1 Phase Motors

ECE 3650 Electrical Machines Athula Rajapakse

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Single-Phase Induction Motors Construction

Rotor: Same as in a three-phase induction motor Stator: Only a single distributed winding

Magnetic field created by the stator winding Unlike a three-phase distributed winding which produce a rotating magnetic field, a single-phase

winding can produce only a pulsating magnetic field. The field gets larger and then smaller but in the same direction

+ve half cycle -ve half cycle

Fig. 1 Animation: http://www-h.eng.cam.ac.uk/help/mjg17/ teach/rotate/phase-a.html

Single-phase Induction Motor Under Starting Conditions

No starting torque since there is no rotating magnetic field. Fig. 2

Induced voltage due to transformer action produces currents in short circuited rotor bars. The resulting rotor flux is inline (but opposite in direction) with the stator flux. Net induced torque: 0)180sin(BB sR SRind BkBk

However, if the rotor begins to rotate, an induced torque will be produced on the rotor. This can be explained using Double-Rvolving-Field Theory or the Cross-Filed Theory.


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Double-Rvolving-Field Theory Stationary pulsating magnetic field can be resolved into two rotating magnetic fields that are equal in magnitude but rotating in opposite directions.

Fig. 3

Air gap field

jtBBSˆ)cos(max

Field revolving in the clockwise direction

jtBitBBCWˆ)sin(ˆ)cos( max2

1max2

1 Field revolving in the counter clockwise direction

jtBitBBCCWˆ)sin(ˆ)cos( max2

1max2

1 Total field

)()()( tBtBtB CCWCWS

t=0o t=45o t=90o

t=150o t=180o t=270o


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Torque-Speed Characteristics

Fig. 4 Net torque is the difference between two torque speed curves

Zero torque at zero speed No starting torque

The above representation is not quite accurate The simultaneous presence of two magnetic fields is not considered.

Three-phase Induction Motor Fig. 5 When the rotor speed is negative

Slip s > 1, rotor resistance is small Motor current is very large

Very high rotor frequency fR = sf Rotor reactance X2 >> R2 /s

Rotor current lags the rotor voltage by almost 90o

Rotor magnetic field is nearly 180o out of phase with stator magnetic field Very small torque

Reduction in torque is partially compensated by the increased current

I 1 R 1 X 1

E 1 E2

I 1 '

R m Xm

I 2 R2 X2

N 1 :N 2

mechanical output power component

R2(1/s-1)

rotor stator

R2(1-s)/s


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Fig. 6 Fig. 7


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Single-Phase Induction Motor

When the rotor is in motion,

Backward flux wave see a slip > 1

Component of rotor current induced by the backward field are greater than that at standstill, and the power factor is lower.

The direction of rotor magnetic field is almost opposite to the field produced by the stator currents

o Reduced backward flux wave.

Forward flux wave see a slip < 1

Component of currents induced by the forward field is less than that at standstill, and their power factor is higher.

The direction of rotor magnetic field is such that it increases magnitude of forward flux wave.

When the speed increases

o the forward flux wave increases

o the backward flux wave decreases Performance of the single-phase induction motor is considerably better than that would be predicted on the basis of forward and backward flux waves.

Torque-Speed Characteristics

(a) without considering effect of rotor field (b) considering the effect of rotor field Fig. 8


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Starting of Single-Phase Induction Motors Since single-phase induction motors produce no intrinsic starting torque, special arrangement is needed.

Split phase windings Capacitor-type windings Shaded stator poles

Single-phase induction motors are classified according to the starting method. All starting techniques are methods of making one of the two rotating fields in the machine stronger than the other, Split-Phase Winding

Fig. 9 Main winding and Auxiliary winding are 90o electrical apart along the stator. Auxiliary Winding

Switched out of the circuit at some set speed by a centrifugal switch Designed to have low X/R ratio Use smaller wire to achieve high R Current in the auxiliary winding leads the current in main winding

Fig. 10


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Torque-Speed Characteristics Fig. 11 Features

Moderate starting torque Used for low starting torque applications Fans, pumps, blowers, etc. Inexpensive Available in the fractional horse power range

Direction of Rotation

Direction is determined by the space angle of the auxiliary winding magnetic field 90o leading or 90o lagging Can be reversed by changing the connection of auxiliary winding while the main winding

connections are kept unchanged

Capacitor Start Motors

Fig 12

Capacitor is connected in series with the auxiliary winding By proper selection of Capacitor value, the mmf of Auxiliary winding can be made equal to that of

Main winding Create a single uniform rotating magnetic field – Behaves like a three-phase induction motor


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Torque-Speed Characteristics Fig. 13 Features

Very high starting torque ~ 300% of the rated torque More expensive than split-phase motors Used in applications those require high starting torque Compressors, pumps, air conditioners, equipment start under load

Permanent Split Capacitor Fig. 14

Starting capacitor does a very good job in improving the torque speed characteristics Capacitor is left in the circuit even during the normal running conditions Operate just like a three-phase induction motor – smooth torque Features Simpler than capacitor start motor – no centrifugal switch At normal loads, they are more efficient Higher power factor Smooth operation Lower starting torque than capacitor start motors

o capacitor size is selected to balance the currents at the normal load conditions o Under starting conditions, current is very high and unbalanced


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Capacitor Start, Capacitor Run Motors Fig. 15 Two Capacitors are used to obtain

Largest possible starting torque Best running conditions Cstart is switched out after a certain speed

Torque-Speed Characteristics Fig. 16 When starting C = Crun+Cstart balances the winding currents yielding high starting torque The permanent capacitor Cstart is just enough to balance the currents at normal speeds Crun= 10-20% of Cstart

Direction of Rotation

Direction of rotation of any capacitor-type motor can be reversed by changing the connections of its auxiliary windings.


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Shaded-Pole Induction Motors Fig 17 No auxiliary winding Has salient poles Each pole is split into two – one portion is surrounded by a short circuited coil called shading ring Changing magnetic flux created by the main winding induces a voltage and therefore a current in

the shading ring The current in a shading ring creates a field that opposes the changes in the field that created it. This opposition retards the flux changes creating slight imbalance between the two oppositely

rotating flux waves Net rotation is from unshaded to the shaded portion of the pole face Direction of rotation cannot be easily changed. Torque-Speed Characteristics Fig 18 Features

Less starting torque Less efficient Used only in very small motors ( 0.05 hp and less) with very low starting torque requirements The cheapest design when it can be used.


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Comparison of single-phase induction motors Ranking from best to worse in terms of starting and running characteristics

Capacitor start, capacitor run motor Capacitor start motor Permanent split capacitor motor Split-phase motor Shaded pole motor

Circuit Model of a Single-Phase Induction Motor

We can use double revolving field theory to develop an equivalent circuit

Only the case of running with main winding is considered Analysis of operation with both winding requires use of symmetrical components

Case -1 : When the motor is stalled Fig. 19

Motor appears like a single phase transformer with short circuited secondary Core loss can be lumped with the rotational losses (or with stray load losses) The machine magnetic field can be resolved into two equal and oppositely rotating magnetic fields Equivalent circuit can be split into two sections, each corresponding to the effects of one of the

two magnetic fields Fig. 20


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Case-2: When running Effective rotor resistance depends on the slip Two magnetic fields – the slip is different for the two magnetic fields

Forward field: s

RS

N

NNs

Backward field: sN

NN

N

NNs

s

RS

s

RSB

2

)(

Fig. 21 Analysis of Single-Phase Induction Motor Performance Using the Equivalent Circuit The net power and torque in the machine is the difference between forward and reverse components. Fig. 22

MsR

MsR

FFF jXjX

jXjXjXRZ

)(

))((

2

2

2

2

MsR

MsR

BBB jXjX

jXjXjXRZ

)(

))((

2)2(

2)2(

2

2

BF ZZjXR

VI

5.05.0111


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Calculation of Output Power and Torque Calculation of the current in rotor impedance branches in forward and backward components is tedious. We can workaround by considering the air gap power.

Air Gap Power (PAG)

Induced torque

Converted Power:

Rotor copper loss (PRCL):

Since the two current components are operating at two different frequencies:

The net mechanical output: Power Flow in a Single-Phase Induction Motor Fig. 23

)5.0(21, FFAG RIP

)5.0(21, BBAG RIP

BAGFAGAG PPP ,,

)5.0(21,, FFRCLFRCL RsIsPP

)5.0()2()2( 21,, BBAGBRCL RIsPsP

BRCLFRCLRCL PPP ,,

sync

AGind

P

AGmindconv PsP )1(

rotconvout PPP


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Example1: A 2.4 kW, 120 V, 60 Hz, capacitor-start motor has the following impedances for the main and auxiliary windings at starting: ZM = 4.5 + j3.7

ZA = 9.5 + j3.5 Find the value of starting capacitance that will place the main and auxiliary winding currents in quadrature at starting.

Example2:

A 1/3 hp, 110 V, 60 Hz, six-pole, split phase induction motor has the following impedances: R1 = 1.52 X1 = 2.10 XM = 58.2

R2 = 3.13 X2 = 1.56 The core losses of this motor are 35W, and the friction, windage and stray losses are 16W. The motor is operating at the rated voltage and frequency with its starting winding open, and the motor’s slip is 5%. Find the following quantities: (a) speed in rpm, (b) stator current in A (c) stator power factor (d) input power (e) air fap power, (f) converted power (g) induced torque, (h) output power (i) load torque, (j) Efficiency


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Universal Motor Torque of a DC motor

Aind IK

where = flux per pole IA = Armature current If the direction of both filed winding and armature winding are reversed at the same time,

AAind IKIK ))(( the direction of torque remains the same. Fig. 24 If an alternating current is applied to both windings, the torque will still be unidirectional, but pulsating as shown in Fig. 2. Fig. 25 DC shunt motor If both windings are connected to the same AC voltage source

Very high inductance in the field coil causes current through it to lag behind armature current Field direction reversal is delayed relative to armature current reversal Instantaneous torque become negative during some intervals The average torque will be unacceptably low


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DC Series Motor When connected to an AC voltage source:

The same current flow through the both windings Instantaneous torque is always positive Could be successfully used as an AC motor

Universal Motor

In order to work with AC, field poles and stator frame need to be completely laminated o Otherwise the Core Loss will be enormous

When the poles and stator are laminated, a DC series motor is called a Universal Motor o Can be run using AC or DC

When the motor is run with AC, commutation is poorer: transformer voltages induced on the coils results in sparking during the commutation

o Much shorter brush life o Source of radio-frequency interference o Poor commutation can be rectified by using a compensation winding

Fig. 26 Equivalent circuit and phasor diagram Torque Speed Characteristics of Universal Motor

Fig. 27 Torque speed characteristics

with DC supply

with AC supply

Torque

Speed


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Torque with AC current is less than that with DC Voltage drop across the reactance at 60 Hz or 50 Hz Small back emf ( KEA )

Smaller flux at a given speed Peak voltage of an AC system is 2 times the rms voltage To avoid saturation voltage rating has to be lowered Therefore, rms flux is significantly low

Characteristics of Universal Motor

Universal motor is light weight Has sharply drooping torques speed characteristics Not suitable for constant speed applications Gives more torque per ampere than other type of single phase motors Operating speeds 1500-15000 rpm

Applications of Universal Motor Vacuum cleaners Hand drills Portable tools Kitchen appliances

Speed Control

Fig. 28 Torque speed characteristics at different terminal voltages


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Speed Control Circuits

Fig. 29 Speed control with SCR (Thyristor)

Fig. 30 Speed control with TRIAC

Example: A 120 V, 60 Hz, 2-pole, universal motor operates at a speed of 8000 rpm and on full load and draws a current of 17.58 A at a lagging power factor of 0.912. The impedance of the series field winding is 0.65 + j1.2 . The impedance of the armature winding is 1.36 + j1.6 . Determine (a) the induced back emf in the armature, (b) the power output, (c) the shaft torque, and (d) the efficiency if the rotational loss is 80 W.

1 Phase Motors

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