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EEE 118: Energy Conversion
Dr. Mongkol Konghirun
Department of Electrical EngineeringKing Mongkuts University of Technology Thonburi
Chapter 10
Single-Phase And Special-Purpose Motors
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10.1 The Universal Motor
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The Universal Motor
The universal motor is essentially the series orshunt DC motor. However, it can be operatedon a single-phase AC power source.
Recall from Chapter 8:ind = KIA (8-49)
When the polarity of the voltage applied to ashunt or series DC motor is reversed, bothdirection of field flux () and the direction ofarmature current (IA) reverse, and resultinginduced torque continues in the samedirection as before
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Torque-Speed CharacteristicThe torque-speed characteristic of a universalmotor is different from one of the samemachine operating from DC voltage for tworeasons:
1. The armature and field windings have quitelarge reactance (as a function of frequency).So, the voltage drop across these reactancesare large. Thus, the EA= K is smaller for agiven input voltage. Then, the motor speed
is slower for a given IAand ind.
2. The peak voltage of an AC system is 2times its RMS value. The magnetic saturationcould occur near the peak current, loweringthe magnetic flux of the motor for a givencurrent. The induced torque is partiallyreduced for a given speed.
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Applications of UniversalMotors
The universal motor has the sharply drooping torque-speedcharacteristic of a DC series motor (EAsignificantlyreduced), so it is not suitable for constant-speed
applications.
However, it is compact, light weight and gives moretorque/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 UniversalMotors
Similar to the DC series motor, the speed of universalmotor is increased when the RMS input voltage isincreased.
10.2 Introduction to Single-PhaseInduction Motors
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Introduction to Single-PhaseInduction Motors
ind = k (BR BS) (4-58)ind = k BRBS sin
= k BRBS sin 180o = 0
where is angle between BRand BS.
The single-phase induction motor hasonly one phase winding sinusoidallydistributed.
The magnetic field in a single-phaseinduction motor does not rotate.Instead, it pulses getting larger firstand then smaller, but always remainingin the same direction during the halfcycle. Thus, there is no startingtorque.
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Introduction to Single-PhaseInduction Motors
However, once the rotor begins toturn, an induced torque will beproduced in it. There are two basic
theories which explain why atorque is produced in the rotoronce it is turning.
1. Double-revolving-field theory ofsingle-phase induction motor
2. Cross-field theory of single-phaseinduction motor
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The Double-Revolving-Field Theoryof Single-Phase Induction Motors
The double-revolving-field theory of single-phase induction motorbasically states that a stationary pulsating magnetic field canresolved into two rotating magnetic fields, each of equal magnitudebut rotating in opposite direction.
The induction motor responds to each magnetic field separately, andthe net torque in the machine will be the sum of the torque due toeach of the two magnetic fields.
The flux density of the stationary magnetic field produced by the stator
current is given byBS(t) = (Bmax cos t)j (10-1)
= BCW(t) + BCCW(t) (10-4)Clockwise-rotating:
BCW(t) = (0.5Bmaxcos t)j + (0.5Bmaxsin t)i (10-2)
Counterclockwise-rotating:BCCW(t) = (0.5Bmaxcos t)j - (0.5Bmaxsin t)i (10-3)
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The Double-Revolving-Field Theoryof Single-Phase Induction Motors
BS(t) = (Bmax cos t)j (10-1)= BCW(t) + BCCW(t) (10-4)
BS = Bmaxj (t=0)
BS = -Bmaxj (t=180o)
BS = 0 (t=90o)
BS = 0 (t=270o)
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The Double-Revolving-Field Theoryof Single-Phase Induction Motors
No Starting torque
Forward and reverse magneticfields are produced by the samecurrent. Both magnetic fields rotate inthe opposite direction. Then, each magnetic fieldproduces own induced torque atrotor. The net induced torque is the
sum of the induced torquesproduced by these two magneticfields. As a result, there is no startingtorque in the motor.
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The Cross-Field Theory of Single-Phase Induction Motors
The cross-field theory of single-phase induction motor is concernedwith the voltages and currents that the stationary stator magneticfield can induce in the bars of the rotor when the rotor is moving.
Rotor voltage is induced in such asway that its flux opposes the BS (see
plane of maximum rotor voltage)
Because of rotors high reactance, theinduced rotor current lags the rotorvoltage by almost 90o.
Since the rotor is rotating in clockwisedirection, at a certain time, thus theplane of maximum rotor current leadsthe plane of maximum rotor voltage by 90o in space.
Finally, the BR is produced by IRasshown.
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The Cross-Field Theory of Single-Phase Induction Motors
Bnet is rotating in acounterclockwisedirection.
BS = 0
BS = 0
BR= 0 BS = 0
BR= 0
BS = |BS|sin(t) 90o
BR= |BR|sin(t-90o) -90owhere |BR|
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Starting Single-Phase InductionMotors
As previously explained, the single-phase inductionmotor has no intrinsic starting torque. There arethree techniques commonly used to start this typeof motor.
1. Split-phase windings2. Capacitor-type windings
3. Shaded stator poles
All three starting techniques are methods of makingone of two revolving magnetic fields in the motorstronger than the other, giving the motor an initialnudge in one direction or the other.
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Split-Phase Windings
Designed to switch out at someset speed.
Main and auxiliary windings areplaced 90 electrical degree apartthe stator of the motor.
Auxiliary winding (small wire): RA/XAhigh IA nearly in phaseVAC
Main winding (big wire): RM/XM low IM nearly lagsVAC by 90o
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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 mainmagnetic field BM.
So, there is a net counterclockwiserotation in the magnetic field.
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Split-Phase Windings
As a result, the auxiliary windingmakes one of the oppositely rotatingstator magnetic fields larger thanthe other one.
The auxiliary winding alsoprovides a net starting torque forthe motor.
The direction of rotation of themotor is determined by whether the
space angle of magnetic field fromthe auxiliary winding is 90o ahead or90o behind the angle of the mainwinding.
The direction of rotation of themotor can be reversed by switchingthe connections of the auxiliarywinding while leaving the mainwindings connections unchanged.
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Capacitor-Start Motors
In the split-phase motors, there are still bothmagnetic fields rotating oppositely during startingbecause IA leads IM not exactly 90
o.
As a result, there are two induced torque(generated by these two oppositely rotating
magnetic fields) in the opposite ways, causing thelow net starting torque.
Thus, the capacitor-start motors are designed toincrease the starting torque in the split-phasemotors.
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Capacitor-Start Motors
By proper selection of C size, IAleads IM by 90
o with the samemagnitude.
When IA leads IM by 90o, there is
only a single uniform rotating statormagnetic field, causing the increaseof the starting torque.
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Permanent Split-Capacitor Motors
In this type, the capacitor is leftpermanently. No centrifugal switch.
At normal loads, they are moreefficient, higher power factor, andsmoother torque than ordinarysingle-phase induction motors.
However, there is a tradeoffbetween the large starting torque
and best running conditionsaccording to the capacitor size.
Because the capacitor cannotbalance the currents under bothstarting (high current) and running(low current) conditions.
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Permanent Capacitor-Start,Capacitor-Run (Two-Value Capacitor)Motors
To get the best performanceunder both starting and runningconditions, two capacitors are used,
calling as capacitor-start andcapacitor-run.
The large capacitor is present inthe circuit during starting, when itensures that the currents in themain and auxiliary windings areroughly balanced, yielding very highstarting torque.
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Shaded-Pole Motors
There is only main winding, noauxiliary windings. Instead, the motor has salient polesand one portion of each pole issurrounded by a short-circuited coilcalled a shading coil. The induced current in the shadingcoil causes the magnetic field withinthe pole, causing the slight imbalancebetween two oppositely rotatingstator magnetic fields.
Then, the starting torque isproduced due to the such imbalanceof two oppositely rotating statormagnetic fields. Shaded-pole motor produce lessstarting torque, less efficient, higherslip, and cheaper than any other typeof single-phase induction motor.
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Comparison of Single-PhaseInduction Motors
Ranking of single-phase induction motors in terms ofstarting and running characteristics,
1. Capacitor-start, capacitor-run motor (mostexpensive)
2. Capacitor-start motor3. Permanent split-capacitor motor4. Split-phase motor5. Shaded-pole motor (least expensive)
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10.4 Speed Control of Single-Phase Induction Motors
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Speed Control of Single-PhaseInduction Motors
For squirrel-cage rotor motors, the speedcontrol 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 aSingle-Phase Induction Motor
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Circuit Analysis with the Single-PhaseInduction Motor Equivalent Circuit (AtStandstill condition)
The equivalent circuit is developedbasing on the double-revolving-fieldtheory.
Only main winding is considered inthe equivalent circuit.
At standstill, the equivalent circuit ofthe motor looks like the one ofsingle-phase transformer.
The pulsating air-gap flux can beresolved into two equal and oppositemagnetic fields.
As a result, it is possible to split therotor equivalent circuit into twosections, each one corresponding tothe effects of one of the magneticfields.
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Circuit Analysis with the Single-Phase
Induction Motor Equivalent Circuit (AtRunning condition)
For the reverse rotating magnetic field(-nsync), the difference between therotor speed and the speed ofreverse 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
For the forward rotating magnetic field(nsunc), the difference between therotor speed and the speed offorward magnetic field is the slip,
s = (nsync-nm)/nsync
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Power-Flow Diagram of a Single-Phase Induction Motor
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Circuit Analysis with the Single-Phase
Induction Motor Equivalent Circuit (AtRunning 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 Single-Phase Induction Motor
Air-gap power for the forward magnetic field:PAG,F = I1
2(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:ind = PAG/sync (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 Single-Phase 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 = indm (10-15)
= ind
(1-s)sync
(10-16)= (1-s)PAG (10-17)
Note: PAG = indsync (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
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Reluctance Motors
Stator structure: same as AC machine (single-phase or three-phasewindings), producing the rotating stator magnetic field.
Rotor structure: the iron salient pole.
The reluctance torque is induced in such away 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 nostarting torque. Therefore, the amortisseur winding forstarting could be used in the reluctance motoras well, so called self-starting reluctancemotor
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Hysteresis Motors
Stator structure: same as AC machine (single-phase or three-phasewindings), producing the rotating stator magnetic field.
Rotor structure: the iron non-salient (smooth cylindrical) pole.
The rotating magnetic field appearing in themachine magnetizes the metal of the rotor. Then, the induced poles are occurred withinthe rotor. The torque is induced because BR lags BS(>0) due to the large hystersis loss of therotor material. It is also a type of the synchronousmachine, rotating at the synchronous speed.
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Stepper Motors
Stator structure: the stator windings are concentrated (not sinusoidallydistributed like AC machine).
Rotor structure: the salient permanent-magnet or reluctance iron pole.
This type of motor is designed torotate a specific number of degreesfor every electric pulse received by thecontrol unit (e.g., 7.5o , 15o per pulse). The mechanical angle correspondsto the electrical angle as follows:
m = (2/P)e (10-18)
2-pole, 3-phaseY-connectedstepper motor
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Stepper Motors
0o
60o
120o
300o240o
180o
Rotorposition
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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:m = (2/P) e (10-19a)nm = (2/P)ne (10-19b)
In this case, each phase is energized by either VDC or VDC (2combinations) while other two phases are not energized. So, there are 6combinations 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 rpmis thereforene = npulses/6 rpm
Substituting ne into equation (10-19b), yieldsnm = (1/3P)npulses (10-20)
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Stepper Motors
Generally, for N-phases, there are 2N pulses per one electricalrevolution. Thus, the electrical speed in rpm becomes
ne = npulses/(2N) rpmwhere npulses = number of pulses per minute.
Substituting ne into equation (10-19b), the mechanical speed in rpm isfinally
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 the2-pole, 3-phase stepper motor, then the speed of motor will be
Given npulses = 1200 pulses/min and P = 2, and N = 3, thennm = (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) areconcentrated (not sinusoidally distributed like AC machine).
Rotor structure: the non-salient permanent-magnet pole
4-phase brushless DC motor
This motor has advantages overconventional DC motors due to theelimination of brushes andcommutators. The driving operation of this motorrequires the rotor position. The basic components of abrushless DC motor are permanent-magnet rotor, stator windings, rotorposition sensor (i.e., Hall elements),and electronic drive and controlcircuits.
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Brushless DC Motors
For 4-phases, there are 8 states perelectrical period. Each state takes the electricaldegree of 45o (=360o/8). Since both VDC and VDC are appliedto the phase windings, so the motor isessentially AC motor, current flowingboth directions (not confused by itsname !!). This operation is called as one-phase on because there is only one-phase winding is energized at all time. The operation could be two-phaseon, i.e., two windings are energized atall time.
360o
45o
180oPhase A
Phase B
Phase C
Phase D
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Brushless DC Motors
360o
45o
180o
Phase A
Phase B
Phase C
Phase D
Hall A
Hall B
Hall C
Hall D
Since the motor is 4-phases,there are 4 Hall sensors (1 Hallsensor per phase). Each Hall sensor is placed the
electrical degree of 45o(=180o/4) apart of each other. The stator voltages aresupplied according to the Hallsignals. When the Hall sensors are notused to detect the rotor position,we call such drive system as
sensorless.
45o
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EEE 118: Energy Conversion
Dr. Mongkol Konghirun
Department of Electrical EngineeringKing Mongkuts University of Technology Thonburi