4.4.3. Frequency

Equation illustrates how the frequency at the grid's end is confirmed to be roughly 50 Hz using PV panels (63) [20].

$$
\Delta \mathbf{f} = - (\Delta P\_{PV}) \mathbf{R} \tag{63}
$$

R is the frequency droop coefficient and is restricted up to 5%.

In reality, there is no way to completely solve power quality problems, but they can be managed or improved to the required level. In this study, a novel HHO-AFOPID controller is used and successfully simulated while retaining the aforementioned power quality issues in the grid-connected system with an SPV interface under normal and perturbed conditions. System perturbation is created from 0.95 s to 1.9 s. To achieve a balanced system quickly, the unbalanced three-phase voltage and current have been controlled using inverter switching pulses. The proposed controller gains fast triggering. The system's voltage is immediately balanced by the gate pulses that are fired in comparison to the other mentioned controllers, i.e., AFOPID, FOPID, and PID.

Figure 8a–c depict the comparative performance assessment in terms of deviation in voltage, frequency, and total harmonic distortion, respectively. While it is clear from the voltage deviation profile that FOPID and AFOPID have shown less deviation than PID, the suggested HHO-AFOPID shows smooth and little change in %VD. The suggested controller's frequency and THD profile also display no frequency fluctuation and practically no THD, which supports the high-quality power produced by the grid-connected PV system and boosts the system's effectiveness.

Tables 5 and 6 compare the performance of several controllers with the proposed controller under changing irradiation and partial shading conditions, respectively. The recommended controller is put to the test against various controllers in terms of undershoot, settling time, ripples, and stability under varying irradiation conditions as measured by IAE and ITAE. In comparison to the other described controllers, the suggested controller exhibits the least undershoot, settling time, and ripple content. The smallest IAE and ITAE further demonstrate HHO-AFOPID's stability across a variety of irradiation conditions.


**Table 5.** Comparative performance analysis of different controllers under changing irradiation conditions.


**Table 6.** Comparative performance analysis of different controllers under the partial shading condition.

**Figure 8.** *Cont.*

**Figure 8.** Power quality analysis on the basis of (**a**) voltage deviations under HHO-AFOPID, (**b**) frequency under HHO-AFOPID, and (**c**) THD analysis under HHO-AFOPID.

In comparison to PID, FOPID, and AFOPID, Table 6 demonstrates that the suggested HHO-AFOPID controller maintains consistency under partial shade conditions in terms of least undershoot, lower settling time, and lower ripple content. When compared to PID, FOPID, and AFOPID, the lowest IAE and ITAE also have the significance of being stable under the given conditions.

In addition to these trials, a literature review was conducted to verify the HHO-AFOPID controller's satisfactory performance analysis, which was based on the case studies listed below. Since earlier times, experts have concentrated on extracting the most energy possible from solar energy. MPPTs are therefore relevant.. Researchers' attention has been drawn to the hybridization of the MPPT algorithm as their study has progressed. Here, numerous other hybrid and non-hybrid controllers are compared to the suggested hybrid HHO-AFOPID MPPT controller in order to provide a comparison of them based on power efficacy and oscillations, and these studies assert that the proposed controller is the best in the aforementioned areas. The suggested controller's performance study with different non-hybrid and hybrid MPPT control topologies is shown in Table 7.

**Table 7.** Comparative performance analysis of the hybrid HHO-AFOPID with other hybridized and non-hybridized MPPT algorithms.

