Transcript
Introduction to Even and Odd Harmonics
Good afternoon, everyone, and welcome to today’s webinar. Today, we are talking about even and odd harmonics. Vinnie here, with me, has written an interesting paper on not just what harmonic distortion is, but especially the difference between even and odd harmonics.
Just to back up a bit, harmonic distortion is a type of volt distortion and current distortion, where we have multiples of the six years fundamental that are present. This paper assumes that yous are somewhat familiar with the concept of harmonics in general. Most utilities see odd harmonics, odd multiples of six years, so the third harmonic, 120 hertz, the fifth harmonic, the seventh harmonic, and those are what utilities deal with every day, as the paper talks about.
Common Odd Harmonics
The third harmonic is very common in single-phase nonlinear loads, like residential situations. The fifth and seventh is very common in three-phase loads, like variable-frequency drives. Mathematically, you see this in terms of multiples of six, plus or minus once, so five and seven, 11 and 13, 17 and 19, or three-phase loads.
There are mathematical reasons why you see the third harmonic, the ninth harmonic, the so-called triplet harmonics, in single phase, and there’s multiples of six, plus or minus one, for three-phase loads.
Even Harmonics Are Rare
But what you don’t normally see are even harmonics, the second harmonic, 120 hertz, or in the fourth harmonic, 240 hertz. Those are almost never there, and as you go towards the 5-19 limits for voltage and current distortion, for shunt, for current, the even harmonic limits are very small, much lower than the odd harmonics.
You don’t see even harmonics very often. They’re not really talked about very often, and here, we’re talking about, one, why that is, what even harmonics are, and how to recognize this in a waveform. What Vinnie points out here is it’s interesting that, in the audio world, when you’re introducing distortion for a warm sound, even harmonics are a feature, not a problem.
Why Even Harmonics Cause Problems
But in the utility world, we don’t like even harmonics, and fundamentally, no pun intended there, that is because even harmonics will just create transformer saturation. An even harmonic is an asymmetry, mathematically, in the top half of the waveform versus the bottom half of the waveform.
In a sine wave, you’ve got a shape that’s above zero and a shape that is below zero, and if those are exactly the same, if one’s a mirror image of the other, mathematically, that translates into no even harmonics. You only have odd harmonics. If there’s any sort of difference in the shape from the top half of the waveform versus the bottom half of the waveform, that asymmetry mathematically means that there must be an even harmonic, one or more even harmonics present.
DC Bias and Transformer Saturation
Now, what that also translates into is an effective, basically DC value. Of course, the entire power grid is AC coupled. We’re going through transformers. Transformers don’t pass DC through them. If there’s a DC bias on a transformer winding, it will tend to saturate the core of the transformer, and as that core becomes saturated, it acts less and less like an ideal transformer and more like your coil of wire.
There’s only so much magnetic field that the coil can handle, and every cycle, if one half has more energy than the other, you’ll accumulate energy in that field until the core saturates. So transformers don’t like even harmonics because of that asymmetry, because of the effective DC component that is usually there with those even harmonics. It’s possible to have even harmonics without a DC value, but generally, an even harmonic translates into some sort of asymmetry that creates transformer PD and closer to saturation.
Loads and Even Harmonics
There’s nothing inherent in loads that cause them to only draw odd harmonics, but in reality, loads that draw even harmonics are less efficient from a power supply standpoint, so manufacturers don’t do that. Generally, they know that they’re not supposed to put even harmonic currents on the line, so you very rarely see this, except in the very simplest loads that are ultra-low power.
Like super low-power LED bulbs. Not like little bulbs that go in a fixture, but like undercounter lights, where it’s just a fraction of a watt. They may be just a single diode. Little, tiny loads like that, that are just a watt or less, half-wave rectifiers that put even harmonics on the line. But in the bulk of the system, you will not see many even harmonic loads. Again, there’s nothing inherent about loads that prevent that from happening. It’s just by design.
Visualizing Harmonics on a Sine Wave
Now, Vinnie has a very interesting visualizer here, and Vinnie can explain how it works.
Yeah. So this helps us kind of visualize what happens on the sine wave when we start adding these harmonics onto it. Typically, some form of loads have odd harmonics, as you can see that as we add, let’s say, some of the third, fifth, and seventh, it’s still symmetrical. The top half and the bottom half are still symmetrical, but when we actually add some of the even ones, we can see some of that asymmetry that we were talking about.
This helped me at least visualize it, because at the time, I could not visualize what was actually happening with it. But actually being able to visualize it with this tool helped a lot, and this is actually where the graph images come from on our whitepaper.
Even Harmonics in Audio Versus Power
What was interesting to me about this, too, was that it’s opposite in the audio world, and this is kind of like what got me introduced into the topic, where the tube amplifiers are extremely sought after because of their warm sound, and it’s because they have the second and the fourth even-order harmonics make the music sound full. But in comparison over here, power engineers will spend millions trying to eliminate the evens. That was kind of the introduction of it to me.
So, when you hear a transformer humming or buzzing, it’s never gonna sound pleasant and warm because there’s no even harmonics in that sound. It’s 60 hertz and then odd harmonics creating that buzz.
How the Human Ear Perceives Harmonics
What was interesting to me too about, from the sound wave, not to derail a little bit, but from what I understood is that if you look at the asymmetry of it, to the human ear, this is actually a lot smoother. The human ear has a range of some harmonics that it can hear, and what it does is kind of blur this, because we don’t hear all the harmonics so we can see.
But in general, we can see that this is a lot smoother to hear than if we have something choppy. That drastic drop over here is like a rigid drop, choppy, and that’s what doesn’t sound as right. It’ll sound off-tune to us where we may not know what we’re listening for, but we can tell when something’s kind of out of tune. Being able to visualize that helped me see that. But obviously, something like this that’s nice and smooth in the audio world is not good in the quality field. So it was a cool little parallel.
Viewing Even and Odd Harmonics in ProVision
Within ProVision and I believe in 3DS too, you can also see the distortion in terms of even versus odds. So if I pull up ProVision, going to pick a random recording, pick a random waveform. That’s a super clean sine wave. But let’s look at the harmonics and we can see the evens and the odds here.
But we can also launch a report. And here we have the total harmonic distortion, including all the harmonics and it’s extremely good, like 0.2%. But we also have the odds and the evens broken out separately. So this is the percent distortion from the evens, and the percentage distortion just from the odds.
If you have a significant fraction, like more than two or three tenths of a percent even harmonics here, that can indicate a problem. So, you can easily separate out the amount of distortion that is contributed by the odds and evens here in this report.
Thanks for attending everyone. Everyone have a great day. Thank you.
