Question

Question 2 (10 marks) (a) A large 3-phase, 4000 V, 60 Hz, slip of 0.01, squirrel cage induction motor draws a current of 375 A and a total active power of 2300 kW when operating at full-load. The stator is connected in wye and the resistance per phase is 0.05 12. The total iron losses are 23 kW and the windage and friction losses are 10 kW. Calculate the following: i) The power factor at full-load ii) The active power supplied to the rotor iii) The total I'R losses in the rotor iv) Efficiency (6 marks) (b) A three phase, wye (star) connected, 400 V, 4 pole, 50 Hz, squirrel cage induction motor has a slip of 6%. Power across the air gap (or rotor input) is 111.9 kW. Calculate i) Rotor speed ii) Voltage induced/phase in rotor circuit iii) Torque developed (corresponding to air gap power) iv) Rotor copper losses per phase. (4 marks)

Answer 1

In the question it is given that , motor draws a Current of 375 A and a total active power of 2300 KW when operating at full load. That means input current/status current = 375 A- And input power / stator ijp power = 2300 kW. And dated voltage = 4000 V. and 60 H2 - And stator is connected in Y and the resistance per phase (R) = 0.052, and slip (s) = 0.01 And Total Iron losses are 23 kW and windage and friction losses ade 10 KW.. As nothing is mentioned about the motor icon loss, we assume that the rotor core loss is negligible. . Statos Iron loss = total ison loss - rotor ison Logs = 23KW -0 = 23KW Now the power flow Diagrams will be Output Input Mech. Mech. Electrical transferred Power Power 2000ss the developed output air gap in rotor at shaft to. Rotor. stator Power Power VP +0 Fiction And Stator Coppos Loss Stator Toon Loss Rotor Coppens Logs Windage Lass

(a) At full load, Pin = 2300 KW. and input voltage (line) = 4000 V. (Vis) (L-1) and input line current = Input phase curent (: stator is stay connected Pin (k-1) - Din (prese) = 375 A. Pin= B Vin (-1) * Tin (1-1x cos d. where caso = power factor, → 2300 x10° = 23 x 4000 x 375 x cos $. = cos $ 2300 x103 - - 0.885270. (Lag) RB X 4000x375 | Power factor at full load = 0.885 Lagging power factor due to the inductive nature of T.M Stator copper loss - 3x{Pistmase) } x R (phase) = 3x (Pin 6-1) ² x R/phase * 3x (375)?x 0.05 = 21.09375 kW :: stator copper loss - 21.09375 kw. And Stator iron 1088 = 23 kw. power transferred to potov = Stator i/p - Stator logs - 2300 kw-21.09375 kW-23 kW. Stator copper Stator icon Logo = 2255.90625 kw. LOSS . The active power supplied to the poter is 2255.90625 KW.

es The power transferred to the rotor is nothing but the input power to the rotor. And The copper loss in potor = Slipx rotor input power . The copper loss (60) I2R loss in the rotor = 0.01 X 2255.90625 KW = 22.5590625 Kw. The total I2R loss in the rotoris 22.5590625 KW| (d) Mechanical por - Mechanical power developed in the rotor is = rotor lip power - potor IR logs = 2255.90625 kw - 22.5590625 kW = 2233.347188 kW And, Mech. power olo at shaft is = Mech power developed in rotos – foiction and windage Logs = 2233.347188 kW – 10 kW = 2223.347188 KW. "Put 100 X100 in efficiency (n)= output x 100 Input Mech. Power opp at shaft Elect: power f/p to Stator - 2223.347188 x10° x100 2300 X 103 - 96.6672% efficiency of motor is 96.6672%

2/ In the question it is given that, a 3-0, y connected, Yoov, 4 pole, 50 H2 Squirrel Cage T.M has a slip of 6%. Power across the air gap (or ao tos input) is 111.9 kW ::V,-€, = 400 v (line-Line) * Ex phase- 400 ( Y connected) Pore (P) = 4, frequency (f) = 50 HZ Seip (s) = 6% (07) 0.06. (a) The synd The synchronous speed (NS) = 12of in R.P.M Ns = 120x50 - 1500 RPM (Revolution - per minute, And slip (8) = Ng - No Ng I where, No= rotor speed in RPM → 0.06 = 1500 - No 1500 * 90= 1500 - Ng Ny = 1500-90= 1410 RPM. in Rotor speed is 1410 RPM. b) As nothing mentioned about the Stator voltage to rotor voltage ratio pu) Stator to rotor tuons datio Let's assume it as 1:1 : The Rotor voltage at standstill (6) - E, And the Induced Rotor voltage at running is equal to SX Ea ss induced

. The induced Rotor voltage/phase = Sx talphase And Ea/phase - El/phase (:&z=6) .: Sx Ealph = Sx ®/ph = 0.06x 400 = 13.8564 v. -Induced ootor voltage/phage in running condi Hon is 13.8564 v. rotor ilp power = Taisgan x Wg And we = a0Ns 212N/60 Als gap power - Tairgap xas (Nm) whose. Taisgaj Tooque developed up corresponding to air gap power And Ws= synchronous speed 60 invad/see) :Tairgap = oo too lp power - 20400 jp power ws 60 x 30400 lp power = 60 x 111.9x10 RTL NS 210 x 1500 :: Tairgap = 74237752 Newton- meter bv Nm : Torque developed codes ponding to aro gap power is 72.37752 Nm. 9 Total Rotoo copper loss = Slipx dotor vyp power = 0.06 x 11.9 Xid = 6714 w od 6.714 KW. And the Rotor Cop! - total Rotor cu- loss - 6714 Kw = 2.238 kw. .:. Rotor copper loss per phase = 2.238 KW