**5. Sensitivity Analysis**

Sensitivity analysis is used to examine how well a system performs in relation to changes in sensitive parameters, such as solar irradiation in the case of a PV-interfaced system. Analyzing the disturbance in sensitive variables is crucial. The variations in sensitive factors and their magnitudes are shown in Table 8.

**Table 8.** Variation of sensitive factors with the magnitude of SPV.


The amount of solar radiation needed to generate electrical energy is solely reliant on the sun's radiation output. The average solar radiation availability each day may be within the range of 5.01 to 10 kW/m2/day. The optimal dimension of a system with the lowest cost of energy is the most desired criterion; hence, this phenomenon has been analyzed on the basis of factors like the total net present cost (TNPC) and levelized cost of energy (LCOE). Equations (64)–(68) can be used to define the cost function of this study, which seeks to minimize TNPC and LCOE [24].

$$TNPC\_{min} = \frac{TAC}{CRF\left(i\_{r\_{\prime}}n\_{p}\right)}\tag{64}$$

TAC is the total annum cost, which includes the capital cost (CC), replacement cost (RC), and maintenance cost (MC) described in Equation (65).

$$\text{TAC} = \text{C}\_{\text{CC}} + \text{C}\_{\text{RC}} + \text{C}\_{\text{MC}} \tag{65}$$

CRF = the factor of capital recovery depending on the basis of the original interest rate (*ir*) and project span *np* is described in Equation (66).

$$\text{CRF}\left(i\_r, n\_p\right) = \frac{i\_r(1+i\_r)^{n\_p}}{(1+i\_r)^{n\_p}-1} \tag{66}$$

$$i\_r = \frac{i\_n - f}{1 + f} \tag{67}$$

*ir* can be calculated using Equation (67) with *in*, which is the magnitude dependent on ROI, and f symbolizes the inflation rate:

$$LCOE\_{\text{min}} = \frac{TAC}{ESPA} \tag{68}$$

*ESPA* = energy served per annum.

The simulation result shows that solar irradiation has are ciprocating effect on TNPC and LCOE, as shown in Figure 9.

The increase in solar irradiation is inversely related to the overall cost parameters according to a thorough analysis of the sensitivity variable of SPV generation or solar radiation with respect to cost parameters. It is possible to deduce cost parameters from a thorough examination of several sensitivity factors in the system, namely net present cost and cost of energy, with an increase in sunray values.

#### **6. Conclusions and Future Directions**

The conducted experiments make it abundantly clear that the suggested controller exhibits the greatest results in terms of qualitative and quantitative analysis when the environment is changing. The reference voltage was produced using the traditional P&O algorithm, which then allowed the nonlinear discrete PID (NDPID) controller to calculate the reference power. The forward Euler formula was used to combine the traditional PID controller with discretized integral and derivative portions. Additionally, the difference between reference power and output power is used to calculate inaccuracy. The HHO further optimizes the AFOPID controller to obtain the best settings for the controller to create an adaptive control law. The switching signal for the inverter is provided by this error. In addition, it has been demonstrated that the resulting topology performs better in terms of the lowest fitness value, improved settling time, and least oscillations under varying environmental conditions and partial shading conditions.To examine the stability of the proposed control methodology, the controller is judged in terms of the integral absolute error (IAE) and integral time absolute error (ITAE) under variable solar radiation intensity and partial shading conditions. In both scenarios, the control topology outperforms by achieving the lowest IAE and ITAE. Due to its fractional calculus property and multicontrol strategy with respect to handling inverter switching, the suggested controller exhibits greater robustness than existing controllers according to the study.

Power quality is assessed in addition to power quantity on the basis of voltage variation, THD, and frequency. In this area, the proposed controller exhibits a suitable response as well. Low THD, lower frequency fluctuation, and lower voltage deviation all point to the suggested control methodology, which improves the system's performance. The suggested control topology achieves the best result even though the impact of power quality issues cannot be totally eliminated or minimized.

Sensitivity analysis was also carried out on the basis of TNPC and LCOE, as the optimal design and reducing energy cost is of utmost priority in grid-interfaced systems. Here, the experiment shows that an increase in solar irradiation results in a reduction in the per unit cost of energy. This analysis will inspire the nation to use solar energy in various applications for techno-economic sustainability.

Furthermore, many cascaded controllers with a number of newly introduced optimization algorithms like mount gazelle optimization (MGO), honey badger algorithm (HBA), and Ebola algorithm may be incorporated to extract the maximum power from a PV source and other renewable energy resources as well. This concept will be helpful for microgrids as well. **Author Contributions:** Conceptualization, A.G., P.K.B., C.S. and A.T.A.; Data curation; Formal analysis, A.G., P.K.B., C.S., A.T.A. and A.R.M.; Funding acquisition, A.R.M.; Investigation, A.T.A., A.R.M. and S.A.; Methodology, A.G., P.K.B., C.S., A.T.A. and A.R.M.; Resources, A.G., P.K.B., C.S., A.T.A., A.R.M. and S.A.; Software, A.G., C.S. and S.A.; Supervision, P.K.B.; Validation, A.T.A., A.R.M. and S.A.; Writing—original draft, A.G., P.K.B., C.S. and A.T.A.; Writing—review & editing, A.G., P.K.B., C.S., A.T.A., A.R.M. and S.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Prince Sultan University, Riyadh, Saudi Arabia.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors would like to thank Prince Sultan University, Riyadh, Saudi Arabia for funding the Article Processing Charges (APCs) of this publication. Special acknowledgments are given to Automated Systems & Soft Computing Lab (ASSCL), Prince Sultan University, Riyadh, Saudi Arabia.

**Conflicts of Interest:** The authors declare no conflict of interest.
