I published something like the following explanation before, on this Forum. I just edited it a bit to more closely answer this question of Wye versus Delta (that answer is at the bottom of this long page). For those who have not seen it before, I'll warn you that the following might be too "mathy" for the tastes of some readers. I have tried to keep the really tough math out, but math has to come into the discussion one way or another.
First of all, you should keep in the back of your mind that harmonics are pure fiction. They do not exist. They are a mathematical model of a real situation, but they are not real in themselves. The "real situation" that they are modeling is a voltage or current curve that does not look like a pure and simple sine wave.
What do I mean by "pure and simple sine wave"? I mean that every peak is constant in height, every valley is constant in depth, the time intervals between peaks and valleys are the same for every cycle, and the curve is smooth. But for some loads, the ones we call "non-linear," the voltage and/or current waves look jagged or clipped or otherwise just plain weird. From the start of one cycle to the start of the next, there is not one smooth positive half and one smooth negative half. Rather, there are lots of miniature peaks and valleys along the way to what should be a single positive peak, and lots more along the way to what should be a single negative peak.
Some brilliant mathematician long ago figured out that any weird wave form can be imitated, as closely to the original as you like, by adding together the following, pure and simple, sine waves:
? One sine wave based on 60 hertz,
? Plus another sine wave based on 2 times 60 hertz,
? Plus another sine wave based on 3 times 60 hertz,
? Plus another sine wave based on 4 times 60 hertz,
? Plus another sine wave based on 5 times 60 hertz,
? Plus another sine wave based on 6 times 60 hertz,
? Plus as many others as you need to make your imitation waveform look like the original.
Each of these sine waves is called a “harmonic.” The one based on 60 hertz is the “fundamental frequency.” The one based on 2 times 60 hertz is called the “second harmonic.” The one based on 3 times 60 hertz is called the “third harmonic.” That pattern continues as far as you want it to.
What you do to determine the amount of harmonics is to calculate how much of the 60 hertz, and how much of the 120 hertz, and how much of the 180 hertz, and how much of the 240 hertz, and how much of the others, you need to put together, to get a close enough approximation of the original signal. That is the real “mathy” part: calculating how much of each harmonic is present. Therefore, "harmonics" is simply a mathematician's tool for approximating a weird looking waveform by adding together a bunch of "more normal looking" sine waves.
The triplens harmonics are the ones that are 3 times, or 6 times, or 9 times, or 12 times, or some other factor of 3 times, the fundamental frequency of 60 hertz. Without going into the math, let me just say that in a power system, all the even harmonics (2nd, 4th, 6th, etc., or equivalently, 120 hertz, 240 hertz, 360 hertz, etc.) disappear. That is the reason that "triplens" is generally defined as the 3rd, 9th, 15th, 21st, and so forth (i.e., there is no 6th or 12th or 18th harmonic present).
Now look at a set of balanced, linear, garden-variety three phase currents. Phase A will be at its positive peak at the same moment that Phases B and C are each at one half of their negative peaks, so the sum is zero. At any moment in time, if you add the three currents, they will sum to zero. Phase B will reach its peak 120 degrees later than Phase A, and Phase C will reach its peak 120 degrees later than Phase B.
Now consider the 3rd harmonic. It runs at 180 hertz (3 times 60). That means that in the time it takes for the 60 hertz signal to go from zero to positive peak to zero to negative peak and back to zero, the 3rd harmonic will have gone through three positive peaks and three negative peaks. In other words, looking at the 3rd harmonic of Phase A, as compared to the original Phase A 60 hertz signal, the 3rd harmonic reaches one peak at the same point in time, and another peak at a point 120 degrees later, and still another peak at a point 240 degrees later.
Next, looking at the 3rd harmonic of Phase B, as compared to the original Phase B 60 hertz signal, the 3rd harmonic reaches peaks at the same point in time, and at a point 120 degrees later, and at a point 240 degrees later.
One again, now looking at the 3rd harmonic of Phase C, as compared to the original Phase C 60 hertz signal, the 3rd harmonic reaches peaks at the same point in time, and at a point 120 degrees later, and at a point 240 degrees later.
So all three phases (of the 3rd harmonics) are reaching peaks at zero degrees, and again at 120- degrees, and again at 240 degrees, and again every 120 degrees thereafter. All three Phases are doing this.
Can you see that one of the peaks of the three Phase A 3rd harmonic (lets call it the first peak of Phase A) will occur at the same point in time as one of the three peaks of the Phase B 3rd harmonic (lets call it the second peak of Phase B), and at the same time as one of the three peaks of the Phase C 3rd harmonic (lets call it the third peak of Phase C)? Put all three of the signals together on the same sheet of graph paper (or the same oscilloscope), and they will look to your eye as three identical signals. Kirchhoff's Law will then tell you that the three must add up to form the total current in the neutral, and that the total is three times any one of the (Phase A or B or C) 3rd harmonics alone.
This is the phenomenon that makes the difference between a WYE and a Delta configuration, as it pertains to triplens harmonics. In the Delta, the 180 hertz signal in the A winding is in perfect sync with the 180 hertz signal in the B winding, and both are in perfect sync with the 180 hertz signal in the C winding. This current will simply flow from one to the next to the next and back to the beginning. By contrast, in a WYE, the three will come together at the one point they have in common: the neutral point. This triplens harmonic current will therefore add together at that point, and you will get three times the current of any winding flowing through the neutral wire.