Transcript Induction Motor - ENCON - Department of ENergy CONversion
•
Induction Motor Drive
Why induction motor (IM)?
– Robust; No brushes. No contacts on rotor shaft – High Power/Weight, Lower Cost/Power ratios – Easy to manufacture – Almost maintenance-free, except for bearing and other “external” mechanical parts •
Disadvantages
– Essentially a “fixed-speed” machine – Speed is determined by the supply frequency – To vary its speed need a variable frequency supply •
Motivation for variable-speed AC drives
– Inverter configuration improved – Fast switching, high power switches – Sophisticated control strategy – Microprocessor/DSP implementation •
Applications
– Conveyer line (belt) drives, Roller table, Paper mills, Traction, Electric vehicles, Elevators, pulleys, Air conditioning and any industrial process that requires variable-speed operation.
• The state-of-the-art in IM drives is such that most of the DC drives will be replaced with IM in very near future.
Dr. Zainal salam; Power Electronics and Drives (Version 2),2002, UTMJB 1
Torque production (1)
• Only “squirrel-cage” IM (SCIM) is considered in this module • Neglecting all harmonics, the stator establishes a spatially distributed magnetic flux density in the air-gap that rotate at a
synchronous speed,
w
1
: w 1 w
e p
where w
e
: supply frequency (in Hz)
p
: pole pairs (
p
=1for 2 pole motor
, p
=2 for 4 pole motor etc) • If the rotor is initially stationary, its conductor is subjected to a sweeping magnetic field, inducing rotor current at synchronous speed.
• If the rotor is rotating at synchronous speed (i.e. equals to
f 1
), then the rotor experience no induction. No current is induced in the rotor.
Dr. Zainal salam; Power Electronics and Drives (Version 2),2002, UTMJB 2
Torque production (2)
• At any other rotor speed, say wm, the speed differential w
i -
w
2
creates slip. Per-unit slip is defined as:
s
w 1 w 1 w
m
; w 1 w
e p
where : w
e
w
m
: supply : rotor frequency frequency
p
: pole pair • Slip frequency is defined as: w
2 =
w
1 -
w
m
.
• When rotor is rotating at w
m
., rotor current at slip frequency will be induced.
• The interaction between rotor current and air-gap flux produces torque.
Dr. Zainal salam; Power Electronics and Drives (Version 2),2002, UTMJB 3
V 1
Single-phase Equivalent Circuit (SPEC)
1:nS R 1 L 1 L 2 R m L m V m V 2 = nSV m R 2 STATOR SIDE
R
1 : Stator resistance
L
1 : Stator leakage inductance
R
2
L
2 : Rotor resistance : Rotor leakage inductance
L m
: Magnetisin g inductance
v
1 : Supply vol tage (phase voltage) ROTOR SIDE Dr. Zainal salam; Power Electronics and Drives (Version 2),2002, UTMJB 4
V 1
SPEC, referred to stator
I 1 R 1 L 1 I 2 L 2 R m L m R 2 S • From previous diagram, SPEC is a dual frequency circuit. On the stator is w
1
and on the rotor w
m
• Difficult to do calculations. • We can make the circuit a single frequency type, by referring the quantities to the stator Dr. Zainal salam; Power Electronics and Drives (Version 2),2002, UTMJB 5
Rotor current
If E the 1 is the back back EMF EMF in the stator phase, then in an equivalent rotor phase with the same effective turns ratio will be E 2 where :
E
2
sE
1 At standstill , i.e
when w m 0 ,
E
2
sE
1 1
E
1
E
1 At synchronou s speed, i.e
when w m 1 ,
E
2 ( 0 )
E
1 0 Hence the current in the rotor phase,
I
2
R
2
E
E
1 2
jsX R
2
jX
2 Note
s
that the 2
R
2
sE
1
jsX
2 quantities are now referred to the stator, but with t he rotor resistance alteration .
Dr. Zainal salam; Power Electronics and Drives (Version 2),2002, UTMJB 6
Performance calculation using SPEC
I 1 R 1 L 1 I 2 L 2 V 1 R m L m R 2 S Input Power :
P in
3
V
1
I
1 cos Note :
V
1 and
I
1 must be phase voltage and current Stator Core copper loss Power : loss :
P ls
across the air gap :
P P lc g
3 3
I V
1 2 1 2 3
I R
2
m
2
R
1
R
2 Rotor copper loss :
P lr
P in
3
I
2 2
P ls R
2
P lc
Dr. Zainal salam; Power Electronics and Drives (Version 2),2002, UTMJB 7
Performance calculation (2)
Gross
P o
P
output
g
P lr
power 3
I
2 2
s R
2 3
I
2 2 : 3
I
2 2
R
2
s
( 1
s
)
P g
( 1
s
) Power at the
P sh
P o
P
shaft
FW
; :
P FW
: friction and windage loss.
Developed (electroma gnetic) torque :
T e
P o
w
m
3
I
2 2
R
2
s
w ( 1
m
s
) Since
s
w 1
T e
But w 1 w 1 3
I
w 2
s
w
p m
2 w 1
e
R
2 ; w
e
w
m
( 1
s
) w 1 , is the supply frequency.
Then,
T e
3
pI
2
s
w 2
e R
2 Dr. Zainal salam; Power Electronics and Drives (Version 2),2002, UTMJB 8
Example calculation
• A single phase equivalent circuit of a 6-pole SCIM that operates from a 220V line voltage at 60Hz is given below. Calculate the stator current, output power, torque and efficiency at a slip of 2.5%. The fixed winding and friction losses is 350W. Neglect the core loss.
V 1 I 1 R 1 0.2
X 1 0.5
I 2 X 2 0.2
X m 20 R 2 0.1
V 1 220V line-to line 220V 127V 3 2.5% 0.025
3 Dr. Zainal salam; Power Electronics and Drives (Version 2),2002, UTMJB 9
Calculation (solution)
X
1 0 .
5 ,
X
2 0 .
2 ,
X m
20
Z in
(
R
1 0 .
2
j
0
jX
1 ) .
5
jX m
//
R
2
s
jX
2
j
20 0 .
1 0 .
025 0 .
1 0 .
025
j
0 .
2
j
0 .
2
j
20 4 .
2 20
o
I
1
V
1
Z in
220 3 4 .
2 20
o
30 .
0 20
o A P in
3
V
1
I
1 cos 10 , 758
W
3 ( 220 3 )( 30 )(cos 20
o
)
P ls
3
I
1 2
R
1 3 ( 30 2 )( 0 .
2 ) 540
W
Power tran sferred to rotor (neglectin g core loss)
P g
P in
P ls
10 , 758 540 10 , 216
W
Gross power
P o
P g
( 1
s
) 10 , 216 ( 1 0 .
025 ) 9 , 961
W
Power at the shaft
P sh
P o
P FW
9 , 961 350 9 , 611
W
Efficiency Output power Input power 9611 10758 89 .
3 % Electromag netic Torque
T e
P o
w
m
78 .
4
N
.
m
( w
e
1
P o p
) ( 1
s
) 2 ( 60 / 9611 3 )( 1 0 .
025 ) Dr. Zainal salam; Power Electronics and Drives (Version 2),2002, UTMJB 10
Starting current
• For the previous example, Calculate the stating current when motor is first switched on to rated applied voltage.
Solution : At standstill ,
s
1
Z in
0 .
2
j
0 .
5
j
20 0 .
1 0 .
1
j
0 .
j
0 .
2 2
j
20
I
1 0 .
76
V
1 220
Z in
0 .
76 3 167
A
Note that the starting current is about 5 times than full load current.
This is common for induction motors.Car
e should be taken when starting induction motors.
Dr. Zainal salam; Power Electronics and Drives (Version 2),2002, UTMJB 11
Approximate SPEC
+
V
1 -
L M R
1
L
1
L
2
R
2
s
Since L m is large, the circuit above can be drawn
I
2
R
1
R
2
s V
1 2 w 1 2
L
1
L
2 2 Power at the rotor (per phase),
P o
I
2 2
R
2
s
Electromag netic (developed ) torque,
T e
3
P o
w 1
s
w 1
R
1
R
2 3
R
2
V
1 2 2 w 1 2
L
1
s
L
2 2 Dr. Zainal salam; Power Electronics and Drives (Version 2),2002, UTMJB 12
Single (fixed supply) frequency characteristics
For a give frequency w 1 , the torque (versus slip) characteri stics can be shown as below.
Note that
s
: w 1 w 1 w
m
; at standsill
s
1 , at sync speed,
s
0 .
w
e
w
m
PLUGGING TORQUE(+) MOTORING
T
(max torque or
em
pull-out torque) w
e
w
m
w
e
w
m
GENERATING
T es
(starting torque) 0 unity slip (standstill) rated slip SLIP,s TORQUE(-) zero slip w
e
(sync.speed) SPEED Dr. Zainal salam; Power Electronics and Drives (Version 2),2002, UTMJB 13
Single frequency characteristics
CURRENT TORQUE 1.0
EFFICIENCY POWER FACTOR rated current Standstill operating point (rated torque) rated slip SLIP 0 synchronous speed Dr. Zainal salam; Power Electronics and Drives (Version 2),2002, UTMJB 14
Single frequency characteristic
• As slip is increased from zero (synchronous), the torque rapidly reaches the maximum. Then it decreases to standstill when the slip is unity.
• At synchronous speed, torque is almost zero.
• At standstill, torque is not too high, but the current is very high. Thus the VA requirement of the IM is several times than the full load. Not economic to operate at this condition.
• Only at “low slip”, the motor current is low and efficiency and power factor are high.
Dr. Zainal salam; Power Electronics and Drives (Version 2),2002, UTMJB 15
Typical IM Drive System
I DC
+
V DC
IM
Modulation Index,
BLOCK DIAGRAM Supply Rectifier and Filter 3-phase Inverter
n
CIRCUIT Dr. Zainal salam; Power Electronics and Drives (Version 2),2002, UTMJB IM 16
Variable speed characteristics
• For variable speed operation, the supply is an inverter.
• The frequency of the fundamental AC voltage will determine the speed of IM. To vary the speed of IM, the inverter fundamental frequency need to be changed.
• The inverter output frequency must be kept close to the required motor speed. This is necessary as the IM operates under low slip conditions.
• To maintain constant torque, the
slip frequency
has to be maintained over the range of supply frequencies. Dr. Zainal salam; Power Electronics and Drives (Version 2),2002, UTMJB 17
Variable voltage, variable frequency (VVVF) operation
• In order for maximum torque production, motor flux should be maintained at its rated value.
m
sin w 1
t
But the back emf is :
e
1
N d
dt
N
w 1
m
cos w 1
t
In RMS,
E
1 1 2
N
w 1 1
m
4 .
44
f
1
N
1
m
or
E
1
f
1 4 .
44
N
1
m
Therefore, in order to maintain t the
E
1
f
1 ratio has he motor flux, to be kept constant.
This is popularly known as the constant Volt/Hertz operation Dr. Zainal salam; Power Electronics and Drives (Version 2),2002, UTMJB 18
Constant Torque region
• Hence for VVVF operation, there is a need to control the fundamental voltage of the inverter if its frequency (and therefore the frequency of the IM) need to be varied.
• To vary the fundamental component of the inverter, the MODULATION INDEX can be changed.
• The rated supply frequency is normally used as the base speed • At frequencies below the base speed, the supply magnitude need to be reduced so as to maintain a constant Volt/Hertz.
• The motor is operated at rated slip at all supply frequencies. Hence a “constant torque” region is obtained. Dr. Zainal salam; Power Electronics and Drives (Version 2),2002, UTMJB 19
Constant Torque Region
TORQUE(+)
f
1
f
2
f
1
f
2
f
3
f
4
f
5
f
3
f
4
f
5 rated torque TORQUE(+) 0 SLIP,s rated torque rated slip SPEED 0 SLIP,s Dr. Zainal salam; Power Electronics and Drives (Version 2),2002, UTMJB SPEED 20
Constant Power region
• Above base speed, the stator voltage reaches the rated value and the motor enters a constant power region.
• In this region, the air-gap flux decreases. This is due to increase in frequency frequency while maintaining fixed voltage.
• However, the stator current is maintained constant by increasing the slip. This is equivalent to field weakening mode of a separately excited DC motor.
Dr. Zainal salam; Power Electronics and Drives (Version 2),2002, UTMJB 21
Constant Power region
TORQUE(+) rated torque 0 TORQUE(+) SLIP,s CONSTANT TORQUE REGION Base speed SPEED "FIELD WEAKENING" 0 SLIP,s Base speed SPEED Dr. Zainal salam; Power Electronics and Drives (Version 2),2002, UTMJB 22
VVVF Summary
0 CONSTANT TORQUE Electromagnetic torque, T e Terminal (supply) voltage, V 1 slip frequency,fs CONSTANT POWER slip,s Base speed SPEED Dr. Zainal salam; Power Electronics and Drives (Version 2),2002, UTMJB 23
Examples
• A three-phase 4-pole, 10 horsepower, 460V rms/60Hz (line-to line) runs at full-load speed of 1746 rpm. The motor is fed from an inverter. The flux is made to be constsnt. Plot the torque-speed graphs for the following frequency: 60Hz, 45 Hz, 30Hz, 15Hz. • A three-phase induction motor is using a three-phase VSI for VVVF operation. The IM has the following rated parameters: • voltage: • frequency: • slip (p.u) • pole pair 415V (RMS) 50Hz 5% 2 – If the inverter gives 415V (RMS) with modulation index of 0.8, calculate the required modulation index if the motor need to be operated at rotor mechanical speed of 10Hz. Dr. Zainal salam; Power Electronics and Drives (Version 2),2002, UTMJB 24