Harmonics: Sequences
The previous article written on Harmonics, found here, discussed looking at harmonics with the Powermaster, and how to read what was seen. This article goes a little more into harmonics, what they are, and what problems they can cause.
What are Harmonics?
Harmonics are sinusoidal voltages or currents having frequencies that are whole multiples of the frequency at which the supply system is designed to operate. In the US, this is 60Hz, thus a 2nd harmonic would have a frequency of 120Hz, a 3rd harmonic would be 180Hz, etc. Some notations show the fundamental as the 1st harmonic. Each harmonic is added to the fundamental, creating a complex wave shape that contains the fundamental and each harmonic, as shown below.
The light blue wave form is the sum of the fundamental 60Hz (dark blue) and the 500 Hz 5th harmonic (the pink waveform).
Harmonic Sequences
To help understand which harmonics can cause problems, harmonics can be divided into what are called sequences. Harmonic sequence refers to the phasor rotation of the harmonic voltages and currents with respect to the fundamental waveform, in a balanced, 3-phase 4-wire system. The three sequences are Positive sequence, Negative sequence and Zero sequence harmonics. The problems caused by the harmonics will be related to their sequence. The below graph shows a few harmonics and the sequence they fall into.
Positive Sequence Harmonics
Positive sequence start with the fundamental, then occur every third one after that. The 1st, 4th, 7th, 10th, 13th, etc, are called positive sequence harmonics. Positive sequence harmonics rotate forward, or in the same direction as the fundamental. These can cause overheating of conductors and transformers due to the addition of the waveforms. If such harmonics are present in a large amount, conductors and transformers must either be sized appropriately to compensate for the additional magnitude, or some form of harmonic mitigation needs to be employed.
Negative Sequence Harmonics
Negative sequence harmonics begin with the 2nd, and occur every third harmonic thereafter. The 2nd, 5th, 8th, 11th and so on are negative sequence harmonics. As opposed to positive sequence harmonics, negative sequence circulate between the phases, in the opposite direction of the fundamental. This opposite rotation causes weakening magnetic fields in motors (especially induction) and results in a loss of mechanical torque.
Zero Sequence Harmonics
Zero sequence harmonics, also more commonly referred to as “triplens” begin with the third, and every third harmonic thereafter. All zero harmonics are a multiple of 3 (3rd, 6th, 9th, 12th, 15th), hence the name triplen. They have zero rotation sequence and circulate between the phase and neutral conductors. These harmonics add up in the neutral conductor (along with currents from the other three phases) and can cause overheating in the neutral. Depending on the magnitude of the harmonic current, the neutral current can at times be upwards of 3 times the phase current, resulting in overheating of the wire and less efficiency all around.
Summary
Any Harmonic with large enough magnitudes are harmful to electrical infrastructure. Understanding what sequence the dominant harmonics belong too, and the possible results of that sequence, will allow one to properly mitigate the harmonics as needed to reduce harm and damage to a system.
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