Delta and 3rd harmonics

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megloff11x

Senior Member
Remembering that you used to remember... I recall that there was a derivation of the benefits of using a delta connection to reduce/eliminate 3rd harmonics. It's probably next to my car keys and a couple of unpaid bills...

Does anyone recall or can name the reference?

Thanks.

Matt
 

ron

Senior Member
The following was from http://www.pge.com/docs/pdfs/biz/power_quality/power_quality_notes/harmonics.pdf
Triplen harmonics cause circulating currents on the delta winding of a delta-wye transformer configuration. When current triplen harmonics on the neutral of a 3-phase 4-wire system reach the transformer, they are reflected to the delta-connected primary where they circulate. The result is transformer heating similar to that produced by unbalanced 3-phase current.​
 

ramsy

Roger Ruhle dba NoFixNoPay
Location
LA basin, CA
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Service Electrician 2020 NEC
Here's a snip from my reference. Please note, this perspective comes from a K-rated Xfmr MFG or OEM News Release, Corporate-controlled media, Marketing Dept., or carpet baggers, if you prefer.

"Transformers configured with a delta - wye connection help to reduce the effects of harmonics. The triplen harmonics are trapped and circulate in the delta primary of the transformer. Since most loads produce high levels of the 3rd harmonic (one of the triplens), the harmonic content reflected back to the source is reduced.

The circulating harmonics in the primary of the transformer creates heat because of their higher frequencies. For this reason, a transformer that can handle the excess heat is needed. This transformer is called a K-rated transformer."


The unqualified claim remains, do K-rated Delta's really trap, or cancel harmonics more than a Wye, and if so does it do so more cost/effectively than other harmonic-mitigating equipment. Any takers?
 
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jim dungar

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A true K-rated transformer is not designed to do anything (different than a non-k-rated one) except tolerate the additional heating caused by the circulating current.
 

charlie b

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Yes, the claim quoted above from the transformer manufacturer is true. Or at least it is true up to the point at which they claim that a K-rated transformer is needed.

There are other methods, including other transformer designs, that can also block or reduce harmonics. The advantage of the K-rated is, as has been said, that it can tolerate the additional heating. The disadvantage is that it permits the additional heating, and therefore requires additional capacity in the cooling system. So if you are doing a cost-benefit comparison, do not forget to take that factor into account.
 

wirenut1980

Senior Member
Location
Plainfield, IN
Can anyone explain why does a delta primary connected transformer "trap" the tripplen harmonic currents and wye does not? I read that the tripplen harmonics travel back to the source on the neutral, and once it hits the transformer is reflected onto the delta primary and circulates. Why does it not keep traveling up the primary lines? And why does it keep traveling upstream in a wye connected primary?
 

steve66

Senior Member
Location
Illinois
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Engineer
wirenut1980 said:
Can anyone explain why does a delta primary connected transformer "trap" the tripplen harmonic currents and wye does not? I read that the tripplen harmonics travel back to the source on the neutral, and once it hits the transformer is reflected onto the delta primary and circulates. Why does it not keep traveling up the primary lines? And why does it keep traveling upstream in a wye connected primary?

I've seen the proof (or at least a pretty good explination) within the last year, and I think it was on this forum. From what I recall, you can probably figure it out by drawing a phasor diagram for the transformers. The three voltages applied to a 3 phase transformer are all 1/3 of a cycle out of phase (5.55ms). But for the third harmonic, that same 5.55 ms equates to an entire cycle. So if you go around the delta and add up all the triplen voltages of each of the three windings (keeping careful track of the phases), they add up to zero.

But for a wye, there is no such thing as going around the loop and adding up the voltages. Each triplen voltage on each winding is applied directly to the input.

That's the best that I remember it.
 

charlie b

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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.
 
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steve66

Senior Member
Location
Illinois
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Engineer
Charlie:

I have to disagree with one minor point. I consider the harmonics to be very real - not just mathmatical tools.

If you have some perfect filters, you could take a complex wave (ie. anything that is not a perfect sine wave) and filter out each harmonic so you are left with only sine waves at different frequencies.

And if you had several sine wave generators, you could create one complex wave from different harmonics.

I think these two examples show that the harmonics are real things, not just abstract ideas.

I think it is kind of like a glass of water. It's usually not necessary to think of the water as billions of molecules. We just think of it as water. But the molecules are still real.

Steve
 

charlie b

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steve66 said:
I have to disagree with one minor point. I consider the harmonics to be very real - not just mathmatical tools.
You are more than welcome to do so. But I disagree back. Your analogy does not work. A glass of water really, really is composed of a large number of molecules. Molecules do not comprise an imaginary model of a real thing. They are themselves real things.

In a non-linear circuit, the thing that is real is the current flowing through the source, the conductors, and the load. Real and physical things (i.e., electrons) are moving through this conductive path, and the rate of their flow does not follow the pattern of a simple sine wave.

I can create a formula, using the set of sine waves I describe above, such that the plot of the formula as a function of time will very closely resemble the actual flow rate of real electrons. But my formula is a mathematical expression; it is not a real or physical thing. I can give you a set of numbers, or in a more practical manner I can have a computer calculate a set of numbers, and I can describe these numbers to you as the amount of harmonic content present in the original signal. But that description does not cause the mathematical model of harmonics to become a real thing.

The original signal was not created by taking a 60 hz signal, and adding a 120 hz signal, and adding a 180 hz signal, and adding a bunch of other signals. Rather, the original signal was created by imposing a voltage on a fluorescent light, or on a welder, or on a variable frequency drive, or on a computer power supply, or on some other non-linear load. That load caused a change in the pattern in which the current flows through it (i.e., change from sine wave to some other weird shape). Harmonics is just a convenient way to describe the non-linear current as the sum of a set of linear currents.
 
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kingpb

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SE USA as far as you can go
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I have to go with Steve.

The term harmonics refers to a distortion of the normally smooth power waveform. Harmonics are actual higher frequency voltages and currents superimposed onto the 60Hz system power, producing a distortion of the normal voltage or current waveform.

Both passive and active harmonic filters can be applied in specific situations. Passive harmonic filters are the most common and are always custom-designed for the application or site. Active harmonic filters are a relatively new technology that will gain market share quickly as their initial cost becomes competitive with the passive variety.

The computation and study of Fourier series, known as harmonic analysis, is a way to break up an arbitrary periodic function into a set of simple terms that can be plugged in, solved individually, and then recombined to obtain the solution to the original problem. But nevertheless, the simple terms, or harmonics are very real values of higher frequency voltages and currents. Harmonics are real quantities, not just a mathematical invention.
 

winnie

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Springfield, MA, USA
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Electric motor research
I fall someplace in between.

Harmonics are clearly a mathematical tool used to describe complex waveforms. But it is also IMHO correct to say that they are real and not simply mathematical expressions. The reason is that these _components_ of the complex waveform will have real physical effects.

If you take a current clamp and put it on the phase conductors, and connect this to a scope, you won't see a set of 10 different sinusoids, you will see a single complex waveform.

If I have a real balanced load, we real third harmonic component to the load current, this will put real current flow on the neutral at 3x the mains frequency. This current flow is a real thing, not just a mathematical expression.

So as I see it, harmonic is a mathematical tool to describe complex waveforms, but the component harmonics are as real as their effects on real systems.

-Jon
 

charlie b

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kingpb said:
I have to go with Steve.
And you are also most welcome to do so.

kingpb said:
Harmonics are actual higher frequency voltages and currents superimposed onto the 60Hz system power, producing a distortion of the normal voltage or current waveform.
No. There is only one current, and it looks weird. To break that single current down to a set of other currents is an analytical technique (with credit given to Mr. Fourier). The results of such an analysis is, well, analytical results. The results of such analysis is not electrons, it is numbers.

There is not a 180 hertz current flowing. There is not a 300 hertz current flowing. There is only one current flowing. It has a weird pattern, and it repeats that pattern 60 times every second.

Do you suppose this is one of those, “you say ‘po-TAAA-to,’ I say ‘po-TAHHH-to’ “ things?
 

wanderer20001us

Senior Member
Every mathmatical equation used in engineering/science/etc is an approximation used to describe and, more impotantly, predict the behavior of the physical world. If you buy into quantum physics and mechanics, the water molecules in the glass are no more 'real' than the harmonics in a given conductor. Let's just agree that molecules and harmonics both have measurable impacts.
 

charlie b

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wanderer20001us said:
Let's just agree that molecules and harmonics both have measurable impacts.
I'll buy that. But I still say it's "po-TAHHH-to." Let's just call the whole thing off.
 

ramsy

Roger Ruhle dba NoFixNoPay
Location
LA basin, CA
Occupation
Service Electrician 2020 NEC
Perhaps these nicely-numbered harmonics originate from the interference pattern of less-orderly mechanics. Like a vibrating string of a musical instrument, "wave form distortion" may more accurately describe what happens before the noise reflects within its confined chamber to cancel some waves then add to others, before settling on a nice, neat, harmonic pattern.

Reactors that filter non-linear loads or rectified noise may not be filters at all, but rather "pattern reflectors" if their reaction pattern is tuned to cancel out the source pattern (harmonic).

Steve & Charlie's description of a 3? Delta circulating 180Hz in a perfect-interference pattern, sounds similar to what modern 6 & 12 pulse bridge rectifiers are attempting, in order to mitigate power-supply noise.

I am now a believer, over-sized or K-factor Xfmrs are still needed for both Wye or Delta at critical-harmonic levels, but only 3? Delta's can cancel frequencies at 180Hz .
 

Sparky Joe

Member
Location
Salt Lake City
steve66 said:
I've seen the proof (or at least a pretty good explination) within the last year, and I think it was on this forum. From what I recall, you can probably figure it out by drawing a phasor diagram for the transformers. The three voltages applied to a 3 phase transformer are all 1/3 of a cycle out of phase (5.55ms). But for the third harmonic, that same 5.55 ms equates to an entire cycle. So if you go around the delta and add up all the triplen voltages of each of the three windings (keeping careful track of the phases), they add up to zero.

But for a wye, there is no such thing as going around the loop and adding up the voltages. Each triplen voltage on each winding is applied directly to the input.

That's the best that I remember it.

Just wanted to say Excellent Post
Thanks for the clarification
 

jtester

Senior Member
Location
Las Cruces N.M.
wirenut1980 said:
Can anyone explain why does a delta primary connected transformer "trap" the tripplen harmonic currents and wye does not? I read that the tripplen harmonics travel back to the source on the neutral, and once it hits the transformer is reflected onto the delta primary and circulates. Why does it not keep traveling up the primary lines? And why does it keep traveling upstream in a wye connected primary?

The posts explaining harmonics have been very interesting, but the answer to this question is much simpler, and doesn't require "cancelling harmonics" etc.

The answer is basded in symmetrical components again, and the connection for the zero sequence part of the delta wye transformer model.

That is quite complicated, but a simple analogy explains it well. A basic rule of transformer operation is that the load flowing in the secondary must flow in the primary. Picture a wye connected secondary, the harmonics flow in and out of the system from the phase wire to the transformer secondary. Note there is no alternate path from the system or from the transformer. The currents in the phase flow in the transformer coil.

The harmonics in the secondary must flow in the primary windings. Picture a wye primary. There is no place out of the winding but into the primary system. Therefor the harmonics will be transferred into the primary system also. Now picture a delta primary. The harmonics flowing in the delta connected winding don't have to flow in the primary phase, they can continue around the delta and complete the circuit without flowing in the primary system at all.

The harmonics aren't cancelled at all, they are given an alternate path to flow in a delta and are contained within the transformer.

Jim T
 
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