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Three-phase motors rarely get along with harmonics. In fact, excessive harmonics tend to act as a brake, reducing efficiency. Therefore, most design efforts have been directed at reducing, masking, or eliminating harmonics either at the point where utility power comes into a plant or where current comes into the motor.

But what if you wound the motor to increase the number of phases beyond three, say to 12, or even higher? Researchers have done that and discovered that instead of damping torque, the harmonics in ac inverter-based motors work with the phases to boost torque.

In the case of a proprietary, patentpending 18-phase prototype, there is 30% more continuous torque and at least three times as much peak torque as comparable three-phase ac motors. The researchers claim that this winding technique retrofits to existing ac units.

The engineers took a three-phase motor and increased the number of phases to the point where each polephase group consisted of only a single slot in the stator winding. This means that an ac motor can operate with upwards of twelve phases. If there's enough stator iron, twenty-four or more phases are possible. And with custom iron, there is no upper limit on phase count.

The factors behind the higher torque are best explained through copper use and harmonics, with harmonic waveforms divided into temporal waves in the power supply current, and spatial waves in the airgap flux.

Spin to harmony

In a typical three-phase motor, the fundamental frequency of the applied current voltage generates the major rotating magnetic field and sets synchronous speed. Analysis shows that the magnetic field rotates at a speed determined by the applied frequency and the number of poles.

Each of the harmonics found in the current generates a rotating field as well. Each field is also subject to the same synchronous speed formula.

Now in a three-phase motor, the fundamental electrical angle between phases is 120°. But windings are on both sides of the stator, so the electrical phase angle between adjacent polephase groups is 60°.

For the fifth harmonic in the drive waveform, the electrical angle between phases is five times this, or 300°. Because sinusoids are periodic functions, 300° is the same as -60°; thus, the phase relation between adjacent phases for the fifth harmonic is precisely opposite that of the fundamental. Therefore, in a three-phase motor, the fifth temporal harmonic generates a rotating field with the same number of poles as that produced by the fundamental, but with negative phase sequence.

Additionally, the fifth harmonic has five times the frequency of the fundamental. Therefore, its rotating field spins at five times the fundamental speed in the reverse direction. This puts a drag on the rotor, which ultimately results in less torque.

What happens, though, if you increase the number of phases, say to five? The fundamental electrical angle between phases becomes 72°, and the angle between pole phase groups is 36°.

For the fifth harmonic, the electrical becomes 360°, and the electrical angle between adjacent pole-phase groups is 180°. Over one 360° cycle of fundamental current flow in the stator, the fifth harmonic will cycle five times.

In five-phase winding, the fifth harmonic current flow produces a tenpole rotating field, rather than a twopole. And it will have a synchronous speed that's the same as that of the fundamental.

Now consider a fifteen phase motor. The phase angle is 24°, with an electrical angle of 12° between adjacent pole-phase groups.

For the fifth harmonic, the electrical angle is 60°, the same as in a tenpole three-phase machine. In fact, a fifteen-phase two-pole winding, fed with fifth harmonic current alone, has exactly the same slot currents as a three-phase ten-pole winding.

In a fifteen-phase motor, then, the fifth temporal harmonic develops a rotating field with five times the poles of the fundamental rotating field. However, because of the fifth harmonic's higher frequency, this field spins at the same synchronous speed as the fundamental field.

Similar reasoning applies to all harmonics. Until the harmonic order is such that its phase angle is greater than 360°, its field will rotate in synchronism with the fundamental field.

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