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8/6/2019 Elx 311 Chap 7 Slides
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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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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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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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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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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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7.3 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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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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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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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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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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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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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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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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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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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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Note: slip @ maxR2, BUT value of max is
independent of R2.
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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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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 ==