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Elx 311 Chap 7 Slides

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    1

    Chapter 7: INDUCTION MOTORS

    7.1 Induction motor construction

    - Stator exactly the same as forsynchronous machines

    - Rotor can be either a Squirrel Cage or Wound Rotor

    Wound Rotor

    - Y-connected 3-phase windingson rotor

    - Accessable via slip rings

    - Can modify torque-speed curveby inserting resistors into rotor

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    2

    7.2 Basic Induction Motor Concepts

    Refer to Electrical Engineering Principles and

    Applications 4th edition by Allan R. Hambley, Chapter 17.

    7.2.1 Rotating Stator Field

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    3

    Chap 17.2.1 cont

    ( ) ( )

    ( ) ( ) ( ) ( )

    ( ) ( )

    ( ) ( ) ( ) ( )

    ( )

    =

    ++=

    ==

    =

    ==

    =

    tKIB

    BBBB

    tItitIti

    tIti

    tKiBtKiB

    tKiB

    mgap

    cbagap

    mcmb

    ma

    ccbb

    aa

    cos23

    240cos120cos

    cos

    240cos120cos

    cos

    The field in the gap rotates counter clockwise with an

    angular speed of.

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    4

    7.2.2 Development of induced torque

    Synchronous Speed:

    - Maximum flux density occurs at t= .- Thus in 2 pole machine, point of max flux rotates anti-

    clockwise at

    =

    dt

    d

    - Similarly a P-pole machines field rotates at:

    2/Psync

    =

    P

    fn esync

    120=

    known as synchronous angular velocity

    How is torque produced:

    - Stator sets up Protating magnetic poles at sync

    - Induces voltages in squirrel-cage conductorsproportional to the velocity of the rotor bars relative to

    the magnetic field: vBleind =

    - Voltages result in currents in rotor conductors

    - Rotor currents establish magnetic poles on rotor: Nr , Sr

    - Interaction of Stator and Rotor poles produces torque:NrSsand SrNs

    HOW CAN I CHANGE THE DIRECTION OF ROTATION??

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    7.2.2 cont

    - Figure for case of purely resistive conductors resultingin maximum induced current directly under stator poles.

    Effect of Rotor Inductance on Torque

    - Equivalent circuit for a rotor conductor

    -cc

    ccccc

    LjsR

    VILjsRZ

    +=+=

    - Current lags hence peakcurrent occurs after stator

    pole passes by hencereduced torque

    - < 90rs - Upper limit to motor speed- Rotor and Stator magnetic

    fields rotate at nsync, butrotor turns at slower speed

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    6

    7.2.3 Concept of Rotor slip

    - Frequency of induced voltages depend on relativespeed (stator field vs rotor) and number of poles

    - Stator field at synchronous speed syncand rotormechanical speed m

    - Hence relative speed or slip speed:slip= sync- m or nslip= nsync - nm

    - Slip is defined as: sync

    msync

    sync

    msync

    n

    nns

    =

    =

    - ( ) ( ) syncmsyncm snsn == 11

    7.2.4 Electrical frequency on the rotor

    - Operates like rotating transformer: Primary = Stator,Secondary = Rotor

    - Induces voltages at slip frequencyslip= ssync- Locked rotor i.e. stationary: Slip s = 1 and fr = fs- At synchronous speed s = 0, fr = 0

    -( )

    ( )msyncr

    ee

    msyncesync

    msync

    r

    er

    nnP

    f

    ff

    P

    nnfn

    nn

    f

    sff

    =

    =

    =

    =

    120

    120

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    7

    7.3 The Equivalent Circuit of an Induction Motor

    7.3.1 Transformer model

    - Circuit elements:o Stator resistance and leakage reactance: R1 and X1o Core Loss resistance RCand Magnetizing reactance Xm

    refer to BH-curves. Why the difference?o E1 = Primary internal stator voltage coupled to secondary

    rotor voltage ER via effective turns ratio aeff.

    - Primary difference wrt transformer lies in effects ofvarying rotor frequency on the rotor voltage ER and therotor impedances RRand XR.

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    8

    7.3.2 Rotor Circuit Model- Stator voltage induces voltage on rotor windings- The greater the relative motion between the rotor and

    stator magnetic fields, the greater the induced rotor

    voltage and frequency: vBleind =

    - Maximum induced voltage at locked rotor condition: ER0- Voltage and frequency directly proportional to slip of the

    rotor: erRR sffsEE == 0 .

    - Rotor contains both reactance and resistanceoRR is independent of slip

    oXRdepends on rotor inductance LRand frequencyof induced voltage and current:

    o ( ) 0222 RReReRrRrR sXLfsLsfLfLX ===== with XR0the locked rotor reactance

    - Resulting equivalent circuit:

    0

    0

    0

    0

    / RR

    R

    R

    RR

    R

    R

    jXsR

    EI

    jsXR

    sEI

    +

    =

    +

    =

    - All rotor affects due to varying rotor speed accountedfor by varying impedance, or rather varying resistance.

    - At low slip RR/s >> XR0, IR varies linearly with slip- At high slip XR0>> RR/s, IR approaches steady state

    value

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    9

    7.3.3 Final PER PHASE Equivalent Circuit

    - Need to refer rotor part of model to the stator side

    22

    0

    2

    2

    20

    '

    1

    jXs

    RjX

    s

    RaZ

    a

    IIEaEE

    RR

    aff

    eff

    RReffR

    +=

    +=

    ===

    - PROBLEM for cage motors: Almost impossible todetermine RR, XR0and aeff.

    - Possible to directly determine referred values (Chap

    7.11)

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    10

    7.4 Power and torque in induction motors

    7.4.1 Losses and Power-Flow Diagram

    - Pin : 3 phase input power- PSCL: Stator copper losses 3I

    2R1- Pcore: Core losses due to hysteresis and eddy

    currents- PAG: Power transferred to the rotor across the

    airgap- PRCL: Rotor copper losses 3I

    2R2- Pconv: Remaining elect energy conv to mech energy- PF&W: Friction and windage losses- Pstray: Stray losses- Pout: Power out available for torque to load- Prot= PF&W+ Pstray+ Pcore: Rotational losses constant

    with changing speed because as => (PF&W+ Pstray)and Pcore

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    11

    7.4.2 Power and Torque in an IM

    ( )

    sync

    AG

    sync

    AG

    m

    conv

    devind

    miscWFconvout

    RCLconvAG

    AGdevRCLAGconv

    AG

    eff

    effRRRCL

    coreSCLinAG

    Ccore

    SCL

    P

    s

    PsP

    PPPP

    s

    P

    s

    PP

    PsPs

    sRIPPP

    sPRIa

    RIaRIP

    s

    RIPPPP

    REP

    RIP

    =

    ===

    =

    =

    =

    ==

    ==

    ====

    ==

    =

    =

    )1(

    )1(

    )1(

    )1(13

    333

    3

    /3

    3

    &

    222

    2

    2

    22

    22

    2

    2

    22

    2

    21

    1

    2

    1

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    12

    7.4.3 Separating PRCL and Pconv

    - Recall:

    ==

    s

    sRIPRIP convRCL

    133 2

    2

    22

    2

    2

    - Hence:

    += s

    sRRs

    R 1222

    - From Electrical Engineering Principles andApplications 4th edition by Allan R. Hambley, Chapter17:

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    13

    7.4.4 Torque-Speed Characteristic- From Electrical Engineering Principles and

    Applications 4th edition by Allan R. Hambley, Ch. 17- Finally the torque-speed characteristic can be

    explained!- Recall:

    o At low slip RR/s >> XR0, IR varies linearly with slipo At high slip XR0>> RR/s, IR approaches steady state

    value

    - Start assuming rotor is at synchronous speed

    - Small slip sresult in sLc

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    14

    7.5 IM Torque-speed characteristics

    7.5.1 Induced Torque from a Physical Standpoint.

    Self read.

    7.5.2 Derivation of IM Induced Torque Equation

    sync

    AG

    sync

    AG

    m

    convdevind

    P

    s

    PsP

    =

    ===

    )1(

    )1(

    s

    RIPAG

    22

    23=

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    15

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    7.5.3 Comments on the IM Torque-Speed curve

    1. Induced torque = 0 at synchronous speed2. TS-curve linear between no load and full load (low slip).3. Pullout torque not be exceeded.

    4. Starting torque > full-load torque5. Torque at fixed slip varies with V

    2.

    6. If rotor speed > sync speed = generator.7. Plugging = reversal of 2 phases to quickly break IM.

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    18

    7.5.4 Maximum (Pullout) Torque in an IM

    sync

    AGind

    P

    =

    Hence ind is maximum when PAG is maximum.

    Sinces

    RIP

    AG

    22

    23= , maximum ind is when power in

    R2/s is max, which is when

    ( )2222 XXR

    s

    RTHTH ++=

    From figure below use principle of maximum

    power transfer.

    Hence slip at pull-out torque:

    ( )222

    2

    XXR

    Rs

    THTH ++

    =(7-53)

    Maximum or pull-out torque from eq 7-50

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    19

    Note: slip @ maxR2, BUT value of max is

    independent of R2.

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    20

    7.11 Determining circuit model parameters

    7.11.1 No-Load Test (open circuit)

    - Only load is friction and windage- Slip is very, very small- Power measured must equal losses in motor

    - ( ) rotmiscWFcoreSCLNLin PRIPPPPPP +=+++== 12

    1& 3 - IM large to create flux through high airgap reluctance,

    hence very small Xmcompared to R2/s: mNL XXX + 1

    -22

    2

    ,1,1 3NLNLNL

    nl

    NLNL

    nl

    NL RZXI

    PR

    I

    VZ ===

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    7.11.2 R1: DC Test

    7.11.3 Blocked-rotor Test (short circuit)

    - Voltage is increased intil current is approx rated current- Measure voltage, current, power- Problem:

    o er sff = hence with s = 1 reactance

    LfLfX er 22 == which is much higher than at

    usual s 0.03.o IEEE recommends operation at 25% of rated

    frequency

    DC

    DC

    I

    VR 2

    11 =

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    22

    7.11.3 cont

    - 1221

    21

    3

    RRR

    I

    PRRR LR

    LRLR ==+=

    - Locked rotor impedance at test frequency ftest:

    o22'

    1

    LRLRLRLR RZXI

    VZ ==

    - Rotor impedance at rated frequency frated:

    o 21

    'XXX

    f

    fX

    LRtest

    rated

    LR+==

    o Usually 21 XX = hence

    LRNLNLm XXXXX 5.01 ==

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    7.11.4 Summary for parameter tests:

    1. Do DC test to get R1.

    2. Do No-Load Test at rated voltagea. Measure: V, I, Pb. Calculate: ZNL, RNL, XNL.

    3. Do (B)locked rotor test at 25% frequency and ratedcurrent:

    a. Measure: V, I, P, ftest

    b. Calculate: ZLR, RLR, XLR.

    4. Calculate Parameters:

    a. 21'

    XXXf

    fX LR

    test

    ratedLR +==

    b. 21 XX =

    c. 12 RRR LR =

    d. LRNLNLm XXXXX 5.01 ==


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