Why is residential wiring known as single phase?

[rattus]

It would be very refreshing to have an honest debate without games and deflections.

Well, just answer the question in a straightforward manner.

 

[Besoeker]

Rather than editing after the fact: φ₀: 0, π/3, 2π/3.

There are six:

Vmsin(ωt)
Vmsin(ωt+π/3)
Vmsin(ωt+2π/3)
Vmsin(ωt+π)
Vmsin(ωt+4π/3)
Vmsin(ωt+5π/3)


All different.

 

[Besoeker]

You are using a legitimate mathematical transformation, but then trying to defend it as though it was a physical transformation. Stick to your mathematical transformation and all would be fine. But it would be really nice and really helpful if we could carry on an honest debate following proper debating etiquette.

If there isn't more than one phase, why does this circuit need two firing pulses per cycle to work correctly?

 

[T.M.Haja Sahib]

Well am I right or wrong? Is the phase of [-sin(wt + PI)] wt, or is it (wt + PI)?

Neither.It is -(wt+PI).Because -sin(wt + PI)= sin[-(wt + PI)].So,what is it you are right or wrong?

 

[rattus]

Neither.It is -(wt+PI).Because -sin(wt + PI)= sin[-(wt + PI)].So,what is it you are right or wrong?

It seems I have an extra PI in the expression. It should read:

Well am I right or wrong? Is the phase of [-sin(wt)] wt, or is it (wt + PI)?

 

[T.M.Haja Sahib]

It seems I have an extra PI in the expression. It should read:

Well am I right or wrong? Is the phase of [-sin(wt)] wt, or is it (wt + PI)?

You mean for extremely small values of 'wt'?

 

[rattus]

You mean for extremely small values of 'wt'?

Now where did you get that notion? There is no limit on the value of wt.

 

[Rick Christopherson]

If there isn't more than one phase, why does this circuit need two firing pulses per cycle to work correctly?

Since when do diodes care about phase? They don't. You misrepresent this as though phase was critical to the function. The reason why it works has nothing to do with how you measure the circuit. Diodes only care about being forward or reverse biased.

Actually, I see these are SCRs, which really makes this an asinine question since they can be triggered by anything, and you don't show the triggers. Nevertheless, the above comment is still true.

 

[rattus]

Since when do diodes care about phase? They don't. You misrepresent this as though phase was critical to the function. The reason why it works has nothing to do with how you measure the circuit. Diodes only care about being forward or reverse biased.

Actually, I see these are SCRs, which really makes this an asinine question since they can be triggered by anything, and you don't show the triggers. Nevertheless, the above comment is still true.

Rick, it is time to quit sniping and add something positive to the discussion!

 

[Rick Christopherson]

Database error made 2 posts

 

[gar]

120315-1025 EDT

Rick:

The circuit containing the diodes, SCRs, or other switches is very much dependent upon the phases connected to the circuit. This is why rbalex's comment that a hex-phase supply is nothing more than a "glorified three-phase" source is a useless description. This description does not improve communication.

If I have a 4 wire 3-phase Y source, 6 diodes, the Y neutral is the negative DC output, and the diodes connect with their anodes to the three 3-phase legs, and all the cathodes to the positive terminal of the filter capacitor, then how do I get a fundamental ripple frequency of 360 Hz from a 60 Hz source? You can't. The frequency will be 180 Hz. You needed a 6-phase input with one diode to each phase leg.

.

 

[Rick Christopherson]

The circuit containing the diodes, SCRs, or other switches is very much dependent upon the phases connected to the circuit. This is why rbalex's comment that a hex-phase supply is nothing more than a "glorified three-phase" source is a useless description. This description does not improve communication.

No, to say that it is phase dependent is a misstatement. Diodes are 2 terminal devices and do not care about phase. They only care about the polarity between those terminals. The way the question is worded specifically makes it appear that the system can only function if you view the voltages as phase opposed versus inversions. That is the part that is deliberately misleading.

It's also a circular argument based on mathematics, when mathematics are not part of my contention. I've made that quite clear.

 

[rbalex]

Besoeker supplied the following graphic is Post 2165 and accepted the following definition in Posts 1537 and 1539:



Definition:

Phase (of a periodic phenomenon ?(t), for a particular value of t) The fractional part t/P of the period P through which ? 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]

The actual definition is underlined. The parenthetic clarifies that the definition applies to periodic phenomena. The ?Note? states a non-mandatory convention.

In the graphic I see six periodic functions ? so the definition applies.

Since time is the only independent variable; I choose a common t₀ = 0 as the ?arbitrary origin.?

At t₀ = 0, two of the functions are zero and have identical periods of 360?. Throughout the period P, at any time t, they have the identical ?fractional part t/P of the period P through which ? has advanced relative to an arbitrary origin? (t₀).

Therefore, those two functions have the same phase.

For those that feel compelled to evaluate this analysis by dredging up and applying an alternate definition of ?same phase,? in the statement above, same is simply an adjective under definition 1a in the link. The ?relevant? factors within the definition are they are periodic functions with a common t_0, initial value and period. How this may or may not apply to other sets is NOT relevant to conventional 120/240V systems.

 

[rattus]

Besoeker supplied the following graphic is Post 2165 and accepted the following definition in Posts 1537 and 1539:

View attachment 6609

Definition:



The actual definition is underlined. The parenthetic clarifies that the definition applies to periodic phenomena. The ?Note? states a non-mandatory convention.

In the graphic I see six periodic functions ? so the definition applies.

Since time is the only independent variable; I choose a common t₀ = 0 as the ?arbitrary origin.?

At t₀ = 0, two of the functions are zero and have identical periods of 360?. Throughout the period P, at any time t, they have the identical ?fractional part t/P of the period P through which ? has advanced relative to an arbitrary origin? (t₀).

Therefore, those two functions have the same phase.

For those that feel compelled to evaluate this analysis by dredging up and applying an alternate definition of ?same phase,? in the statement above, same is simply an adjective under definition 1a in the link. The ?relevant? factors within the definition are they are periodic functions with a common t_0, initial value and period. How this may or may not apply to other sets is NOT relevant to conventional 120/240V systems.

Nonsense!

There are three pairs of inverses. Their zero points coincide, but their negative to positive crossings do not.

There are six phase constants, count them, six phases.

 

[rbalex]

Nonsense!

There are three pairs of inverses. Their zero points coincide, but their negative to positive crossings do not.

There are six phase constants, count them, six phases.

Yes - so? That isn't a requirement of the definition. What part of 'The “Note” states a non-mandatory convention," don't you understand? Or did you even read the definition?

 

[rbalex]

In my previous post only "but their negative to positive crossings do not" should have been in bold. Responding from an iPad is sometimes difficult to get the formatting straight.

 

[rattus]

Yes - so? That isn't a requirement of the definition. What part of 'The ?Note? states a non-mandatory convention," don't you understand? Or did you even read the definition?

The arbitrary reference applies to all waves in the system. By your thinking we could use a different reference for all six. Now would that make sense? We could claim there is only one phase if we measured all to different references.

It is clear as day. However you try to twist the definitions around, there are six different phase constants. There are six different phases.

 

[mivey]

If I may reword: Transformer connection are what they really are. The physical relationship between a transformer's terminals output are based on the reality of its connections.

And taking voltages from different terminals and in different winding directions produces the phase shifts we have in transformers.

Echoing back what I got from your wording: The assignment of voltage directions is mathematically equivalent to a phase shift.

Almost. The assignment of voltage directions is mathematically equivalent to a time shift. While they are not time shifts, taking voltages from different terminals and in different winding directions produce what we refer to as phase shifts.

Summarizing, what I infer from your wording:
The "physical realities" of of transformer connections can be ignored, it is only the arbitrary assignment of mathematical references that counts.

I would contend that your inference is not based on the evidence. It would not be possible for one to use the transformer configurations in my examples if one were to ignore the physical realities of the transformer connections.

 

[Rick Christopherson]

Almost. The assignment of voltage directions is mathematically equivalent to a time shift. While they are not time shifts, taking voltages from different terminals and in different winding directions produce what we refer to as phase shifts.

Thank you. This is correctly stated.

 

[mivey]

The reversal of polarity indicated does happen, but it happens at the output by the attachment of the connections to the transfomer.

Connecting to the transformer is how we get our voltages so what is your point? A voltage is defined by its reference. The current in the winding moves in the same linear direction for both halves. That has nothing to do with the positive voltage direction as I can also get currents moving in the same linear direction using phase-opposed voltages.

I have been saying I have both added and subtracted windings to change voltage as needed...Many different voltages and phase angles can be obtained.

Which is what I am saying, so where's the beef?

In the single phase example, an infinite variety of connection changes can only yield two different phase angles, 0 and 180, which is the special case of reversal of the leads polarity. All sums add linearly and there is no phase displacement in a second dimension. The 0 to 180 deg rotation is a one dimensional solution on the same line.

There is very little about AC that is one-dimensional. The complex math that we use with AC is not a one-dimensional operation, even for single-phase.