4.5.3. Phase Adjustment

Phase adjustment is done through controller selection. A proportional integral (PI) controller is selected for that purpose. The transfer function of the PI controller is expressed by (45).

$$G\_c = k\_p + \frac{k\_i}{s} \tag{45}$$

The value of *kp* and *ki* are selected in such a way so that |*Gc*| is 0 dB at *fc* and frequency can be swept for all the frequency less than *fc*.The value of *kp* could be ≈*k* and the value of *ki* can be determined by (46).

$$k\_i = k\_P \omega\_z \tag{46}$$

where, *ω<sup>z</sup>* is the angular form of zero frequency *fz*. The value of *fz* should be less than the desired control frequency, *f* , of injected AC current. The relationship can be expressed by (47).

$$f\_z < f < f\_c \tag{47}$$

The parameters used for phase and gain adjustment are in Table 3. The loop controller transfer functions are shown in Figure 9.

**Table 3.** Parameters for proposed controller.

