Chuck Yung
EASA Senior Technical Support Specialist
I used to joke that if you mention harmonics, engineers get excited while the eyes of non-engineers glaze over. The truth is that harmonics can be easily understood when explained in layman’s terms. Harmonics are simply multiples of the fundamental frequency, with positive, zero or negative sequence. The fundamental frequency is line frequency – also called the first order harmonic -- that being 60 Hz in North America or 50 Hz in most of the rest of the world.
Other harmonic numbers (5th, 7th, etc.) can be viewed as that order times the fundamental frequency, or visualized as having that number of waveforms in the same distance as a single waveform of the fundamental. So in a 60 Hz system, the 5th harmonic is 5x60 or 300 Hz. There will be 5 complete waveforms in the span of a single 60 Hz waveform. When the positive and negative portions of the sine wave are symmetrical, even number harmonics are non-existent.
Any harmonic that is a multiple of three, in the three-phase world, is a zero-sequence harmonic; and, when we are considering a sinusoidal power system, cancels out (except for synchronous alternators, which are outside the scope of this discussion).
If you need a refresher from high school mathematics, there are quite a few online programs that allow you to combine different frequency sine waves, so you can see what happens when different frequencies are combined. One was used to generate the combined waveforms of Figure 1. The first harmonic (Figure 1-A) is what causes an electric motor to rotate. Positive sequence harmonics, other than the first harmonic, distort the sine wave but are acting to rotate the rotor in the desired rotation (Table 1). Negative sequence harmonics distort the sine wave but also are rotating in the direction opposite the rotation of the rotor. They rob the motor of torque and can cause significant heating of the rotor.
There are certain coil pitches with two-pole motors that result in excessive slot spatial harmonics (see Currents, January 2004). But a bigger concern at present is the effect of harmonics on motors operating from a VFD (variable frequency drive). Specifically, when a rotor core surface is blued from heating, that is usually due to negative sequence harmonics, as in Figure 2.
Eddy-current losses vary as the frequency raised to the 1.5 power (some say it is the frequency squared). Consider that a rotor is intended to only “see” line frequency at the moment of
starting and that the rotor frequency diminishes in proportion to the slip. At half speed, the rotor frequency is half of line frequency, and when the motor reaches operating speed, the rotor frequency is only about one or two Hz. When a drive introduces a 5th harmonic, the rotor “sees” the negative sequence of five times the line frequency or 300 Hz in the 60 Hz countries and 250 Hz in the rest of the world. Considering that:
(300 Hz negative sequence / 2 Hz slip frequency) ^1.5 = 1837
Or, for the 50 Hz world:
(250 Hz / 2 Hz) ^1.5 = 1397
If the 5th harmonic was of the same magnitude as the fundamental frequency, the rotor experiences eddy-current surface heating of approximately 1800 times (1400) as compared to normal operation on sinusoidal power. If the magnitude of the 5th harmonic was 10% of the fundamental, then rotor heating could be 180 times as great.
The bottom line is that a blued rotor core should prompt a discussion with the customer about installing a harmonic filter or load reactor between the motor and drive. It offers an opportunity to reduce motor failures, improve efficiency and increases reliability. Note: There are some cases where flash heating and quenching of the rotor is part of the manufacturing process, so a blued rotor is not always indicative of a negative sequence harmonic.
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