# NCEES QUESTION 533



## rmsg (Sep 26, 2018)

Can Anybody please help me with NCEES Question 533 of _*third harmonics rms neutral current*_. I don't have a clue how it was solved and neither could find any useful information online on calculation of RMS neutral current of third harmonics. _(see enclosed)_


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## Flyer_PE (Sep 26, 2018)

When you do the time domain math on a 3 phase system, you find that the triplen harmonics (primarily 180 hz but it occurs at higher multiples of 3) actually add on the neutral rather than cancel one another out.


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## rmsg (Sep 26, 2018)

Flyer_PE said:


> When you do the time domain math on a 3 phase system, you find that the triplen harmonics (primarily 180 hz but it occurs at higher multiples of 3) actually add on the neutral rather than cancel one another out.


So if third harmonics phase rms current would have been 7A instead of 3A _(as given in the question)_ , then what would have been the Neutral third harmonics RMS current ?


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## Flyer_PE (Sep 26, 2018)

^21 (7+7+7) if they are balanced at 7 amps/phase.  At 180 Hz, the current vectors are no longer separated by 120 degrees.


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## jnspark (Sep 27, 2018)

Check out the following link Triplen Harmonics as it will give a good overview.  I will not present math or equations as I don't know them, but with 3rd harmonics, a triplen harmonic, you need to also think in terms of symmetrical components and KCL.  The third harmonic is zero sequence current, also known as ground fault current.  It is what is sometimes called circulating current and is a simple summing of all the currents.

As far as I understand it, and I am not a PE yet just someone dealing with protection and grounding banks, the major problem with ground fault current and triplen harmonics occurs in a system with a grounding connection.  So the key part of the NCEES question will be the mention of a 3-phase 4-wire system.  If this was a 3-phase 3-wire system, meaning floating-wye or Delta, then there is no source of ground fault current and I believe the answer would be zero, unless KCL is a myth and the world is really flat.

There are tons of links out there, just search "triplen harmonics" .

Good luck to all of us in October!


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## Nashi (Sep 27, 2018)

I found another very good document on Harmonics and want to share because it helped me...Six tough topics about harmonic distortion. https://www.schaffner.com/fileadmin/media/downloads/white_paper/Schaffner_Whitepaper_Harmonic_distortion.pdf


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## Nashi (Sep 27, 2018)

Check out page 18 of the pdf..."If the network is distorted by current harmonics, the triplen harmonics will add up in the neutral so that the current in the neutral can exceed the current of each phase of the individual phase currents up to factor three."


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## JayD (Mar 5, 2020)

Isn't it neutral current should be zero? Because for a balanced 3 phase 4 wire system there is no current flow through the neutral.

Please comment.


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## JayD (Mar 5, 2020)

JayD said:


> Isn't it neutral current should be zero? Because for a balanced 3 phase 4 wire system there is no current flow through the neutral.
> 
> Please comment.


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## Orchid PE (Mar 5, 2020)

JayD said:


> Isn't it neutral current should be zero? Because for a balanced 3 phase 4 wire system there is no current flow through the neutral.
> 
> Please comment.


Triplen harmonics are additive in the neutral, even for balanced currents.

Notice in the image below how the triplen harmonics for phases A, B, and C are all in phase. The fundamental frequency waveforms sum to zero, but the triplen harmonics add.


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## JayD (Mar 5, 2020)

Thank you so much. Is it true about the 5th harmonic too ?

Same problem: balanced system with 5th harmonic currents. What will be the neutral current?


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## Orchid PE (Mar 5, 2020)

JayD said:


> Thank you so much. Is it true about the 5th harmonic too ?
> 
> Same problem: balanced system with 5th harmonic currents. What will be the neutral current?


Only the triplen harmonics, which are odd multiples of 3.


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## JayD (Mar 5, 2020)

I have few more questions about neutral current and harmonics:

1. For a balanced three phase system 3rd harmonics will be three in the system (and hence flow through neutral) only if any non-linear load is there in the system?

2. Is there third harmonics are present only in 3-phase, 4 wire Wye system not in delta system?

3. For a 3-phase to ground fault we say, Ia+Ib+Ic=0 and In=0 too.

Is it correct to say that during 3-phase fault current in the neutral is zero ? 

4. Also the multiple of 3 of 3rd harmonics are zero sequence harmonics. So is it in a 3-phase balanced system the other positive and negative sequence harmonics cancel out each other??


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## Orchid PE (Mar 6, 2020)

I think a better way to state this is: For a balanced three phase system, harmonics of _any order_ can be produced by non-linear loads. Only _triplen _(odd multiples of 3: 3, 9, 15, 21, etc.) harmonics will flow in the neutral.

I think you're on the right track. I would suggest reading up on how zero sequence harmonics circulate in the delta winding of transformers.

I think what you're asking is what happens to the zero sequence harmonics during a 3-phase-to-ground fault? If we're trying to prep for the PE exam, I wouldn't worry about harmonics _and_ a 3-phase-to-ground fault occurring the same problem.

If I'm understanding your question correctly, yes. The positive and negative sequence harmonics cancel out, and the zero sequence harmonics (triplen) add.


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