional!

How do you justify that?

Where is the REFERENCE? Without a reference we must conclude that you don't know what you are taking about, or maybe just bamboozling us. I think it is the latter.

 

[rbalex]

Then -sin(wt) = sin(wt + PI); which clearly shows the argument to be wt + PI

You ignored the negative sign! Again! No fair! Dirty pool! Unprofessional!

How do you justify that?

Where is the REFERENCE? Without a reference we must conclude that you don't know what you are taking about, or maybe just bamboozling us. I think it is the latter.

Because that's how identities work - surely an MSEE from SMU would know that. The sign is irrelevant in any of the formal definitions.

 

[rattus]

Because that's how identities work - surely an MSEE from SMU would know that. The sign is irrelevant in any of the formal definitions.

You can drop the nonsense about identities. We know a sinusoid shifted by PI is the inverse of the unshifted wave.

The sign is NOT irrelevant to anyone who knows anything about mathematics.

If the sign is irrelevant, then -sin(wt) = sin(wt); when wt is 0 or PI

They taught me not to ignore negative signs on pain of failing the course.

Where is your REFERENCE??

 

[mivey]

Your identities merely show that a wave shifted by PI is the inverse of the unshifted wave. We already know that. So why keep harping about it as if you have discovered something new and mysterious?

Hear, Hear!

The sign is NOT irrelevant to anyone who knows anything about mathematics

Hear, Hear! X 2

The minus sign in front of the function is part of the phase constant and gives the other part of the path direction. The amplitude is the maximum distance from the center of oscillation and gives the path length. We don't have negative lengths.

 

[rattus]

Why sign matters:

Why sign matters:

Consider the function,

[-sin(wr)]

If we ignore the MINUS sign, we are left with sin(wt) and we come to the erroneous conclusion that the argument of [-sin(wt)] is (wt).

But if we include the MINUS sign, as the brackets indicate we should, we must first 'expand' (not reduce) the function to sin(wt + PI) with its true argument (wt + PI). The wave is shifted by PI, or -PI, take your pick, and its phase constant is (wt + PI).

That is how identities work!!

We now are back to the function we started with which just demonstrates that the majority of this discussion has been an exercise in nonsense!!

 

[gar]

120312-1011 EST

Many posts back I presented a question relative to a spinning disk kWh meter. I did not provide sufficient information in that post. I am somewhat repeating the question, but in a somewhat different form.

A spinning disk kWh meter is connected to a two wire single phase power company source. A 10 A resistive load is placed on the house side of the meter. The meter will spin forward at a speed proportional to the load current.
Meter speed = K * avg ( V_s*sin (wt) * I_load*sin (wt) )
Meter speed = K * V_s * I_load / 2

Change the device on the house side from a resistor to a generator of 10 A. What does the kWh meter do?
Relative to the voltage what is the phase angle of the current thru the meter and how does this compare with the phase angle when the house was a resistive load?

By rbalex's definition of same phase both the resistive load current and the generator current are the same phase.
Meter speed = K * avg ( V_s*sin (wt) * I_load*sin (wt + Pi) )
Meter speed = - K * avg ( V_s*sin (wt) * I_load*sin (wt) )
Meter speed = - K * V_s * I_load / 2
But the meter response is quite different. It runs backwards.

Why create a definition for "same phase" that does not agree with common usage, contributes no useful value in communication, and really creates problems? So we are back to a question of what "same" means.

.

 

[rattus]

Why create a definition for "same phase" that does not agree with common usage, contributes no useful value in communication, and really creates problems? So we are back to a question of what "same" means.

.

Hear! Hear!

I think it means 'nonsense'.

 

[jim dungar]

Here is a reference which provides access to a graphing java applet.
http://www.intmath.com/trigonometric-graphs/1-graphs-sine-cosine-amplitude.php

[h=2]Sine Graph Java Applet[/h]
It lets you enter an equation and then play with changing the magnitude. As you move between positive and negative values, you will notice the waveform never shifts in time (it stays at t0).
For example, the waveform for a*sin(x+PI) is identical to that of -a*sin(x).

 

[rattus]

Here is a reference which provides access to a graphing java applet.
http://www.intmath.com/trigonometric-graphs/1-graphs-sine-cosine-amplitude.php

[h=2]Sine Graph Java Applet[/h]
It lets you enter an equation and then play with changing the magnitude. As you move between positive and negative values, you will notice the waveform never shifts in time (it stays at t0).
For example, the waveform for a*sin(x+PI) is identical to that of -a*sin(x).

Yes, of course, we already know that. The crux of the matter though is the claim that wt is the argument of [-sin(wt)]. The brackets emphasize the fact that the MINUS sign must not be ignored.

 

[rbalex]

Other than my very first Post 51, I have always used a definition to work from (Post 132)

Since then, I have also accepted or proposed two additional definitions and used routinely accepted mathematical principles from trigonometry and algebra.

[1] Phase: The angular position of a quantity. For example, the phase of a function f(ωt+φ₀) as a function of time is: φ(t)= ωt+φ₀

[Weisstein, Eric W. "Phase." From MathWorld--A WolframWeb Resource. http://mathworld.wolfram.com/Phase.html:]

[2] Phase: Phase is the fractional part of a period through which time or the associated time angle wt has advanced from an arbitrary reference.

[Kerchner and Corcoran, Alternating-Current Circuits, Wiley,1951]

[3] phase (of a periodic phenomenon ƒ(t), for a particular value of t)The fractional part t/P of the period P through which ƒ has advanced relative to an arbitrary origin.

Note: The origin is usually taken at the last previous passage through zero from the negative to the positive direction.

[IEEE Std 100 The IEEE Standard Dictionary of Electrical and Electronic Terms]

​

All three definitions support my position when applied properly. That is: any voltage function V(t) of a conventional120/240V system may be written with an identical phase. That is:

V(t) = ?Vm Sin(ωt+φ₀+Nπ)

Since time (NOT displacement) is the only independent variable, (ωt+φ₀+Nπ) or its equivalent derived from an identity is the argument and phase of all voltage functions of a conventional 120/240V system.

Of course, no one else is obligated to use those definitions; they are simply the basis for my position. However the very point I made in Post 51 was, without a common definition, it is impossible to resolve the issue.

I can’t read minds either, but it seems to me that the “two-phase” advocates are putting the cart before the horse and prefer the effect rather than the cause to be the basis for defining phase. Edit Add: Sort of like the tides push the moon around the earth. I prefer the cause.

 

[gar]

120312-1203 EST

Jim:

Magnitude is a non-negative number. From http://en.wikipedia.org/wiki/Magnitude_(mathematics)

HistoryThe Greeks distinguished between several types of magnitude,[citation needed] including:

Positive fractions
Line segments (ordered by length)
Plane figures (ordered by area)
Solids (ordered by volume)
Angles (ordered by angular magnitude)
They proved that the first two could not be the same, or even isomorphic systems of magnitude.[citation needed] They did not consider negative magnitudes to be meaningful, and magnitude is still chiefly used in contexts in which zero is either the lowest size or less than all possible sizes.

From: http://en.wikipedia.org/wiki/Magnitude_(vector)

In linear algebra, functional analysis and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to all vectors in a vector space, other than the zero vector. A seminorm, on the other hand, is allowed to assign zero length to some non-zero vectors.

A simple example is the 2-dimensional Euclidean space R2 equipped with the Euclidean norm. Elements in this vector space (e.g., (3, 7)) are usually drawn as arrows in a 2-dimensional cartesian coordinate system starting at the origin (0, 0). The Euclidean norm assigns to each vector the length of its arrow. Because of this, the Euclidean norm is often known as the magnitude.

From: http://www.allaboutcircuits.com/vol_2/chpt_1/3.html
again magnitude relates to size, and size does not normally include something smaller than zero.

From: http://dictionary.reference.com/browse/magnitude

3. greatness of size or amount.

Thus, when the sine wave goes from k * sin wt to k * sin (wt + Pi), k is the non-negative magnitude of the waveform, there is a 180 degree phase shift. When you watch the output of an LVDT as it passes thru null there is actually a shift from 0 phase difference thru all values to Pi. If the LVDT was ideal, then there would be a discrete shift from 0 to Pi.

.

 

[mivey]

Here is a reference which provides access to a graphing java applet.
http://www.intmath.com/trigonometric-graphs/1-graphs-sine-cosine-amplitude.php

Sine Graph Java Applet


It lets you enter an equation and then play with changing the magnitude. As you move between positive and negative values, you will notice the waveform never shifts in time (it stays at t0).
For example, the waveform for a*sin(x+PI) is identical to that of -a*sin(x).

From your link:

Amplitude

The a in the expression y =a sinx represents the amplitude of the graph. It is an indication of how much energy the wave contains.

The amplitude is the distance from the "resting" position (otherwise known as the mean value or average value) of the curve. In the interactive above, the amplitude can be varied from 10 to 100 units.

Amplitude is always a positive quantity. We could write this using absolute value signs. For the curves y = a sin x,

amplitude = |a|

Sine Graph Java Applet

Here's another trigonometric graph interactive to play with. In this Java applet, you can vary the amplitude by using the slider at the bottom. You can also change the function to whatever you like. Try changing it to a*cos(x) and see that the amplitude changes as the value of a changes.

You can also see the effect of a negative in front of the a value.

In other words, the negative in front of the function is not part of the amplitude but is part of the phase constant.

 

[mivey]

Of course, no one else is obligated to use those definitions; they are simply the basis for my position.

The whole industry uses that same definition but does not reach the same conclusion as you. You are mis-using the definition. It is your position that is in error.

I said it before and I'll say it again: I know what you are ultimately trying to illustrate. There are ways to express what you are trying to illustrate. You are trying to force a bad extrapolation and it just will not work. There is a larger single-phase voltage but that does not mean that there are not two smaller voltages that can differ in phase.

Trying to manipulate the definition and math to conclude that two smaller phases have the same phase is not the same as saying two smaller phases can co-exist with a larger phase. A single-phase larger voltage can co-exist with smaller in-phase voltages, and a single-phase larger voltage can co-exist with smaller phase-opposed voltages.

 

[rbalex]

The whole industry uses that same definition but does not reach the same conclusion as you. ...

Well industry - as he is wont to do, the weasel that never accepted a formal defintion before has spoken for you. If you are of the "one - phase in a single phase system" it is time for you to speak foir yourselves.

 

[rattus]

Just the facts Ma'am!

Just the facts Ma'am!

Facts are that the secondary of a single phase transformer is center tapped. This CT is taken as a reference which defines two phases according to one definition.

These two phases manifest themselves as V1n on L1 and V2n on L2. They are of course inverses of each other, but one is no more real or important than the other. We know this without turning on a scope or concerning ourselves with the transformer wiring.

To say these waves are 'of the same phase' is ridiculous. Out of phase waveforms simply cannot be 'of the same phase'. Go figure.

Any attempt to misinterpret a trig identity to claim 'same phase' is even more ridiculous!

Still a single phase service though.

 

[__dan]

120312-1203 EST

Jim:

Magnitude is a non-negative number. From http://en.wikipedia.org/wiki/Magnitude_(mathematics)


From: http://en.wikipedia.org/wiki/Magnitude_(vector)


From: http://www.allaboutcircuits.com/vol_2/chpt_1/3.html
again magnitude relates to size, and size does not normally include something smaller than zero.

From: http://dictionary.reference.com/browse/magnitude


Thus, when the sine wave goes from k * sin wt to k * sin (wt + Pi), k is the non-negative magnitude of the waveform, there is a 180 degree phase shift. When you watch the output of an LVDT as it passes thru null there is actually a shift from 0 phase difference thru all values to Pi. If the LVDT was ideal, then there would be a discrete shift from 0 to Pi.

.

mmm, gar

The mathematical description is reducible to a one dimensional coordinate system. All possible connections and solutions to the two winding single core system reside linearly, along the same line. There is no variance or projection in a second dimension.

Thus, displacement or magnitude from the origin, with sign, is the essential quantity and the phase angle is the redundant, unecessary quantity. Except for the special case where rotation by 180 deg = multiplication by (-1), there is no application for the phase angle. Phase angle = zero for all other cases applying to the two secondary winding single core transformer. Recall your parters constant arguement to stop looking at the transformer. Looking at the actual does not support the arguement they are making.

Phase angle = 180 is an artifact of describing a one dimensional problem with a two dimensional polar coordinate system. An artifact of making the description unecessarily complex or obscuring the underlying actual. What is the phase angle if the measurememts are taken with a method that maintains consistency with the winding turn direction ? The transformer itself offers two windings that are consistent in turn direction. Your analysis does not clearly convey this, it conveys the opposite.

Recall this inquiry was for mechanics who have their hands on the terminals. Do you really want to instruct them, "forget about the sign (polarity wrt the winding turns direction) and pay attention to the phase shift". There is no phase angle other than the special case of reversing the leads 180 deg.

 

[__dan]

Facts are that the secondary of a single phase transformer is center tapped. This CT is taken as a reference which defines two phases according to one definition.

These two phases manifest themselves as V1n on L1 and V2n on L2. They are of course inverses of each other, but one is no more real or important than the other. We know this without turning on a scope or concerning ourselves with the transformer wiring.

To say these waves are 'of the same phase' is ridiculous. Out of phase waveforms simply cannot be 'of the same phase'. Go figure.

Any attempt to misinterpret a trig identity to claim 'same phase' is even more ridiculous!

Still a single phase service though.

Yes, but if I measure the sum at the output, I get 240 volts. If the voltage sources were truly 180 out of phase, their sum would be zero. They are in fact connected in series for you at the factory, so their voltages sum. Certainly you can reverse the leads 180 relative to the winding turn direction to make the scope display the artifact that supports your premise. However, the display artifact is something caused by you, by ignoring the winding turn direction, and your failure to maintain consistency with it. Recall your constant advice to forget the transformer. Your premise relies on forgetting the transformer.

Measure the voltage with a method that is consistent with the winding turn direction. This is the underlying physical reality provided to you by the factory. Given this requirement (include the transformer in your analysis), what is the phase shift.

 

[david luchini]

Yes, but if I measure the sum at the output, I get 240 volts. If the voltage sources were truly 180 out of phase, their sum would be zero. They are in fact connected in series for you at the factory, so their voltages sum.

This is not correct. I suggest that you too take Jim's refresher course on Phasors in post #1999.

zx
In a tail-to-point configuration we ADD the phasors together.
In a tail-to-tail or a point-point configuration we SUBTRACT them.

Two voltage phasors of 120<0 and 120<180 are connected tail-to-tail. They must be subtracted, not added to find the total voltage across both phasors together.

120<0 - 120<180 = 240<0.

 

[__dan]

This is not correct. I suggest that you too take Jim's refresher course on Phasors in post #1999.



Two voltage phasors of 120<0 and 120<180 are connected tail-to-tail. They must be subtracted, not added to find the total voltage across both phasors together.

120<0 - 120<180 = 240<0.

Look at the dot marking for a two winding single core secondary. The dots are arranged head to tail, not tail to tail. This is fixed and built for you at the factory.

Head to tail is correct, the phasors add, and the sum is 240 volts. The phase angle is added in the measuring process, how the leads are connected to the transformer, not internally by the transformer itself.

 

[david luchini]

Look at the dot marking for a two winding single core secondary. The dots are arranged head to tail, not tail to tail. This is fixed and built for you at the factory.

Head to tail is correct, the phasors add, and the sum is 240 volts. The phase angle is added in the measuring process, how the leads are connected to the transformer, not internally by the transformer itself.

It makes no difference where the dot markings are for a two winding single core secondary when performing circuit analysis. You can use any reference frame you want, but you must then use the proper convention to combine the two voltages.

You are free to use Van and Vnb. These phasors would be head-to-tail. 120<0 + 120 <0 = 240<0

You are free to use Van and Vbn. These phasors would be tail-to-tail. 120<0 - 120<180 = 240<0

You are free to use Vbn and Vna. These phasors would be head-to-tail. 120<180 + 120<180 = 240<180

You are free to use Vbn and Van. These phasors would be tail-to-tail. 120<180 - 120<0 = 240<180

It is incorrect to use Van and Vbn (tail-to-tail) and to ADD them together to find the voltage across both windings. The must be subtracted to find the voltage across both windings.