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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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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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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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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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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

eee118 ch10 final

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