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7.8: Harmonic Phase Sequences

  • Page ID
    1439
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    In the last section, we saw how the 3rd harmonic and all of its integer multiples (collectively called triplen harmonics) generated by 120o phase-shifted fundamental waveforms are actually in phase with each other. In a 60 Hz three-phase power system, where phases A, B, and C are 120o 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:

    02335.png

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

    12141 (1).png

    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:

    12142.png

    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:

    12143.png


    This page titled 7.8: Harmonic Phase Sequences is shared under a GNU Free Documentation License 1.3 license and was authored, remixed, and/or curated by Tony R. Kuphaldt (All About Circuits) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.