Harmonic phase sequences
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, and/or in mathematical terms:
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:
Sequence especially matters when we're
dealing with AC motors, since the mechanical rotation of the rotor
depends on the torque produced by the sequential "rotation" of the
applied 3-phase power. Positive-sequence frequencies work to push the
rotor in the proper direction, whereas negative-sequence frequencies
actually work against the direction of the rotor's rotation.
Zero-sequence frequencies neither contribute to nor detract from the
rotor's torque. An excess of negative-sequence harmonics (5th, 11th,
17th, and/or 23rd) in the power supplied to a three-phase AC motor will
result in a degradation of performance and possible overheating. Since
the higher-order harmonics tend to be attenuated more by system
inductances and magnetic core losses, and generally originate with less
amplitude anyway, the primary harmonic of concern is the 5th, which is
300 Hz in 60 Hz power systems and 250 Hz in 50 Hz power systems.
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