triple harmonics

[Sparky Joe]

Can anyone explain to me how triplens work, how they are created and why they can put more current on the neutral? doesn't this go against Kirchoff's law?

I think I have a good idea; on multiwire circuits where only the imbalance is handled by the neutral, when you get a triple harmonic: the third phase(in refferrence to the first) is actually on the same cycle as the triplen, though it cannot balance it because it itself hasn't 'pushed' as much current as it is trying to recieve.

Am I on the right track? Or is my own explanation too difficult to understand?

 

[infinity]

Here is the blue collar explanation of triplen harmonics. In the world of perfect sine waves in a 3 phase, 4 wire Wye system, the three phases will cancel each other in the neutral. When you start to add devices that distort the sine wave, such as some types of lighting ballasts or computer power supplies the current in the common neutral no longer cancels but becomes additive. This would theoretically allow the neutral current to become up to 1.73 times the phase current. There are some other posts here that give detailed engineering analysis of how this works. Trying searching the archived posts for a lot of debate on the theory of harmonics and who is pushing the entire concept.

 

[jtester]

A triplen harmonic is basically a 180 hz wave, 60x3. If you draw our typical 3 phase 60 hz waves, they cancel out because at any moment the sum of the three values of current equal zero. Draw out 3 60 hz sine waves each displaced by 120 degrees and you will see what I mean.

Now if you draw those waves displaced by 120 degrees as 180 hz waves, triplen harmonics, you will see that they peak at the same time. They do not cancel as in the 60 hz drawing.

That is the simple reason that they add.

Jim T

 

[charlie b]

Can anyone explain to me how triplens work, how they are created and why they can put more current on the neutral? doesn't this go against Kirchoff's law?

I'll give it a try. I'll start by saying that Kirchhoff's Law will remain intact. I'll then 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.

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. Therefore, "harmonics" is simply a mathematician's tool for approximating a weird looking waveform through the addition of 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.

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, In other words, 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 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.

 

[Sparky Joe]

Thanks for the very explanatory post, and I'll say that math doesn't bother me.
I don't think I was too far off base about the similar peaks creating the added current. But what you said makes much better sense.
So is it possible then to have a wave with several different frequencies in it? I guess what I'm asking is; is a cycle defined by how often it peaks? Being that, by your description it may peak several times within one standard 60Hz wave. Or does it have to drop below the refferrence to be called a cycle, or is that essentially what your mathematical description of a harmonic is describing, that there are actually several waves happening within one though only the outlying and stongest one is visible?
And is what causes these drops or peaks within a standard wave due to electronic switching devices 'sucking' power from the wave at that exact moment, then switching off to put on a corresponding peak?
Sorry if I sound like a child asking "why is the sky blue" and of course I will understand if don't get a response(mostly becasue what I've said makes no sense). But I do really appreciate the satisfying of my curiosity.
-Joe

 

[winnie]

Joe,

I do believe that you have the gist of it. This is really about looking at different aspects of the same thing. Here is me repeating much of what has been said above:

The frequency of a 'periodic function' is not defined by the zero crossings, but instead by the repetitions of the same shape. With something simple like a sine wave or a square wave, the repetitions of the same shape happen every other zero crossing. But with some sort of complex wave shape, you could have many zero crossings before you repeat, or with something simple like an AC voltage added to a larger DC voltage, you might have no zero crossings at all.

Any reasonable waveform can be considered as a sum of simpler waveforms. Each of these simpler waveforms will have its own frequency. So you can have a periodic function which has a _single_ frequency. But you could consider this periodic function to be a sum of different sine waves, each with its own frequency. As a very weak analogy, a trip North-East of 1 mile could be considered the _sum_ of a trip East of 0.71 miles and a trip North of 0.71 miles.

Similarly, a 60Hz _square wave_ could be considered the _sum_ of a 60Hz sine wave plus a 180Hz sine wave of 1/3 the amplitude plus a 300Hz sine wave of 1/5 the amplitude plus a 420Hz sine wave of 1/7 the amplitude.....These higher frequency sine waves are 'harmonic components'.

When you ask what causes harmonics, you need to first specify: voltage or current harmonics. Current harmonics are caused by any device that does not draw current exactly in proportion to the applied voltage. Power electronic devices that only conduct for a portion of the supply voltage waveform are a perfect example. Power electronic loads can create really ugly current consumption patterns, where the harmonic components are larger than the fundamental or base frequency component. These are current harmonics which can cause neutral overloading.

But the current harmonics will interact with the supply, and change the shape of the supplied voltage waveform. This changed voltage shape is called voltage harmonics, and it can cause interference with other loads on the system, even perfect sinusoidal loads.

-Jon

 

[catchtwentytwo]

Can anyone explain to me how triplens work, how they are created and why they can put more current on the neutral? doesn't this go against Kirchoff's law?

Take a look at some of the Application Notes at Fluke, especially:
Troubleshooting Harmonics http://us.fluke.com/usen/support/appnotes/default?category=AP_PQ(FlukeProducts)&parent=APP_NOTES(FlukeProducts)
Dranetz-BMI has some recorded training courses http://wpt.interwise.com/wpt/portal/dbtraining/default.asp?WhichTab=2
Just set the From:(mm/dd/yyyy) to 01/01/20001 to see all 3 pages.

 

[charlie b]

So is it possible then to have a wave with several different frequencies in it? I guess what I'm asking is; is a cycle defined by how often it peaks?

Winnie had the right answer to this question, but let me put it another way.

Don't start by thinking of sine waves or frequencies. Instead, look for patterns. If you see a series of ups and downs and zero crossings, at the end of which you see the same series begin again, and at the end of the second series you see it starting all over again, then you have a pattern. Pick a point and call it the beginning of the pattern. Figure out how much time elapses before the pattern begins again. Then figure out how many times the pattern repeats itself during a period of one second.

So you don't actually have "several different frequencies," you have only one. The number of times per second that the pattern repeats will be the frequency of that pattern.

But it is hard to work with a weird pattern of ups and downs and zero crossings. It is much easier to work with sine waves. That is where harmonic analysis comes into the picture. Any pattern that repeats itself can be modeled as a set of sine waves, as I described earlier. The analysis will tell you how much of each harmonic frequency (i.e., how much 60 hz, how much 120 hz, how much 180 hz, etc.) it would take to create a pattern that closely resembles the one you are trying to model.

Nowadays there are electronic devices that you could plug into the original signal and that will give you the results of a harmonic analysis. It will tell you about the various frequencies that are in the original signal. But you should keep in mind that this is just a mathematical model of the original signal. In truth, as I stated above, the original signal has one and only one frequency: the frequency at which it repeats its basic pattern.