220v question

[David L Morse]

Please explain. If you have 2 voltages that are oscillating at the same frequency and one is at the peak positive voltage when the other is at the peak negative voltage, then in electrical terms, they are said to be 180 degrees out of phase. That is the situation you have with 240VAC. I must admit I can't remember hearing 240VAC referred to as 2 phase, but that doesn't seem to me to be too far from correct. I am curious about the teminology.

A two phase system has sources that differ by 180/2= 90(+/-180)degrees. A three phase system has 180/3=60(+/-180)degrees. The +/-180 is, as Chris said, invisible so for three phase we usually refer to the balanced 0 and+/-120 phases from 60-180=-120 and -60+180=120.

Three phase systems are used for power transmission because the symmetry optimizes transmission costs. Two phase is used for things like stepper motors.

Why is the 180degree difference hidden? Imagine having a phase meter. If you measure the phase of an ac signal between two wires as 0degrees you can then reverse the measurement probes and read 180degrees. The act of reversing the probes has not created a new phase, it merely shows the difference in reference points.

[Rick Christopherson]

A two phase system has sources that differ by 180/2= 90(+/-180)degrees. A three phase system has 180/3=60(+/-180)degrees. The +/-180 is, as Chris said, invisible so for three phase we usually refer to the balanced 0 and+/-120 phases from 60-180=-120 and -60+180=120.

Three phase systems are used for power transmission because the symmetry optimizes transmission costs. Two phase is used for things like stepper motors.

Why is the 180degree difference hidden? Imagine having a phase meter. If you measure the phase of an ac signal between two wires as 0degrees you can then reverse the measurement probes and read 180degrees. The act of reversing the probes has not created a new phase, it merely shows the difference in reference points.

Do you just make this stuff up as you go along? Why would you divide 180 by the number of phases, when a cycle is 360 degrees? Did you do that because you couldn't explain 2-phase and wanted something convenient?

There is also no such thing as +/-180 in the definition. Just because you moved your test probes, doesn't mean it redefines the system. So you don't start out at your 60 degrees and miraculously jump to 120 degrees by moving your probes. It's a sinusoidal function and mathematically defined as v(t) = V_mSin (ωt + Φ), where Φ is the phase shift of 0, 120, or 240.

[Art Mann]

You don't have two waveforms. You have a single waveform coming from the single winding of a center-tapped transformer. The only reason why you think you are seeing one voltage positive to the other's negative is because you have chosen a voltage reference point to be in the middle. That is the hidden minus sign I mentioned above.

Using the center tap as a common voltage reference point may be convenient to think about, but if you actually performed a circuit analysis on the system you would have the transformer simultaneously supplying and consuming power. The current and voltage in one half of the transformer would be in opposition.

In short, it is a 240 volt transformer, but we get the 120 volts by tapping into the middle of it.

Yes. I thought about it after I went to bed last night and decided it was a stupid idea. I guess there is no simple term that is self explanatory. I was thinking about someone who posted in another thread who seemed to have an idea that 240V is kind of like stacking two 1.5Vdc batteries end to end in series to get 3 volts. I was hoping to come up with an easy terminology that explained the difference.

[Rick Christopherson]

I was thinking about someone who posted in another thread who seemed to have an idea that 240V is kid of like stacking two 1.5Vdc batteries end to end in series to get 3 volts.

That's actually not a bad analogy, and I have used it in similar discussions. (Here is the graphic I created for that very topic 5 years ago on the Mike Holt Electrical forum.)

It is actually what reveals why you don't have a phase shift or inversion. If the two halves of the transformer were literally 180 degrees out of phase (or inverted), then you would never get 240 volts phase-to-phase (shown to the right below). When you reverse your voltmeter probes, it makes it appear to be inverted, but it is actually a double-negative, and the second minus sign is easy to overlook (shown to the left below). Changing the voltage probe orientation is analogous to taking a red magic marker and crossing out the +/- designations on the battery and writing your own on there. It doesn't physically change the battery, just the printing on the side of it.

[Ole Anderson]

I might have been the one to suggest that referring to 240 v as two phase would make sense. Well, while it makes common sense (1 hot for single phase 120, 2 hots for 240 ("2 phase") and 3 hots for 3 phase) for talking purposes, it certainly doesn't from a true electrical perspective. I under stood that when I Googled "three phase power" and got a bunch of these images, which I understand now to be how the wave form of each phase looks when displayed simultaneously: .

[David L Morse]

Do you just make this stuff up as you go along?

This post was in response to Art's question of why 2 phase is not 2 voltages that differ by 180degrees. Art is not the only person here to struggle with this, it's a common source of confusion and it doesn't seem to have been addressed in a way that makes it crystal clear to everyone. Lot's of people have asked Ole's question "why, if three phase is spaced 360/3 = 120 degrees isn't 2 phase 360/2 = 180 degrees?". So, if trying to come up with an explanation that gives a more intuitive understanding of some difficult concepts is "making it up as I go" then sure, mea culpa.

Why would you divide 180 by the number of phases, when a cycle is 360 degrees?

Because dividing 360 by the number of phases gives the wrong answer in all but a few special cases.

Did you do that because you couldn't explain 2-phase and wanted something convenient?

I can explain 2 phase just fine. It's dividing 360 by 2 that has that problem.

Well of course I want the formula to be convenient. Why should I have to use different formulas for even and odd number of phases and balanced or unbalanced configurations. One general solution that works for all cases is certainly to be preferred over multiple special formulas and should allow for better understanding of the underlying fundamentals.

Just because you moved your test probes, doesn't mean it redefines the system.

About that I said "The act of reversing the probes has not created a new phase, it merely shows the difference in reference points." so I think we are in agreement there. Reversing a pair of leads does not change the number of phases in a system.

So you don't start out at your 60 degrees and miraculously jump to 120degrees by moving your probes.

Agreed. If we start at 60degrees and then reverse the leads we (no miracle) jump to 240degrees (or -120degrees if the range switch on your phase meter is set to '-180 to +180' instead of '0 to 360').

Sorry Rick if you think some of the above are cheap shots but I felt I had to address all of your points. No offense intended. Let's move on to some ideas.

Start with a 2 pole 3 phase generator. We have three windings and if we make no connection between them we have six wires. Add a 2 pole three phase motor, again with three separate windings. If we are careful to observe polarity and sequence we can connect the windings on the generator to those on the the motor in such a way that the magnetic field inside the motor is a nearly exact replica of the field in the generator. This is a connection of winding to winding, six wires with no common points. Phase 1 winding of the generator is connected to Phase 1 winding of the motor. Phases 2 and 3 the same. It takes six wires to connect the generator to the motor. If we take one lead from each winding and connect them to a common point (call it ground or neutral if it helps) we can reduce the interconnect count to four. There are eight possible combinations (three windings with each having two possible connections =2^3 combinations) of common connection. Using the generator shaft as a reference we then can show eight different phase configurations, one from each of the connection options: [0,120,240], [60, 180, 300], [0,60,120], [60,120,180], [120,180, 240], [180, 240, 300], [240, 300, 0], and [300,0,60].

The left column is oscilloscope-like representations, the center column is phasor diagrams and the last column is a listing of the phase shifts relative to the generator axle.

Note that the first two configurations are really the same thing, differing only by a rotation of 60degrees. The last six are also related to one another by rotations of multiples of 60degrees. After removing rotationally similar configurations we are left with two fundamentally different arrangements. One is symmetrical and balanced [0,120,240] and the other is unbalanced [0,60,120]. They both work but only the balanced one can be used in a Delta configuration and the advantages of that are so great that you rarely, if ever, see unbalanced 3 phase. But regardless of which of the eight possibilities we choose the motor and generator can't tell the difference. The magnetic fields inside are identical no matter which wiring arrangement we use.

Looking at the 'scope plots we can also that the zero crossing are all equally spaced at 60degrees.

Moving on to 2 phase we can do the same analysis as was done for 3 phase and get the following:

Here we have 2^2=4 combinations but only one basic configuration, the other three are just shifted by multiples of 90degrees. There's no balanced arrangement here and so no equivalent to the 3 phase Delta configuration. Here again the zero crossings are evenly spaced at 90degrees.

To be complete we might as well look at single phase. 2^1=2 combinations which is really just one and it's 180degree rotated mate. Zero crossings separated by 180degrees.

We can now try to generalize this to an N phase system. Let's look at the generator (motor) first. This simplest rotary electromagnetic machine has two poles (there is no monopole magnet). For N phases the number of physical poles is #ofPoles*N = 2*N. These physical poles are evenly spaced at 360/2N degrees =180/N degrees. There are 2^N possible arrangements of winding connections with phase differences of various multiples of 180/N degrees. There are 2N zero crossings in a period with equal spacing of 180/N.

This applies for any N, even or odd. For the case of N odd two of the 2^N arrangements result in balanced configurations with phase spacing of 2*180/N degrees = 360/N degrees. These two balanced arrangements are displaced from one another by 180/N degrees.

So try this on for size:

For a polyphase system of N phases generated by a generator with equally spaced physical poles we can describe the relationship between those phases as follows:

Connect one lead from each phase to a common point such that you get a series of phases k*(180/N) where k=0..N-1 and then on any number of those reverse the leads to add a 180 degree shift.

That works for N even or odd. If N is odd you can reverse the leads k odd or k even and get a symmetrical system with equal angles between phases of 2*180/N = 360/N.

Here's how that works for N = 5.


On the left are the five phasors equally spaced at 36 degrees. The ones in red correspond to k = 1 and k = 3. Reversing the leads of thos two geneerator coils shifts the phase by 180 degrees leading to the phasor diagram on the right.

DISCLAIMER! The above is not intended to be a definition of polyphase systems. It applies to a limited number of cases and has many implied constraints. A polyphase system requires no logic to the selection of phase differences. The only real definition is that it's a number of sources that differ in phase. Here's the IEC definition:

Set of m interrelated sinusoidal integral quantities of the same kind, where m is an integer greater than one, all quantities having the same period but usually different phases

Note 1 – In some cases the phases differ by an integral multiple, including zero, of 2Pi .

Note 2 – Polyphase systems of voltages, electric currents and linked fluxes are commonly used.

Note 3 – The qualifiers two-phase, three-phase, four-phase, six-phase and twelve-phase are used for m = 2, 3, 4, 6, 12, respectively.

Note 4 – The concept of polyphase system can, under certain conditions, be extended to non-sinusoidal periodic quantities.

The high-leg delta transformer connection has phases of [0, 90, 120, 240]. It has four different phases so in a general way it could be called a four phase system except it's different from what we have already named four phase. Would you call it a mixed 2 phase / 3 phase system? How about six phase missing two phases? I guess it's a good thing someone already named it "high-leg delta".

With tapped transformers any polyphase system can be converted into any other. Google "Scott-T" for a transformer arrangement that converts between 2 phase and 3 phase.

[Art Mann]

The reason I changed my mind about calling 240VAC a "2 phase" voltage is the issue of the transformer. If there is no center tap on a 240VAC secondary, then you can simply tie one lead to some hard earth ground and measure 240VAC between it and the other lead. In that case, it is obviously not 2 phase. I don't know of an application that uses a transformer that way but there certainly could be. Come to think of it, you don't have to reference either lead to anything but the other.

Edit: I just read the David Morse explanation again and it finally made sense. It has been 30 years since I last studied the subject and I am more than a little rusty.