1/7/2013
EEE 118: Energy Conversion
Dr. Mongkol Konghirun
Department of Electrical Engineering
King Mongkut’s University of Technology Thonburi
Chapter 10
Single-Phase And SpecialPurpose Motors
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10.1 The Universal Motor
The Universal Motor
The universal motor is essentially the series or
shunt DC motor. However, it can be operated
on a single-phase AC power source.
Recall from Chapter 8:
τind = KφIA
…(8-49)
When the polarity of the voltage applied to a
shunt or series DC motor is reversed, both
direction of field flux (φ) and the direction of
armature current (IA) reverse, and resulting
induced torque continues in the same
direction as before
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Torque-Speed Characteristic
The torque-speed characteristic of a universal
motor is different from one of the same
machine operating from DC voltage for two
reasons:
1. The armature and field windings have quite
large reactance (as a function of frequency).
So, the voltage drop across these reactances
are large. Thus, the EA = Kφω is smaller for a
given input voltage. Then, the motor speed ω
is slower for a given IA and τind.
2. The peak voltage of an AC system is √2
times its RMS value. The magnetic saturation
could occur near the peak current, lowering
the magnetic flux of the motor for a given
current. The induced torque is partially
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reduced for a given speed.
Applications of Universal
Motors
The universal motor has the sharply drooping torque-speed
characteristic of a DC series motor (EA significantly
reduced), so it is not suitable for constant-speed
applications.
However, it is compact, light weight and gives more
torque/amp than any other single-phase motor.
Typical applications for this motor are vacuum cleaners,
drills, similar portable tools, and kitchen appliances.
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Speed Control of Universal
Motors
Similar to the DC series motor, the speed of universal
motor is increased when the RMS input voltage is
increased.
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10.2 Introduction to Single-Phase
Induction Motors
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Introduction to Single-Phase
Induction Motors
The single-phase induction motor has
only one phase winding sinusoidally
distributed.
The magnetic field in a single-phase
induction motor does not rotate.
Instead, it pulses getting larger first
and then smaller, but always remaining
in the same direction during the half
cycle. Thus, there is no starting
torque.
τind = k (BR × BS)
…(4-58)
τind = k BRBS sin γ
= k BRBS sin 180o = 0
where γ is angle between BR and BS.
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Introduction to Single-Phase
Induction Motors
However, once the rotor begins to
turn, an induced torque will be
produced in it. There are two basic
theories which explain why a
torque is produced in the rotor
once it is turning.
1. Double-revolving-field theory of
single-phase induction motor
2. Cross-field theory of single-phase
induction motor
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The Double-Revolving-Field Theory
of Single-Phase Induction Motors
The double-revolving-field theory of single-phase induction motor
basically states that a stationary pulsating magnetic field can
resolved into two rotating magnetic fields, each of equal magnitude
but rotating in opposite direction.
The induction motor responds to each magnetic field separately, and
the net torque in the machine will be the sum of the torque due to
each of the two magnetic fields.
The flux density of the stationary magnetic field produced by the stator
current is given by
BS(t) = (Bmax cos ωt)j
…(10-1)
= BCW(t) + BCCW(t)
…(10-4)
Clockwise-rotating:
BCW(t) = (0.5Bmaxcos ωt)j + (0.5Bmaxsin ωt)i
…(10-2)
Counterclockwise-rotating:
BCCW(t) = (0.5Bmaxcos ωt)j - (0.5Bmaxsin ωt)i
…(10-3)
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The Double-Revolving-Field Theory
of Single-Phase Induction Motors
BS = Bmax j (ωt=0)
BS = 0 (ωt=90o)
BS(t) = (Bmax cos ωt)j
…(10-1)
= BCW(t) + BCCW(t) …(10-4)
BS = -Bmax j (ωt=180o)
BS = 0 (ωt=270o)
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The Double-Revolving-Field Theory
of Single-Phase Induction Motors
No Starting torque
• Forward and reverse magnetic
fields are produced by the same
current.
• Both magnetic fields rotate in
the opposite direction.
• Then, each magnetic field
produces own induced torque at
rotor.
• The net induced torque is the
sum of the induced torques
produced by these two magnetic
fields.
• As a result, there is no starting
torque in the motor.
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The Cross-Field Theory of SinglePhase Induction Motors
The cross-field theory of single-phase induction motor is concerned
with the voltages and currents that the stationary stator magnetic
field can induce in the bars of the rotor when the rotor is moving.
• Rotor voltage is induced in such as
way that its flux opposes the BS (see
plane of maximum rotor voltage)
• Because of rotor’s high reactance, the
induced rotor current lags the rotor
voltage by almost θ ≈ 90o.
• Since the rotor is rotating in clockwise
direction, at a certain time, thus the
plane of maximum rotor current leads
the plane of maximum rotor voltage by
θ ≈ 90o in space.
• Finally, the BR is produced by IR as
shown.
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The Cross-Field Theory of SinglePhase Induction Motors
BS = |BS|sin(ωt) ∠90o
BR = |BR|sin(ωt-90o) ∠θ-90o
where |BR|<|BS| due to losses in the rotor, and θ = 80o.
BS = 0
BR = 0
BR = 0
BS = 0
BS = 0
Bnet is rotating in a
counterclockwise
direction.
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10.3 Starting Single-Phase
Induction Motors
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Starting Single-Phase Induction
Motors
As previously explained, the single-phase induction
motor has no intrinsic starting torque. There are
three techniques commonly used to start this type
of motor.
1. Split-phase windings
2. Capacitor-type windings
3. Shaded stator poles
All three starting techniques are methods of making
one of two revolving magnetic fields in the motor
stronger than the other, giving the motor an initial
nudge in one direction or the other.
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Split-Phase Windings
Main winding (big wire):
⇒ RM/XM low
⇒ IM nearly lags VAC by 90o
Main and auxiliary windings are
placed 90 electrical degree apart
the stator of the motor.
Designed to switch out at some
set speed.
Auxiliary winding (small wire):
⇒ RA/XA high
⇒ IA nearly in phase VAC
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Split-Phase Windings
As a result, IA leads IM
• Since IA leads IM, so the magnetic
field BA peaks before the main
magnetic field BM.
• So, there is a net counterclockwise
rotation in the magnetic field.
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Split-Phase Windings
• As a result, the auxiliary winding
makes one of the oppositely rotating
stator magnetic fields larger than
the other one.
• The auxiliary winding also
provides a net starting torque for
the motor.
• The direction of rotation of the
motor is determined by whether the
space angle of magnetic field from
the auxiliary winding is 90o ahead or
90o behind the angle of the main
winding.
• The direction of rotation of the
motor can be reversed by switching
the connections of the auxiliary
winding while leaving the main
winding’s connections unchanged.
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Capacitor-Start Motors
• In the split-phase motors, there are still both
magnetic fields rotating oppositely during starting
because IA leads IM not exactly 90o.
• As a result, there are two induced torque
(generated by these two oppositely rotating
magnetic fields) in the opposite ways, causing the
low net starting torque.
• Thus, the capacitor-start motors are designed to
increase the starting torque in the split-phase
motors.
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Capacitor-Start Motors
By proper selection of C size, IA
leads IM by 90o with the same
magnitude.
When IA leads IM by 90o, there is
only a single uniform rotating stator
magnetic field, causing the increase
of the starting torque.
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Permanent Split-Capacitor Motors
• In this type, the capacitor is left
permanently. No centrifugal switch.
• At normal loads, they are more
efficient, higher power factor, and
smoother torque than ordinary
single-phase induction motors.
• However, there is a tradeoff
between the large starting torque
and best running conditions
according to the capacitor size.
• Because the capacitor cannot
balance the currents under both
starting (high current) and running
(low current) conditions.
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Permanent Capacitor-Start,
Capacitor-Run (Two-Value Capacitor)
Motors
• To get the best performance
under both starting and running
conditions, two capacitors are used,
calling as “capacitor-start” and
“capacitor-run”.
• The large capacitor is present in
the circuit during starting, when it
ensures that the currents in the
main and auxiliary windings are
roughly balanced, yielding very high
starting torque.
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Shaded-Pole Motors
• There is only main winding, no
auxiliary windings.
• Instead, the motor has salient poles
and one portion of each pole is
surrounded by a short-circuited coil
called a “shading coil”.
• The induced current in the shading
coil causes the magnetic field within
the pole, causing the slight imbalance
between two oppositely rotating
stator magnetic fields.
• Then, the starting torque is
produced due to the such imbalance
of two oppositely rotating stator
magnetic fields.
• Shaded-pole motor produce less
starting torque, less efficient, higher
slip, and cheaper than any other type
of single-phase induction motor.
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Comparison of Single-Phase
Induction Motors
Ranking of single-phase induction motors in terms of
starting and running characteristics,
1. Capacitor-start, capacitor-run motor (most
expensive)
2. Capacitor-start motor
3. Permanent split-capacitor motor
4. Split-phase motor
5. Shaded-pole motor (least expensive)
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10.4 Speed Control of SinglePhase Induction Motors
Speed Control of Single-Phase
Induction Motors
For squirrel-cage rotor motors, the speed
control techniques are
• Vary the stator frequency
• Change the number of poles
• Change the applied terminal voltage
(commonly used)
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10.5 The Circuit Model of a
Single-Phase Induction Motor
Circuit Analysis with the Single-Phase
Induction Motor Equivalent Circuit (At
Standstill condition)
•
•
•
•
•
The equivalent circuit is developed
basing on the double-revolving-field
theory.
Only main winding is considered in
the equivalent circuit.
At standstill, the equivalent circuit of
the motor looks like the one of
single-phase transformer.
The pulsating air-gap flux can be
resolved into two equal and opposite
magnetic fields.
As a result, it is possible to split the
rotor equivalent circuit into two
sections, each one corresponding to
the effects of one of the magnetic
fields.
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Circuit Analysis with the Single-Phase
Induction Motor Equivalent Circuit (At
Running condition)
For the forward rotating magnetic field
(nsunc), the difference between the
rotor speed and the speed of
forward magnetic field is the slip,
s = (nsync-nm)/nsync
For the reverse rotating magnetic field
(-nsync), the difference between the
rotor speed and the speed of
reverse magnetic field is the slip
(-nsync-nm)/(-nsync)
= (nsync+nm)/nsync
= (nsync-nsync)/nsync+(nsync+nm)/nsync
= (2nsync -nsunc + nm)/nsync
= 2-(nsync-nm)/nsync
= 2-s
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Power-Flow Diagram of a SinglePhase Induction Motor
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Circuit Analysis with the Single-Phase
Induction Motor Equivalent Circuit (At
Running condition)
The forward impedance:
ZF = RF + jXF = (R2/s+jX2)(jXM)/[(R2/s+jX2)+jXM]
…(10-5)
The reverse impedance:
ZB = RB + jXB = (R2/(2-s)+jX2)(jXM)/[(R2/(2-s)+jX2)+jXM]
…(10-6)
The stator current:
I1 = V/(R1+jX1+0.5ZF+0.5ZB)
…(10-7)
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Powers and Torques in a SinglePhase Induction Motor
Air-gap power for the forward magnetic field:
PAG,F = I12(0.5 RF)
…(10-8)
Air-gap power for the reverse magnetic field:
PAG,B = I12(0.5 RB)
…(10-9)
Total air-gap power in a single-phase induction motor:
PAG = PAG,F − PAG,B
…(10-10)
Induced torque in a single-phase induction motor:
τind = PAG/ωsync
…(10-11)
Rotor copper losses in a single-phase induction motor:
PRCL = PRCL,F + PRCL,B
…(10-12)
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Powers and Torques in a SinglePhase Induction Motor
Forward rotor copper losses:
PRCL,F = sPAG,F
…(10-13)
Reverse rotor copper losses:
PRCL,B = sPAG,B
…(10-14)
Total converted power in a single-phase induction motor:
Pconv = τindωm
…(10-15)
= τind(1-s)ωsync
…(10-16)
= (1-s)PAG
…(10-17)
Note: PAG = τindωsync (see equation (10-11)).
Output power in a single-phase induction motor:
Pout = Pconv – Pcore – PF&W – Pstray
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Example Problem
Example 10-1 on page 663
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10.6 Other Types of Motors
Reluctance Motors
Stator structure: same as AC machine (single-phase or three-phase
windings), producing the rotating stator magnetic field.
Rotor structure: the iron salient pole.
• The reluctance torque is induced in such a
way that BR line up with BS.
• It is a type of the synchronous machine,
rotating at the synchronous speed.
• Like the synchronous motor, it has no
starting torque.
• Therefore, the amortisseur winding for
starting could be used in the reluctance motor
as well, so called “self-starting reluctance
motor”
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Hysteresis Motors
Stator structure: same as AC machine (single-phase or three-phase
windings), producing the rotating stator magnetic field.
Rotor structure: the iron non-salient (smooth cylindrical) pole.
• The rotating magnetic field appearing in the
machine magnetizes the metal of the rotor.
• Then, the induced poles are occurred within
the rotor.
• The torque is induced because BR lags BS
(δ>0) due to the large hystersis loss of the
rotor material.
• It is also a type of the synchronous
machine, rotating at the synchronous speed.
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Stepper Motors
Stator structure: the stator windings are concentrated (not sinusoidally
distributed like AC machine).
Rotor structure: the salient permanent-magnet or reluctance iron pole.
2-pole, 3-phase
Y-connected
stepper motor
• This type of motor is designed to
rotate a specific number of degrees
for every electric pulse received by the
control unit (e.g., 7.5o , 15o per pulse).
• The mechanical angle corresponds
to the electrical angle as follows:
θm = (2/P)θe
…(10-18)
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Stepper Motors
Rotor
position
0o
60o
120o
180o
240o
300o
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Stepper Motors
Pulse number 1 (va = VDC)
Initial rotor position ≠ 0o
Pulse number 1 (va = VDC)
Rotor position = 0o
Pulse number 2 (vc = -VDC)
Rotor position = 60o
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Stepper Motors
• The mechanical speed corresponds to the electrical speed as follows:
ωm = (2/P) ωe
…(10-19a)
nm = (2/P)ne
…(10-19b)
In this case, each phase is energized by either VDC or –VDC (2
combinations) while other two phases are not energized. So, there are 6
combinations for energizing three phases.
In other words, there are 6 pulses per electrical revolution. With the
given number of pulses per minute (npulses), the electrical speed in rpm
is therefore
ne = npulses/6
rpm
Substituting ne into equation (10-19b), yields
nm = (1/3P)npulses
…(10-20)
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Stepper Motors
Generally, for N-phases, there are 2N pulses per one electrical
revolution. Thus, the electrical speed in rpm becomes
ne = npulses/(2N)
rpm
where npulses = number of pulses per minute.
Substituting ne into equation (10-19b), the mechanical speed in rpm is
finally
nm = (1/NP)npulses
…(10-21)
Note: nm = (2/P)ne …(10-19b)
For example, if the control system sends 1200 pulses per minute to the
2-pole, 3-phase stepper motor, then the speed of motor will be
Given npulses = 1200 pulses/min and P = 2, and N = 3, then
nm = (1/(2*3))*1200 = 200 rpm
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Example Problem
Example 10-2 on page 674
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Brushless DC Motors
Stator structure: the stator windings (three-, four-, or more- phases) are
concentrated (not sinusoidally distributed like AC machine).
Rotor structure: the non-salient permanent-magnet pole
• This motor has advantages over
conventional DC motors due to the
elimination of brushes and
commutators.
• The driving operation of this motor
requires the rotor position.
• The basic components of a
brushless DC motor are permanentmagnet rotor, stator windings, rotor
4-phase brushless DC motor position sensor (i.e., Hall elements),
and electronic drive and control
circuits.
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Brushless DC Motors
45o
Phase A
180o
Phase B
Phase C
Phase D
360o
• For 4-phases, there are 8 states per
electrical period.
• Each state takes the electrical
degree of 45o (=360o/8).
• Since both VDC and –VDC are applied
to the phase windings, so the motor is
essentially AC motor, current flowing
both directions (not confused by its
name !!).
• This operation is called as onephase on because there is only onephase winding is energized at all time.
• The operation could be two-phase
on, i.e., two windings are energized at
all time.
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Brushless DC Motors
180o
Hall A
Phase A
45o
Hall B
Phase B
Hall C
Phase C
45o
Hall D
Phase D
360o
• Since the motor is 4-phases,
there are 4 Hall sensors (1 Hall
sensor per phase).
• Each Hall sensor is placed the
electrical degree of 45o
(=180o/4) apart of each other.
• The stator voltages are
supplied according to the Hall
signals.
• When the Hall sensors are not
used to detect the rotor position,
we call such drive system as
“sensorless”.
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1/7/2013
EEE 118: Energy Conversion
Dr. Mongkol Konghirun
Department of Electrical Engineering
King Mongkut’s University of Technology Thonburi
25