lecture 10 - induction machine iii
DESCRIPTION
principle of induction motorTRANSCRIPT
Induction Motor III
ELEC 2032(3)Electromechanical System
Course Instructor: Dr S. Goolaup
21st March 2012
Recap
Stator and Wound Rotor windings induced EMF
Torque Speed Characteristics
Equivalent circuit for stator
Power Flow
Rotor Equivalent CircuitRrs
Air Gap Power Pag Ir
2Rr
s Ir
2Rr Ir2Rr
1 ss
Prcl Pmech
Pag : Prcl : Pmech 1 : s :1 s
Torque per phase
Pmech Tmechm m 2nm
60Tmech
Pag
s
Equivalent Circuit Model
No Load Test, Blocked Rotor Test and DC resistance of Stator Windings
Pin
Stator Core Loss
Stator Cu Loss ( )
Pag
Rotor Core Loss
Rotor Cu Loss ( )3I1
2R13I2
2R2
Pmech
Friction and Windage Losses
Pout(shaft)
(Pshaft)
MotoringPower
Pshaft Tshaftm
Pshaft Pmech Pf ,w
Efficiency
Useful power output:Total input power
Pshaft
Pin
Power Factor
Power Factor = cosr
Pin
Sin
For a 3 phase system:
Sin 3VlineI line
*
Example 2A 60Hz, 11.19KW, 460V, 3phase, 6pole, Y connectedinduction motor driving a load at a speed of 1185 rev/min.The total rotational losses are 166 W and the motorparameters referred to the stator (ohms/phase):R1 = 0.20 R2 = 0.25 XM=42.0X1 = 1.20 X2= 1.29 RC = 317
Determine:(a) line current (b) Apparent power (c) equivalent rotor current (d) stator copper loss (e) core loss (f) Air gap power (g) mechanical power and torque developed (h) shaft torque
Approximate Equivalent Circuit
High Power Motors I1 is very small> 2 KWFractional Horsepower
still need to use equivalent circuit
Approximate Equivalent Circuit
Fixed supply voltage and frequencyCore losses, Friction and windage losses are constant at alloperating speed
Rotational losses
Performance Characteristic
Pmech Tmechm Pmech I2' 2 R2
'
s(1 s)
Tmech I2' 2 R2
'
s(1 s)
1m
m (1 s) s
Tmech I2' 2 R2
'
s1 s
Performance Characteristic
I2' 2 V1
2
R1 R2
'
s
2
X1 X2'
Tmech V1
2
R1 R2
'
s
2
X1 X2' 2
R2'
s s
For small s(nm≈ns)
Tmech V1
2
R2'
s s
Linear Characteristic near synchronous speed
Large s (nm ≥ 0)
Torque varies inversely with s
Tmech V1
2
X1 X2' 2
R2'
s s
For fixed s(nm = constant)
Tmech V12
Torque varies as square of supply voltage
Performance Characteristic
Performance CharacteristicMaximum Torque
dTmech
ds 0 Tmech
V12
R1 R2
'
s
2
X1 X2' 2
R2'
s s
Quotient Rule
g(s) R2
'
s
h(s) R1 R2
'
s
2
X1 X2' 2
Performance Characteristic
ST max R2
'
R12 X1 X2
' 2 1
2
Tmax 1
2 s
V12
R1 R12 X1 X2
' 2
12
Maximum torque is independent of rotor circuit resistance
R2 determines speed of Maximum
Torque
Performance Characteristic
If Stator resistance, R1 is small
ST max R2
'
X1 X2'
Tmax 1
2 s
V12
X1 X2'
Maximum Torque inversely proportional to Leakage Reactance
Maximum torque to Torque at any speed
Tmax
T
sT max2 s2
2sT maxs
Effect of Rotor ResistaceST max
R2'
R12 X1 X2
' 2 1
2
ST max R2' Rext
Rotor I2R loss dissipated in externalresistance
Rotor heating lower during starting andacceleration period
Starting of Squirrel Cage MotorDraws a large current at start - Low Torque and Power Factor∼5 to 8 time the Full Load Current
Large Current leads to overheating of motor
Reduced Voltage StartingAuto-TransformerR: Running contact
S: Starting contacts
Start: S are closed & R is open
Running: S are open & R is closed
Starting of Squirrel Cage Motor
Star-Delta 1: Star 2: Delta
Running - Delta
Starting - Star
Solid State Voltage Controller
Stator Windings
Control Speed
Reduce Voltage ⇒ Reduce Torque
Example 3A 3 phase, 460V from a Y-connected supply, 1740 rpm 60Hz, 4pole wound-rotor induction motor has the following parameter per in ohms/phase:R1 = 0.25 R2’ = 0.20X1 = X2’ = 0.5 Xm=30
The rotational losses are 1700W. With rotor terminals short circuited find:
(a) (i) starting current when started direct on full voltage(ii) Starting Torque
(b) Full load (i) slip (ii) current (iii) Torque (iv) Motor Efficiency (v) Internalefficiency (Pag:Pmech)
(c) (i) Slip at which maximum torque is developed (ii) Maximum Torque
(d) For maximum torque to occur at start, what is the additional resistance tobe connected per phase?
