Zero Sequence Currents

Yes to the second question.

Look up Fourier Series. It will tell you what happens. It doesn't matter how many phases are involved.

The two hot lines are 180 degrees apart in phase. 2nd, 4th, 6th, ... etc harmonics will add in the neutral line.

Good day Guest : Okay, so if I understand correctly--- when you have three desktop computers (PC), each operating at 120vac ( line to neutral) on a 120/208vac/ 3phase-4wire system, and one PC is on phase A, the 2nd PC is on phase B, and the 3rd PC is on phase C ---- the 3rd,9th,15th harmonic currents that each of these PC s draw will ADD up in the common neutral !? But if there are two PCs, one on phase A (120v) and the other on phase B (120v)(180 degrees apart), of a 120/240vac/1phase-3wire system, What happens to the 3rd,9th,15th harmonics ? Do they just not appear and instead we have 2nd,4th,6th harmonics that ADD up in the common neutral ?? Or is the case that we retain the triplen harmonics but that they do not add up in the common neutral as would be the case in a 3 phase-4wire system ??

Here is a good explanation of your problem, right down to the power supplies in your PC's.

You are talking about two different things:

1)zero sequence : this is one of the sequences obtained in an unbalaced system using the Fortescue Rheorem(look at it!) or Symmetrical Components Theory.

2)harmonics: they are the result of the decomposition of a periodic wave into their harmonics, according to the Fourier Series

In a system neutral, only the zero sequence will occur.

A single phase system may be considered as a periodic wave. You may decompose the single phase system into the positive, negative and neutral components, exactly as described in the later Fortescue Theorem.

Regards