Transcript INDUCTION MOTOR (squirrel cage)

MEP 1523
ELECTRIC DRIVES
INDUCTION MOTOR
Scalar Control
(squirrel cage)
Scalar control of induction machine:
Control of induction machine based on steady-state
model (per phase SS equivalent circuit):
Rs
Is
Llr’ Ir’
Lls
+
Vs
–
Lm
+
Eag
Im
–
Rr’/s
Scalar control of induction machine
Te
Pull out
Torque
(Tmax)
Te
Intersection point
(Te=TL) determines the
steady –state speed
TL
Trated
s
sm
rated
rotor s
r
Scalar control of induction machine
Given a load T– characteristic, the steady-state speed
can be changed by altering the T– of the motor:
Pole changing
Synchronous speed change with
no. of poles
Discrete step change in speed
Variable voltage (amplitude),
variable frequency
Using power electronics converter
Operated at low slip frequency
Variable voltage (amplitude),
frequency fixed
E.g. using transformer or triac
Slip becomes high as voltage
reduced – low efficiency
Variable voltage, fixed frequency
e.g. 3–phase squirrel cage IM
600
V = 460 V
Rr=0.2  Lr = Ls = 0.5/(2*pi*50)
500
Lm=30/(2*pi*50)
400
f = 50Hz
Torque
Rs= 0.25 
p=4
300
Lower speed  slip higher
200
100
0
Low efficiency at low speed
0
20
40
60
80
w (rad/s)
100
120
140
160
Variable voltage, variable frequency
Constant V/f operation
At low slip
Variable voltage, variable frequency – Constant V/f
If Φag is constant  Te α slip frequency
Variable voltage, variable frequency – Constant V/f
How do we make  ag constant ?
Approximates constant air-gap flux when Eag is large
Eag = k f ag
 ag = constant

E ag
f

V
f
Speed is adjusted by varying f - maintaining V/f to
approximate constant air-gap flux
Variable voltage, variable frequency – Constant V/f
Characteristic with constant  ag
900
800
50Hz
700
30Hz
Torque
600
500
10Hz
400
300
200
100
0
0
20
40
60
80
100
120
140
160
Variable voltage, variable frequency
Constant  ag  constant V/f
Vs
Vrated
Constant slope
frated
f
Variable voltage, variable frequency
Constant V/f – open-loop
Rectifier
3-phase
supply
VSI
IM
C
f
Ramp
s*
+
V
Pulse
Width
Modulator
rate limiter is needed to ensure the slip
change within allowable range (e.g. rated
value)
Variable voltage, variable frequency
Constant V/f – open-loop
Simulation example: 415V, 50Hz, 4 pole, Rs = 0.25, Rr = 0.2,
Lr=Ls= 0.0971 H, Lm = 0.0955, J = 0.046 kgm2 , Load: k2
is
In1 Out1
To Workspace2
Subsystem
isd
Va
Out1
isq
ird
speed
Signal 1
Signal Builder
In1
Rate Limiter
Out2
Vb
Vd
Scope
irq
Out3
Constant V/Hz
Vq
Vc
Te
Induction Machine
speed
torque
To Workspace1
To Workspace
Scope1
Variable voltage, variable frequency
Constant V/f – open-loop
Simulation example: 415V, 50Hz, 4 pole, Rs = 0.25, Rr = 0.2,
Lr=Ls= 0.0971 H, Lm = 0.0955, J = 0.046 kgm2 , Load: k2
constant_vhz_withoutBoost/Signal Builder : Group 1
50
Signal 1
40
30
20
10
0
0
0.5
1
1.5
2
Time (sec)
2.5
3
3.5
Variable voltage, variable frequency
Constant V/f – open-loop
Simulation example: 415V, 50Hz, 4 pole, Rs = 0.25, Rr = 0.2,
Lr=Ls= 0.0971 H, Lm = 0.0955, J = 0.046 kgm2 , Load: k2
450
400
350
300
250
200
150
100
50
0
-50
0
20
40
60
80
100
120
140
160
Variable voltage, variable frequency
Constant V/f – open-loop
Simulation example: 415V, 50Hz, 4 pole, Rs = 0.25, Rr = 0.2,
Lr=Ls= 0.0971 H, Lm = 0.0955, J = 0.046 kgm2 , Load: k2
With almost no rate limiter
500
200
150
400
100
50
0
300
-50
200
0
0.5
1
1.5
0
0.5
1
1.5
600
400
100
200
0
-200
0
-100
0
20
40
60
80
100
120
140
160
180
200
Variable voltage, variable frequency
Constant V/f – open-loop
Simulation example: 415V, 50Hz, 4 pole, Rs = 0.25, Rr = 0.2,
Lr=Ls= 0.0971 H, Lm = 0.0955, J = 0.046 kgm2 , Load: k2
With 628 rad/s2
450
400
200
350
150
100
300
50
250
0
200
-50
0
0.5
1
1.5
0
0.5
1
1.5
150
600
100
400
50
200
0
0
-50
-20
0
20
40
60
80
100
120
140
160
-200
Variable voltage, variable frequency
Constant V/f – open-loop low speed problems
Problems with open-loop constant V/f
At low speed, voltage drop across stator impedance is
significant compared to airgap voltage - poor torque
capability at low speed
Solution:
(i) Voltage boost at low frequency
(ii) Maintain Im constant  stator current control
Variable voltage, variable frequency
Constant V/f – open-loop low speed problems (i) voltage boost
500
450
400
350
300
250
200
150
100
50
0
0
20
40
60
80
100
120
140
160
180
• Torque deteriorate at low frequency – hence compensation commonly
performed at low frequency
• In order to truly compensate need to measure stator current – seldom
performed
Variable voltage, variable frequency
Constant V/f – open-loop low speed problems (i) voltage boost
500
450
400
With voltage
boost of Irated*Rs
350
300
250
200
150
100
50
0
0
20
40
60
80
100
120
140
160
180
• Torque deteriorate at low frequency – hence compensation commonly
performed at low frequency
• In order to truly compensate need to measure stator current – seldom
performed
Variable voltage, variable frequency
Constant V/f – open-loop low speed problems (i) voltage boost
Voltage boost at low frequency
Vrated
Linear offset
Boost
Non-linear offset – varies with Is
frated
Variable voltage, variable frequency
Constant V/f – open-loop low speed problems (i) voltage boost
Idc
Rectifier
3-phase
supply
+
Vdc
-
VSI
IM
C
f
Ramp
s*
+
V
+
Vboost
Pulse Width
Modulator
Variable voltage, variable frequency
Constant V/f – open-loop low speed problems (i) Constant Im
ag, constant → Eag/f , constant → Im, constant (rated)
Controlled to maintain Im at rated
Rs
Is
Llr’
Lls
Ir’
+
Lm
Vs
Eag
maintain at rated
–
+
Im
–
Rr’/s
Variable voltage, variable frequency
Constant V/f – open-loop low speed problems (i) Constant Im
From per-phase equivalent circuit,
• Current is controlled using currentcontrolled VSI
Im 
Rr
s
j  ( L lr  L m ) 
Is 
• The problem of stator impedance drop is
solved
• Dependent on rotor parameters –
sensitive to parameter variation
j  L lr 
Is 
j L r 
 r
j  
1 r
Rr
s
Rr
s

R
L r  r

s

j  slip T r  1
 r
j  slip 
1 r
Is

 T r  1

Im
Im ,
Variable voltage, variable frequency
Constant V/f – open-loop low speed
problems (i) Constant Im
VSI
3-phase
supply
Rectifier
IM
C
Current
controller
*
+
PI
-
slip
+
r
+
|Is|
s
Current reference generator
Tacho
Variable voltage, variable frequency
Constant V/f
Problems with open-loop constant V/f
Poor speed regulation
Solution:
(i) Slip compensation
(ii) Closed-loop control
Variable voltage, variable frequency
Constant V/f – poor speed regulation: (i) slip compensation
Motor characteristic
AFTER slip
compensation
T
Tload
Motor characteristic
BEFORE slip
compensation
T2
T1
ωs1*
ωr1
ωslip1 ω
slip1
ωr2≈ωs1*
ωs2*=ωs1*+ωslip1
ωr (rad/s)
Variable voltage, variable frequency
Constant V/f – poor speed regulation: (i) slip compensation
Idc
Rectifier
3-phase
supply
+
Vdc
-
VSI
IM
C
f
Ramp
s*
+
+
+
Slip speed
calculator
Vdc
Idc
V
+
Vboost
Pulse Width
Modulator
Variable voltage, variable frequency
Constant V/f – poor speed regulation: (i) slip compensation
How is the slip frequency calculated ?
Idc
+
INV
Vdc

Pdc= VdcIdc
Pmotor,in= Pdc – Pinv,losses
STATOR
ROTOR
Pmotor,in
Pair-gap
Stator Copper
lossess
Stator Core
losses
Variable voltage, variable frequency
Constant V/f – poor speed regulation: (i) slip compensation
How is the slip frequency calculated ?
Pair-gapc = Tesyn
Te = Pair-gap/syn
For constant V/f control,
Te
 slip

Te , rated
 slip , rated
 slip  T e
 slip , rated
T e , rated
Variable voltage, variable frequency
Constant V/f – poor speed regulation: (i) closed-loop speed
• Require speed encoder
• Increase complexity