9th Harmonic: Triplen Harmonic & Neutral Current
Three-phase system demonstration — 9th harmonic currents become in-phase
and add in the neutral conductor
Phase A 9th Harmonic
0 A
Phase B 9th Harmonic
0 A
Phase C 9th Harmonic
0 A
Neutral Current
0 A
Why does the 9th harmonic add in the neutral?
The 9th harmonic is a triplen harmonic because 9 = 3 × 3. In a balanced three-phase system, the fundamental currents are separated by 120°. However, the phase displacement of the 9th harmonic is 9 × 120° = 1080°, which is equivalent to 0°. Therefore, the 9th-harmonic currents in phases A, B and C are in phase with each other.
The 9th harmonic is a triplen harmonic because 9 = 3 × 3. In a balanced three-phase system, the fundamental currents are separated by 120°. However, the phase displacement of the 9th harmonic is 9 × 120° = 1080°, which is equivalent to 0°. Therefore, the 9th-harmonic currents in phases A, B and C are in phase with each other.
For the simulation, each phase carries the same 9th-harmonic current. Instead of cancelling in the neutral, the three currents add:
IN = IA9 + IB9 + IC9
IN ≈ 3 × I9
For example, if each phase contains 10 A of 9th-harmonic current, the neutral can carry approximately 30 A of 9th-harmonic current, assuming ideal equal harmonic currents and ignoring other system effects.
Engineering note: Triplen harmonics such as the 3rd, 9th
and 15th can be especially important in four-wire three-phase systems.
Excessive neutral harmonic current can cause conductor overheating and
additional transformer losses. Actual systems should be evaluated using
harmonic measurements and applicable electrical standards.