# 10.8: Harmonic Phase Sequences

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- 1439

In the last section, we saw how the 3rd harmonic and all of its integer multiples (collectively called *triplen *harmonics) generated by 120^{o} phase-shifted fundamental waveforms are actually in phase with each other. In a 60 Hz three-phase power system, where phases ** A**,

**, and**

**B****are 120**

**C**^{o}apart, the third-harmonic multiples of those frequencies (180 Hz) fall perfectly into phase with each other. This can be thought of in graphical terms, (Figure below) and/or in mathematical terms:

*Harmonic currents of Phases A, B, C all coincide, that is, no rotation.*

If we extend the mathematical table to include higher odd-numbered harmonics, we will notice an interesting pattern develop with regard to the rotation or sequence of the harmonic frequencies:

Harmonics such as the 7th, which “rotate” with the same sequence as the fundamental, are called *positive sequence*. Harmonics such as the 5th, which “rotate” in the opposite sequence as the fundamental, are called *negative sequence*. Triplen harmonics (3rd and 9th shown in this table) which don’t “rotate” at all because they’re in phase with each other, are called *zero sequence*.

This pattern of positive-zero-negative-positive continues indefinitely for all odd-numbered harmonics, lending itself to expression in a table like this: