1. Three Phase Induction Motors

2. Lecture 3 3 Induction Motor Equivalent Circuit Rotor Frequency
Rotor Emf, Current, Impedance
Rotor Equivalent circuit
Load Representation
Power Stages
Lecture 3 Exercise
Summary
Dept of E & E, MIT Manipal
L3 – 01

3. Equivalent Circuit Ic V1 Rc Xm R2 Xr=sX2 I1 E1 Er= s E2 Im Rotor
Dept of E & E, MIT Manipal
L3 – 02 Rc Xm V1 R2
Xr=sX2 I1 E1
Er= s E2 Ic Im
Rotor
Air Gap
Stator R1 X1
Stator
V1 = Supply voltage
R1 = Stator Winding Resistance
X1 = Stator Leakage Reactance
I1 = Stator Winding Current
Rc = Core Loss Resistance
Xm = Magnetising Reactance
E1 = Stator Self Induced Emf
Rotor
Er = Rotor Induced Emf under Running Conditions
s = Operating Slip
E2 = Standstill Rotor Induced Emf
R2 = Rotor Winding
X2 = Rotor Leakage Reactance at Standstill
Xr = Rotor Leakage Reactance under Running Condition

4. Rotor Frequency For rotor speed N, relative speed = NS - N
f = Frequency of ac supply, Hz
P = No. of poles
NS = Speed of RMF, rpm
s = fractional slip
fr =frequency of rotor, Hz
Note
At instant of starting, N = 0, s = 1, fr = f
Dept of E & E, MIT Manipal
L3 – 03

5. Rotor Emf
At standstill, s = 1, max relative speed, max rotor induced emf
If E2 = per phase rotor induced emf at standstill, E2  NS
If E2r = per phase rotor induced emf under running conditions,
E2r  (NS - N)
Thus for any slip,
Dept of E & E, MIT Manipal
L3 – 04

6. Rotor Equivalent circuit
Dept of E & E, MIT Manipal
L3 – 05
Rotor windings offer resistance, represented by R2
Presence of leakage flux, represented by X2
Standstill
Operating
Emf E2
E2r = s E2
Resistance R2
Reactance X2
X2r = s X2
Impedance
Z2= R2 + j X2
Z2r= R2 + j ( s X2 )
Current I2
I2r R2
X2r
E2r
I2r

7. Rotor Equivalent circuit cont’d …
Dept of E & E, MIT Manipal
L3 – 06 R2
X2r
E2r
I2r
E2r = per phase rotor induced emf = s E2
R2 = per phase rotor resistance
X2r = per phase rotor leakage reactance = s X2
I2r = per phase rotor current
s = operating slip X2 E2
I2r

8. Load Representation X2 X2 R2 E2 E2 I2r I2r
Dept of E & E, MIT Manipal
L3 – 07 X2 E2
I2r R2 X2 E2
I2r
Variable Rotor resistance can be split into two parts :
Resistor R2 to represent the rotor side copper loss
Resistor RL to represent the electrical equivalent of mechanical load
Mechanical load on the
motor is represented by

9. PNet = PGross – PFriction & Windage Loss
Power Output
Dept of E & E, MIT Manipal
L3 – 08 R2 X2 E2
I2r
Gross Power Output
(Rotor Output)
Net Power output
(actual Power output
or Shaft output)
PNet = PGross – PFriction & Windage Loss

10. Torque
Dept of E & E, MIT Manipal
L3 – 09 R2 X2 E2
I2r
TSh = Tg – TFw

11. Torque Slip Characteristics – Squirrel Cage
Dept of E & E, MIT Manipal
L3 – 10
Torque, Nm
Tmax
Low to medium slip region
High slip region
Tst sM
s = 1
Slip, %
s = 0

12. R2 < (R2 + y) < (R2 + 2y) < (R2 + 3y)
Torque Slip Characteristics – Slip Ring
Dept of E & E, MIT Manipal
L3 – 11
R2 < (R2 + y) < (R2 + 2y) < (R2 + 3y)
Torque, Nm
Slip, % sM
sM = 1 R2
R2 + y
R2 + 2y
Tmax
Tst
R2 + 3y

13. Lecture 3 Exercise
[1] A 3, 50 Hz, 6 pole induction motor has a no load slip of 1 % and a full load slip of 3 %. Determine (a) synchronous speed (b) no load speed (c) full load speed (d) frequency of rotor current at standstill (d) frequency of rotor current at full load
1000rpm,990 rpm,970 rpm,50Hz,1.5Hz
[2] A 3, 50 Hz, 4 pole induction motor has a star connected rotor. The per phase rotor resistance is 0.1  and per phase standstill reactance is 2 . If the induced emf between the slip rings is 100 V, full load speed is 1460 rpm, determine (a) slip (b) rotor induced emf (c) per phase rotor reactance (d) rotor current. Assume the slip rings are short circuited.
2.67%,1.50,0.052 ,13.3A
[3] A 3, induction motor has a star connected rotor. The rotor emf between the slip rings at standstill is 50 V. The rotor resistance and standstill rotor reactance are 0.5  and 3  respectively. Determine (a) per phase rotor current at starting if a star connected rheostat of 6  per phase is connected across the slip rings (b) full load rotor current and for a full load slip of 4 % (c) per phase rotor emf under full load condition
Dept of E & E, MIT Manipal
L3 – 12

14. Lecture 3 Summary Induction Motor as a generalized Transformer
Rotor Equivalent circuit
Electrical equivalent of mechanical load
Power Output
Gross Power Output, Friction & Windage Loss, Shaft Output
Torque
Gross Torque, Shaft Torque, Friction Torque
Torque slip characteristics
Dept of E & E, MIT Manipal
L3 – 13