How does harmonic phase shifting work including a detailed mathematical explanation to reduce system harmonics?

In this video, we're going to talk about a subject that a lot of people ask questions about-- harmonic cancellation with phase shifting transformers.

So with two variable frequency drives connected to a common bus and motors connected to those drives, the harmonics that come out of those typical six-pulse drives will have a current waveform that look like this. So the drives will look like this. And what happens is the total current is basically just two times that. So it's 1 plus 1 equals 2.

Before we put isolation transformers and phase-shifting transformers in here to get cancellation, we're going to demonstrate how harmonics add up on power systems. So we're going to go to a part of the system over here where we're actually going to show you how that works.

We're going to actually combine these harmonics from drives. We're going to put two different drives on and show how those harmonics add up together. So we'll turn one on. We'll take a look at the waveform.

And you see the harmonics coming out of one of the drives. And now, if we take a look at the harmonic spectrum, the harmonic spectrum from that has your typical fifth and seventh harmonics-- what you'd expect. And so the fifth harmonic right now is about 10.9 amps. Now if I turn on the second drive, what we end up with is about twice that amount of harmonic current. So as expected, 1 plus 1 equals 2, and that's the harmonics that come out of both drives.

Now what we're going to do is we're going to turn those drives off. And we're going to go back to the paper, and we're going to describe what happens when we put two drives on, but with phase-shifting transformers.

So now with phase-shifting transformers, we would put in this situation, where we have, for example, a delta y on one side-- delta y on one side-- and this could be a delta delta or, in fact, it could be a delta zigzag, which effectively gives you a 0 degree phase shift. So you get 0 degrees here and you get 30 degrees here. So the same harmonics come out of these drives that we saw in the other picture.

But what happens up here is this transformer has 0 degree phase shift of harmonics come out the same. This transformer, the harmonics kind of look like this, or the waveform kind of looks like this. And so when you add these two together, we get what's not now a six-pulse system, but rather a 12-pulse system. And we end up with a current that looks fairly linear. So let me show you that in the actual waveforms that we can see from the two drives coming on.

So I'm going to turn this over to a combination where we put one drive on. And if we look at that situation, we have the isolation transformer where we're going around. It's the delta delta transformer. Now if we look at the actual waveforms from that, the harmonics look very similar. But if we look at the actual waveforms, the harmonics look the same. But then when we put on the fourth drive, or the one that actually-- the other drive, where we have the phase shifting, or the 30-degree phase shift-- you can see that now we have what's similar to a 12-pulse situation.

So now if I get on my harmonic spectrum, we actually have the fifth and seventh go away. Now if we turn drive number one off, what we're going to see is the harmonic currents come back from that drive that's now on, the one that went through the delta y transformer. And we can now see that the wave shape is, as I showed you, a little bit different.

Now what's interesting about this is, let's just look at one of the harmonics, the fifth harmonic. And what we're going to do is we're going to look at the fifth harmonic here on phase A. And the fifth harmonic is 9 amps at minus 62 degrees. Now what we're going to do is we're going to turn that drive off and we're going to turn drive number one back on.

And we'll see that the harmonic currents from that drive come in at about the same amount or magnitude, about almost nine amps again, but the phase angle is about 114 degrees. So now if we put both of them on together-- we put the other drive on with it-- now we get that fifth and seventh to cancel out, but your 11th and 13th basically adds up together. So going back to the paper now, let's talk about how that worked.

Again, we had no phase shift here. So we expect the wave shape to add up to be similar-- or to go through the transformer and look very similar. This one here, the wave shape changed, and this is a 30-degree phase shift. So we're saying the fifth and seventh from here cancel with the fifth and seventh from here. And what happens is we don't end up with fifth and seventh flowing this way. So no fifth and seventh going this way, but we do end up with 11th and 13th-- which ends up being this 12-pulse system.

How does that work? Well, if you take each harmonic order-- the positive, negative, and zero sequence harmonics for each-- we say plus, minus, zero, plus, minus, zero. And that pattern continues. Plus, minus, zero, plus, minus. So if we look at just the fundamental, the fundamental we say is a vector or phaser that rotates in this direction.

So phase A's at zero, rotates this direction, phase B follows, and phase C follows that. So a negative sequence harmonic would actually rotate the opposite direction. So how do we get the fifth and seventh to cancel from one side to the other?

First of all, all of these harmonics on the left side stay exactly the same. The fifth harmonic on the right side is five times as fast as the 60-hertz. So the phase shift is 5 times 30 degrees, but it's actually in the opposite direction. It's a negative sequence harmonic. It's in the opposite direction of the 60-hertz. So if the 60-hertz is going ahead 30 degrees and this one goes the other direction 30 degrees but times 5, we end up with 150 degrees this way and 30 degrees this way. The net effect is 180 degrees.

It's like we always talk about two vehicles leaving at the same time going in opposite directions. One goes 30 this way-- 30 miles this way, or whatever-- and we say the other one goes 150 miles this way. The difference in that is 180 miles. In this case, we're 180 degrees out of phase.

And so what that actually means is when the fifth harmonic comes up from the bottom on this side, the fifth harmonic looks like this; and then when the fifth harmonic comes up from this side, it looks like exactly the opposite. So those two added together in this path up here go away, because they add up to zero.

And the seventh harmonic, because the seventh harmonic is a positive sequence harmonic, it actually rotates the same direction as the 60-hertz. So imagine 210 degrees, or seven times 30, going this way. 210 degrees. And we're going the same direction, or 30 degrees with the fundamentals. So the net difference, again, is 180 degrees. So as we look at the fifth and seventh coming up through power system, we're actually canceling out the fifth and seventh from both sides.

So as we wrap up, the key point here is we take two six-pulse drives, we put them through phase-shifting transformers, and we create a 12-pulse system. Seems complicated, but at the end of the day, as we saw with the minus 61 or so degrees and 114, 115 degrees positive, you saw the fifth harmonic was exactly almost equal and opposite, or 180 degrees apart. And that's how it works.