Energy ECE341 Conversion (Spring 2011)
Topic 4: Induction Machine
Physical construction: Chap. 7: 1
Basic concepts and equivalent circuit: Chap. 7: 2, 3
Parameter measurement: Chap. 7: 11
Power, speed, and torque: Chap. 7: 4-6
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Induction Machines: the Name
The name induction machine because the rotor voltage
(which produces the rotor current and rotor magnetic
field) is induced in the rotor winding rather than being
physically connected by wires.
A distinguishing feature is that no DC field current, nor
permanent magnet is required to run this machine.
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Induction Machines: Construction
Machine Construction:
Stator: An induction motor has the same physical
stator as a synchronous machine.
Rotor: is of two types.
1.Squirrel Cage Rotor or simply cage rotor
(Work horse of the industry)
2.Wound rotor (Not a popular type of machine)
b axis
ib
2 / 3
a axis
2 / 3
ia
2 / 3
ic
( b)
c axis
(a )
Figure 11-9 (a) Three-phase stator; (b) squirrel-cage rotor.
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Induction Machines with Squirrel-cage Rotor
The rotor of many induction generators has copper or
aluminum bars shorted together at the ends, looks
like a cage
Can be thought of as a pair of magnets spinning
around a cage
Rotor current iR flows easily through the thick
conductor bars
Work horse of industrial applications, low cost,
minimum maintains, and rugged construction.
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Nikola Tesla: Inventor of Induction Motor
Nikola Tesla (1856 to 1943) is one of the key
inventors associated with the development of todays
three phase ac system. His contributions include the
induction motor and polyphase ac systems.
Unit of flux density is named after him
Tesla conceived of the induction motor while
walking through a park in Budapest in 1882.
He emigrated to the US in 1884.
The Tesla Coil in OSUs
High Voltage and Power
Electronics
Laboratory
operates at 3 MV.
Statue of Nikola Tesla
at Niagara Falls
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Tesla and Renewable Energy/Energy Efficiency
Most wind turbines are based on induction machines
because of its low cost and less need for maintenance !
http://www.youtube.com/watch?v=y2RQttpahqk
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Operation Sequence from Standstill
Rotating magnetic field of stator revolves at synchronous
speed
Flux lines cut rotor conductors, voltage is induced in rotor
conductors
Rotor currents can flow in short circuited conductors
eind
Rotor currents generate rotor flux and interact with stator
magnetic flux; torque is produced; rotor starts to move;
The induced voltage and current in the rotor winding
change polarity with the rotating magnetic field. The
induced torque was kept at the same direction. The rotor
starts to rotate!
BS
BS
Bw
ind
ind
eind
eind
i
i
S
BS
Steady state speed is smaller than synchronous speed
i
ind
eind
BS
ind
i
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Slip Rate Concept
nsync =
60 f sync
s=
P/2
=
120 f sync Rotation speed
P
nsync nm
nsync
of stator
magnetic field.
nm = (1 s )nsync
n m ns 0.5ns
0.5ns n s
8
nm : the rotation speed
of the rotor.
nslip = nsync nm
1.5ns
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Rotor Electric Frequency
Rotor electric frequency is the relative frequency between synchronous
frequency and rotor speed multiplied by P/120, which can simply be written
as
f r = sf sync.
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Exercise
Question:
A six-pole induction motor is supplied by a synchronous generator having
four poles and running at 1500 RPM, if the speed of the induction motor is
750 RPM, what is the rotor electric frequency?
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Rotor Voltage
At standstill:
nm = 0
Induced rotor voltage
s =1
f r = f sync
Er = kf r Nm = kf sync Nm
When the rotor accelerates
Induced rotor voltage
Er = kf r Nm = ksf sync Nm
When the rotor reaches synchronous speed
Induced rotor voltage Er = kf r Nm = ksf sync Nm = 0
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Induction Machine as a Motor
The rotating magnetic field in the stator causes the rotor to
spin in the same direction
As rotor approaches synchronous speed of the rotating
magnetic field, the relative motion becomes less and less
If the rotor could move at synchronous speed, there would be
no relative motion, no current, and no force to keep the rotor
going
Thus, an induction machine as a motor always spins
somewhat slower than synchronous speed
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Induction Machine as a Motor
As load on motor increases, rotor slows down
When rotor slows down, slip increases
Breakdown torque increasing slip no longer satisfies
the load and rotor stops
rotor Braking- is forced to operate in the opposite
direction to the stator field
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Induction Machine as a Generator
The stator requires excitation current
from the grid if it is grid-connected
In wind generation, wind speed forces generator shaft to
exceed synchronous speed
Slip is negative because the rotor spins faster than
synchronous speed
Slip is normally less than 1% for grid-connected
generator
Typical rotor speed
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Single Phase Model
Single phase model
I2
I1
R1
IR
IM
jX1
a eff
jXM
RC
jXR
v
E1
RR
v
ER
Similar as transformer model;
The rotor side may have different frequency from the stator side, thus
the rotor side component can not be directly referred to the stator side.
The total rotor resistance stands for the winding power loss and output
mechanical power
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Rotor Equivalent Circuit
IR
jXR
Rotor model
RR
v
ER
IR
Standstill:
s =1
f r = f sync
v
IR =
v
ER 0
RR + jX R 0
jX R 0
v
ER0
RR
At synchronous speed, the only active power consumption at the rotor side is
the winding power loss. Thus, when referred to synchronous speed frame,
RR can be seen as the winding resistance.
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Rotor Equivalent Circuit: Refer to the Stator Side
Rotating:
X R = sX R 0
IR
v
IR =
v
v
ER = sER 0
jXR
v
v
sE R 0
ER 0
=
RR
RR + jsX R 0
+ jX R 0
s
RR
v
ER
RR
IR
IR
jX R 0
jX R 0
RR / s
v
ER0
1 s
RR
s
v
ER0
v
Note: ER 0 is at synchronous frequency
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Equivalent Circuit and Power Flow
I1
I2
R1
jX 2
R2
IM
jX1
RC
2
R2 = aeff RR
jXM E
1
1 s
R2
s
RR = R2
2
X 2 = aeff X R 0
Pout = loadm
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Power Loss
Pout = load m
PSCL = 3I12 R1
PAG = Pin PSCL Pcore
Pcore = 3E / RC
2
1
2
PRCL = 3I 2 R2
2
Pconv = PAG PRCL = 3I 2 R2 (
1 s
)
s
PRCL = sPAG
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Parameter Measurement
No load test
Rotor spins at the speed close to synchronous speed, thus slip rate is very
small,
1 s
R2
>> R2
s
.
In general cases
1 s
R2
>> X 2
s
I1
1 s
R2
>> X M
s
I2
R1
jX 2
RC >> X M
I1
R2
IM
jX1
RC
jXM
X M + X 1 >> R1
1 s
R2
s
20
jX1
I1
jXM
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Parameter Measurement
Locked rotor test
There is no mechanical power, the only active power is the rotor winding
resistive loss.
I1
I2
jX 2
I1
I2
jX 2 R 2
R1
1 s
R2
s
jXM
RC
jX1
R1
IM
jX1
I1
I1
jX 2
jXM
RC
X M >> R2 + jX 2
R2
RC >> R2 + jX 2
jX1
R1
R2
IM
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Torque Equations (I)
ind =
Pconv
m
=
(1 s) PAG
P
= AG
(1 s )sync sync
2
PAG = 3I 2
R2
s
I1
I2
R1
V
2
ind = 3I 2
jX 2
R
max
s sync
R2
IM
jX1
RC
ns
1 s
R2
s
jXM E
1
X M >> X 1 , X 2
RC >> R1 , R2
I1 I 2
22
ind = 3
V2 R2 / s
s [( R1 + R2 / s) 2 + ( X 1 + X 2 ) 2 ]
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Torque Equations (II)
Startup torque
ind = 3
V2 R2 / s
s [( R1 + R2 / s) 2 + ( X 1 + X 2 ) 2 ]
ind _ startup = 3
S=1
Maximum (pullout) torque
Maximum torque happens at the condition that
At this condition
ind _ max 3
S _ max
R2
V2 R2
s [(R1 + R2 ) 2 + ( X 1 + X 2 ) 2 ]
d ind
=0
d ( R2 / s)
R + ( X1 + X 2 )2
2
1
V2 R2
2s ( R1 + R12 + ( X 1 + X 2 ) 2 )
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Starting the Motor
Most three phase induction motor can be started by simply plug the three
phase terminal into standard three phase power outlet.
One concern is that at startup, if rated voltage at rated frequency is applied to
the motor, there will be inrush current 5-7 times higher than rated current.
Sometime this inrush current will cause voltage dip in the power network to
which it connected.
With V/F control, inrush current can be very
well controlled.
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Still, It is also Good to Know the Old Ways
Speed control by
Change number of poles
Change the line frequency
Change line voltage
Change rotor resistance
(Text book pp. 436-444)
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Variable Slip Example: Vestas V80 1.8 MW
The Vestas V80 1.8 MW turbine is
an example in which an induction generator
is operated with variable rotor resistance
(opti-slip).
Adjusting the rotor resistance changes the
torque-speed curve
Operates between 9 and 19 rpm
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From generator to load: ECE 341 Topics
Synchronous Generator in the
concentrating solar power plant
Step-up Transformer
Three Phase 765 kV High
Voltage Lines
Induction machines
and power electronics
in home appliance and
Electrical Vehicles
Three Phase 22 kV
Distribution Lines
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Step-down Transformer
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