Lecture 10 - Induction Machine III

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?