Harmonics Practice Problem Question

[BebeshKing PE]

Hello, I need help for the answer, solution and explanation for this kind of Harmonic Problem. Thanks.


A three-phase, four wire balanced wye-connected load is connected to a balanced three-phase four wire source. The following harmonic data is recorded:




Order




Frequency




RMS amps measured per phase




3




180




100




5




300




20




7




420




15




9




540




10


Assume no harmonics of higher order than the ninth are present. What would be the RMS current measured in the neutral?

 

[Orchid PE]

[Nonsense answer]

 

[BebeshKing PE]

@Chattaneer PE, thank you for your solution. I just have a few questions though:

1. Is it the total harmonic current(including the positive and negative sequence) flowing into the neutral? 

2. Should it be just the triplen harmonics(zero sequence) which is the 3rd and 9th harmonics will contribute to the neutral conductor?

3. Based on Wildi’s book, these triplen harmonics adds up in the neutral and 3 times greater.
So I would assume that the harmonic current in the neutral is 3(3rd harmonics  plus 9th harmonics) = 3(100+10)=330A??

I’m not really sure and I’m confuse, that’s why I needed help with you guys.. Please see attached the reference from Wildi. 
 

thank you,

 

[Orchid PE]

@Chattaneer PE, thank you for your solution. I just have a few questions though:

1. Is it the total harmonic current(including the positive and negative sequence) flowing into the neutral? 

2. Should it be just the triplen harmonics(zero sequence) which is the 3rd and 9th harmonics will contribute to the neutral conductor?

3. Based on Wildi’s book, these triplen harmonics adds up in the neutral and 3 times greater.
So I would assume that the harmonic current in the neutral is 3(3rd harmonics  plus 9th harmonics) = 3(100+10)=330A??

I’m not really sure and I’m confuse, that’s why I needed help with you guys.. Please see attached the reference from Wildi. 

1. This doesn't have anything to do with symmetrical components (positive, negative, zero sequence).

2. I was taught it was the odd order harmonics, not just the triplen.

3. Idk where he gets "three times" from, but there's no way it's three times.

Can you send the next couple of paragraphs for that section of his book? I'll also check some books I have here in a little bit.

 

[BebeshKing PE]

@Chattaneer PE, see attached continuation from Wildi.

 

[Orchid PE]

@BebeshKing

After some reading, I brushed up on the harmonics from a few books.

1. The square root of the sum of the RMS currents squared is the total rms of the current (not in the neutral). So if you needed to calculate Irms per phase including harmonics, use this formula.
   
2. For a balanced load, the fundamental, even, and odd cancel out in the neutral, except the triplen.
   
3. The triplen (3, 9, 15, etc.) are 3x the RMS in the neutral, because each phase is additive.
   

So I think what you had, 3*(100 + 10) = 330 A is correct.

 

[Orchid PE]

From another book:

 

[DLD PE]

Great stuff!  Thanks I read the example problem at the start of this and it stumped me as well.  Not sure where that problem came from but I'm curious to know.  Here is another article I came across that explains triplen harmonics well:

https://electrical-engineering-portal.com/what-are-triplen-harmonics

 

[BebeshKing PE]

@Chattaneer PE @MEtoEE, Thank you for all your responses.

 

[Orchid PE]

Great stuff!  Thanks I read the example problem at the start of this and it stumped me as well.  Not sure where that problem came from but I'm curious to know.  Here is another article I came across that explains triplen harmonics well:

https://electrical-engineering-portal.com/what-are-triplen-harmonics

I was reading through this article, and thought it looked familiar. It's literally the same wording that's in my book.

 

[DLD PE]

What's the name of your book (the one with the page 1409)?  I have Wildi, Graffeo, Blackburn and Glover.  Glover doesn't even cover harmonics that I can see.  

 

[Orchid PE]

What's the name of your book (the one with the page 1409)?  I have Wildi, Graffeo, Blackburn and Glover.  Glover doesn't even cover harmonics that I can see.  

Standard handbook for electrical engineers, 17th edition.

 

[DLD PE]

I don't know if I've heard of anyone having that book.  Do you recommend it?

 

[Orchid PE]

I don't know if I've heard of anyone having that book.  Do you recommend it?

I'm going through it now. It covers a lot of topics. I wish I had bought it before I took the exam. From what I've seen, it appears it could be a great reference for the exam.

 

[DLD PE]

I have two books, Power Systems Analysis (Grainger) and a protection book by Blackburn.  Both of those are very difficult for me to read.  I have the Glover book and I really like it so far, but I haven't delved into the problems that much, plus I have the 6th edition and no solution manual.

 

[BebeshKing PE]

I have two books, Power Systems Analysis (Grainger) and a protection book by Blackburn.  Both of those are very difficult for me to read.  I have the Glover book and I really like it so far, but I haven't delved into the problems that much, plus I have the 6th edition and no solution manual.

@MEtoEE, I have the same references as yours too. So far, I like the Glover for the protection topics, Grianger for the Transmission lines, and Wildi for the Machine.

@Chattaneer PE, does the Standard Handbook for Electrical Engineers reference has plenty sample/practice problems?

 

[Orchid PE]

@MEtoEE, I have the same references as yours too. So far, I like the Glover for the protection topics, Grianger for the Transmission lines, and Wildi for the Machine.

@Chattaneer PE, does the Standard Handbook for Electrical Engineers reference has plenty sample/practice problems?

It doesn't have any practice problems.