# How does a three-phase transformer work with phases sharing a common core?

Google search reveals a lot of pictures of three-phase transformers. Looks like a common setup is to have three pairs of winding and a shared core. The core typically consists of three "bars" in parallel and each pair of windings is wrapped onto its own "bar" and the "bars" are connected on both ends so the core is closed and effectively it is one single core of complex shape and each pair of windings occupies its dedicated place on the core.

-----------  << the two horizontal bars are free
|    |    |
|    |    |  << windings are wrapped onto this vertical bars
|    |    |  << each pair occupies a separate bar
|    |    |
|    |    |
-----------


Now as I see it each phase will induce its own magnetic flux and since each phase is offset by 120 degrees its flux will also be offset and those three fluxes should mix and more or less annihilate each other (full annihilation should happen when all phases are loaded equally) and so the transformer should not output any power on the secondary windings. However three-phase transformers work just fine.

How does a three-phase transformer work with magnetic flux of each phase passing through the common core?

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Related – Dean Feb 17 '12 at 12:49
Did you ever heard about law of conservation of energy? It is one of the basic principles of our existence. The phases cannot "annihilate" themselves when put together. – Al Kepp Feb 17 '12 at 23:49
@Al Kepp: Actually current in the neutral wire is exactly zero when all phases are equally loaded - right because of currents summing up and "annihilating" each other. I expected fluxes to behave the same way. – sharptooth Feb 20 '12 at 6:14
@sharptooth: In an ideal 3-phase case, current goes forward and back in those 3 phase wires. It is not "annihilated" anywhere. Fourth wire isn't used, but that's not because of "annihilation" - it's because current goes in both directions in the three phase wires and doesn't need any additional wire. – Al Kepp Feb 20 '12 at 18:33

You are correct that in each winding, the magnetic field varies in phase with the current in the windings. What you're having a problem with is the concept of flux being 'annihilated' at where the cores are joined.

It's helpful here to think about 'magnetic circuits'. Think about a single phase transformer for a moment; the core completes a loop that passes through the windings, so the field from the windings has a closed path. Now think about a three phase transformer. Look at the phase A winding. It has a certain amount of field that needs to be returned from one end of the winding to the other. You could just close it on itself, and do the same with phases B and C, and have three separate single-phase transformers, and it would get the job done, but it would be wasteful of material. Consider that the phase relationship of the currents means that, at any given moment, the fields from phases B and C added together are equal and opposite to that of phase A. It doesn't matter which phase you look at, the fields from the other two add to cancel. You see, where you were surmising that the fields annihilated eachother, what in fact happens is that they complement one another, and provide the right amount of magnetic return path. This lets you use less core material, and so economics dictates that's the way to go.

It's a bit like what happens to the currents in a Y-connected three phase load; the currents sum to zero, but it's not that they annihilate one another, it's that they form balanced return paths for one another.

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I like the magnetic-circuit analogy. Magnetic fields don't have associated particles the way electric currents do, but they behave somewhat as though they do: a current through a coil of wire may be thought of as pushing magnetic "stuff" (flux) out one end which then wants to go around the coil and flow back in the other; anything that impedes this flow will receive energy. At any given time, in a vertically-mounted three-phase transformer, if two coils are moving a certain amount of flux upward, the third coil will move twice as much downward, thus letting flux move... – supercat Oct 15 '12 at 17:53
...smoothly, entirely within the transformer core. – supercat Oct 15 '12 at 17:54

The key here is that each individual core has the primary and secondary pairs for that phase on it. While you are correct that for the transformer as a whole the fluxes should sum to zero, in each individual core you effectively only see the flux for that particular phase - the entire flux does not pass through each of those cores.

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Then why use a closed single core instead of just three separate bars? – sharptooth Feb 16 '12 at 13:00
@sharptooth Maybe there is a neutral winding? – clabacchio Feb 16 '12 at 13:01
Efficiency would be my guess - closing the transformer means you aren't having to deal with losses from the flux outside the core. – Rory Alsop Feb 16 '12 at 13:02
@sharptooth - The magnetic flux is much higher for a closed core. Think of the magnetic lines which remain concentrated in the core instead of spreading through the air. – stevenvh Feb 18 '12 at 10:14

If the following commands are copied and pasted in MATLAB, you will have a triple phase in a period with frequency of 1.

t=0:0.000001:(2*pi); y1=220*sin(t-(pi/6));y2=220*sin((t-(pi/6))+(2*pi/3));y3=220*sin((t-(pi/6))+(4*pi/3)); plot(t,y1,t,y2,t,y3);grid on

Magnetic flux that flows in each leg of 3-phase transformer is same as three phase current waveforms. There are 6 important areas in a period because there are 3 phases which divide a period into three areas with 120 degrees, and in each area there are 2 phases that one of them is increasing and another one is decreasing and their curves will cut the other. So, every one of third is divided in two parts and we have 6 important areas. In every one of sixths; one phase core injects flux in other two phases' core or two phases core inject flux in one other phase core.

Blue Red Green

0 to pi/3 ↑ ↓ ↓ 1 phase is injecting

Pi/3 to 2pi/3 ↑ ↑ ↓ 2 phases are injecting

2pi/3 to pi ↓ ↑ ↓ 1 phase is injecting

Pi to 4pi/3 ↓ ↑ ↑ 2 phases are injecting

4pi/3 to 5pi/3 ↓ ↓ ↑ 1 phase is injecting

5pi/3 to 2pi ↑ ↓ ↑ 2 phases are injecting

But the most important thing that should not be ignored is; some fluxes are flowing into the oil of transformer and because of financial limitation it is ignored. But in power plant transformers I have seen these solutions: 1- Using 5 legs transformer core. In these transformers, there are two legs beside nearest phases and their volume is half of main legs. 2- Using shell type transformers which coils are covered with core and dispersal flux is very low. 3- Using core parts on transformer tanks that don't have any connection with the main core and make a less lose way for dispersal flux.

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Interesting answer, but it doesn't address the original question. – Dave Tweed Oct 15 '12 at 15:40