IM 5 #Cotha_728888888866667777777655.pdf

IM motor

1. Three-Phase Induction Motor
Part-05
ShadhonChandra Mohonta
Assistant Professor
Dept. of EEE, RUET, Rajshahi.
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2. Reference Books
.
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3. Torque Under Running Conditions
Let,therotoratstandstillhaveperphaseinducede.m.f.E2,
reactanceX2andresistanceR2.Thenunderrunningconditions
atslips,
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4. Torque Under Running Conditions
Runningtorque,
Itmaybeseenthatrunningtorqueis:
(i)directlyproportionaltoslipi.e.,ifslipincreases(i.e.,motor
speeddecreases),thetorquewillincreaseandvice-versa.
(ii)directlyproportionaltosquareofsupplyvoltage(E2V,
constant).
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4)E (
)sX(R
RsEK
)sX(R
RsEK

)sX(R
RsE
)sX(R
R
)sX(R
sE

)E ( cosIcosIET
22
2
2
2
2
2
21
2
2
2
2
22
2
2
2
2
22
2
2
2
2
2
2
2
2
2
2
222222r

+
=
+

=
+


+

+



5. Torque Under Running Conditions
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6. Maximum Torque under Running Conditions
Inordertofindthevalueofrotorresistancethatgives
maximumtorqueunderrunningconditions,differentiateexp.(i)
w.r.t.sandequatetheresulttozeroi.e.,
Thusformaximumtorque(Tm)underrunningconditions:
Rotorresistance/phase=Fractionalslip×Standstillrotor
reactance/phase
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6( ) () 
( )
( )
22
2
2
22
2
2
2
2
2
22
2
2
2
2
22
2
2
2
2
2
2
22
22
2
21r
sXRor XsR or
0sX2XsRor
0
XsR
sRsX2XsRREK
ds
dT
==
=−+
=
+
−+
= ()i............
)sX(R
RsEK
)sX(R
RsEK
T
2
2
2
2
2
2
21
2
2
2
2
22
r
+
=
+

=

7. Maximum Torque under Running Conditions
Slipcorrespondingtomaximumtorqueiss=R2/X2
PuttingR2=sX2ineq.(i),weget
Substitutingvalueofs=R2/X2ineq.(i)
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7()ii....
R2
sEK
or
X2
EK
Tor
R2
RsEK
or
Xs2
XEsK
T
2
2
2
2
m2
2
22
2
2
2
22
2
m 






 
=







 
= ( )
( )
2
2
21
2
2
2
22
2
2
2
2
2221
m
X2
EK
XXRR
REXRK
T =
+
= m-N
X2
E
N2
3
T have we,
N2
3
K Since,
2
2
2
s
m
s
1


=

=

8. Maximum Torque under Running Conditions
Itisevidentfromtheaboveequationsthat:
(i)Thevalueofrotorresistancedoesnotalterthevalueofthe
maximumtorquebutonlythevalueoftheslipatwhichit
occurs.
(ii)Themaximumtorquevariesinverselyasthestandstill
reactance.Therefore,itshouldbekeptassmallaspossible.
(iii)Themaximumtorquevariesdirectlywiththesquareofthe
appliedvoltage.
(iv)Toobtainmaximumtorqueatstarting(s=1),therotor
resistancemustbemadeequaltorotorreactanceat
standstill.
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9. Torque-Slip Characteristics
Themotortorqueunderrunningconditionsisgivenby;
Ifacurveisdrawnbetweenthetorqueandslipforaparticular
valueofrotorresistanceR2,thegraphthusobtainediscalled
torque-slipcharacteristic.Fig.
showsafamilyoftorque-slip
characteristicsforaslip-range
froms=0tos=1forvarious
valuesofrotorresistance.
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9constant. ,E if ;
)sX(R
RsK
)sX(R
RsEK
T
22
2
2
2
21
2
2
2
2
22
r

+
=
+

=

10. Torque-Slip Characteristics
Thefollowingpointsmaybenotedcarefully:
i.Ats=0,T=0sothattorque-slipcurvestartsfromthe
origin.
ii.Atnormalspeed,slipissmallsothatsX2isnegligibleas
comparedtoR2.
So,Ts/R2 ...asR2isconstant.
s
Hencetorqueslipcurveisastraightlinefromzerosliptoaslip
thatcorrespondstofull-load.
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11. Torque-Slip Characteristics
iii.Asslipincreasesbeyondfull-loadslip,thetorqueincreases
andbecomesmaximumats=R2/X2.Thismaximumtorque
inaninductionmotoriscalledpull-outtorqueorbreak-
downtorque.Itsvalueisatleasttwicethefull-loadvalue
whenthemotorisoperatedatratedvoltageandfrequency.
iv.Tomaximumtorque,theterm??????
2
??????
2
2
increasesveryrapidly
sothat??????
2
2
maybeneglectedascomparedto??????
2
??????
2
2
.
??????∝Τ????????????
2
??????
2
2
∝Τ1??????…….asX2isconstant.
Thusthetorqueisnowinverselyproportionaltoslip.Hence
torque-slipcurveisarectangularhyperbola.
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12. Torque-Slip Characteristics
v.Themaximumtorqueremainsthesameandisindependent
ofthevalueofrotorresistance.Therefore,theadditionof
resistancetotherotorcircuitdoesnotchangethevalueof
maximumtorquebutitonlychangesthevalueofslipat
whichmaximumtorqueoccurs.
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13. Effect of Change in Supply Frequency in Torque
and Speed
Largefrequencychangesoftentakeplaceonisolated,low-
powersystemsinwhichelectricenergyisgeneratedbymeans
ofdieselenginesorgasturbines.Examplesofsuchsystemsare:
emergencysupplyinahospitalandtheelectricalsystemona
shipetc.
Themajoreffectofchangeofsupplyfrequencyisonmotor
speed.Iffrequencydropsby10%,thenmotorspeedalsodrops
by10%.Machinemeantfor50Hzcausesproblemwhen
connectedto60-Hz.Everythingruns(60-50)×100/50=20%
fasterthannormal.So,wehavetousegearstoreducespeed.
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14. Full-Load Torque and Maximum Torque
Let??????
??????betheslipcorrespondingtofull-loadtorque,then
??????
??????∝
??????
??????
??????
2
2
+(??????
????????????
2)
2
and??????
??????∝
1
2??????
2
Wherea=R2/X2=resistance/standstillreactanceperphase
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14()( )
2
f
2
f
2
f
2
22
22f
2
2f
2
2
22f
m
f
sa
as2
sXR
XRs2
XsR
XRs2
T
T

+
=
+
=
+
=

15. Starting Torque and Maximum Torque
Wherea=R2/X2=resistance/standstillreactanceperphase
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15( )
22
22
22
2
2
2
2
22
m
s
2
m
2
2
2
2
2
s
a1
a2
X/R1
X/R2
XR
XR2
T
T
X2
1
T
XR
R
T
+
=
+
=
+
=

+


16. ?
1.Derivetheequationofrotortorqueunderrunning
condition?
2.Whenthetorqueunderrunningconditionismaximumand
alsofindthemaximumtorqueunderrunningcondition?
3.Describetherelationbetweentorqueandslipwithnet
diagram.
4.Findtherelationbetween(a)full-loadtorqueandmaximum
torque(b)startingtorqueandmaximumtorque
5.Example:34.10–34.23(Book:B.L.Theraja)
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