Single Phase vs. Two Phase

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steve066

Senior Member
There is still a lot of discussion that I believe revolves around the "single phase" vs. "two phase" argument. I completely stayed out of the 2500 post thread mostly because I thougth both "single phase" and "two phase" were equally correct.

Since then I've realized one name is more correct than the other name (at least in the mathmatical sense).

So how do we decide what to call single phase, and what to call two phase? I don't think that has been answered yet.

The general principle in math is to keep problems as simple as possible. If we can work a problem using only real numbers ,1,2, 3, 4.... and -1,-2,-3,-4.... that's how we work the problem. We don't add complex numbers or multiple dimensions.

For example, if we add 2+2=4, it is a one dimensional problem. We don't say its 2+0i + 2 +2i = 4 + 0i. Working the problem that way gives the correct answer, but its much more complex than necessary.

Likewise, if we are working a physics problem that deals in two dimensions (maybe the path of a projectile motion), we don't normally worry about the third dimension, and we certainly don't add a 4th dimension.

The same applies to AC circuits - we don't call a delta system a 12 phase system when we only have to work with 3 phases. We should only call a system 2 phase if there is some reason we can't work out all the details of a circuit by considering only one phase.
 

steve066

Senior Member
Here is the simple explaination, no phasor or vector math is necessary.

If we consider our center tapped transformer, make Va is the voltage on the bottom winding (from the bottom terminal to the center tap). The reference point for this voltage is the bottom terminal.

Make Vb is the voltage on the top winding (from the center tap to the top winding). The reference point for this voltage is the center tap.

Make Vc the voltage across both windings (from the bottom to the top). The reference point for this voltage is the bottom terminal.

All three voltages are in phase. The find the total voltage, we only have to add. Va+Vb = Vc.

Single phase, only one phase is necessary, and we don't even have to think about phase.

For example, Say Va = 2 volts at angle zero, and Vb = 2 volts. Then Vb is also at angle zero, and Vc is 4 volts at angle zero.

If you draw it out, it is intuitive, and no more complex than a DC circuit.
 

steve066

Senior Member
OK, one more post. Here is the mathmetical proof that a center tapped transformer is a single phase circuit. (As if the fact that the entire world calls it single phase isn't proof enough.)

Once again, if we can represent all the voltages with a single phase, that's what we do. In mathmatics, this is called linear independence. We don't write equations with 12 variables when only one variable will do. If you ever get the chance to learn some linear algebra, it will tell you more than you ever wanted to know about linear dependence and independece.

Here is an official looking definition from Wikipedia:

A linear combination of any system of vectors with all zero coefficients is zero vector of V. If this is the only way to express zero vector as a linear combination of v1, v2, …, vk then these vectors are linearly independent. Given a set of vectors that span a space, if any vector
f1290186a5d0b1ceab27f4e77c0c5d68.png
was a linear combination of other vectors (and so the set is not linearly independent), then the span would remain the same if we removed
f1290186a5d0b1ceab27f4e77c0c5d68.png
from the set. Thus, a set of linearly dependent vectors is redundant in the sense that a linearly independent subset will span the same subspace.

You can read more here: http://en.wikipedia.org/wiki/Linear_algebra

and here: http://en.wikipedia.org/wiki/Linearly_independent

What this tells us is that if we can write one voltage as a constant times another voltage, they are not independent. If they are not independent, they do not have different phases.

Its trivial to show using Va and Vb that if we use the center tap as the reference point, Va = -1 * Vb. Therefore, they are not independent, and they do not have different phases.

Perhaps some will object to calling a wave and its inverse in phase. Maybe its better to just say they are not of the same phase.

But the real focus should be on the fact that the two voltages are not independant. That alone makes the circuit single phase.
 
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iwire

Moderator
Staff member
Location
Massachusetts
Man this subject is really becoming the engineers version of ground up or down. :D

So much wasted effort, so much stress for the people involved.

For what? :?
 
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Strathead

Senior Member
Location
Ocala, Florida, USA
Occupation
Electrician/Estimator/Project Manager/Superintendent
I din't read the 1500 post threads, but this reminds me of something I learned in 1st year Geometry. Proofs and theorums. Proove that 2 plus 2 equals 4. You can only do this if you can proove that 1 plus 1 equals 2, but 1+1=2 is a theory. There is no proof. So all mathmatics is based on the theory that 1+1=2. So maybe it isn't single phase after all.:):D;):p:happyno::happyyes::roll:
 

rattus

Senior Member
There is still a lot of discussion that I believe revolves around the "single phase" vs. "two phase" argument. I completely stayed out of the 2500 post thread mostly because I thougth both "single phase" and "two phase" were equally correct.

Since then I've realized one name is more correct than the other name (at least in the mathmatical sense).

So how do we decide what to call single phase, and what to call two phase? I don't think that has been answered yet.

The general principle in math is to keep problems as simple as possible. If we can work a problem using only real numbers ,1,2, 3, 4.... and -1,-2,-3,-4.... that's how we work the problem. We don't add complex numbers or multiple dimensions.

For example, if we add 2+2=4, it is a one dimensional problem. We don't say its 2+0i + 2 +2i = 4 + 0i. Working the problem that way gives the correct answer, but its much more complex than necessary.

Likewise, if we are working a physics problem that deals in two dimensions (maybe the path of a projectile motion), we don't normally worry about the third dimension, and we certainly don't add a 4th dimension.

The same applies to AC circuits - we don't call a delta system a 12 phase system when we only have to work with 3 phases. We should only call a system 2 phase if there is some reason we can't work out all the details of a circuit by considering only one phase.

First, no one is saying we should call single phase service two phase. We are saying that the split phase service splits the secondary voltage into TWO voltages with TWO phase angles PI radians apart.
That is, we look at the voltages ON L1 and ON L2 relative to a common point which is the neutral. These voltages are what they are regardless of what we call them.

You can of course choose another reference point to make all voltages in phase. But, what if we need to know V2n (not Vn2), we would have to write,

V2n = -120Vrms@0

That is a bit clumsy I think.

Mivey has posted several references which show that the practice of using the neutral as a reference is well established. So why fight it? You can always do it your way.

BTW, V1n and Vn2 are in phase and of the same phase, but they are NOT inverses.
V1n and V2n are inverses, but they are neither in phase nor of the same phase.
A sine wave and its inverse CANNOT be in phase or of the same phase.
 
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K8MHZ

Senior Member
Location
Michigan. It's a beautiful peninsula, I've looked
Occupation
Electrician
Man this subject is really becoming the engineers version of ground up or down. :D

So much wasted effort, so much stress for the people involved.

For what? :?

To increase our carbon footprint.

Did you know Google's data center used just under 3 million mega watt hours in 2010? That's more than Salt Lake City.

I wonder what the MH servers draw.

Seriously, the discussion has similarities to a sort of an addiction. Or a virus. One you can't kill, it just keeps popping up on new threads.

From a mod point of view, if the discussion gets so heated that insults start to fly, the subject should be considered for inclusion in the taboo category.
 

Rick Christopherson

Senior Member
So how do we decide what to call single phase, and what to call two phase? I don't think that has been answered yet.
Actually it was answered several times. It's called single phase because there is only one physical phase, and the second phase is only an apparent phase; present only mathematically. That's what was revealed with the "noise" discussion that shows there is no physical phase shift.
 
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