A 3-phase, 4-pole, wound-rotor induction motor has a rating of 110 kW, 1760 r/min, 2.3 kV, 60 Hz. Three external resistors of 2 Ω are connected in wye across the rotor slip-rings. Under these conditions the motor develops a torque of 300 Nm at a speed of 1000 r/min.
a. Calculate the speed for a torque of 400 Nm.
b. Calculate the value of the external resistors so that the motor develops 10 kW at 200 r/min.

Question

Accepted Answer

a. The given conditions are

[latex]\begin{aligned}T_{ n } &=300 N \cdot m \s_{ n } &=(1800-1000) / 1800=0.444\end{aligned}[/latex]

All other conditions being fixed, we have for a torque of 400 Nm the following:

[latex]\begin{aligned}s_{ x } &=s_{ n }\left(T_{ x } / T_{ n } ight)=0.444(400 / 300) \&=0.592\end{aligned}[/latex]

The slip speed [latex]=0.592 imes 1800=1066 r / min[/latex]

Consequently, the motor speed is

[latex]\begin{aligned}n &=1800-1066 \&=734 r / min\end{aligned}[/latex]

Note that the speed drops from 1000 r/min to 734 r/min with increasing load.

b. The torque corresponding to 10 kW at 200 r/min is

[latex]\begin{aligned}T_{ x } &=9.55 P / n \&=9.55 imes 10000 / 200 \&=478 N \cdot m\end{aligned}[/latex]

The rated torque is

[latex]\begin{aligned}T_{ ext {rated }} &=9.55 P / n \&=9.55 imes 110000 / 1760 \&=597 N \cdot m\end{aligned}[/latex]

Because [latex]T_{ x } ext { is less than } T_{ ext {rated }} ext {, }[/latex] we can apply Eq. 2. The slip is

[latex]s_{ x }=s_{ n }\left[\frac{T_{ x }}{T_{ n }} ight]\left[\frac{R_{ x }}{R_{ n }} ight]\left[\frac{E_{ n }}{E_{ x }} ight]^{2}[/latex] (Equation 2)

[latex]s_{ x }=(1800-200) / 1800=0.89[/latex]

All other conditions being fixed, we have, from Eq. 2

[latex]\begin{aligned}s_{ x } &=s_{ n }\left(T_{ x } / T_{ n } ight)\left(R_{ x } / R_{ n } ight) \0.89 &=0.44(478 / 300)\left(R_{ x } / 2 ight)\end{aligned}[/latex]

and so

[latex]R_{ x }=2.5 \Omega[/latex]

Three 2.5 Ω , wye-connected resistors in the rotor circuit will enable the motor to develop 10 kW at 200 r/min.

Question 14.3: A 3-phase, 4-pole, wound-rotor induction motor has a rating ...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions