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A three phase motor may be run from a single phase power source.
(Figure
below) However, it will not self-start. It may be hand started in
either direction, coming up to speed in a few seconds. It will only
develop 2/3 of the 3-φ power rating because one winding is not used.
3-φ motor runs from 1-φ power, but does not start.
The single coil of a single phase induction motor does not produce a
rotating magnetic field, but a pulsating field reaching maximum
intensity at 0o and 180o electrical. (Figure )

Single phase stator produces a non-rotating, pulsating magnetic
field.
Another view is that the single coil excited by a single phase
current produces two counter rotating magnetic field phasors, coinciding
twice per revolution at 0o (Figure
above-a) and 180o (figure e). When the phasors rotate to
90o and -90o they cancel in figure b. At 45o
and -45o (figure c) they are partially additive along the +x
axis and cancel along the y axis. An analogous situation exists in
figure d. The sum of these two phasors is a phasor stationary in space,
but alternating polarity in time. Thus, no starting torque is developed.
However, if the rotor is rotated forward at a bit less than the
synchronous speed, It will develop maximum torque at 10% slip with
respect to the forward rotating phasor. Less torque will be developed
above or below 10% slip. The rotor will see 200% - 10% slip with respect
to the counter rotating magnetic field phasor. Little torque (see torque
vs. slip curve) other than a double frequency ripple is developed from the
counter rotating phasor. Thus, the single phase coil will develop
torque, once the rotor is started. If the rotor is started in the
reverse direction, it will develop a similar large torque as it nears
the speed of the backward rotating phasor.
Single phase induction motors have a copper or aluminum squirrel cage
embedded in a cylinder of steel laminations, typical of poly-phase
induction motors.
One way to solve the single phase problem is to build a 2-phase
motor, deriving 2-phase power from single phase. This requires a motor
with two windings spaced apart 90o electrical, fed with two
phases of current displaced 90o in time. This is called a
permanent-split capacitor motor in Figure
below.
Permanent-split capacitor induction motor.
This type of motor suffers increased current magnitude and backward
time shift as the motor comes up to speed, with torque pulsations at
full speed. The solution is to keep the capacitor (impedance) small to
minimize losses. The losses are less than for a shaded pole motor. This
motor configuration works well up to 1/4 horsepower (200watt), though,
usually applied to smaller motors. The direction of the motor is easily
reversed by switching the capacitor in series with the other winding.
This type of motor can be adapted for use as a servo motor, described
elsewhere is this chapter.
Single phase induction motor with embedded stator coils.
Single phase induction motors may have coils embedded into the stator
as shown in Figure
above for larger size motors. Though, the smaller sizes use less
complex to build concentrated windings with salient poles.
In Figure
below a larger capacitor may be used to start a single phase
induction motor via the auxiliary winding if it is switched out by a
centrifugal switch once the motor is up to speed. Moreover, the
auxiliary winding may be many more turns of heavier wire than used in a
resistance split-phase motor to mitigate excessive temperature rise. The
result is that more starting torque is available for heavy loads like
air conditioning compressors. This motor configuration works so well
that it is available in multi-horsepower (multi-kilowatt) sizes.
Capacitor-start induction motor.
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