Question 7.1: A DFIG is operating in the motoring mode at a subsynchronous......
A DFIG is operating in the motoring mode at a subsynchronous speed at a lagging power factor (drawing Q_s from the grid). Calculate the signs of various quantities in this mode of operation.
\begin{aligned}\omega_{\text {slip }} & =\omega_{d A}=+ \hspace{30 pt}\hspace{30 pt} \hspace{30 pt} \hspace{30 pt} \hspace{30 pt}\quad \quad \text{(7-23)}\\ s & =\frac{\omega_{\text {slip }}}{\omega_{ \text{syn} }}=+ \hspace{30 pt} \hspace{30 pt} \hspace{30 pt} \hspace{30 pt} \quad \quad \; \quad\; \; \; \text{(7-24)}\\ T_{e m} & =+ \hspace{30 pt} \hspace{30 pt} \hspace{30 pt} \hspace{30 pt} \hspace{30 pt} \hspace{30 pt}\quad \enspace \; \text{(7-25)}\\ P_s & =\nu _{s q} i_{s q}=\omega_d \lambda_{s d} i_{s q}=+ \hspace{30 pt} \hspace{30 pt} \hspace{30 pt} \enspace\enspace \; \, \enspace \; \text{(7-26)}\\ \therefore i_{s q} & =+ \hspace{30 pt} \hspace{30 pt} \hspace{30 pt} \hspace{30 pt} \hspace{30 pt} \hspace{30 pt}\enspace \; \, \enspace \; \text{(7-27)}\\ & i_{r q}=- \hspace{30 pt} \hspace{30 pt} \hspace{30 pt} \hspace{30 pt} \qquad \hspace{30 pt}\enspace \; \enspace \> \text{(7-28)}\\ & Q_s=\nu _{s q} i_{s d}=\omega_d \lambda_{s d} i_{s d}=\underbrace{+}_{\text {given }}\hspace{30 pt} \hspace{30 pt} \quad \enspace \; \enspace \text{(7-29)}\\ & \therefore i_{s d}=+ \hspace{30 pt} \hspace{30 pt} \qquad \hspace{30 pt} \hspace{30 pt}\quad \enspace \quad \; \text{(7-30)}\\ & P_r=\nu _{r q} i_{r q}=s \omega_d \lambda_{r d} i_{r q}=-\> \hspace{30 pt} \quad \quad \hspace{30 pt}\; \> \, \text{(7-31)}\\ & Q_r=\nu _{r q} i_{r d}=s \omega_d \lambda_{r d} i_{r d} \\ & i_{r q}=-\left(\text { since } i_{s q}=+\right) \hspace{30 pt} \hspace{30 pt} \quad \enspace \hspace{30 pt}\; \text{(7-32)}\\ & i_{r d}=+\text { taken as positive but } i_{r d}<i_{m d} \hspace{30 pt} \quad \, \> \text{(7-33)}\\ & \nu _{r d}=0 \hspace{30 pt} \hspace{30 pt} \hspace{30 pt} \hspace{30 pt} \hspace{30 pt} \quad \quad \enspace \; \text{(7-34)}\\ & \nu _{r q}=s \omega_d \lambda_{r d}=+ \hspace{30 pt} \hspace{30 pt} \hspace{30 pt} \hspace{30 pt} \enspace \enspace \; \text{(7-35)} \end{aligned}
\begin{bmatrix} \nu _A(t) \\ \nu _B(t) \\ \nu _C(t) \end{bmatrix}=\sqrt{\frac{2}{3}}\begin{bmatrix} \cos \left(\theta_{d A}\right) & -\sin \left(\theta_{d A}\right) \\ \cos \left\lgroup\theta_{d A}+\frac{4 \pi}{3}\right\rgroup & -\sin \left\lgroup\theta_{d A}+\frac{4 \pi}{3}\right\rgroup \\ \cos \left\lgroup\theta_{d A}+\frac{2 \pi}{3}\right\rgroup & -\sin \left\lgroup\theta_{d A}+\frac{2 \pi}{3}\right\rgroup \end{bmatrix}\begin{bmatrix} \nu _{r d} \\ \nu _{r q}\end{bmatrix} \text {. }\text{ (7-36)}
Various space vectors are shown in Fig. 7-4.
