ECE 3300 ELECTRIC MACHINERY FALL 2016 HOMEWORK #7
DUE: 11/21/2016
1.
Problem #4.34 pp. 197.
2.
A three-phase induction motor is wound for 4 poles and is supplied from a 50-Hz system.
(a)
Determine the synchronous speed ωs.
(b)
Calculate the rotor speed ωm when the slip is 4%.
(c)
The rotor runs at a speed of 600 rpm.
(i)
Determine the new slip snew.
(ii)
Determine the rotor frequency fr.
3.
A 1100-V delta-connected induction motor has a star-connected slip-ring rotor with a
transformation ratio of 3.8. The rotor resistance and standstill leakage reactance are 0.012
Ω and 0.25 Ω, respectively. Neglect stator impedance and magnetizing current.
(a)
(i)
Determine rotor phase voltage E2 at standstill.
(ii)
Determine the rotor impedance Z2 per phase in Ω.
(iii)
Determine the rotor current I2 at start with slip-rings shorted.
(b)
Determine the rotor power factor at start with slip-rings shorted.
(c)
The runs with a slip of 4% with slip-rings shorted.
(i)
Determine rotor impedance Z2 per phase in Ω.
(ii)
Determine the rotor phase voltage E2.
(iii) Determine the rotor current I2.
(iv)
Determine the power factor.
(d)
The starting current is 100 A in the stator supply lines.
(i)
Determine the rotor current I2.
(ii)
Determine the rotor phase voltage E2.
(iii)
Determine the external resistance Rext per phase required.
4.
A 3-phase, slip-ring, induction motor with star-connected rotor has an induced emf of
120 volts between slip-rings at a standstill with normal voltage applied to the stator. The
rotor winding has a resistance per phase of 0.3 Ω and standstill leakage reactance per
phase of 1.5 Ω.
(a)
The rotor is running short-circuited with 4 percent slip.
(i)
Determine rotor phase voltage E2 at standstill.
(ii)
Determine the rotor impedance Z2 per phase in Ω.
(iii)
Determine the rotor current I2 at start with slip-rings shorted.
(b)
The rotor develops maximum torque.
(i)
Determine new slip snew.
(ii)
Determine the rotor impedance Z2 per phase in Ω.
(iii)
Determine the rotor current I2 at start with slip-rings shorted.