the magnetising current 9

[vijayppatel13]

The magnetising current inrush in a transformer is rich in 3rd harmonic?
yes or no?

 

[crisleon]

1. The magnetising current inrush in a transformer is "rich" in 3rd harmonic? yes or no?
NO
2. The magnetising current inrush in a transformer is "rich" in 2nd harmonic? yes or no?
YES

 

[jraef]

But his homework question doesn't pose any other scenarios!

"If I had eight hours to chop down a tree, I'd spend six sharpening my axe." -- Abraham Lincoln
For the best use of Eng-Tips, please click here -> faq731-376

 

[Skogsgurra]

I would say that third harmonics is a possibility. Yes - or no. Then again, what about first harmonics?

Gunnar Englund

http://www.gke.org

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100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

 

[electricpete]

I'm with Gunnar. There can definitely be a lot of 3rd harmonics in inrush. However 3rd harmonic also can show up from other power system and ct pheonomena. In contrast even harmonics don't show up from many sources other than inrush and turn out to be a reliable harmonic to use for harmonic restraint.

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[electricpete]

I have done a simulated inrush based on simple single-phase model with non-linear iron.

Results are attached. 3rd harmonic is 22% of fundamental.

Harmonic/Mag / Fraction of fundamental
1 34.10 1.000
2 10.81 0.317
3 7.42 0.217
4 1.10 0.032
5 0.23 0.007
6 0.70 0.021

I had a problem uploading spreadsheet, but did show a screenshot attached. Will keep trying to upload spreadsheet.



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[electricpete]

Sorry, the harmonic content that I listed in previous corresponded to a longer interval over which the dc decayed. I repeated over a shorter interval and resuls as follows:

Harmonic/Mag / Fraction of fundamental1 68.13 1.000
2 19.98 0.293
3 3.87 0.057
4 2.89 0.042
5 1.90 0.028
6 0.65 0.010

This time spreadsheet updated successfully (I made it smaller)

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[waross]

Now the question hangs on semantics.
Will 21.7% or 22% be considered "Rich".
A comment Pete;
I like to see trends rather than a single example. When dealing with non-linear issues, a single example may be misleading, unintentionally of course.
Can you easily plug in lower voltage levels (minus 10%, minus 20%)?
It will be interesting to see if the ratios of harmonics stay about the same and if different, how much and in what direction.
I suspect that a lower voltage may result in less saturation and lower harmonics, but how much less (and I may be wrong).
Yours
Bill


Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[electricpete]

I like to see trends rather than a single example. When dealing with non-linear issues, a single example may be misleading, unintentionally of course.

The spreadsheet is a tool/model for consideration. I think the contents (model) is pretty transparent, but then again I wrote it. Even without the any computer aides at all, I think we can easily say the typical inrush time waveform with sharp repeating peaks every 1/60th of a second will fourier transform into harmonics of 60 hz generally starting highest at 1st and decreasing from there including both even and odd harmonics. The spreadhsheet graphically illustrates this. How exacting an analysis is required to quantify these results and their variability depends on your purpose (I have no intent in investing time on it).

If you want to look at other scenarios, that is one advantage of a simulation over a measurement… you can vary parameters in attached spreadsheet to see effect. Voltage is one… Phase angle of closing is another…. Magnetic parameters is another. (Of course measurements have other advantages and measurements /simulations compliment each other imo). You are welcome to try it if you like… see instructions tab… don’t’ forget the F9.

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[jghrist]

See the attached for measured harmonics while energizing a 100-24.9 kV 30/40/50 MVA delta-grd wye transformer.

 

[dpc]

jghrist,

Very cool - thanks for sharing.

David Castor

http://www.cvoes.com

 

[electricpete]

I would like to mention that particular transformer posted by jghrist has a distintive feature that the 3rd harmonic is very close to zero. I believe that aspect is representative of some but not all transformers (not that anyone said it was).

Some references below imply regarding the presence of 3rd harmonic in the inrush current :

"Typical inrush currents contain substantial amounts of second and third harmonics and diminishing amounts of higher orders."

[quote="Art and Science of Protective Relaying" by G.E.]
Harmonic Component Amplitude in Percent of Fundamental
2nd 63.0
3rd 26.8
4th 5.1
5th 4.1
6th 3.7
7th 2.4[/quote]

[quote="Power System Protection" by Anderson]
3. Third harmonic. The inrush current also contains large amounts of third harmonic
current, in about the same proportion as the second harmonic. In three-phase transformers,
the third harmonic currents in the three phases are all in phase, and may not
appear in the line current of delta connected banks. It is also important to note that
third harmonics currents are likely to flow as the result of CT saturation.[/quote]

I focused on 3rd harmoinc above because that was the question. And as we all know 2nd is more useful for discrimination of inrush.

Also I'd like to apologize to Bill / waross.... rereading my reply above sounds like some kind of over-reaction. Your very point is the one that I repeated in this post.

Also that post of mine seemed to imply that it would be valuable for someone to run my simulation with various values to study it... which is just plain silly because that model is very crude to begin with (no 3-phase attributes, no residual magnetism, etc etc). If the word "model" implies something fancy, that's not what that spreadsheet is.


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[waross]

No problem Pete.
What I am wondering: How to phrase this?
I understand that inrush may be mitigated somewhat by first energizing at a lower voltage and then stepping up to working voltage.
With that understanding, I wonder if the ratio of the harmonics would be the same in a transformer energized at 80% or 90% of normal voltage as the ratio when energized at full voltage.
This information may then transfer to transformers designed to work at different flux densities.
I understand that 2nd harmonics result from saturation and odd harmonics result from a distorted waveform. These effects are related but may not be exactly the same.
Yours
Bill

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[electricpete]

Attached I did what Bill suggested, vary the voltages. Summary is in slide 1 and repeated below:

H 100% 90% 80% 70% 60
1 1.00 1.00 1.00 1.00 1.00
2 0.29 0.32 0.36 0.41 0.47
3 0.06 0.04 0.02 0.02 0.09
4 0.04 0.05 0.07 0.07 0.06
5 0.03 0.02 0.01 0.01 0.05
6 0.01 0.02 0.03 0.03 0.01

For this particular model, there is a clear pattern that as we increase voltage, the 3rd harmonic goes up and the 2nd harmonic goes down. What is the conclusion, I'm not sure, but I'm open to comments what insight this gives and how it might relate to real transformers.

fwiw, in slide 8, I included Fourier analysis of a what would be current output of a halfwave rectifier feeding a resistive load (sin pulse for half cycle, zero for other half of cycle).
1.00 1.00
2.00 0.25
3.00 0.11
4.00 0.06
5.00 0.04
6.0 0.03
It is of course not a realistic recreation of a transformer inrush, but it is the simplest waveform that resembles the transformer inrush and has the advantage that you could calcualte it by algebra (instead of numerically). But I was too lazy to do that.

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[electricpete]

Whoops, the 3rd harmonic actually changes direction. I added one more point on each end to verify that. Results below and updated powerpoint attached.

H 110% 100% 90% 80% 70% 60% 50%
1 1.00 1.00 1.00 1.00 1.00 1.00 1.00
2 0.27 0.29 0.32 0.36 0.41 0.47 0.53
3 0.07 0.06 0.04 0.02 0.02 0.09 0.21
4 0.03 0.04 0.05 0.07 0.07 0.06 0.01
5 0.03 0.03 0.02 0.01 0.01 0.05 0.05
6 0.00 0.01 0.02 0.03 0.03 0.01 0.04

Does it mean anything to you Bill? I'm not sure what to make of it.

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[electricpete]

Attached is corrected slide for 100% voltage
My apologies for excess number of posts.
I'm done now.

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[waross]

Thanks Pete. That's great. Have another lps
The numbers seem to be going in the opposite direction to what I expected. Now I'm going to spend a few days digesting this.
Thanks again.
Yours
Bill

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[vijayppatel13]

thanks to all..

 

[electricpete]

Sorry, one more correction on the coefficients of the half-wave rectified waveform. They tell a different story which heavily favors the even harmonics:
1 1.00
2 0.42
3 0.00
4 0.08
5 0.00
6 0.04

I double checked the other reported frequency components and they are correct.

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[Skogsgurra]

The first three answers to the OP were very much tongue-in-cheek. I think we all thought it was a student question that was going to be RFd. Pete did an investigation that says that there is some third harmonic but mostly second (because of the saturation). So, don't RF this thread, please.

Gunnar Englund

http://www.gke.org

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100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...