Single Phase Theroy

[SAC]

This is how I see it. "Phase" means "angle". No matter how many wires, if you can connect the loads in an appropriate manner such that the "angle" of the sine wave is the same for all the loads, it is a "single phase" system. Note that with a 120/240, it is possible to connect loads to the three appropriate conductor pairs such that voltage seen by the loads them will all have the same "angle". The "inversion" is really not a phase difference - it is a difference in how the loads are connected to the sources. If you see an inversion, you just need to reverse where the "positive" and "negative" terminals of the load are connected in order to "fix it". With references shown for "positive" and "negative" references:

(+)------------------- (+)
                  120v (a)
                       (-)
240v      (G) --------
                       (+)
                  120v (b)
(-)------------------- (-)

Loads connected to the 240v, 120v(a), and 120v(b) references all have the same "Phase".

 

[Rick Christopherson]

Which is accurate? My statement that an exclusive identification is silly, or the idea that an exclusive representation is made by the voltage waveform?

If you are thinking the latter: Given a waveform that is already cycling steadily and that the batteries could be any of the four combinations mentioned before, please identify any moment along that waveform that would allow you to identify which of the four configurations is exclusively represented. Hint: it would be impossible.

Ummm...the one where the current opposes the voltage....or the one where your Red Sharpie re-identification opposes the chemical equation of a battery.

I can't believe you guys are still arguing this topic after...what's it been...several years?!?!?

 

[greendriv]

http://forums.mikeholt.com/showthread.php?t=123720

Over 200 posts, for your reading pleasure.

Jim, thanks. I am interested about this topic too. Thanks for your answer.

 

[rattus]

This is how I see it. "Phase" means "angle". No matter how many wires, if you can connect the loads in an appropriate manner such that the "angle" of the sine wave is the same for all the loads, it is a "single phase" system. Note that with a 120/240, it is possible to connect loads to the three appropriate conductor pairs such that voltage seen by the loads them will all have the same "angle". The "inversion" is really not a phase difference - it is a difference in how the loads are connected to the sources. If you see an inversion, you just need to reverse where the "positive" and "negative" terminals of the load are connected in order to "fix it". With references shown for "positive" and "negative" references:

(+)------------------- (+)
                  120v (a)
                       (-)
240v      (G) --------
                       (+)
                  120v (b)
(-)------------------- (-)

Loads connected to the 240v, 120v(a), and 120v(b) references all have the same "Phase".

Yes, you can look at it this way, but why? Why have two references when one will do?

And, no one has provided anything more than an opinion that a phase inversion is somehow different from a phase shift of 180 degrees. You could be picky and claim that there is no lead or lag as we see in reactive circuits, but that is a weak argument.

It is a simple matter to show mathematically that an inverted sinusoid is identical to that sinusoid shifted 180 degrees.

So let's see a solid reference that proves that an inverted sinusoid is different from a phase shifted sinusoid.

 

[SAC]

Yes, you can look at it this way, but why? Why have two references when one will do?

And, no one has provided anything more than an opinion that a phase inversion is somehow different from a phase shift of 180 degrees. You could be picky and claim that there is no lead or lag as we see in reactive circuits, but that is a weak argument.

It is a simple matter to show mathematically that an inverted sinusoid is identical to that sinusoid shifted 180 degrees.

So let's see a solid reference that proves that an inverted sinusoid is different from a phase shifted sinusoid.

I look at it that way because it is simple, and seems to explain the industry terminology. Had the industry so chosen, it could have called such a service "two phase" - but it didn't. I present an explanation as to why that may be - the circuit can be arranged so that for analysis all sources really are the "same phase", including the sign. Engineering uses many such methods to simplify circuit analysis that are based on pragmatism in getting the problem solved, and not on mathematical purity. Are you saying that my explanation is at odds with the industry convention, or that you didn't agree with the lack of mathematical purity in my explanation?

 

[Rick Christopherson]

Are you saying that my explanation is at odds with the industry convention, or that you didn't agree with the lack of mathematical purity in my explanation?

The reason why this topic has been argued for several years and across several threads is simply a matter of how some posters choose to view the system, but then mistakenly "define" the system based on their point of reference, discounting all other views in the process.

An analogy to this would be driving down a road with a 55 mph speed limit, but the person connected their speedometer up backward, showing a negative vehicle speed. Then arguing that they couldn't possibly be speeding at 60 mph because their speed was negative 60 mph.

It is one thing to choose a reference point that some think is convenient, but it is an entirely different matter to define the system (for everyone else) based on that chosen reference point. The chosen reference point is the sole source of the negative sign or 180 degree phase angle. The electrons have not changed their relative direction of flow relative to the conductor(s) in the transformer, nor have you altered the chemical reaction in a battery by using a sharpie marker to re-identify the terminals.

The posters have chosen a relative reference point which is contradictory to the physical devices. At some point in the analysis, a negative sign must be injected to align the equations with the physical devices. Failure to do so will eventually lead to an analysis where the result opposes the physical movement of the electron flow. These same posters have concealed this negative sign in many forms during previous discussions in an effort to "force" their relative reference point to "appear" as though it were absolute.

 

[rattus]

I look at it that way because it is simple, and seems to explain the industry terminology. Had the industry so chosen, it could have called such a service "two phase" - but it didn't. I present an explanation as to why that may be - the circuit can be arranged so that for analysis all sources really are the "same phase", including the sign. Engineering uses many such methods to simplify circuit analysis that are based on pragmatism in getting the problem solved, and not on mathematical purity. Are you saying that my explanation is at odds with the industry convention, or that you didn't agree with the lack of mathematical purity in my explanation?

SAC, I am only saying that the notion that an inversion does not produce a 180 degree phase shift is false and there is no authoritative reference to support that false notion.

Now I must agree that this inverted waveform is not a second phase.

 

[SAC]

It is one thing to choose a reference point that some think is convenient, but it is an entirely different matter to define the system (for everyone else) based on that chosen reference point. The chosen reference point is the sole source of the negative sign or 180 degree phase angle. The electrons have not changed their relative direction of flow relative to the conductor(s) in the transformer, nor have you altered the chemical reaction in a battery by using a sharpie marker to re-identify the terminals.

The posters have chosen a relative reference point which is contradictory to the physical devices. At some point in the analysis, a negative sign must be injected to align the equations with the physical devices. Failure to do so will eventually lead to an analysis where the result opposes the physical movement of the electron flow. These same posters have concealed this negative sign in many forms during previous discussions in an effort to "force" their relative reference point to "appear" as though it were absolute.

Agreed. I don't believe the references I defined in my example system have that complexity. At any given point in time, all the defined references will have the same polarity. When the 240v (+) terminal is at a higher potential than the 240v (-) terminal, so will both the 120v (+) terminals be at a higher potential then their corresponding (-) terminal. So the references chosen are consistent with the physical behavior of the system. My guess is that some would prefer to always treat the (G) terminal as (-), though that doesn't seem to be a method that produces the most concise description of the system.

 

[SAC]

SAC, I am only saying that the notion that an inversion does not produce a 180 degree phase shift is false and there is no authoritative reference to support that false notion.

I agree that mathematically that is true for a sine wave. However, when talking about real-world single phase services it certainly isn't always true in practice. For example, consider a distortion in the phase that supplies the transformer for the single phase service in question, such as a clipping on the "positive" half of the cycle. Will the resulting waveforms on the two 120v sources resemble a 180? phase shift, or an inversion?

 

[mivey]

Ummm...the one where the current opposes the voltage....or the one where your Red Sharpie re-identification opposes the chemical equation of a battery.

As you know, an AC source is not quite the same as a DC source. That is why the analogy only works in part.

I can't believe you guys are still arguing this topic after...what's it been...several years?!?!?

And because there is a tendency by many to adopt convention without understanding the physical principles behind it, the question will continue to come up long after we are gone. I have no problem accepting the conventional notation (and it is what I use in the workplace), but I also choose to understand why the conventional notation works and to understand the limitations of that notation.

 

[mivey]

I look at it that way because it is simple, and seems to explain the industry terminology.

Correct. It is absolutely in line with industry notation.

Had the industry so chosen, it could have called such a service "two phase" - but it didn't.

Also correct. What many continue to fail to see is that both systems produce exactly the same output voltages. Both source systems are represented by the voltage outputs. Both sources map to exactly the same outputs.

A center-tapped transformer is a single-phase load on the primary system. It is the most reasonable means to get the voltage outputs being discussed. With that said, there is no reason one could not use two different 180 degree displaced sources (not just an inversion, but real 1/2 cycle time-shifted waveforms) to provide the exact same outputs.

I present an explanation as to why that may be - the circuit can be arranged so that for analysis all sources really are the "same phase", including the sign.

An absolutely valid option, but just as valid as the other option. Both systems can co-exist and could actually be tied together with no problem. Even though both systems exist with no difference (other than what would be observed at the time of creation), we only use one name (single-phase) and it is the name that makes the most sense to use.

The conventional use of one of the names does not mean the other system does not exists. To deny that would be denying the physics of the system.

 

[rattus]

I agree that mathematically that is true for a sine wave. However, when talking about real-world single phase services it certainly isn't always true in practice. For example, consider a distortion in the phase that supplies the transformer for the single phase service in question, such as a clipping on the "positive" half of the cycle. Will the resulting waveforms on the two 120v sources resemble a 180? phase shift, or an inversion?

I am of course speaking of pure sinusoids which are assumed in linear circuit analysis. Fact is that both V1n and V2n would be distorted, then neither waveform could carry a phase angle.

 

[mivey]

The reason why this topic has been argued for several years and across several threads is simply a matter of how some posters choose to view the system, but then mistakenly "define" the system based on their point of reference, discounting all other views in the process.

I think you err here. Some of us do not discount the other view but say that both are valid. It is not an either/or proposition because both the single-phase system and two-phase system produce the same output voltages in this unique case.

If you mean I discount the view that only one reference is valid, you are correct. I say both references are valid.

An analogy to this would be driving down a road with a 55 mph speed limit, but the person connected their speedometer up backward, showing a negative vehicle speed. Then arguing that they couldn't possibly be speeding at 60 mph because their speed was negative 60 mph.

It is not just about negative signs. It is the source that can be represented by the output voltages. I think a better analysis is to have a vehicle made of two front halves of front-wheel drive cars connected together moving up and down a two-way path (saw that on some show the other day where two teams competed to build a two-headed car).

Single-phase configuration: Connect them back-front-back-front and you would call the the direction of travel forward and backward. Connect them front-back-front-back and you would call the the direction of travel backward and forward. It would be the same direction of travel for both halves.

Two-phase configuration: Connect them front-back-back-front and the direction of travel would be opposite for both halves. Same for back-front-front-back.

Think about two single-phase sources with a 180? displacement:

Start with two waveforms that are actually shifted in time by 180?. You would have two separate single-phase sources. Let them have one ungrounded conductor and one grounded conductor for each source. Let V represent the voltage of the ungrounded conductor referenced to ground. Let V' represent the first source and let V" represent the time-shifted source.

Feed these two sources into two duplicate transformers with the ungrounded conductor on H2 for both (say H2' and H2"). V_H2'@0? = V_H2"@180?. There has been no finagling with the polarity of the transformers to get this phase difference. It is really a function of a shift in time, not just an inversion. On the load-side we have V_X2'@0? = V_X2"@180?.

How would you connect these two transformers to get a dual voltage output? To add transformer outputs, we make one connection of different terminals (X1'-X2'-tie-X1"-X2" or X2'-X1'-tie-X2"-X1"). To subtract transformer outputs, we make one connection of the same terminals (X1'-X2'-tie-X2"-X1" or X2'-X1'-tie-X1"-X2"). If we add two phase-opposed voltages we get zero output. If we subtract two phase-opposed voltages we get a 2V output.

Now think about two single-phase sources with a 0? displacement:

Start with two waveforms that are not shifted in time. You would have two separate single-phase sources. Let them have one ungrounded conductor and one grounded conductor for each source. Let V represent the voltage of the ungrounded conductor referenced to ground. Let V' represent the first source and let V" represent the second source.

Feed these two sources into two duplicate transformers with the ungrounded conductor on H2 for both (say H2' and H2"). V_H2'@0? = V_H2"@?. Again, there has been no finagling with the polarity of the transformers to get the phase agreement. On the load-side we have V_X2'@0? = V_X2"@180?.

How would you connect these two transformers to get a dual voltage output? To add transformer outputs, we make one connection of different terminals (X1'-X2'-tie-X1"-X2" or X2'-X1'-tie-X2"-X1"). To subtract transformer outputs, we make one connection of the same terminals (X1'-X2'-tie-X2"-X1" or X2'-X1'-tie-X1"-X2"). If we add two in-phase voltages we get a 2V output. If we subtract two in-phase voltages we get zero output.

Looking at both systems, we can obtain configurations that produce a 2V output.

In the second case (the in-phase case), we can actually replace the two in-phase sources with a single stronger source, then feed its flux through a single-phase transformer core with a center-tapped secondary to get the same voltage outputs we had before.

Alternatively, we could also combine the fluxes from the two sources in a common core but it would not be as efficient. Instead of using two separate fluxes, we were able to use a stronger source and a stronger single flux to get the same voltages we obtained before using two fluxes.

Also, this does not mean the case of using two fluxes created from two phase-opposed voltages no longer is a possibility. It simply means we choose to use the more efficient means of creating the voltages.

As for combining the fluxes in a phase-opposed case, we could combine the fluxes by subtraction, then send this combined flux through a single-phase core with a center-tapped secondary, then separate the flux back into two parts by feeding the center-tapped secondary through a pair of isolation transformers (i.e. separate cores) to get our original phase-opposed voltages back.

The point being, the output voltages can represent either type source configuration because both type sources (either in-phase or phase-opposed sources) can produce the exact same voltage outputs. Just because we chose one particular way of creating the voltages do not mean the voltages can't represent either source.

 

[mivey]

The electrons have not changed their relative direction of flow relative to the conductor(s) in the transformer

Not the point. The point is the difference in time can be represented by the phase-opposed voltages and unless we were there at the time of creation, it is impossible to tell the difference.

nor have you altered the chemical reaction in a battery by using a sharpie marker to re-identify the terminals.

Some batteries can be charged and discharged but that doesn't mean you have altered physics. Besides, to try to make the battery analogy work in the other post, the batteries were being flipped around in regular cycles to emulated the AC cycle (so we could always have a single direction of current from the battery cell but a cycling direction of current coming out of the battery box).

The posters have chosen a relative reference point which is contradictory to the physical devices.

Absolutely incorrect. See above. To me, it is not about how the voltages were created (a single transformer, two transformers, a phase-shifting function generator circuit, etc) but what kind of sources can the output voltages represent. The single-phase transformer is a single-phase transformer and the single flux through the single core makes that a given. The voltage waveforms are what I am discussing and they could have been created with a single transformer or multiple transformers.

At some point in the analysis, a negative sign must be injected to align the equations with the physical devices. Failure to do so will eventually lead to an analysis where the result opposes the physical movement of the electron flow.

Incorrect. It is about the movement of the electrons based on a relative point in time. The electrons from wave A started their life moving "forward" at time a. The electrons from wave B started their life moving "forward" at time a + 1/2 cycle. In other words, the B electrons were moving forward when the A electrons were moving back-wards. To get them to move in synchronization, we did indeed make a polarity change and tied the two strings together in reverse.

You are arguing the case (case #1) that all electrons in a single source were originally moving forward at the same time. To get the end result of them moving in opposite directions, we must break the source and align the halves in the opposite directions. I agree that is a valid case.

For a two-source scenario, you would arguing the case (case #2) that all electrons in both source were originally moving forward at the same time. To get the end result of them moving in opposite directions, we align the sources in the opposite directions. I agree that is a valid case.

I say there is also a case that exists (case #3) where the electrons in one source were originally moving in the opposite direction from the electrons in the other source at the same time. To get the end result of them moving in the same direction, we align them in opposite directions. You fail to recognize this as a valid case.

I do not say there is a case (case #4) where a single source has electrons moving in two different directions.

I do say that the electrons moving forward in half A and the electrons moving forward in half B can represent the two sources of case #2 aligned in the same direction, or the two sources of case #3 aligned in opposite directions and that it would be impossible for us to look at the steady-state output and tell the difference.

These same posters have concealed this negative sign in many forms during previous discussions

On the contrary, I am not trying to conceal anything, but rather show the nature of the physics of the system from a general standpoint rather than by its conventional name. I have tried my best to use different analogies and examples to clarify my statements, not conceal any part of it.

in an effort to "force" their relative reference point to "appear" as though it were absolute.

There is no absolute reference point. To define a voltage, one must either pick a reference point or accept one that someone else has already picked. I have argued that the selection of a reference point is a choice, not an absolute. X1 and X2 are BOTH valid choices.

 

[mivey]

My guess is that some would prefer to always treat the (G) terminal as (-), though that doesn't seem to be a method that produces the most concise description of the system.

Not always, but it is certainly a reasonable choice when feeding a load like a two-diode full-wave rectifier.

 

[rattus]

What is your preference?

What is your preference?

Mivey, which reference point would you use for:

4-wire wye?

3-wire 1-ph?

Delta?

 

[mivey]

I agree that mathematically that is true for a sine wave. However, when talking about real-world single phase services it certainly isn't always true in practice. For example, consider a distortion in the phase that supplies the transformer for the single phase service in question, such as a clipping on the "positive" half of the cycle. Will the resulting waveforms on the two 120v sources resemble a 180? phase shift, or an inversion?

Since we now have a time-creation reference, we can identify it as an inversion. Suppose the two secondary voltages were run through separate power conditioners to clean up the signal? Now you are back to two clean signals with no identifying marks.

A single-phase transformer is still a single-phase transformer. I'm not advocating calling it a two-phase transformer, I'm just saying it can provide exactly the same two voltage signals you could get from two individual single-phase transformers that were fed by two different 180? displaced voltages.

Suppose the two voltages were creating using a function generator that really provided two phase-opposed voltages? It would not make any difference as we would use the voltages the same way we did with the single-phase transformer.

You are mixing the method of creation with the voltages we have been supplied. The question is: what source systems can the voltages we have represent? Specific traditional methods do not cover all of the physics of the systems in general. That is the trouble with the labels we use not always matching the general physical case.

Other than efficiency and practicality, there would be nothing preventing the same two secondary voltages from being supplied by two different generators feeding two different transformers with 180? displaced voltages.

 

[mivey]

Mivey, which reference point would you use for:

4-wire wye?

3-wire 1-ph?

Delta?

Depends on the load and what I am doing.

 

[Rick Christopherson]

You guys crack me up with the amount of time and energy you spend defending your position. You base your position on the foundation of a grounded, center-tapped transformer with a zero reference at the grounded center-tap, yet as soon as someone calls attention to the common core of this transformer, you want to jump away like a hot potato into the hypothetical of isolated voltage sources and electrons with differing histories.

If you want to stick to hypotheticals, you won't get any argument from me, but I kind of think that the electrician(s) that started the discussion might call foul.

Pick your stance and stick with it. If you want to choose the phase shift and minus sign, then you need to also stick with isolated sources. If you want to represent this as real-world, then you are stuck with a common-core transformer and you can no longer interject your phase shift and minus sign. Rhetorical question: Does this also mean you have two isolated sources at the primary too?

The people you are misleading in these threads have the right to know that you are not referring to real-world applications.

 

[Rick Christopherson]

...... I'm just saying it can provide exactly the same two voltage signals you could get from two individual single-phase transformers that were fed by two different 180? displaced voltages.

I didn't notice this at the time of my previous posting, but nevertheless this is what should be strongly pointed out to those reading this thread.

The whole basis of this discussion is that you are dealing with non-real-world applications with isolated secondaries and isolated primaries. If either one of which is linked, then you can no longer interject your time shift.