Question

Please use exact methods and not approximations!

7.15. A three-phase, 460 V, 60 Hz, 1760 rpm, wound-rotor induction motor has the following equivalent circuit parameters Ri=0.25 ohm : R'= 0.2 ohm : Xi = 1.2 ohm : X2,= 1.1 ohm : 'Ku = 35 ohm The motor is connected to a 3ph, 460V, 60Hz supply and is star-connected. Use the simplified equivalent circuit. Initially the external rotor resistance is set to zero. (a) Calculate the speed (in rpm) at which maximum torque occurs. (b) Using the torque equation, calculate the output torque at the following speeds i) synchronous, (ii) rated speed, (iii) speed corresponding to maximum torque, (iv) locked rotor (0 rpm) (d The total effective rotor resistance R2' is adjusted by adding external rotor resistance. What is the total effective rotor resistance required to give maximum torque at standstill? What is the starting torque under this condition?
Ans 7.15. (a) 1644 rpm [ See slide 7.5.2 to find the slip corresponding to maximum torque, then find synchronous speed based on the rated speed and the supply frequency using the method in Slide 7.2.5] (b)(i) 0 Nm) 111.2 Nm (iii) 218.9 Nm (iv) 40.88 Nm (d) 2.314 ohms, 218.9 Nm (this of course is equal to the maximum torque calculated earlier)

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