Elec467 Power Machines &
Transformers
Electric Machines by Hubert, Chapter 6
Topics: Single phase induction motors
Single Phase inertia
Single phase induction motors can not develop a rotating field nor motor torque without
auxiliary methods because they only have two poles. A squirrel cage rotor locks into
position and doesn’t move as seen in (a) above. The main idea is to develop a
quadrature field axis by initiating rotor rotation by mechanical or other means.
Quadrature Field Theory
Once the rotor is moving a “quadrature” field is created at right angle to the direct axis
field. It is created by the speed voltage of the rotor turning thru the existing field. The
following rotor bars continue to hold the quadrature field up and the rotor picks up speed.
Effect of adding a pole
Starting torque is called locked
rotor torque, TLR. This is the
formula to calculate the torque
required to start the split-phase
motor.
TLR  ksp I mw I aw sin 
Variables for the split-phase motor
ksp = machine constant
Iaw = current in auxiliary winding
Imw = current in main winding
α = difference twn current phases
A phase-splitter eliminates mechanical starts by initially creating
the rotating field. Once the rotor starts the phase-splitter circuit
can be shut down as the quadrature field takes over.
Shade-pole motor
This single phase motor uses a split stator with one of the forks wrapped
with a copper ring that acts like a short-circuited secondary of a
transformer. This secondary winding creates an mmf (that collapses)
which opposes the regular field thus creating a field across the face of the
stator that is irregular, stronger on one edge than the other. It sweeps
across the face of the stator starting the rotor rotation when the
quadrature takes over.
Modifications 3Ø motor from 1Ø
With a couple of capacitors, you can create a phase shift
and run a three phase motor from a one phase source. This
motor has a starting capacitor that adds extra capacitance to
assist the starting torque. The motor should then be derated
to 2/3 of the three phase rating.
Elec467 Power Machines &
Transformers
Electric Machines by Hubert, Chapter 7
Specialty machines: Reluctance,
Stepper, Linear, and Universal
Salient Poles
Machines such as reluctance motor and hysteresis motor are used
for timing devices such as tape recorders, turntables and other
device with constant speed requirements. They are an induction
motor with a modified squirrel-cage rotor shaped by notches, flats
or barrier slots that provide routing paths for magnetic flux to poles
that are formally known as salient poles. Salient means projecting
or prominent. Shaping the flux across the power gap makes this
machine a reluctance machine.
Reluctance Motor
Reluctance formulas
For a reluctance machine, at no load the centerline of the salient
poles line up with the rotating field produced by the stators and
rotates at synchronous ns. With increasing load the salient poles
lags behind the rotating field by an angle called the torque angle,
δrel, while in synchronous rotation with the field. When the angle
exceeds 45°, the motor runs as an induction machine.
2
Trel  K  V  sin 2 rel 
 f
Trel is the average value of the reluctance torque
K is a constant that varies according to the machine
V is the applied voltage and f is the line frequency
 represents the angle in electrical degrees (lower case delta)
A hysteresis motor has a rotor that is a cylinder made of a
permanent magnet. The operation is quite similar to the
reluctance machine with a torque angle, δh.
Variable-Reluctance Motors
• A stepper motor is a variable-reluctance motor.
• The rotor composed of salient poles.
• The stator has one or more poles than the
rotor.
• Depending on the position of the rotor when
one (or more) of the stators is energized will
cause the reluctance of the magnetic path to
vary.
Stepper motor workings
Step angle calculation

Ns  Nr
Ns Nr
 360
B = step angle in space degrees
Ns = number of stator poles (also called teeth)
Nr = number of rotor salient teeth
Control of when the rotor steps, how fast, and in which direction
can be done with a microcontroller circuit. In figure 7.7 (f) the
switches are connected to output I/O pins of the embedded
processor.
Input would be a zero-biased potentiometer
connected to an ADC input. As long as at least one stator pole
is energized, the rotor would be held steady in one position
thus enabling a locked position to be selected by the user.
Half-step operation
By turning on two of the stator poles at the same time, the rotor will be
repositioned half-way between two poles in what would be called a
half-step. This doubles the resolution. Further improvement in the
resolution can be accomplished by incrementally increasing the current
in the adjacent stator to full value where the rotor becomes position ½
between the two stators then decreasing the current in the original
stator. This is called micro-stepping.
Restoring torque
The holding torque (static
torque) seen in (a) is
equal to the maximum
load-torque that can be
held without having the
rotor slip poles.
The
angle when slipping poles
occurs is twice the step
angle. This is measured
by use of a torque wrench
applied to the rotor shaft.
Stepper motor constructed
using a permanent magnet
This design allows the flux from
a permanent magnet to be
added to the electromagnetic
flux of the stator to give added
holding power. In the
construction of the rotor, the
toothed sections attached to
either side of the permanent
magnet are misaligned with
each other but arranged so that
just one south/north pole of the
rotor will align with one
north/south pole of the stator.
In (a) and (c) there are ten rotor
poles but for the purposes of
calculating the step size there
are only 5 .
Linear induction motor
In these diagrams, the flux field is moving to the right as seen by the two positions of Us for the
same flux line. This causes a current to develop in the conducting rail such that flux bunching
occurs causing a mechanical movement in the same direction as the sweeping field. Reversing
the flux will cause the movement to reverse.
LIM synchronous speed
LIM stands for Linear Induction Motor and is one method use to implement high-speed rail
lines. In the above diagram the primary is connected to the AC supply. The windings are
laid in a straight line for a two-pole machine with one coil per phase per pole. The
connections between poles (wye/delta) are not shown. The train would be connected to
the rail. The pole pitch  is the span of the coils.
U s  2f
Us = synchronous speed (m/s)
 = pole pitch (m)
f = supply frequency (Hz)
U  U s (1  s)
U = 2nd speed (m/s)
s = slip
s
U s U
Us
Universal motor
The rotor is called the armature that is connected in series with the stator (called series-field windings). The
torque is proportional to the flux density (created by series-field windings) and the current in the armature.
When the motor is running the rotor in the positions seen above is generating maximum flux with the current
peaking in the rotor and the series-field windings but 90 space degrees later, the rotor isn’t cutting many flux
line and the voltage is zero-crossing just as the commutators are shorted out by the brushes.
Elec467 Power Machines &
Transformers
Electric Machines by Hubert, Chapter 8
Topic: Synchronous motors
Rotor for a synchronous machine
Word play:
The stators for a synchronous machine are called the armature but they act
exactly the same way as the stators of an induction motor. This terminology
is opposite to the Universal motor just mentioned in the last chapter and DC
motors.
The rotor of a synchronous machine is made up of two overlapping winding:
(1) like a squirrel cage winding (aka: pole-face, amortisseur, and damper) and
(2) wound rotor winding (aka: excitation, magnetic, field coils, field).
Salient-pole synchronous rotor
When the motor
is turned on the
squirrel-cage
winding are used
to accelerate the
rotor to near
synchronous
speed. Then the
field coils on the
rotor are turned
on making the
squirrel cage
bars into an
electromagnet
called field poles.
Shaft mounted DC exciter
The field coils are powered by a DC motor attached to the shaft of the synchronous
motor. The voltage is brought from the commutators of the DC motor to the slip rings
of the rotor to power up the field coil. This in effect makes the rotor act like a
permanent magnet and bring the motor up to synchronous speed with zero slip and a
torque angle controlled by the load.
Torque Angle
By varying the voltage in the field coils (rotor) the power across the power gap can
feed voltage back into the AC supply by the counter-emf generated by the rotor
electromagnets sweeping the armature (stator) coils. Synchronous machines built
expressly for this purpose have no external shafts and are called synchronous
condensers that “float” on the bus.
Power factor
This chart allows you to estimate the armature current based on the
excitation voltage (per phase) and rated load. It also lets you
determine whether or not you have the machine contributing a
leading or lagging power factor to the grid.
Types of torque
changes with power angle
The power angle is changed by varying the DC current supplied
to the field coils of the rotor from the DC exciter motor attached
to the shaft.