How can I simulate a third harmonic in the positive sequence system?

Power Quality

Third harmonics are usually simulated in the zero sequence system. This entry shows how to shift the zero sequence contributions into the positive sequence domain by introducing phase shift corrections.


An ideal symmetrical system has the following phase shifts for harmonics of the nth order:

A: 0°
B: -n*120°
C: n*120°

For the third harmonic, for example, the phase shifts amount to:
A: 0°
B: -360°
C: 360°

They appear only on the zero sequence domain. To account for third harmonics in the positive sequence domain, the following phase shift corrections need to be entered:
A: 0°
B: (n-1)*120°
C: -(n-1)*120°

If the above mentioned third harmonic is phase shifted as follows:
A: 0° + 0° = 0°
B: -360° + (3-1)*120° = -120°
C: 360° - (3-1)*120° = 120°
This is entirely in the positive sequence domain.
In the attached library (LibraryHarmonics.pfd) the spectrum of a 12-pulse converter can be found, where the 1.5th, 2nd and 3rd harmonics have been corrected with the above formula.