Download E701 ELECTRICAL MACHINES III

Rajagiri School of Engineering and Technology
E701
ELECTRICAL MACHINES III
Assignment I
1. The frequency of e.m.f in the stator of a 4 pole induction motor is 50 Hz and that in the rotor
is 1.5 Hz. What is the slip and at what speed the motor is running?
2. A 3.3kV, 20 pole, 50 Hz, 3 phase Induction Motor has rotor resistance and standstill
reactance of 0.014Ω and 0.113Ω per phase respectively. Calculate (a) speed at which torque
developed is maximum (b) the ratio of FL torque to maximum torque, if FL torque is
delivered at 288 r.p.m.
3. A 580V, 6 pole, 50 Hz, 3 phase Induction Motor develops 20 hp at 950 r.p.m with a p.f. of
0.86. The mechanical losses total 1 hp. Calculate for this load (a) the rotor copper loss (b)
torque output in Nm (c) Line current. Assume Stator loss total as 1 kW.
4. The power input to a 500V, 6 pole, 50 Hz, 3 phase Induction Motor running at 975 r.p.m is
40kW. Stator losses total 1 kW and Mechanical losses total 2 kW. Calculate the (a) slip (b)
rotor copper loss (c) ŋ of the motor.
5. An Induction Motor has an ŋ of 90% when the load is 50 hp. At this load, the stator copper
loss, rotor copper loss and iron loss are all equal. The mechanical losses are one third of the
iron loss. Calculate the slip.
6. A 6 pole, 50 Hz, 3 phase Induction Motor runs on FL with a slip of 4%. Given the rotor
standstill impedance per phase as (0.01+j0.05) Ω. Calculate the available maximum torque in
terms of FL torque. Also determine the speed at which maximum torque occurs.
7. The power input to a 4 pole, 50 Hz, 3 phase Induction Motor is 42 kW, the speed being 1455
r.p.m. The stator losses are 1.2 kW and mechanical losses are 1.8 kW. Find (a) the rotor input
(b) rotor copper loss (c) ŋ
8. A 8 pole, 50 Hz, 3 phase Slip ring Induction Motor has a standstill rotor impedance per phase
as (0.04+j0.15) Ω. Find the speed at which maximum torque occurs.
9. The power input to a 3 phase Induction Motor is 60kW. The Stator losses total to1 kW. Find
the total mechanical power developed and the rotor copper loss per phase, if the motor is
running with a slip of 3%.
10. A 440V, 6 pole, 50 Hz, 3 phase Induction Motor delivers a mechanical load of 15 kW at 950
r.p.m with a p.f. of 0.84. The mechanical losses total 0.75 kW. Calculate for this load the
following quantities. (a) slip (b) the rotor copper loss (c) the input if the stator losses total 1.5
kW (d) the line current.
11. A 6 pole, 50 Hz, 3 phase Induction Motor develops 5 kW at 950 r.p.m. What is the stator
input and ŋ if stator loss is 300 W.
12. A 400 V, 50 Hz, 3 phase Slip ring Induction Motor with a star connected rotor has 3 slip
rings brought out to the terminal box. The induced e.m.f between slip rings is 60V on open
circuit at standstill condition with 400V, 50 Hz applied to the stator. The resistance and
standstill reactance of each rotor per phase are 0.6Ω and 4 Ω respectively. Calculate the
current per phase in the rotor (a) at standstill when the rotor is connected to a star connected
impedance with resistance 5 Ω and reactance 2 Ω per phase and (b) when running short
circuited with a slip of 4%.
13. The power input to the rotor of a 400V, 50 Hz, 4 pole, 3 phase slip ring induction motor is 75
kW. The rotor e.m.f makes 100 complete alternations per minute. Calculate (a) the rotor
speed (b) mechanical power developed (c) rotor resistance per phase, if the rotor current is
60A.
©DEE_JRN_2009
Rajagiri School of Engineering and Technology
14. A 500V, 4 pole, 50 Hz, 3 phase delta connected Induction Motor has a stator impedance per
phase of (0.05+j0.20) Ω. The equivalent rotor impedance at standstill is the same. The
magnetizing current is 50A and the core loss is 2000W. The mechanical loss is 750W.
Calculate the output, input and p.f at a rotor speed of 1470 r.p.m.
15. A 400 V, 4 pole, 50 Hz, 3 phase Induction Motor has a star connected stator whose
impedance is represented by (0.5+j1.5) Ω. The equivalent resistance and standstill leakage
reactance of the rotor referred to the stator phase are 1 Ω and 2 Ω respectively. Determine the
current drawn from the supply and torque in synchronous watts when the motor is running at
a speed of 1400 r.p.m.
16. A 500V, 4 pole, 50 Hz, 3 phase delta connected Induction Motor gave the following results
on no-load and short circuit tests.
No-load Test (line values)
400V 3A 645W
Short circuit Test (line values)
200V 12A 1660W
The friction and windage losses amount to 183W. Determine the working and the
magnetizing components of no-load current, no-load p.f., no-load resistance Ro and reactance
Xo, equivalent resistance and reactance per phase as referred to primary, power factor on short
circuit and short circuit current with normal applied voltage of 400V across the stator. Stator
resistance may be assumed to be 5 Ω. Also draw the approximate equivalent circuit referred
to stator.
17. A 400V, 6 pole, 50 Hz, 3 phase delta connected Induction Motor gave the following results
on no-load and short circuit tests.
No-load Test (line values)
400V 8A 0.16 p.f.
Short circuit Test (line values)
200V 39A 0.36 p.f.
Determine the mechanical output, torque and slip when the motor draws a current of 30A
from the mains. Assume the stator and rotor copper losses to be equal.
18. The following test results relates to a 30kW, 500V, 6 pole, 3 phase, 50 Hz delta connected
induction motor.
No-load Test
500V 18A 1.2 kW
Short circuit Test
250V 100A 11 kW
Stator resistance per phase is 0.6 Ω. Construct the circle diagram and find (a) line current, p.f.
and slip at FL and (b) the maximum output
19. Draw the circle diagram of a three phase delta connected 30hp, 500V, 4 pole, 50 Hz Cage
Induction Motor. The figures given below give the measurements of line current and voltage
and readings of 2 wattmeters.
No load test :
500V
8.3A +2.85kW
-1.35kW
Block rotor test :
100V
32A
-0.75kW
+2.35kW.
Find from circle diagram for full load (i) Line current (ii) Power factor (iii) Efficiency (iv)
Max.O/P
20. A 400 V, 3 phase, 6 pole, 50Hz Induction motor gave the following test results.
No load Test
: 400V 7A 0.15 pf.
Blocked rotor test : 200V 38A 0.35 pf.
The stator is delta connected and the resistance between two terminals is 0.1Ω. Determine
the Out put, Torque developed in Nm and Efficiency when the input current is 25A.
©DEE_JRN_2009