# Study-of-induction motor

EXERCISE: STUDY OF AN INDUCTION MOTOR

We consider a squirrel cage induction motor powered by a network with a frequency of 50 Hz and voltages between phases equal to 380 V. It was subjected to the following tests:

– No-load absorbed power : Pa0 = 360W             – No-load current: I0 = 3.6A                        – Rotation speed: N0 = 2995rpm
– Absorbed power : Pa0 = 4560W                        – Current : 8.1A                                              – Rotation speed: N = 2880rpm
The windings of the stator are coupled in star; The resistance of each of them is r = 0.75Ω .  Iron losses in the stator Pfs are estimated at 130 W.
1- What is the synchronism speed Ns ? Deduce the slip g under load.
a) Calculate the Joule losses Pjos at the stator.
b) Justify that in addition to rotor iron losses, the Joule losses in the rotor are negligible.
c) Deduce the mechanical losses Pmec.
a) Calculate the stator Joule losses Pjs and the Joule losses in the rotor Pjr
b) Calculate the useful power Pu and torque Cof the motor
c) Calculate the efficiency of the motor η
4- The motor now drives a pump whose moment of the resistive torque Cr is proportional to the rotation speed and is 18 Nm at 3000rpm. In its useful part, the mechanical characteristic Cu (N) of the motor can be assimilated to a straight line. Determine the rotation speed N of the motor-pump unit.

CORRECTION

1)Ns = 3000tr/min ;   g = (3000 – 2880)/3000 = 4%

a) Pjs = 3×R ×I02 = 3× 0.75 ×3.62 = 29W

b) At no-load, the slip g is negligible.           Pjr = g× Ptr;  Therefore, the Joule losses in the rotor are negligible.

c) Pmec = Pa0 – Pjos – Pfs = 201W

a) Pjs = 3×RI2 = 3×0.75×8.12 = 148W

b) Pjr = gPtr = g(Pa – Pjs – Pfs) = 0.04×(4560 – 148 – 230)  = 171W;       Pu = 4282 – 171 – 201 = 3910W ;    Cu = Pu/Pa = 3910/(2880×π/30) = 13Nm

c) η = Pu/Pa = 3910/4560 = 85,7%

4)  Cr (Nm) = 0,006 N (tr/min)       Cu = 0 à 3000 tr/min          Cu= 13,0 à 2880 tr/min           So Cu() = 324 − 0.108 (tr/min)

Operation point: Cu = Cr ⇒324-0.108 N = 0.006 N             N =2842 tr/min