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EE2005 - Electrical Machines Tutorial 6 11 April 2015 1. An induction machine has a stator impedance of 1.0 + j 3.0 Ω, rotor impedance of 1.0 + j 2.0 Ω and a no-load shunt impedance of 10 + j 50 Ω. The voltage per phase is 240 V and Rc =19 Ω. Estimate at a slip of 5%: (a) stator current (b) equivalent rotor current (c) mechanical power developed and (d) power factor 2. A star connected squirrel cage induction machine rated 7.5 kW, 230 Volts, 4 pole, three phase 50 Hz has its full load torque at slip of 0.04. It has R1 = 0.36 Ω, X1 = X2 = 0.47 Ω, R2 = 0.222 Ω and Xm = 15.5 Ω per phase. Assuming that the shunt branch is connected across the supply terminal, estimate: (a) maximum electromagnetic torque at rated voltage and frequency. (b) slip at maximum torque. (c) developed starting torque at rated voltage and frequency. 3. A 3 phase 400 V star connected induction motor has a stator impedance 0.06 + j 0.2 Ω and equivalent rotor impedance 0.06 + j 0.22 Ω. Determine: (a) maximum gross power output. (b) slip at which maximum gross power is observed. 4. Following are results from a 400 V three phase delta connected induction motor. No load test : 400 V; 3.0 A; 645 W. Short circuit test : 200 V; 12.0 A; 1660 W. Friction and windage loss : 190 W. Estimate: (a) loss and magnetising components of no-load current (b) no-load power factor (c) no-load resistance R0 and reactance X0 . (d) equivalent resistance and reactance per phase as referred to stator. (e) power factor under blocked rotor conditions. (f) blocked rotor current with normal applied voltage of 400 V across stator Assume stator resistance as 5 Ω/phase. 5. A 200 V three phase star connected induction motor takes 25 A at a line voltage of 30 V with rotor locked . With this line voltage power input to the motor is 440 W, and core loss is 40 W. The DC resistance between a pair of stator terminal is 0.1 Ω. If the ratio of AC to DC resistance is 1.6, find:

(a) equivalent leakage reactance/phase (b) stator and rotor reactance/phase 6. A 460 V, 50 HP, 60 Hz, 4-pole induction machine is supplying rated load at 1755 rpm. Calculate: (a) slip of the rotor and frequency of induced currents in the rotor. (b) Angular velocity of the stator flux with respect to stator and with respect to rotor. (c) Angular velocity of the rotor flux with respect to stator and with respect to rotor. 7. A 3-φ, 400 V, 4-pole, 50 Hz squirrel cage induction motor operating at rated voltage and frequency delivers full rated load at 1370 rpm. The machine can develop a maximum torque of 2.3 times the full rated value at 675 rpm. Determine the starting torque of the machine in per unit based on its full load torque. Neglect the core and rotational losses. 8. A 3-φ, 400 V, 4-pole, 50 Hz wound rotor induction machine rated at 10 kW has star connected rotor windings with resistance of 0.16 Ω/phase and standstill rotor reactance of 0.27 Ω/phase. The motor, when operating with short circuited slip rings at a rotor current of 31.1 A and a slip of 0.035, develops 60 Nm torque. Find the magnitude and phase of a balanced three phase supply that should be connected across the slip rings so that the machine develops the same torque (60 Nm) at a slip of 0.02. Assume that the frequency of the three phase supply connected to the slip rings is maintained equal to the slip frequency. 9. A 30 kW, 3-φ, 230 V, 6-pole, 50 Hz, ∆ connected induction motor has the following equivalent circuit parameters in Ω/phase Y: R1 = 0.045 Ω R2 = 0.054 Ω X1 = 0.29 Ω X2 = 0.28 Ω Xm = 9.6 Ω (a) Calculate the starting current and starting torque of the machine when connected directly to a source of rated voltage. (b) If the machine is supplied from an autotransformer connected to a 230 V supply, with a tap setting of 65%, calculate the starting current and the current drawn by the autotransformer from the supply. (c) What would be the starting current and starting torque if the stator windings are disconnected and reconnected to form a Y network? 10. The blocked rotor test on a 37 kW, 440 V, 50 Hz, 6-pole, Y-connected, 3-φ induction motor gave the following results: Vl−l = 230 V , I = 140 A, cosφ = 0.35. The motor drives a load having a constant torque of 300 Nm. Estimate the maximum percentage reduction in supply voltage possible before the motor stalls. Assume that the copper losses are equally divided between the stator and the rotor. Neglect magnetising current. 11. Using the looking-in impedance approach for the equivalent circuit as seen by the rotor side, derive the expression for the torque developed in a P-pole induction machine. Derive the expression for the slip at maximum torque, and the maximum torque developed in the motoring mode. ******************

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