A 3 phase 50 Hz, 12 pole, 200 kW slip-ring induction motor drives a fan whose torque is proportional to the square of speed. At full load, the motor slip is 0.045. The rotor resistance measured between any two slip-rings is $61 m \Omega$ .

What resistance should be added in the rotor circuit to reduce the fan speed to 450 rpm?

Question

A 3 phase 50 Hz, 12 pole, 200 kW slip-ring induction motor drives a fan whose torque is proportional to the square of speed. At full load, the motor slip is 0.045. The rotor resistance measured between any two slip-rings is $61 m \Omega$ .

What resistance should be added in the rotor circuit to reduce the fan speed to 450 rpm?

Accepted Answer

For the rotor circuit is it is fair to assume that

[latex] R_{2} / s>>X_{2} [/latex]

So we will neglect [latex] X_{2}[/latex]

[latex] R_{2}=61 / 2=30.5 m \Omega[/latex]

[latex] \omega_{s}=\frac{120 f}{P} imes \frac{2 \pi}{60}=\frac{4 \pi f}{P}=\frac{4 \pi imes 50}{12}=52.36 rad / s[/latex]

[latex] \omega=(1-s) \omega_{s}=(1-0.045) imes 52.36=50 rad / s[/latex]

At full load [latex] 200 imes 10^{3}=\omega T ext { (fan) }=50 T[/latex]

Or [latex] T( ext { fan })=4000 Nm[/latex]

Rotor current [latex] T=\frac{3}{\omega_{s}} \frac{I_{2}^{2} R_{2}}{p}[/latex]

[latex] 4000=\frac{3}{52.36} imes \frac{I_{2}^{2} imes 30.5 imes 10^{-3}}{0.045}[/latex]

Or [latex] I_{2}=321 A[/latex]

Rotor circuit voltage (stand still)

[latex] E_{2}=I_{2}\left(R_{2} / s ight)=321 imes \frac{30.5 imes 10^{-3}}{0.045}=217.6 V[/latex]

The fan speed is to be reduced to

[latex] n=450 rpm [/latex] or [latex] \frac{450 imes 2 \pi}{60}=47.12 rad / s[/latex]

Slip, [latex] s=\frac{500-450}{500}=0.1[/latex]

[latex] I_{2} ext { (new) }=\frac{217.6}{R_{t} / s}=\frac{21.76}{R_{t}}, R_{t}=[/latex] total rotor resistance

[latex] T ext { (new) }=4000 imes\left(\frac{47.12}{50} ight)^{2}=3552 Nm[/latex]

[latex] T ext { (new) }=\frac{3}{\omega_{s}} \frac{I_{2}^{2}(n \omega) R_{t}}{s(n \omega)}[/latex]

[latex] 3552=\frac{3}{52.36} imes \frac{(21.76)^{2} R_{t}}{R_{t}^{2} imes 0.1}[/latex]

From which we find [latex] R_{t}=76.4 m \Omega[/latex]

[latex] R_{ ext }=76.4-30.5=45.9 m \Omega[/latex] (to be added)

Question 9.13: A 3 phase 50 Hz, 12 pole, 200 kW slip-ring induction motor d...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions