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the magnetising current
9

the magnetising current

the magnetising current

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

RE: the magnetising current

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

RE: the magnetising current

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: Eng-Tips.com Forum Policies  

RE: the magnetising current

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

Gunnar Englund
www.gke.org
--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

RE: the magnetising current

3
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.  

=====================================
(2B)+(2B)'  ?

RE: the magnetising current

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.

 

=====================================
(2B)+(2B)'  ?

RE: the magnetising current

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)

=====================================
(2B)+(2B)'  ?

RE: the magnetising current

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

RE: the magnetising current

Quote:

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.  

=====================================
(2B)+(2B)'  ?

RE: the magnetising current

jghrist,

Very cool - thanks for sharing.   

David Castor
www.cvoes.com

RE: the magnetising current

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 :

Quote (Areva / Alstom "Network Protection and Automation Guide"):


"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 ("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.

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.
 

=====================================
(2B)+(2B)'  ?

RE: the magnetising current

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

RE: the magnetising current

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.

=====================================
(2B)+(2B)'  ?

RE: the magnetising current

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.

=====================================
(2B)+(2B)'  ?

RE: the magnetising current

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

RE: the magnetising current

(OP)
thanks to all..
 

RE: the magnetising current

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.

=====================================
(2B)+(2B)'  ?

RE: the magnetising current

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

RE: the magnetising current

Quote:

I would like to mention that particular transformer posted by jghrist has a distintive feature that the 3rd harmonic is very close to zero.
This may be true.  The reason that we did the analysis is that the second harmonic current was inadequate to restrain the GE Type BDD differential relay and it tripped on energization.  We adjusted the relay to be more sensitive.
 

RE: the magnetising current

Guys

I'm running up a new dry cast transformer tomorrow. No load on it yet but it will feed some 11kV pumps in the coming weeks. I'm connecitng a Ranger 7000T power quality analyser to get a feel for it's effect on the system, including harmonics. I'll post the results tomorrow evening (GMT) just for interest.  

RE: the magnetising current

Gunnar: "The first three answers to the OP were very much tongue-in-cheek".
I can't agree with your opinion. My very first answer was absolutely serious.
Question was "yes or no?" and my answer was "no". In addition I stated the similar question referring to the 3-rd harmonic and I answered "yes".
By and large Pete's data confirmed it.
Regards
CL

RE: the magnetising current

Sorry. I understood the whole thing wrong.

Gunnar Englund
www.gke.org
--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

RE: the magnetising current

No problem.
I found that in my text above the last-but-one sentence should be correctly in such a way: "In addition I stated the similar question referring to the 2-nd harmonic and I answered "yes".
A mistake may be a fatigue symptom.

Regards
CL  
 

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