*4.2. Feed-Forward Controller*

Due to the presence of coupling terms in the new MIMO system (20), and in this study, to eliminate the coupling terms, a feed-forward controller was designed, as expressed in (22):

$$\begin{aligned} \mu\_P &= \frac{2}{3} L v\_P + \frac{2}{3} L \omega Q + \frac{2}{3} R P + V\_{\text{pcc}} \\ \mu\_Q &= -\frac{2}{3} L v\_Q - \frac{2}{3} R Q + \frac{2}{3} L \omega P \end{aligned} \tag{22}$$

where feedback controller inputs are *v<sup>P</sup>* and *v<sup>Q</sup>* and can be calculated using (23):

$$\begin{aligned} v\_P &= F\_P + P\_{ref}^\bullet\\ v\_Q &= F\_Q + Q\_{ref}^\bullet \end{aligned} \tag{23}$$

where *F<sup>p</sup>* and *F<sup>Q</sup>* are the de-fuzzified output of the real and reactive power FLCs.

Finally, the genuine control inputs *u<sup>α</sup>* and *u<sup>β</sup>* were obtained using (24).

$$\mu\_{\alpha} = \frac{-\mu\_{Q}\upsilon\_{p\emptyset} + \mu\_{P}\upsilon\_{p\alpha}}{V\_{p\text{cc}}^{2}}$$

$$\mu\_{\beta} = \frac{\mu\_{P}\upsilon\_{p\emptyset} + \mu\_{Q}\upsilon\_{p\alpha}}{V\_{p\text{cc}}^{2}}\tag{24}$$

These two control inputs using αβ-abc transformation were converted to 3-ph control signals, which were used to generate the control signals for the VSI switches using sinusoidal pulse width modulation (SPWM). SPWM was chosen in this study because the harmonics of lower and higher order can be reduced or eliminated easily using this technique.
