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1 JRE SCHOOL OF Engineering Class Test-1 Examinations September 2014 Subject Name Electromechanical Energy Conversion-II Subject Code EEE -501 Roll No. of Student Max Marks 30 Marks Max Duration 1 hour Date 12 th September 2014 Time 9:20 AM to 10:20 AM For EE branch only NOTE: ATTEMPT ALL SECTIONS. Attempt all questions. SECTION A (3 x 5 = 15) 1) Explain why three-phase induction motor cannot attain synchronous speed. 2) Draw torque-slip characteristics of three-phase induction motor and explain the effect of change of rotor resistance on it. Mention stable and unstable region. 3) Draw phasor diagram of three-phase induction motor under running condition. 4) Describe the concept of rotating magnetic field in the operation of three-phase induction motor. 5) Derive the relationship between supply frequency and rotor induced emf frequency. SECTION B (5 x 1 = 5) Attempt any one question. 6) A 4 pole, 50 Hz, three-phase induction motor has rotor resistance and reactance per phase of 0.02 Ω and 0.1 Ω respectively. What must be the value of external resistance per phase to be added in the rotor circuit such that starting torque is two-third of the maximum torque? 7) Derive the torque equation of a three-phase induction motor and condition for the maximum torque. Justify that maximum torque does not depend on rotor resistance. SECTION C (10 x 1 = 10) Attempt any one question. 8) A 6-pole, 50 Hz, three-phase induction motor running on full load develops a useful torque of 160 Nm when the rotor emf makes 120 complete cycles per minute. Calculate the shaft power output. If the mechanical torque lost in friction is 10 Nm, compute the efficiency. The total stator loss is given to be 800 W. 9) A three-phase, start connected 400 V, 50 Hz, 4 pole induction motor has following parameters referred to stator: R 1 = 0.15 Ω, X 1 = 0.44 Ω, R 2 = 0.12 Ω, X 2 = 0.44 Ω, X m = 30 Ω, neglect core loss resistance (R c). Find stator current and input power factor at rated voltage and slip of 4%. ********* Page 1 of 8

2 Solution of Class test-1 SECTION A Ans.1 Induction motor runs on the principle of torque created between rotational magnetic field and the current flowing through the closed rotor connection. Now as long as N r and N s are different, there will be torque. The moment when N r (rotor speed) becomes = N s (synchronous speed of stator flux), torque will be vanished and hence the motor can't run. Ans.2 The three-phase induction motor torque under running conditions is given by The following points should be analyzed as: (i) At s = 0, T = 0 so that torque-slip curve starts from the origin. (ii) At normal speed, slip is small so that sx 2 is negligible as compared to R 2. Hence torque slip curve is a straight line from zero slip to a slip that corresponds to full-load. (iii) As slip increases beyond full-load slip, the torque increases and becomes maximum at s = R 2 /X 2. This maximum torque in an induction motor is called pull-out torque or break-down torque. Its value is at least twice the full-load value when the motor is operated at rated voltage and frequency. (iv) After the maximum torque, the term sx 2 >> R 2 Thus the torque is now inversely proportional to slip. Hence torque-slip curve is a rectangular hyperbola. (v) The maximum torque remains the same and is independent of the value of rotor resistance. Therefore, the addition of resistance to the rotor circuit does not change the value of maximum torque but it only changes the value of slip at which maximum torque occurs. (vi) At s = 1 i.e. (at the time of starting), T = T st >1. Torque-slip characteristics of three-phase induction motor Page 2 of 8

3 Ans.3 Ans.4 Phasor diagram of three-phase induction motor under running condition Page 3 of 8

4 Page 4 of 8

5 . Page 5 of 8

6 Ans.5 The relationship between supply frequency and rotor induced emf frequency can be derived as follows: The frequency of a voltage or current induced due to the relative speed between a vending and a magnetic field is given by the general formula; 120 Where, N = Relative speed between magnetic field and the winding P = Number of poles For a rotor speed N r, the relative speed between the rotating flux and the rotor is Ns-N r. Consequently, the rotor current frequency f is given by; Ans.6 SECTION B Given that, P=4, f=50 Hz, R 2= 0.02Ω, X 2= 0.1Ω, T st= (2/3) T m Now, =, Ω Ω Page 6 of 8

7 Ans.7 The torque produced by three phase induction motor depends upon the following three factors: the magnitude of rotor current, the flux which interact with the rotor of three phase induction motor and is responsible for producing emf in the rotor part of induction motor and the power factor of rotor of the three phase induction motor. Hence Where, T is the torque produced by induction motor, φ is flux responsible of producing induced emf, I 2 is rotor current, cosθ 2 is the power factor of rotor circuit. The flux φ produced by the stator is proportional to stator emf E 1. i.e φ α E1 We know that transformation ratio K is defined as the ratio of secondary voltage (rotor voltage) to that of primary voltage (stator voltage). Hence φ α E2. Now putting the value of flux φ, rotor current I 2, power factor cosθ 2 in the equation of torque we get, If we want to find the maximum value of some quantity then we have to differentiate that quantity with respect to some variable parameter and then put it equal to zero. In this case we have to find the condition for maximum torque so we have to differentiate torque with respect to some variable quantity which is slip, s in this case as all other parameters in the equation of torque remains constant. So, for torque to be maximum, Now differentiate the above equation by using division rule of differentiation. On differentiating and after putting the terms equal to zero we get, Substituting the value of this slip in torque equation, we get the maximum value of torque as, From the above equation it is concluded that, 1. The maximum torque is directly proportional to square of rotor induced emf at the standstill. 2. The maximum torque is inversely proportional to rotor reactance. 3. The maximum torque is independent of rotor resistance. 4. The slip at which maximum torque occur depends upon rotor resistance, R2. So, by varying the rotor resistance, maximum torque can be obtained at any required slip. Page 7 of 8

8 Ans.8 SECTION C. = 87.29%. Ans.9 Given that, R 1 = 0.15Ω, X 1 = 0.44 Ω, R 2 = 0.12 Ω, X 2 = 0.44 Ω, X m = 30 Ω, s= 0.04 As per the given problem statement, R c is neglected Ω The equivalent circuit is shown below cos Page 8 of 8

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