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    ThreeThree--Phase Induction MotorPhase Induction Motor(Asynchronous )(Asynchronous )

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    2

    Contents

     

    Introduction

     

    Rotating Magnetic field

     

    Construction and Principle of Operation

     

    Equivalent Circuit

     

    Performance Characteristics

     

    Starting Methods

     

    Speed Control

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    3

    Laws of Electromagnetism

     

    Faraday’s Law

     

    Lenz’s Law

     

    Fleming’s Right Hand rule

     

    Fleming’s Left Hand rule

     

    Interaction of two magnetic fields

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    4

    Faraday’s Law ofElectromagnetic Induction

     

    When the magnetic fluxthrough a circuit ischanging an induced

    EMF is setup in thatcircuit and its magnitudeis proportional to the

    rate of change of flux”

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    5

    Lenz’s Law

     

     “

     

    The direction of an

    induced EMF is suchthat its effect tendsto oppose the changeproducing it” 

    http://h/123/Lenz.avi

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    6

    Fleming’s Right Hand rule

    Used to measure the direction of

    induced current in a conductor when

    cut by a magnetic field.

    Fleming’s Left Hand rule

    Used to measure the direction of

    motion of a current carryingconductor when placed in

    magnetic field.

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    7

    Interaction of two magnetic fields

    Electromagnetics

    Stator 

    Rotor 

    http://c/Documents%20and%20Settings/user/Local%20Settings/Temporary%20Internet%20Files/Content.IE5/4LU4EGW8/DC_motor.avi

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    8

     

    About 65% of the electric energy in the United States isconsumed by electric motors.

     

    In the industrial sector alone, about 75% is consumed by

    motors and over 90% of them are induction machines.

     

    Simple construction, Robust, Cheap

    Introduction

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     MOTOR

    9

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    Production of three phase

    rotating magnetic field (RMF)

     

    RMF may be set up in two-phase or three-phasemachines.

     

    The number of pole pairs must be the same as the

    number of phases in the applied voltage.

     

    The poles are displaced from each other by an

    angle equal to the phase angle between theindividual phases of the applied voltage.

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    + When Current positive and going into

     

    When Current negative and coming from

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    Rotating Magnetic Field

     p f n s

    s120

    When three-phase balanced currents

    are applied to a three-phase winding,

    (aa', bb', cc', displaced from each other

    by 120 electrical degrees in space), a

    rotating magnetic flux is produced.

    The speed at which the magnetic flux rotates is called the

    synchronous speed ns

     

    ,

    Where  f s is the supply frequency and p is the total numberof poles.

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    Rotating Magnetic Field (Cont.)

     

    Currents in different phases of AC Machine

    1 Cycle

    Amp

    timet0 t1 t2 t3 t4

    t01 t12

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    MMF due to ac current in phase “a” 

    Axis of phase a

    a’a’

    -90 -40 10 60 110 160 210 260-1

    -0.8

    -0.6

    -0.4

    -0.2

    0

    0.

     

    2

    0.4

    0.6

    0.8

    1

    Fa

    Space angle (

     

    ) in degrees

    t0

    t01

    t12

    t2

    at1

    a

    a

    Fa

    +

    .

    Axis of

     phase a

    Pulsating mmf 

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    a

    a’

    c’  b’

     b c

    Fc

    F b

    Fa F

    t = t0

    a

    a’

    c’  b’

     b c

    Fc

    F

    F b

    t = t1

    F

    a

    a’

    c’  b’

     b c

    F b

    Fa

    Fc

    t = t2

    a

    a’

    c’  b’

     b c

    Fc F bF t = t3

    -93 10 113 216-1.5

    -1

    -0.5

    0

    0.5

    1

    1.5

    Space angle () in degrees

    FFa Fc

    F b

    t = t0

    MMF due to three-phase currents in three-

    phase winding

    MMF’s at various instant ( Rotating mmf )

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     b a    c

    Time

    t 1 t 3t 2

    Rotating Magnetic Field

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     b a    c

    Time

    t 1 t 3t 2

    ia

    ic

    ib

     b

     c

     a a

     c

     b

    Rotating Magnetic Field

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     b a    c

    Tim

    t 1 t 3t 2 

    ia  

    ic 

    ib 

     b 

     c 

     a 

    max2

    max

    2

    max23  

    max2

    max2

    3 max2

    max2

    max2

    max

    2

     At t1

     At t 2

     At t 3

    Rotating Magnetic Field

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    Rotating Magnetic Field

    www.ewh.ieee.org

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    Principle of Operation

    If the stator windings are connected

    to a three-phase supply; a rotating field

    will be produced in the air-gap. This field

    rotates at synchronous speed ns. This

    rotating field induces voltages in the

    rotor windings. Since the rotor circuit is

    closed, the induced voltages in the rotor

    windings produce rotor currents thatinteract with the air gap field to produce

    torque. The rotor will eventually reach a

    steady-state speed nm that is less than

    the synchronous speed ns.

    The difference between the rotor

    speed and the synchronous speed is

    called the slip, s ,

    www.ewh.ieee.org

    s

    s

    n

    nnS

     

    s

    sS 

       

    60

    n2    n 

     

    in rpmω  in rad/s

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    Analytical expression for the rotating mmf 

    An analytical expression may be obtained for the resultant mmf wave at

    any point in the air gap, defined by an angle .

    )120cos()120cos(cos

    )()()()(

       

        

    cba

    cba

     Ni Ni Ni

    F F F F 

    The currents ia

     

    , i b

     

    and ic are function of time thus

    )120cos()120cos(

    )120cos()120cos(coscos)(

      

         

    t  NI 

    t  NI t  NI F 

    m

    mm

    )cos(2

    3

    )240cos(

    2

    1)cos(

    2

    1

    )240cos(2

    1)cos(

    2

    1

    )cos(

    2

    1)cos(

    2

    1)(

    t  NI 

    t  NI t  NI 

    t  NI t  NI 

    t  NI t  NI F 

    m

    mm

    mm

    mm

      

        

        

         

    0 /

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    Construction

    1- STATOR

    A three-phase windings is put in slots cut on the inner

    surface of the stationary part. The ends of these

    windings can be connected in star or delta to form athree phase connection. These windings are fed from a

    three-phase ac supply.

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    Construction (Cont.)

     2- Rotorit can be either:

    a- 

    Squirrel-cage (brushless)

     

    The squirrel-cage windingconsists of bars embedded inthe rotor slots and shorted at both ends by end rings.

     

    The squirrel-cage rotor is the

    most common type because itis more rugged, moreeconomical, and simpler.

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    /rotor winding/rotor winding

    Short circuits allShort circuits all

    rotor bars.rotor bars.

    25

    Squirrel Cage Induction Motor (SCIM)

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    Construction (Cont.)

     b- 

    Slip ring (wound-rotor)The wound-rotor winding has the same

    form as the stator winding. The windings

    are connected in star. The terminals ofthe rotor windings are connected to three

    slip rings. Using stationary brushes

     pressing against the slip rings, the rotorterminals can be connected to an

    external circuit.

    26

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    Construction-Wound Rotor Induction Motor (WRIM)

    Cutaway in a

    typical wound-

    rotor IM.

     Notice the

     brushes and the

    slip rings

    Brushes

    Slip rings

    27

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    APPLICATION OF SLIP RING

    MOTOR

    compressor Central air conditoining

    29

    Wound rotr 

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    ADVANTAGES OF SLIP RING AND

    SQUIRREL CAGE MOTOR

    SQUIRREL CAGE SLIP RING

    cheaper and more robustslightly

    the starting torque is muchhigher and the starting current

    much lower 

    higher efficiency and power

    factor 

    the speed can be varied by means

    of external rotor resistors

    explosion proof, since the

    absence of slip-rings and brusheseliminates risk of sparking.

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    Principle of Operation

     

    If the stator windings are connected to athree-phase supply; a rotating field will be produced in the air-gap. This field

    rotates at synchronous speed ns. Thisrotating field induces voltages in therotor windings. Since the rotor circuit isclosed, the induced voltages in the rotor

    windings produce rotor currents thatinteract with the air gap field to producetorque. The rotor will eventually reach a

    steady-state speed nm that is less than thesynchronous speed ns.

     

    The difference between the rotor speedand the synchronous speed is called the

    slip, S , and is defined as

     s

     m s

     n

     n nS  

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    Definitions

     

    nm = the rotor speed (the motor speed) w.r.t. stator

     

    ns

    = the speed of stator field w.r.t. stator or the synch. speed

     

    nr = the speed of rotor field w.r.t rotor

     

    S = the slip

     

     f s = the frequency of the induced voltage in the stator (stator

    or supply frequency)

     

     f r = the rotor circuit frequency or the slip frequency

    S mS r  snnnn   Slip rpm

    S S mS r r  f S nS 

     pnn

     pn

     p f    )(

    120)(

    120)(

    120

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    Induced EMF

    w p phrms K  N  f  E    44.4

    The instantaneous value of the induced voltage

    in N turns coil is given by:

    )90sin(2)cos(

    )sin(

    t  f  N t  N e

    t  Let 

    dt 

     N e

    mm

    m

          

       

     

    The r.m.s. value of the induced voltage per phase is

    where

     N  ph is the number of turns in series per phase

     f is the frequency

      p

    is the flux per pole

    K w is the winding factor 

     phase voltage is 1/√3

    of the normal voltage

     phase voltage is equal

    to the line voltage.

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    2

    1

    2

     N 

     N 

     E 

     E 

     

     I 1

     X 1 R1

     N 1

     I  

     E 1V  

     I c

     X c Rc

     I r   I 2

    2  R2

    2  E 2

    1

    2

    2

    12

     I 

     I 

     N 

     N 

     I 

     I 

    • 

    At standstill 

    (nm= 0 , S = 1)The equivalent circuit of an induction motor at standstill is the

    same as that of a transformer with secondary short circuited.

    Equivalent Circuit Per Phase

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    • 

    At standstill 

    (nm= 0 , S = 1)

    The equivalent circuit of an induction motor at standstill is the

    same as that of a transformer with secondary short circuited.

    V 1

     I 2’

     R1  R2’ X 1  X 2

     X c Rc

     I c I 1

     I 2’

     E 1

     

    = E 2’  All values are

    per phase

    Where

    E2

     

    = per-phase induced voltage in the rotor at standstill

    X2 = per-phase rotor leakage reactance at standstill

    Equivalent Circuit Per Phase

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    Equivalent Circuit Per Phase (cont.)

     

    At any slip S

    When the rotor rotates with speed nm

     

    the rotor circuit

    frequency will be:

      Therefore induced voltage in the rotor at any slip S will

     be

     

    E2S

    = S E2

     

    , similarly X2S

    = SX2

    and the rotor equivalent circuit per-phase will be:

    S r   f S  f  

    sX2   X2

      X2

    R2

     

    (1-S)/S

    I2

    sE2   R2

    I2

    E2   R2

     

    /S

    I2

    E2

    R2

     2 2

     2

     2 2

     2 2

     jX  ) s /  R(  E

     jSX  RSE I 

     

     

    Where

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     I 2  I 1

     X 2  X 1 R1  R2 /s  N 1 : N 2

     E 2

     I  

     E 1

     I c

     X c RcV  

    Combined Equivalent Circuit

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     I 2’ 

     I 1

    2’1 R1  R2’  /s 

     E 1  E 2’ 

     I c

    c RcV  

    2

    2

    12

    ' 2

     N 

     N  R R

     

      

     

    2

    2

    12

    ' 2

     N 

     N  X  X 

     

      

     

     

     

     

     

    1

    22

    ' 2

     N 

     N  I  I 

    Combined Equivalent Circuit

      2’

    1 R1  R2’  /s 

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     I 2’ 

     I 1

    2’

    1 R1  R2’ 

     E 1  E 2’ 

     I c

    c RcV   )s1(s

     R' 2

    )s1(s

     R Rs

     R' 

    2' 2

    2

     I 2

    ’ 

     I 1

     E 1  E 2’ 

     I c

    c RcV  

    Equivalent Circuit of IM

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    Equivalent Circuit of IM

     I o

    V 1

     I 1

     E 1

    '

    2 R

     RS '

    2)1(  

    Stator CircuitStator Circuit  Rotor Circuit Rotor Circuit

     Airgap & Airgap &

     Magnetic Circuit  Magnetic Circuit 

    1 X 

    '

    2 X 

    m

     X 

     I’2

    c R

     Load + Load +

     Rotational losses Rotational losses

    1 R

    2’

    1R1 R2’

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    Equivalent to transformer’s

    load

    Equivalent to transformer’ssecondary windings

    Equivalent to transformer’sprimary windings

     

     I 2’ 

     I 1

    21 R1  R2  

     E 1  E 2’ 

     I c

    c RcV   )s1(s

     R' 2

    2’

    1R1 R2’

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     I 2’ 

     I 12

    ’  R2’ 

     E 1  E 2’ 

    1 R1

    c

     I c

     RcV   )s1(s

     R' 2

     

     I 2’ 

     I 1

    21 R1  R2  

     E 1  E 2’ 

     I c

    c RcV   )s1(s

     R' 2

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     I 2’ 

     I 1

     X eq  Req 

     X c

     I c

     RcV   )s1(s R' 2  

    ' 21eq

    21eq

     X  X  X 

     R R R

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    Equivalent Circuit Per Phase (cont.)

    1-The Complete Equivalent Circuit per phase

     I o

    V 1

     R1 I 1

     E 1

    '

    2 R

     RS '

    2)1(  

    Stator CircuitStator Circuit  Rotor Circuit Rotor Circuit Airgap & Airgap &

     Magnetic Circuit  Magnetic Circuit 

    1 X  '

    2 X 

    m X 

     I’2

    c R

     Load + Load +

     Rotation losses Rotation losses

    R 2‘

     

    /S

     I 1

    V 1  X m=2  f 1 Lm

     R1  X 1=2  f 1 L1

    I

    X2’

     

    =2  f 1 L2

    I2’

    2-IEEE-Recommended Equivalent Circuit

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    Equivalent Circuit Per Phase (cont.)

    3-Thevenin Equivalent Circuit

    In order to simplify the computations, IEEE recommended equivalent circuitcan be replaced by the following Thevenin’s equivalent circuit.

    If 

    12

    1

    2

    1)(

    V  X  X  R

     X V 

    m

    m

    th

     2 m1

     21  ) X  X (  R  

    1

     2

     th1

     2

     m1

     m

     th

     R K  R ) X  X 

     X (  R  

     

    1 th1

     m1

     m th V  K V 

     X  X 

     X V   

     

     th th

     m11

    11 m th  jX  R

     ) X  X (  j R

     ) jX  R(  jX  Z  

    1 th  X  X   and

    Xth

    Vth

    Rth

     Air  gap

      X2’

    R’2

     

    /S

      I2’

    DETERMINATION OF THE EQUIVALENT

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    1. No-Load Test ( S = 0 )

    Measured values V oL = V 1L , I   L , and Pot = W 1 ± W 2

    Calculate the per phase values V 0 , I  

     

    and P0= P ot 

     

     /3 

    )sin()cos()cos(0

    omoc

    o

    o I  I  I  I 

     I V 

    P

        

     

    m

    m

    c

    c I 

    V  X 

     I 

    V  R 00

    V 0

     I m

     X m Rc

     I c

     I 

    V

    W1A

    W2

    I.M.

     No Load

    DETERMINATION OF THE EQUIVALENT

    CIRCUIT PARAMETERS (cont.)

    DETERMINATION OF THE EQUIVALENT

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    2. Blocked rotor Test (S =1)

    Measured values V bL < V 1L , I bL , and Pbt = W 1 

     

    ± W 2 

    Calculate the per phase values V b , I b and Pb = Pot /3

    V

    W1A

    W2

    I.M.

     R1

     

    +R ’2  X 1

     

    +X’2

     Z  bV b

     I b

     Blocked 

    2&

    ,,

    2112

    22

    21221

    b

    b

    bbb

    b

    b

    b

    b

    b

    b

     X  X  X  R R R

     R Z  X  X  X  I 

    V  Z 

     I 

    P R R R

    DETERMINATION OF THE EQUIVALENT

    CIRCUIT PARAMETERS (cont.)

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    Power Flow In Induction Motors

    = 3V 1 I 1cos 

    dev

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    Power Flow In Induction Motors

    S  R I P

     R I P

     R I P

    dev

     RCL

     AG

    )1()(3

    )(3

    )(3

    22

    2

    2

    2

    2

    22

    2

    )1(::1:: S S PPPdev RCLGA

     

    P AG

     I mV 1

     I 2’

     R1  R2’ X 1  X 2

     X m Rc

     I c I  I 1

     I 2’

     R2’(1-S)

    S

    Power Flow In Induction Motor

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    50

     nput Power (Pin )

     tator Losses:

    Copper losses (P cu 1 )

    Core losses (Piron

     ) 

    irgap Power (P g )

    eveloped Power (P d  )  otor Copper Losses (P cu 2 )

     otational Losses (P rotational  )  Output Power (P out )

    Power Flow In Induction Motor

    Power Flow In Induction Motor

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    51

     

    11in cos I V 3P    

    m

    2

    iron

    1211cu

     R

    V 3P

     R I 3P

    sd ' 22' 

    2g T 

    s

     R) I (3P    

    gcu Ps R I P   '22'22 3

    Protational   T Pout    

       d gd  T sPss R I P   )1()1(3

    '

    22'2

    )1(::1:: 2 ssPPP d cug  

     I 2’

     I 1

     X 2’

     X 1 R1  R2’

     E 1   E 2’

     I c

     X c RcV  )s1(s

     R' 2

    Power Flow In Induction Motor

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    Power relations

    3 cos 3 cosin L L ph ph

    P V I V I    

    21 13SCLP I R

    ( ) AG in SCL coreP P P P

    2

    2 23 RCLP I R

    conv AG RCLP P P

    ( )out conv f w strayP P P P

    52

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    Example

    53

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    54

    Solution

    100 hp, 460 V, 8 pole, 60 Hz, star connected, 3-phase IMV ph

     

    = 460/√3 = 265.6 V

    a) Machine parameters

     No Load Test  :

    Vnl

     

    = 460/√3 = 265.6 V, Inl

     

    = 40 A , Pnl

     

    = 4200/3 = 1400 Wcos (nI

     

    ) = Pnl

     

    / (VnI

     

    * Inl

     

    ) = 1400/ (265.6*40) = 0.132

    nI 

    = 82.4°

    Ic

     

    = Inl

     

    cos (nI

     

    )= 40* cos(82.4°) = 5.27 A , R c

     

    = Vnl

     

    / Ic

     

    = 50.38 .

    Im

     

    = Inl

     

    sin (nI 

    ) = 40* sin(82.4°) = 39.65 A , Xm

     

    = Vnl

     

    / Im

     

    = 6.7  . Blocked rotor test  :V bl = l00/√3 = 57.74 V, I bl = 140 A , P bl

     

    = 8000/3 = 2666.67 W

    R 1

     

    +R '2

     

    = P bl

     

    / (l bl

     

    )2

     

    = 0.136

    But R 1

     

    = (0.152/2) * 1.11 = 0.084 , so R '2

     

    = 0.052Z bl

     

    = V bl

     

    / I bl

     

    = 0.412  .X bl =√{(Z bl

    2

     

    -(R 1

     

    +R '2

     

    )2} = 0.39 X1

     

    = X'2

     

    .= 0.39/2 = 0.195

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    55

    195.0084.0895.6732.1

    7.6*)195.0732.1( j

     j

     j j Z 

    in 

    in Z 

     b) For nm

     

    = 873 rpm

    ns

     

    = 120*f s

     

    / P = 120*60/8 = 900 rpm

    S = (ns

     

    - nm

     

    )/ns

     

    = 0.03

    IEEE recommended equivalent circuit per phase

    1.623 + j0.771 = 1.797 25.41I1 = V 1

     

    / Zin = 147.75 A

     p.f. = cos(25.41)= 0.903 lagPin

     

    = 3 V1

     

    I1

     

    cos() = 3 *265.6*147.75*cos (25.41) = 106308 WP

    AG

     

    = Pin

     

    -3I1

    2

     

    R l

     

    = 100806 W

    PRCL

     

    = s * PAG

    = 3024 W

    Pdev

     

    = PAG

     

     –PRCL

     

    = 97782 W

    Rotational losses = Pnl (total)

     

     – 3 (Inl

     

    )2

     

    R 1

     

    = 4200 – 

     

    3 (40)2

     

    (0.084) = 3797 W

    Pout

     

    = Pdev

     

     –Rotational losses = 97782-3797 = 93985 W

    Efficiency = Pout

     

    / Pin

     

    = 0.884

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    Problem

    56

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    57

    Performance Characterstics

    2

    2

    2'

    2

    '

    2

    )(  X  X s

     R R

    V  I 

    thth

    th

     

      

     

    22

    2'

    2

    2'

    2

    )(

    3

     X  X S 

     R R

     RT 

    thth

    th

    s

     

      

     

     

    Xth

    Vth

    Rth

     Air  gap

      X2’

    R’2

     

    /S

      I2’

    Torque / speed Curve

    Consider Thevenin’s equivalent circuit

    The rotor current referred to stator side is:

    And the developed torque T is :

    ss

     AG

    s

     AG

    m

    dev R I P

    S PP

    T      

    2

    2

    2)(3

    )1(

    )1(  

    Speed p.u.

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    58

    Torque/Speed Curve (cont.)

     Maximum torque

    Starting torque

    Starting Torque:

    at starting S =1, so the starting torque is:

    22

    2

    2

    2'

    2

    )(3

     X  X  R RV  RT 

    thth

    th

    s

    St 

     

    S Tmax

    For maximum torque

    which fromdS 

    dT ,0

    2/12'

    2

    2

    '2

    max])([  X  X  R

     RS 

    thth

    2/12'

    2

    2

    2

    max])()[(2

    3 X  X  R R

    V T ththth

    th

    S    

    Stable

    Unstable

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    Torque-speed characteristics

    Typical torque-speed characteristics of induction motor 59

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    60

    Torque/Speed Curve (cont.)

    )(2

    3

    )( '2

    2

    max'

    2

    '

    2

    max X  X 

    T and  X  X 

     R

    S th

    th

    S th

    T   

    )()/()/(

    )/()/()(

    )()/(

    )()/(

    max

    2

    max

    '

    2

    2

    max

    '

    2

    2

    max

    '

    2

    2'

    2

    max

    2'

    2

    2

    max

    '

    2

    2'

    2

    2'

    2max

    T T T 

    T thT 

    th

    S  RS  R

    S  RS  R

     X  X S  R

     X  X S  R

    S S 

    S S 

    max

    2max

    2

    max

    2

    If the stator resistance is small, so R th

     

    may be neglected

    and the ratio between the maximum torque and the torque developed at

    any speed is given by:

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    Problem

    61

    Torque Characteristics

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    62

    Torque Characteristics

    2

    2'

    21

    '

    2

    eq X s

     R

     R

    V  I 

     

     

     

     

     

     I 2’ 

     I 1 X eq  Req 

     X c

     I c

     RcV   )s1(s

     R' 2  

     

    d d 

    PT   )1()(

    3 '22'2 s

    s

     R I   

     

     

     

     

     

    2

    2'

    2

    1

    '

    2

    2 )1(3

    eq X s

     R

     Rs

    s RV 

     

    Consider The approximate equivalent circuit. The rotor current referred

    to stator side is

    Torque Characteristics

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    63

    Torque 

    n s 

    1

    0ns

    Tst

    T

    max

    smax

    s

    s

    s

    s

    n

    nns

     

       

     

     

     

     

    2

    2'

    21

    '

    2

    2

    3

    eqs

    d d 

     X s

     R Rs

     RV PT 

      

    Torque Characteristics

    Torque Characteristics

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    64

    smax

    T maxT 

    Torque

    s

    1

    0

    st 

    Small Slip

     Large Slip

     Maximum Torque

    Torque Characteristics

    Maximum Torque

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    65

    Maximum Torque

     

     

     

     

    2

    2'

    21

    '

    2

    23

    eqs

     X s

     R

     Rs

     RV PT 

     

     

    2eq

    21

    2max X  R

     Rs

    2

    eq211s

    2

    max

     X  R R2V 3T 

     

    0s

    T d 

    Set 

    Starting of IM

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    66

    Starting of IM

    • 

    Problems: –  

    High starting current

     – 

     

    Low starting torque

    Starting of Induction Motor

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    67

    Starting of Induction Motor

    2

    eq

    2' 

    21

    ' 2

     X  R R

    V  I 

    st 

     

     I 2’ 

     I 1 X eq  Req 

     X c

     I c

     RcV   )s1(s

     R' 2  

    Starting by Reducing Voltage

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    68

    Sta t g by educ g o tage

     

    Torque

    n s 

    s max 

    T st 1 

    T  max T st 2

    V 2 < V 1

    V 1

    2eq2' 

    21

    ' 2

     X  R R

    V  I 

    st 

    2eq

    21

    ' 2

    max X  R

     Rs

    2eq

    211s

    2

    max

     X  R R2

    V 3T 

     

    22212

    23

    eq

    s

    st 

     X  R R

     RV T 

     

    Starting by Reducing Voltage

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    69

    g y g g

    • 

    Starting current is reduced (good)

     

    Starting torque is reduced (cannot start heavy

    loads)

    • 

    Maximum torque is reduced (Motor acceleration

    is low)•

     

    Speed at maximum torque is unchanged

    Starting by Adding Rotor Resistance

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    70

    g y g

    Torque 

    n s 

    s max 

    T st1 T st3=T max 

    T st2 

     Radd3  Radd2

     Radd1

     Radd3 > Radd2 > Radd1

    2eq2' 

    21

    ' 2

     X  R R

    V  I 

    st 

    2eq

    21

    ' 2

    max X  R

     Rs

    2eq

    211s

    2

    max

     X  R R2

    V 3T 

     

    22212

    2

    3

    eq

    s

    st 

     X  R R RV T 

     

    Starting by Adding rotor resistance

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    71

    g y g

    • 

    Starting current is reduced (good)

    • 

    Starting torque is increased (good)

    • 

    Maximum torque is unchanged (Motoracceleration is high)

    • 

    Speed at maximum torque is reduced

    Methods Of Impro ing Starting Torq e

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    72

    Methods Of Improving Starting Torque

     

    In creasing the resistance of the rotor conductors

     

    Using a combination of high and low resistance

    Conductors

     

    Using a wire wound rotor connected to variable

    resistor 

    Torque/Speed Curve for varying R

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    73

    Torque/Speed Curve for varying R2

     

    The maximum torque isindependent of the rotorresistance. However, the value of

    the rotor resistance determinesthe slip at which the maximumtorque will occur. The torque-slipcharacteristics for various values

    of are shown.

     

    To get maximum torque atstarting::

    )(

    )(23

    '

    2

    '

    2

    max

    '

    2

    2

    max

     X  X 

     RS 

     X  X V T 

    th

    th

    th

     

    )(..1 22max  X  X  ReiS  thT   

    T

    NL~nsn

    T

    r1nr2nr3nn

    r3n

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    Maximum Torque

    Effect of rotor resistance on torque-speed characteristic74

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    75

    Stator current and input power factor

     

    From the IEEE recommended equivalent circuit, the input impedance Zinis:

     

    The stator current I1

     

    is :

     

    And the input power factor is :

     p.f. = cos ()

        

     inin

    m

    m

    in

     Z  Z 

     X  X  jS 

     R

     jX S 

     R jX 

     jX  R Z '

    2

    '

    2

    '2

    '

    2

    11

    in Z V  I  11 

    R 2‘ /SV 1  jX m

     R1  jX 1 jX2

     I 1

     I 1

    p.f.

     

    01

    s

    T  st

     art

     No-load Starting

    Typical Induction MotorTypical Induction Motor

    CharacteristicsCharacteristics

     Maximum or

     pull-out torque

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    76

    Classes of squirrel-cage motors

     

    According to the National Electrical Manufacturing Association

    (NEMA) criteria, squirrel-cage motors are classified into class A, B,

    C or D. The torque-speed curves and the design characteristics for

    these classes are :

    Rated

    Load Slip

    Starting

    Torque

    Starting

    Current

    Class

    < 5% Normal Normal A

    < 5% NormalLow B

    < 5%HighLowC 

    8-13 %Very HighLow D

     A D

    C

    B

    Speed control of induction motorsSpeed control of induction motors

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    77

    Speed control of induction motorsSpeed control of induction motors

     

    1- Stator voltage Control

    Rotor

    T

     

     Vs2

    i

    a

    i

     L

    v A

     N 

    1

    4

    v B

     N vC 

     N 

    3

    6T 

    5

    T 2

    i

    b

    i

    c

     N  B

     A

    Rotor

    T

    NL~nsn

    T

    r1nr2nr3nn

    r3n>r2n>r1n

    1V

    2V

    3V

    3V>2V>1V

    V decreasing

    Speed control of induction motorsSpeed control of induction motors

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    78

    Speed control of induction motorsSpeed control of induction motors

     

    2- Stator Frequency Controlnm=(1-S)ns , ns= 120 f s /P

    Torque-Speed curves at different

    stator frequencies with constantvoltage supply

    Rotor

    i L

     N  B

     A

     Rectifie

    AC→

     

    DC

     Inverter 

    DC →

     

     AC

    f Control

    filter

    ns1

    ns3

    1

    3

    2

    1 > f 2 > f 3

    Speed 

    Torque

    ns2

      

      

    2

    2

    21

    2

    23

    eq

    s

     X s

     R Rs

     RV T 

     

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    79

    Speed control of induction motorsSpeed control of induction motors

     

    3. Rotor voltage Control (Slip-Energy Recovery)

    For wound rotor induction motor only

     Advantages: Advantages:• Very simple

    • Very useful at starting:

    (high starting torque & low starting current)

     Drawbacks: Drawbacks:• Low efficiency:extra losses

    • Slow control

    • unbalance problems if the three

    resistors are unequal.

    a-

     

    Classical technique:

    Variation of rotor circuit resistance

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    80

    Speed control of induction motorsSpeed control of induction motors

     b-

     

    An alternative methods of varying rotor-circuit resistance

    Using three-phase diode bridge and a single variable resistor 

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    81

    Speed control of induction motorsSpeed control of induction motors

    c-

     

    Slip-Energy Recovery System

    Diode Rectifier  Controlled Inverter 

    Starting of Induction Motors

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    82

    Starting of Induction Motors

    1-

     

    Direct-On-Line Starting

    Induction motors when started by connecting them directly across

     

    the

    supply line take 5 to 8 times their full-load current. This initial excessive

    current may cause large line voltage drop that affects the operation of otherelectrical equipment connected to the same lines. This method is

     

    suitable

    for small motors up to 10-hp rating.

    2-

     

    Auto-transformer 

    A three-phase step-down autotransformer may be employed as a reducedvoltage starter. As the motor approaches full speed, the autotransformer is

    switched out of the circuit.

    Starting of Induction Motors

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    83

    R ext

     

    decreases

    Starting of Induction Motors

    3- 

    Star-delta methodThe normal connection of the stator windings is delta

    while running. If these windings are connected in star

    at starting, the phase voltage is reduced, resulting in

    less current at starting. As the motor approaches thefull speed, the windings will be connected in delta.

    4-

     

    A solid-state controller 

    The controller can provide smooth starting.

    5-

     

    Using an external resistance in series with the rotor 

    For wound rotor induction motor only. The external

    resistance can be chosen to get high torque and low

    current at starting and can be decreased as motor

    starts up.

    SINGLE PHASE INDUCTION

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    The single-phase induction machine is the most

    frequently used motor for refrigerators, washing

    machines, clocks, drills, compressors, pumps, andso forth.

     

    The single-phase motor stator has a laminated iron

    core with two windings arranged perpendicularly.

     

    One is the main and

     

    The other is the auxiliary winding or starting

    winding

    MOTOR

    84

    Nameplate

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    85

    Nameplate

    SINGLE PHASE INDUCTION

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    MOTOR

    86

     MOTOR

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    MOTOR

     

    This “single-phase”

    motors are truly two-

    phase machines.

     

    The motor uses a

    squirrel cage rotor,

    which has a laminated

    iron core with slots.

     

    Aluminum bars are

    molded on the slots and

    short-circuited at bothends with a ring.

    Stator with laminated

    iron core Slots with winding

    Bars

    Ring to short

    circuit the barsStarting winding

    +

     _ 

    Main winding

    Rotor withlaminated

    iron core+

     _ 

    Single-phase induction motor.

    87

    SINGLE PHASE INDUCTION

    MOTOR

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    MOTOR

    Squirrel cage rotor