Question 3.AE.10: Compute the mmf and its angular velocities for an induction ......
Compute the mmf and its angular velocities for an induction machine with the following time and space harmonics:
(a) A_1=1 pu, A_H=0.05 pu, I_{m1}=1 pu, I_{mh}=0.05 pu, H=5, and h=5.
(b) A_1=1 pu, A_H=0.05 pu, I_{m1}=1 pu, I_{mh}=0.05 pu, H=13, and h=0.5.
a) For A_1=1 pu, A_H=0.05 pu, I_{m1}=1 pu, I_{mh}=0.05 pu, H=5, and h=5 one obtains the rotating mmf as
\begin{aligned} F_{\text {total }}= & 1.5 \cos \left(\theta-\omega_1 t\right)+0.075 \cos \left(\theta-5 \omega_1 t\right) \\ & +0.075 \cos \left(5 \theta+\omega_1 t\right)+0.00375 \cos \left(5 \theta-5 \omega_1 t\right) \end{aligned}with the angular velocities
\frac{d \theta_{h=1}}{d t}=\omega_1, \frac{d \theta_{h=5}}{d t}=5 \omega_1, \frac{d \theta_{H=5}}{d t}=-\omega_1 / 5, \frac{d \theta_{H=5, h=5}}{d t}=\omega_1 (E3.10-1)
b) For A_1=1 pu, A_H=0.05 pu, I_{m1}=1 pu, I_{mh}=0.05 pu, H=13, and h=0.5 one obtains the rotating mmf as
\begin{aligned} F_{\text {total }}= & 1.5 \cos \left(\theta-\omega_1 t\right)+0.075 \cos \left(\theta-0.5 \omega_1 t\right) \\ & +0.075 \cos \left(13 \theta-\omega_1 t\right)+0.0035 \cos \left(13 \theta-0.5 \omega_1 t\right) \end{aligned}with the angular velocities
\frac{d \theta_{h=1}}{d t}=\omega_1, \frac{d \theta_{h=0.5}}{d t}=0.5 \omega_1, \frac{d \theta_{H=13}}{d t}=\omega_1 / 13, \frac{d \theta_{H=13, h=0.5}}{d t}=\omega_1 / 26 (E3.10-2)