# Single Phase or Polyphase?

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#### jim dungar

##### Moderator
Staff member
So we have you down for camp #2: "I'm going to have to see if these voltages were taken from a single-phase transformer before I can tell if they actually have a 180? angular difference or if your meter is playing mathematical tricks on you." :grin:
If you treat the source as a black box you can analyze it any way you want.

If you want to connect multiple sources togther, how they are created is very important.

#### LarryFine

##### Master Electrician Electric Contractor Richmond VA
So we have you down for camp #2: "I'm going to have to see if these voltages were taken from a single-phase transformer before I can tell if they actually have a 180? angular difference or if your meter is playing mathematical tricks on you." :grin:
No, I'll just take several voltage measurements and then make up my mind.

If A-N + N-B > A-B, it's not 1ph.
If A-N + N-B = A-B, it is 1 ph.

#### gar

##### Senior Member
100324-0810 EST

sin (t) = sin (t + x) if and only if x = N*2*Pi

Anything else is a different phase.

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#### LarryFine

##### Master Electrician Electric Contractor Richmond VA
sin (t) = sin (t + x) if and only if x = N*2*Pi

Anything else is a different phase.
I sure wish I knew whether that means you agree with me.

#### gar

##### Senior Member
100325-0731 EST

Larry:

It probably means I do not agree with you.

If I have two sine waves that extend in time from minus infinity to + infinity, then only at phase shifts of integer multiplies of 360 degees are the waveforms in phase. Any other shift and the waveforms are of different phases. A phase shift of 0.000000000000000001 or smaller that is not precisely 0 makes the waveforms not identical in phase.

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#### LarryFine

##### Master Electrician Electric Contractor Richmond VA
Larry:

It probably means I do not agree with you.
Awww.

#### mivey

##### Senior Member
If you want to connect multiple sources togther, how they are created is very important.
It certainly can be a consideration, but still does not dictate what we choose to use as a reference. We can still wire our circuit using two voltages with opposing phase angles rather that two voltages with the same phase angle.

If you have a 120/240 volt source, what person in their right might would seek to add another transformer and bring in a different 120 volt source because they need a second 120 volt sources in phase opposition? It is not a math trick, it is a physical wiring connection that gives you two voltages that are not in phase.

What is confusing the whole deal seems to be the concept of reversing polarity. A phase just a single alternating emf across two wires. Chosing a polarity for one voltage does not dictate the polarity of the others. Some transformer connections even make use of the fact that you can use them in a polarity that is different from the others in the bank. What you wind up with is a physical difference in the output voltage, not a mere "math trick".

Truly if you swap the two wire ends, you have swapped the polarity and it is just the negative of the other. There is nothing that says there is a universal constant for determining which of the two wires should be the reference end.

The addition of the center-tap now gives us two different pairings. Now we have two voltages that are equal in magnitude. We can now supply two different circuits with two different emfs. We can choose to connect these so they can either have the same phase angle or not. It is a physical connection and is how the system is defined. The polarity of one voltage does not dictate the polarity of the other.

You will get the same voltages even if you use two completely different primary sources. Nothing in how these two voltages are created is going to ultimately determine how we use these two separate phases as far as the polarity is concerned.

The reason we call 120/240 single-phase is because that is how it is used. We have single-phase 240 volt loads, and single-phase 120 volt loads (two different sets of loads: one set for each side of the winding).

There is nothing that says we can't use the two 120 volt sources together in phase opposition to supply two phases to a two-phase load.

#### mivey

##### Senior Member
100325-0731 EST

Larry:

It probably means I do not agree with you.

If I have two sine waves that extend in time from minus infinity to + infinity, then only at phase shifts of integer multiplies of 360 degees are the waveforms in phase. Any other shift and the waveforms are of different phases. A phase shift of 0.000000000000000001 or smaller that is not precisely 0 makes the waveforms not identical in phase.

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Maybe one day we will be able to measure with enough resolution to find that magical point near 180 degrees where a physical phase difference turns into a simple math trick.

#### LarryFine

##### Master Electrician Electric Contractor Richmond VA
There is nothing that says we can't use the two 120 volt sources together in phase opposition to supply two phases to a two-phase load.
True, but with them wired in series with a neutral point, the line-to-line voltage will depend on the relative phase angles.

Only a 180-degree opposition will produce a line-to-line voltage twice that of the line-to-neutral voltage. (Okay, in theory.)

#### mivey

##### Senior Member
True, but with them wired in series with a neutral point, the line-to-line voltage will depend on the relative phase angles.

Only a 180-degree opposition will produce a line-to-line voltage twice that of the line-to-neutral voltage. (Okay, in theory.)
That is exactly right. With a 90? difference you will have a 1.414X (sqrt[2]) multiplier. With a 120? difference you will have a 1.73X (sqrt[3]) multiplier. But there is no reason why a 90? or 120? difference is any less of a math trick than a 180? difference.

It is a mathematical fact that applying a negative sign is the same as adding 180? to a number in polar form. The scalar math function and the polar math function just happen to coincide at that point. That does not turn the physics of the situation into a math trick.

Every now and then, something in the physical world matches a prime number. That just means the physical something is not a multiple of smaller whole-number physical somethings. It might be interesting, but does not hinder the physical world. Math is a tool that helps us model the physical world.

In fact, we hope that we can make the math agree with the physical world. We can take math and make things that do not model the physical world, but it is not helpful to the task at hand. We constantly strive to make models to describe what we see so we can predict behavior. We should be happy when the math agrees, not call it a math trick.

#### jim dungar

##### Moderator
Staff member
It certainly can be a consideration, but still does not dictate what we choose to use as a reference.

My point has been, that the number of 'phases' should not depend on the presence or absence of a neutral (the reference is arbitrary to the definition), you have been saying that the use of a neutral changes the number of phases (the choice of reference is critical to your definition).

There are industry standards for choosing reference points of transformer windings (these are based on the physics of transformers). I have been saying that these standards should be considered.

As you point out, some combinations of transformer windings are intended to be additive while others are subtractive. A common dry type single phase 120/240V 3-wire transformer is an additive connection of two 'in phase' windings X1->X2 plus X3->X4 (following ANSI convention). A common oil filled POCO 120/240V 3-terminal transformer is a single winding with a center tap where the X1 terminal defines the polarity of the secondary winding.

#### mivey

##### Senior Member
My point has been, that the number of 'phases' should not depend on the presence or absence of a neutral (the reference is arbitrary to the definition), you have been saying that the use of a neutral changes the number of phases (the choice of reference is critical to your definition).
It is simple to see that a two terminal transformer has but one voltage to offer. It is also simple to see that a three terminal transformer has more than one voltage offering. I don't see how you can say any different. You are trying to say that the voltages we take from the transformer must be used in phase. I disagree and say that we can use them in phase opposition as well.

With voltages in phase opposition, you can have a two-phase system of voltages serving a load that requires two voltages in phase opposition. If the voltages are in phase, you do not have one system, but you have two systems, each having one voltage and the voltages are serving single-phase loads.
There are industry standards for choosing reference points of transformer windings (these are based on the physics of transformers). I have been saying that these standards should be considered.
Industry standards for how the transformer terminals are labeled have nothing to do with what we decide to use as a reference when we take the voltages from the transformer. If you say there is, I say: Prove it. And pack plenty of provisions because you will be a long time finding the proof.
...is a single winding with a center tap where the X1 terminal defines the polarity of the secondary winding.
It is a polarity indicator for the transformer windings. It is not a polarity restriction for our circuit that means we have to use the voltages in a X1-X2-X3-X4 polarity.

#### gar

##### Senior Member
100326-1327 EST

This is a slight digression, but related.

It is common to parallel two secondaries that are in phase, and this should produce no circulating current because both voltages are assumed to be identical and therefore there is no voltage difference between them.

From a practical point of view there may be slight differences in both amplitude and phase. Because the subject of this thread is phase assume the amplitudes are identical but slight phase differences may exist. Then what is the voltage difference.

From trig identities:
sin t - sin (t + dT) = 2 * cos (t/2 + (t+dT)/2) * sin (t/2 - (t+dT)/2)
or
sin t - sin (t + dT) = 2 * cos (t + dT/2) * sin (dT/2)
If we work in degrees, for angles under 10 deg, then both sin and tan are approximately x * 0.0175 where x is in degrees.
Thus, sin (dT/2) is approximately 0.0175 * dT / 2. Then
sin t - sin (t + dT) = 0.0175 * dT * cos (t + dT/2)

Therefore, the amplitude in RMS is approximately 0.0175 * dT * Vrms of one input. At a 1 degree difference the approximate source voltage creating circulating current is 0.0175 * Vrms.

As you load the two secondaries the circulating current diminishes and becomes load current. This is all a function of the internal impedances of the secondaries.

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#### jim dungar

##### Moderator
Staff member
Industry standards for how the transformer terminals are labeled have nothing to do with what we decide to use as a reference when we take the voltages from the transformer.
You treat the transformer as a 'black box', and choose the phasing to make your math work. I choose to follow the industry standard of transformer connections when defining the number of phases, and my math also works.

I say two in-phase voltages add to a 1-phase 2-wire voltage or to a 1-phase 3-wire multi-voltage, how the load is wired is immaterial.

You say two out-of-phase voltages add(?) to a 1-phase 2-wire voltage or to a 2-phase 3-wire multi-voltage, how the load is wired is paramount.

#### jim dungar

##### Moderator
Staff member
It is common to parallel two secondaries that are in phase...
This is why it is important to consider (or at least acknowledge) the industry standard terminal identification methodology.

I say that a pair of series connected windings will create what appears to be 2 out-of-phase voltages when the neutral is used as a reference and what appears to be 2 in-phase voltages when an end point is used as a reference. However the construction of the transformer dictates the voltages' actual relationship to each other.

#### mivey

##### Senior Member
You treat the transformer as a 'black box', and choose the phasing to make your math work. I choose to follow the industry standard of transformer connections when defining the number of phases, and my math also works.
I have shown you where your method has inconsistencies.
I say two in-phase voltages add to a 1-phase 2-wire voltage or to a 1-phase 3-wire multi-voltage, how the load is wired is immaterial.

You say two out-of-phase voltages add(?) to a 1-phase 2-wire voltage or to a 2-phase 3-wire multi-voltage, how the load is wired is paramount.
The system wiring does make a difference. Grounding a particular terminal determines what voltages we have available for a system that uses the ground as a reference. That should be obvious.

Even a 3-phase wye can be used to supply three individual single-phase circuits as well as supplying one three-phase circuit (forgetting the two-phase debate for a moment). The transformer can be a source for both so we usually call it a source of the higher order: a three-phase source.

It is a matter of how we define the system of voltages being used. The source is capable of supplying more than one system type and we generally label it by the highest order system that it can provide.

#### mivey

##### Senior Member
This is why it is important to consider (or at least acknowledge) the industry standard terminal identification methodology.

I say that a pair of series connected windings will create what appears to be 2 out-of-phase voltages when the neutral is used as a reference and what appears to be 2 in-phase voltages when an end point is used as a reference. However the construction of the transformer dictates the voltages' actual relationship to each other.
The voltages not only appear to be out of phase, they really are out of phase if wired that way. The fundamental rule of defining a voltage is defining a reference point. The transformer absolutely does not by any stretch of the imagination tell us which terminal we must use as a reference point in our circuit. The relative voltage relationships of the windings and the wiring of our circuit are not the exact same thing.

#### gar

##### Senior Member
100326-1830 EST

I want to repeat the concept of an earlier post of mine.

If two voltages are identical, then you can parallel them with no resulting circulating current. This is the case if X1 and X3 are connected together, then the voltage difference between X2 and X4 is zero and X2 and X4 can be connected.

This is not the case when X2 is connected to X3, then the voltage difference between X1 and X4 is double that of either X1 to X2 or X3 to X4, and big sparks fly when X1 and X4 are connected together.

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#### jim dungar

##### Moderator
Staff member
The fundamental rule of defining a voltage is defining a reference point.

Your number of phases change when you move your reference, but you say I am being inconsistent.

Take our example of two identically connected 240 series connected windings with a (1) 240V load and (1) 480V load. For you to define the number of phases requires you to know which terminal of the transformer is the reference point, but you say we should ignore how it is connected.

#### jim dungar

##### Moderator
Staff member
100326-1830 EST

I want to repeat the concept of an earlier post of mine.

If two voltages are identical, then you can parallel them with no resulting circulating current. This is the case if X1 and X3 are connected together, then the voltage difference between X2 and X4 is zero and X2 and X4 can be connected.

This is not the case when X2 is connected to X3, then the voltage difference between X1 and X4 is double that of either X1 to X2 or X3 to X4, and big sparks fly when X1 and X4 are connected together.

The two 240V voltages are X1->X2 and X3->X4. They are in phase, based on industry convention.

When they are connected in series they remain two in phase voltages of X1->X23->X4, with a single resultant additive voltage of 480V.

So the transformer is connect using industry standards of X1->X23->X4. Now you come along and connect your o-scope to X23 and see 2 out of phase waveforms of X1->X23 and X4->X23, so you say they are out of phase. I connect my scope to X1 and I see 2 waveforms in phase of X1->X23 and X1->X4. The only change to the relationship of the two waveforms X1->X2 and X3->X4 has been how we connect the scope.

Or, are you saying that as soon as I connect two voltages in series a second phase is created because the magnitude of the sum of the voltages (X1-X4) is different than magnitude of each individual (X1-X23)?

I guess I am lost about your point "and big sparks fly when X1 and X4 are connected together." X1 and X4 are the opposite ends of effectively a single conductor, if they were at the same potential we would not have a voltage between them. But the same thing 'sparks will fly' can be said about both X1-X23 and X4-X23.

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