Harmonic summation and cancellation can be a tricky subject. For example, why do 3rd harmonics sum in the neutral but cancel phase-to-phase?
To answer those questions, I created an Excel spreadsheet (attached at bottom of this article) that allows you to dial in various harmonics and see just what happens in the neutral as well as when measuring phase-to-phase voltage on two harmonic laden phases.
(https://pps2.com/images/smf/poweranalysis/harmonic_cancel_diagram.jpg)
HINT: Summation and cancellation of 3rd harmonics are easier to understand when we remember that they are zero sequence. That means that each phase harmonic is in-phase with each other.
Have fun!
Here's a quick screencast tutorial: https://pps2.com/v/1/hmc.php (https://pps2.com/v/1/hmc.php)
Here's the same application, but this one includes 3-phase plotting.
(https://pps2.com/images/smf/poweranalysis/3-phase_harmonics.jpg)
Here's a video tutorial on how to use this version:
https://pps2.com/v/s/1/3h.php (https://pps2.com/v/s/1/3h.php)
(https://pps2.com/images/smf/poweranalysis/3-phase_harmonics_video.jpg) (https://pps2.com/v/s/1/3h.php)