Odd, even, negative sequence and triplen are all interesting adjectives associated with harmonics. Usually, even harmonics are a rarity. However, in the past couple of years, even harmonics have increasingly appeared in data sent to me by customers. This doesn’t necessarily mean that there is an increase in even harmonics in today’s electrical environment; it’s just that I see it more often.
The concept of harmonics has been discussed before and is probably well known to most electrical contractors. The two most common effects of harmonics—excessive current levels in neutral conducts and the overheating of electromagnetic equipment—are also well known. How those adjectives address different types of harmonics is less familiar to most people, as well as the value this additional wording provides.
Harmonic numbering starts with zero—the direct current (DC) component of the mostly alternating current signal—whether voltage or current. The No. 1 component is the fundamental frequency, which in most cases is the dominant frequency component, whether 50 or 60 Hz in most power applications.
The odd and even terminology is fairly obvious: two, four, six, eight, etc., are the evens, and three, five, seven, etc., are the odds. Harmonics that can be evenly divided by three receive the “triplen” adjective. This makes three, six, nine, etc., part of the triplen harmonics. The “two” adjective as often combined to further narrow them down to the “odd triplens,” the three, six, 15 and so on.
Another method of describing harmonics is the sequencing component terms—positive, negative and zero. These terms are often use by utility engineers, but have a place in harmonics, though sometimes are controversial. It is basically a grouping of three, where the fundamental is a positive-sequence harmonic; the second is negative sequence and third is zero sequence. It then repeats with the fourth being positive, fifth negative and so on.
Now that we are all on the same page with the terminology, what is the value of descriptors? It basically takes a complex set of squiggly waveforms and turns them into a couple of key indicators of what the potential source and problems are with such in an industrial or commercial facility.
We’ll start with the evens. Because of the symmetrical nature of how most loads operate, even harmonics are unusual, as they distort the symmetry around the half cycle and quarter cycle points on the sine wave (see Figure 1). Depending on the amount of the different harmonic levels and their phase angles, it can shift the signal so it isn’t symmetrical on the top and bottom half of the waves, which is like a DC-bias. Such things make transformers unhappy, as their world exists in the AC domain only.
This example shows how multiple zero crossings can occur, which wreaks havoc on clocking circuits that are based on having only two zero crossings per cycle.
The effects of triplen odd harmonics come into play in three-phase systems. In a four-wire wye circuit, the triplen harmonics will become additive in the neutral conductor, rather than canceling out as the fundamental does.
Since odds are more prevalent, the triplen odds get the attention for overheating neutrals, sometimes to the point of ignition of flammable material. Figure 2 shows that 25 percent of third harmonic contribution per phase results in almost an equal neutral signal to the phase conductors. In a delta circuit, such harmonics have no neutral conductor to “escape” on, so they just circulate round and round, generating extra heat that the transformer must contend with by having its operating limits derated.
The final example, Figure 3, shows the seventh harmonic—a negative sequence harmonic. In a normal counterclockwise rotation of the fundamental frequency, the seventh harmonic is rotating in a clockwise fashion, or opposite the fundamental. In an AC motor, this will also result in extra heating and require further derating, as it is trying to turn the motor in the wrong direction, like a braking torque.
Hence, knowing the meaning and effect of a few extra adjectives on harmonics can replace scanning through countless waveforms and spectrum analysis graphs to determine what is there, and what the affect is on the infrastructure of your facility. EC
BINGHAM, a contributing editor for power quality, can be reached at 732.287.3680.