5
6. (i) Describe an auto-transformer starter. From the expression for power input per phase (ec torque) show that for a turns ratio n of 4-§ : 1 , for the auto-transformer.
VS V R„ • the power input to the motor/phase = ‘- n2z 2 P direct on-line torque 3
• the motor starting torque =
• using a star/delta starter the motor starting torque is the same as the auto-transformer above.
(ii) If a motor produces a starting torque of 70 Nm with a starting current of 55 amperes when controlled by a direct-on-line starter, what will be the starting torque and starting current when using a star/delta starter?
7. (i) Given that the rotor emf at any slip Er = sEo where Eo is the rotor phase voltage at standstill, show mathematically that for a 3 phase induction motor where R2 is the rotor phase resistance and X2 is the rotor phase reactance that:
(a) the rotor current per phase can be expressed as:
ir 1 VR2 + (2 SX2 )
3E0
R2 (b) the power factor is cos 0 —
VR2 + ( sx2 )2
6 (c) power input per rotor phase can be expressed as: s2 E0 2 R2 Power per phase =
R22 + (sX2
)2
(ii) If the torque output per phase is proportional to the power input per phase ignoring losses it can be shown that:
T .4 sR2 ‘2 Ri + (sX2)
then show by differentiating with respect to the slip s, that maximum torque occurs when: R2 = sX2
(iii) A two-pole wound rotor induction motor has a rotor resistance of 0.8 ohms per phase and a rotor leakage reactance of 7 ohms. At what speed will the motor produce maximum torque when fed from a 50 Hz supply? What resistance must be added to the rotor circuit to give maximum starting torque?
