Understanding Harmonic Phase Sequences in Three-Phase Power Systems
In the previous section we showed that the third harmonic and its integer multiples—known as triplen harmonics—generated by 120° phase‑shifted fundamental waveforms are actually in phase with one another.
In a standard 60 Hz three‑phase system, where phases A, B, and C are spaced 120° apart, the third‑harmonic multiples (180 Hz) align perfectly in phase across all three phases.
Both graphical illustration and mathematical formulation can be used to understand this behavior:
Harmonic currents of Phases A, B, C all coincide, that is, no rotation.
Extended Mathematical Table with Odd-Numbered Harmonics
If we extend the table to include higher odd‑numbered harmonics, a clear pattern emerges regarding the rotation—or sequence—of these frequencies:
Harmonics that rotate with the same sequence as the fundamental, such as the 7th, are termed positive‑sequence. Those that rotate in the opposite sequence, like the 5th, are called negative‑sequence. The triplen harmonics (3rd, 9th, etc.) that do not rotate at all—remaining in phase with each other—are classified as zero‑sequence.
This positive‑zero‑negative‑positive pattern repeats indefinitely for all odd‑numbered harmonics, which can be succinctly expressed in the following table:
Related Worksheets
- Mixed‑Frequency Signals Worksheet
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