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BEE 4123Electrical Machines & Drives
Chapter 3Chapter 3
Induction MotorsInduction Motors
Module Outlines
Induction Motor Construction Basic Induction Motor Concepts The Equivalent Circuit of an Induction Motor Power and Torque in an Induction Motor Induction Motor Torque-Speed Characteristics Starting Induction Motors Speed Control of Induction Motors Determining Circuit Model Parameters Induction Motor Ratings
Induction Motor Construction
The single-phase induction motor is the most frequently used motor in the world.
Most appliances, such as washing machines and refrigerators, use a single-phase induction machine
Highly reliable and economical
Power Supply
Rotor
Stator
Shaft
Induction Motor Construction
Using amortisseur windings, no DC field circuit. Called “induction machines” because the rotor
voltage is induced in the rotor windings instead of physically connected by wires.
Mostly used as motor, rarely as generator. 2 types of rotor – squirrel cage & wound rotors. Most motors use the squirrel-cage rotor because
of the robust and maintenance-free construction.
Induction Motor Construction
Squirrel-cage rotor
Induction Motor Construction
Squirrel cage rotor This rotor has a laminated iron core with slots, and is mounted
on a shaft. Aluminum bars are molded in the slots and the bars are short
circuited with two end rings. The bars are slanted on a small rotor to reduce audible noise. Fins are placed on the ring that shorts the bars. These fins work
as a fan and improve cooling.
Rotor bars (slightly skewed)
End ring
Induction Motor Construction
Wound rotor Large or older motors use a
wound rotor with three phase windings placed in the rotor slots.
The windings are connected in a three-wire wye.
The ends of the windings are connected to three slip rings.
Resistors or power supplies are connected to the slip rings through brushes for reduction of starting current and speed control.
Basic Induction Motor Concepts
IRBS
BR
Bnet
R
ER
Net voltageMaximum induced voltage
Maximum induced current
Apply 3-phase voltage
to stator, 3-phase currentflowing in stator
produces BS.
Apply 3-phase voltage
to stator, 3-phase currentflowing in stator
produces BS.
P
fn esync
120 IBveind )(
BR and BS rotate at nsync, but rotor turns at a slower speed.
BR and BS rotate at nsync, but rotor turns at a slower speed.
The Development of Induced Torque
SRind BkB
Basic Induction Motor ConceptsThe Concept of Rotor Slip
The voltage induced in rotor bar depends on the speed of the rotor relative to the magnetic fields.
2 terms to define the relative motion: Slip speed -- difference between synchronous speed
and rotor speed:
Slip -- relative speed expressed on p.u. basis:
msyncslip nnn
sync
slip
n
ns
sync
msyncs
syncm nsn )1(
Basic Induction Motor Concepts
The Electrical Frequency on the Rotor
Induction motor also called as rotating transformer due to its induced voltage and current.
Primary (stator) & Secondary (rotor). Unlike transformer, frequency not necessarily same at
secondary and primary. If rotor is locked, fr = fs or fe.
If rotor at nsync, fr = 0.
If rotor rotate in between the above speeds,
er sff )(120 msyncr nnP
f
The Equivalent Circuit An induction motor has two magnetically coupled circuits:
the stator and the rotor. The latter is short-circuited. This is similar to a transformer, that the secondary side is
rotating and short-circuited. The motor has balanced three-phase circuits;
consequently, the single-phase representation is sufficient. Both the stator and rotor have windings, which have
resistance and leakage inductance. The stator and rotor winding are represented by a
resistance and leakage reactance connected in series.
The Equivalent Circuit A transformer represents the magnetic coupling between
the two circuits. The stator produces a rotating magnetic field that induces
voltage in both windings. A magnetizing reactance (XM) and a resistance
connected in parallel represent the magnetic field generation.
The resistance (RC) represents the eddy current and hysteresis losses in the iron core.
The induced voltage is depend on the slip and the turn ratio.
The Equivalent Circuit
The Transformer Model of an Induction Motor
Stator Rotor
jXR
RR
IR
ER
R1I2
E1VP
I1
jXMRC
IM
aeffjX1
The Equivalent Circuit
Magnetization curve (Wb)
(A-turns)
Induction motor
Transformer
The curve is more shallower because of the air gap in an induction motor that increases the reluctance of the flux path. More magnetizing current is needed!
The curve is more shallower because of the air gap in an induction motor that increases the reluctance of the flux path. More magnetizing current is needed!
The Equivalent Circuit
The Rotor Circuit Model
The magnitude of induced rotor voltage is directly proportional to slip (s) of the rotor; largest during locked-rotor and smallest during synchronous speed with stator magnetic field.
RR is constant but XR is dependent of slip.
LRR sEE During locked-rotor
RrRrR LfLX 2
The Equivalent Circuit
The Rotor Circuit Model
By fr=sfe,
Rotor current,
LRR sXX
jXR=jsXLR
ER=sELR RR
IR
+
-
LRR
LR
RR
RR jXsR
E
jXR
EI
/ LRReqR jXsRZ /,
The Equivalent Circuit
Final Equivalent Circuit (Per phase circuit)
Referred rotor circuit to stator side (similar to transformer – secondary referred to primary).
SS
SSP
SSP
ZaZ
a
III
aVVV
2'
'
'
LRR
eff
eff
R
LReffR
jXs
RaZ
a
II
EaEE
22
2
'1
TransformerTransformer Induction motorInduction motor
The Equivalent Circuit
Per-phase Equivalent circuit of induction motor
I1
V
jX1 R1
E1
jX2
R2/s RcjXM
IM
I2
LReff
Reff
XaX
RaR
22
22
Power and Torque
Transformer has electric power output from secondary, but induction motor has no electric power output from rotor as it is shorted out.
Only mechanical power output from rotor.
Pout=loadm
Pstray (Pmisc.)
Pfriction and windage losses
Pcore (Core losses)
PSCL (Stator copper loss)
Pin=3VTILcos
PRCL (Rotor copper loss)
Air-gap powerindm
PAG Pconv
I2R
Mechanical power
RC
Power and Torque
I1
V
jX1 R1
E1
jX2
R2/s RcjXM
IM
I2
22
11
1
11
jXsRjBG
jXRZ
Z
VI
MC
eq
eq
Power and Torque
The stator copper losses
The core losses
The air-gap power
The rotor copper losses
1213 RIPSCL
Ccore GEP 213
s
RIPPPP coreSCLinAG
2223
222
2 33 RIRIP RRRCL
AGRCL sPP
Power and Torque
The electrical power is then converted to mechanical power, called Pconv or developed mechanical power.
The output power,
s
sRI
PPP RCLAGconv
13 2
22
AG
AGAG
RCLAGconv
Ps
sPP
PPP
)1(
miscWFconvout PPPP &
Power and Torque
The induced torque or developed torque,
sync
AG
sync
AG
m
convind
P
s
Ps
P
)1(
)1(
Power and Torque
I1
V
jX1 R1
E1
jX2
R2(1-s)/s Rc jXM
IM
I2
(SCL)
(Core loss)
R2
(Pconv)
(RCL)
s
sRR
s
RRconv
122
2
Torque-Speed CharacteristicsI1
V
jX1 R1
E1
jX2
R2/s jXM
I2
V
jX1 R1
VTHjXM+-
jX1 R1
jXM)(
)(
11
11
M
MTH XXjR
jXRjXZ
VXXR
XV
M
MTH 2
121 )(
Thevenin Equivalent Voltage Thevenin Equivalent Impedance
Torque-Speed Characteristics
Since XM>>X1, XM>>R1 and XM+X1>>R1,
jXTH RTH
E1
jX2
R2/s VTH+-
I2
VXX
XV
M
MTH
1
2
11
M
MTH XX
XRR
1XXTH
Torque-Speed Characteristics
From the circuit,
The magnitude of I2,
The air-gap power,
2222 jXjXsRR
V
ZZ
VI
THTH
TH
TH
TH
222
2
2XXsRR
VI
THTH
TH
22
22
22
222
33
XXsRR
sRV
s
RIP
THTH
THAG
Torque-Speed Characteristics
The rotor-induced torque,
][
32
22
2
22
XXsRR
sRVP
THTHsync
TH
sync
AGind
Torque-Speed CharacteristicsTypical induction motor torque-speed characteristic curve
in
d (%
of
full
lo
ad)
100
200
300
400
500Pullout torque
Full-load torque
Starting torque
nsync
Mechanical Speed
Torque-Speed CharacteristicsTorque-speed characteristic curve (extended operating ranges)
in
d (%
of
full
lo
ad)
nm2nsyncnsync Mechanical Speed
Generator region
Motor regionBraking region
max
-800
400
Torque-Speed Characteristics
Torque and power converted versus motor speed
100
200
300
400
500
600
700
800
250 20001000
15
30
45
60
75
90
105
120
Ind
uce
d t
orq
ue
(N-m
)
Po
wer
(kW
)
Mechanical speed (r/min)
Torque-Speed Characteristics
Maximum (Pullout) Torque
Maximum torque occurs when the air-gap power is maximum and it is equal to the power consumed in load resistor, R2/s.
Maximum power transfers to R2/s when the magnitude is equal to the magnitude of the source impedance, Zsource.
2jXjXRZ THTHsource
22
22 )( XXRs
RTHTH
Torque-Speed Characteristics
The slip at pullout torque,
The pullout torque,
22
2
2max
)( XXR
Rs
THTH
])([2
32
22
2
maxXXRR
V
THTHTHsync
TH
Starting Induction Motor
Simply start the induction motors by connecting them to the power line may cause voltage dip in the power system.
For wound-rotor induction motor, the insertion of extra resistance increases the starting torque and reduces the starting current.
For squirrel-cage induction motor, the starting current is depends on the rated power (Sstart in kVA) and the rated voltage (VT in V),
) )( ( factorlettercoderhoursepoweratedSstart
T
startL
V
SI
3
Starting Induction Motor
The code letter factor (in kVA/hp) is given on the nameplate. The example of code letters,
Nominal code letter
Locked rotor, kVA/hp
A 0-3.15
B 3.15-3.55
C 3.55-4.00
D 4.00-4.50
Starting Induction Motor
Starting circuit is use to reduce the starting current, but it also reduce the starting torque.
Common approach is to reduce the motor’s terminal voltage during starting by using autotransformers.
1 1 12 22
3 3
Line terminals
Motor terminals
Th
ree-
ph
ase
auto
tran
sfo
rmer
Speed Control of Induction Motors
2 techniques to control the speed of induction motor:
i. Vary the nsync (changing fe and pole)
ii. Vary the slip (changing VT and rotor resistance)
Changing Pole Old technique, greatly obsolete nowadays!
Speed Control of Induction Motors
Changing Line Frequency From the below equation,
To decrease the magnetization current, voltage applied to the stator need to be decreased. Thus maximum power rating of the motor must be decreased to avoid motor overheat.
tN
Vt
P
M
cos fe , Excessive magnetization current flow in the motor!
cos3 LLIVP
Speed Control of Induction Motors
Changing the Line Voltage The motor torque is proportional to (Vapp)2. The changing of torque will vary the motor speed and
it can be analyzed from the torque-speed characteristic curve.
Sometimes used on small motors driving fan.
Changing Rotor Resistance It is applicable for wound-rotor induction motors only
by inserting extra resistances. The extra resistances seriously reduces the efficiency
of the motor. Used only for short periods.
Determining Circuit Model Parameters
Why important? To determine the torque-speed curve of the real induction motor.
What parameters? R1, R2, X1, X2, and XM.
What tests? DC Test – to find stator resistance, R1.
No-load test – to find Znl = X1+XM.
Locked-rotor test – to find RLR=R1+R2 and XLR=X1+X2.
Determining Circuit Model Parameters
DC voltage is applied to stator windings. Since it is DC, thus, no eind and I2, and jX=0.
I1 is adjusted to I1,rated and voltage between terminals is measured. The total resistance, 2R1,
A
VVDC (variable)
Current limiting resistorI1=I1,rated
R1
R1
R1
DC
DC
I
VR 12
DC Test
R1 R2
R2(1-s)/sjXM
jX1 jX2
RC
I2=0
IM
I1
V
+
-
R1
RF&W= R2(1-s)/s
jXM
jX1
RC
I1
V
+
-
R1
RF, W, & core >> XM
jXM
jX1
V
+
-
Determining Circuit Model ParametersNo-load Test
Initial equivalent circuit
Initial equivalent circuit
Since R2(1-s)/s >> R2 and R2(1-s)/s >> X2.
Since R2(1-s)/s >> R2 and R2(1-s)/s >> X2.
Combining RF&W and RC
Combining RF&W and RC
P1 AV
Variable voltage, variable frequency, three-phase power source P2 A
A
IA
IB
IC
No load 3
CBAL
IIII
Mnl
eq XXI
VZ 1
,1
miscWFcorerot PPPP &
rotSCLin PPP 1213 RIPSCL
Determining Circuit Model ParametersLocked-rotor Test
PAV
Adjustable voltage, adjustable frequency, three-phase power source PA
A
IA
IB
IC
Locked rotor
a
b
c
R1
R2/s=R2jXM
jX1 jX2
RC
I2I1
V
+
-
tester fff
ratedLCBA
L IIII
I ,3
MC
C
M
XR
jXRR
jXRX
and neglect So22
22
Determining Circuit Model Parameters
One problem with this test: During normal operating conditions, s of the motor is only 2-4%, and resulting the frotor is in the range of 1-3 Hz.
The fe,rated (50/60 Hz) does not represent the normal operating conditions of the rotor.
A typical compromise is to use a frequency (ftest) 25% or less of fe,rated, examples: 12.5 Hz and 15 Hz.
Locked-rotor Test
Determining Circuit Model Parameters
The input power to the motor,
The magnitude of total impedance in motor circuit,
The total equivalent reactance at normal operating frequency,
Locked-rotor Test
cos3 LTin IVP
L
TLR
I
V
I
VZ
31
sincos'
LRLRLRLRLR ZjZjXRZ
21 RRRLR '2
'1
' XXX LR and
21' XXX
f
fX LR
test
ratedLR
Induction Motor Ratings Typical ratings on the nameplate of induction motor:
Output power Voltage Current Power factor Speed Nominal efficiency NEMA (National Electrical Manufacturers
Association) design class (Class A, B, C, and D). Starting code