induction motor1 ac machine stator ‘a’ phase axis ‘b’ phase axis ‘c’ phase axis 120 0
Post on 22-Dec-2015
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induction motor 1
AC Machine Stator
‘a’ phase axis
‘b’ phase axis
‘c’ phase axis
1200
1200
1200
induction motor 21 Cycle
Amp
timet0t1 t2 t3 t4
t01 t12
Currents in different phases of AC Machine
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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 (theta) in degrees
t0
t01
t12
t2
a
MMF Due to ‘a’ phase current
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a Fc
-93 10 113 216-1.5
-1
-0.5
0
0.5
1
1.5
a’
c’ b’
b c
a
a’
c’ b’
b c
a
a’
c’ b’
b c
a
a’
c’ b’
b c
Fb
Fa F
FbFc
F
Fa
F
Fb
Fc Fc Fb
F
Space angle () in degrees
FFa Fc
Fb
t = t0= t4
t = t1t = t2 t = t3
t = t0= t4
RMF(Rotating Magnetic Field)
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Video of the unfolded rotating magnetic field
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RMF(Rotating Magnetic Field)-Analogy with DC machines
The salient field structure in DC machines is mimicked along with speed in an AC machines by a multiphase (2 or more) winding. The number of poles are
determined by winding distribution and is independent of the number of phases.
The rotational speed is determined by the supply frequency and the number of poles, such that an observer in air-gap counts same
number of poles per second, meaning the more the number of poles the slower the machine will run and vice-versa.
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Induction Motor•Most popular motor today in the low and medium horsepower range
•Very robust in construction
•Speed easily controllable using V/f or Field Oriented Controllers
•Have replaced DC Motors in areas where traditional DC Motors cannot be used such as mining or explosive environments
•Of two types depending on motor construction: Squirrel Cageor Slip Ring
•Only Disadvantage: Most of them run with a lagging power factor
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Squirrel Cage Rotor
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Slip Ring Rotor
•The rotor contains windings similar to stator.
•The connections from rotor are brought out using slip rings thatare rotating with the rotor and carbon brushes that are static.
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Torque Production in an Induction Motor
•In a conventional DC machine field is stationary and the current carrying conductors rotate.
•We can obtain similar results if we make field structure rotating and current carrying conductor stationary.
•In an induction motor the conventional 3-phase winding sets up the rotating magnetic field(RMF) and the rotor carries the current carrying conductors.
•An EMF and hence current is induced in the rotor due to the speed difference between the RMF and the rotor, similar to that in a DC motor.
•This current produces a torque such that the speed difference between the RMF and rotor is reduced.
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Slip in Induction Motor
•However, this speed difference cannot become zero because that would stop generation of the torque producing current itself.
•The parameter slip ‘s’ is a measure of this relative speed difference
s
s
s
s
n
nns
where ns,s,f1 are the speeds of the RMF in RPM ,rad./sec and supply frequency respectivelyn, are the speeds of the motor in RPM and rad./sec respectively
•The angular slip frequency and the slip frequency at which voltage is induced in the rotor is given by
11
22122 ,, E
N
NsEsffs s turnsRotorNturnsStatorN 21
polesofpp
fns #;
120 1
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Induction Motor Example
A 100 hp, 460V, 8 pole, 60 Hz, star connected3 phase induction motor runs at 891 rpm under full load. Determine the synchronous speed in rpm, slip, slipfrequency (frequency of the rotor circuit),slip rpm at full load. What is the speed of the rotor field relative to (i) rotor structure, (ii)stator structure, (iii) stator rotating field?
Voltage induced in rotor under full load? N2/N1=0.5
Solution on Greenboard
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Induction motor Equivalent Circuit
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Relation between air-gap, gross mechanical power and rotor copper loss
ssPPP mechag :1:1:: 2
Internal efficiency = sP
P
ag
mech 1
Implies lower the slip higher is the induction motor efficiency
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Example problem related to theformula shown in the previous
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Approximate Equivalent Circuit
•Assumes negligible magnetizing current
• Note Rc has been removed.The sum of core losses and the windage and friction loses are treated as constant. This is because as speed increases rotor core lossdecreases (lower f2) but windage and frictionloses increase.With decrease of speed the converse is true. Thus the sum is constant at any speed and is termed as rotational loss.
j
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IEEE Equivalent Circuit
•Assumes 30-50% magnetizing current and drop across R1+jX1 notnegligible
• As before, the sum of core losses and the windage and friction loses are treated as constant.
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Thevnin’s equivalent of theIEEE Equivalent Circuit
• This is done by applying Thevenin’s theorem and treating the rotor side as load
111
21 ,,,
XX
XKXXRKRVKV
m
mthththththth
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Determining equivalent circuit parameters
j
Uses no-load test and blocked rotor tests to determine them
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Example problem related to no-load and blocked rotor test
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Performance Characteristics(1)
syn
ag
mech
mechmech
pf
synsynmech
agmechmechmech
PPT
s
sPss
RITP
14
222
;)1(
);1()1(
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Performance Characteristics(2)
s
R
XXsRR
VT
s
RI
PPT
thth
th
synmech
synsyn
ag
mech
mechmech
'2
2'2
2'2
2
'22'
2
)()/(
1
1
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Performance Characteristics(3)
Case 1: )( zerotoclosesmalls
'2
'2
'2
XXs
Rand
Rs
RThen
th
th
sT
sR
VT
mech
th
synmech
)(
1'2
2
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Performance Characteristics(4)
Case 2: )(arg onetocloseels
'2
'2 XX
s
RRThen thth
sT
s
R
XX
VT
mech
th
th
synmech
1
)(
1 '2
'2
2
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Performance Characteristics(5)Combining case 1 and 2 the approximate torque speed characteristics would look approximately like:
Tmech
Speed (n)
Tmax
nm ns
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Performance Characteristics(6)How to obtain Tmax? By differentiating the following equation with respect to s and equating it to zero.
s
R
XXsRR
VT
thth
th
synmech
'2
2'2
2'2
2
)()/(
1
One can obtain the following:
Slip at maximum torque =])([ 2'
22
'2
max
XXR
Rs
thth
T
)()(
1
2)(2
1
)(2
1
1'2
2
1'2
2
2'2
2
2
max
RsmallLL
Vp
XX
V
XXRR
VT
th
th
th
th
syn
ththth
th
syn
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Performance Characteristics(7)(Speed Control)
Speed control by varying rotor resistance (varyTmax by varying sTmax)
(inefficient)
Speed control by varying supply voltage and frequency
(Vth/1)(efficient)
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Performance Characteristics(8)
s
R
XXsR
VT
th
th
synmech
'2
2'2
2'2
2
)()/(
1
Also using
)( '2
'2
max XX
Rs
thT
and
for small R1 one can write the following:
ss
ss
T
T
T
T
mech max
max
2
22max
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Example problem based on the formula on previous to express maximum torque and starting torque in terms of rated torque
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Performance Characteristics(9)
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Example problem related to efficiency calculation of induction motor based on equivalent circuit parameters
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Related to the problem in the previous slide
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Different modes of IM operation
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Different modes of IM operation
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Example problem on variable frequency supply using a slip-ringinduction motor
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Speed control of SRIM with ext. resistors
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Applications of SRIM
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Wind Power applications of SRIM
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