**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.


**6.5 Bathymetric characteristics necessary for promoting CRC**

The topography of the reefal bay allows it to produce signature dynamics driven primarily by over-the-reef flow, wind and tidal forcings. Waves break over the reef and the generated flow feed reef-parallel currents that in turn supply a major channel outflow. The channel (Figure 13) features significantly in this system and its prominence is the main bathymetric difference from other more popularly studied reef systems such as atolls, platform and

The Hydrodynamic Modelling of Reefal Bays –

**7. Conclusion**

loop (open CRC);

regime.

expansion.

**8. Summary**

bay system:

of wind and tide regimes to driving gyre emanations.

giving rise to a persistent circulation;

was primarily responsible for bay extension;

Placing Coral Reefs at the Center of Bay Circulation 175

bay circulation around the reef, revealing signature patterns, and deriving the contributions

The hydrodynamic modelling and tracking simulations were able to reproduce field observations, allowing the following signatures to be developed for characterizing the reefal

A characteristic bathymetry comprised of reef arms broken by prominent channel,

 A reef-centered circulation that continuously looped the reef (circum-reef circulation or CRC) to form either a closed gyre (closed CRC) or to flow along the fore-reef as open

The dominance of the CRC alternating between reef arms and dictating which reef arm

The persistence of particularly one reef arm's CRC regardless of the wind or tidal

These signatures are now identified with the reefal bay system, where the reef is shown to be central to inducing the circum-reef circulation or CRC that encourages re-circulation of inner bay waters, and that this CRC formation is not found in non-reefal bays, where there is an absence of emergent reef between headlands. Driving forces such as wind, over-the-reef flow and tidal changes were responsible for maintaining the CRC including its contractions and emanations. These findings are important in their implications for stabilizing and protecting these systems as well as the shoreline of which they are a part. Incorporating the reef-parabola geomorphology as the centre of circulation gives predictability to other bay features such as the physicochemical, geo-physical and biological dynamics, which are all affected in greater part by local circulation. Many of these bays, for example, function as nurseries for marine and terrestrial species where their planktonic stages are directly influenced by current patterns and regimes. Identifying the CRC will aid in locating and protecting habitats conducive to plankton viability and survival, including reef growth and

Research on reefal bays revealed that inner bay waters exiting the channel between reefs recirculated into the back-reef, and that this circulation was localized and permanent around reefs as the signature circulation. The distinctive topology of reef arms subtending the headland and separated by a prominent channel induced particles to circulate the reef in expanding and contracting gyres. Gyres expanded by as much as 98% of the horizontal distribution, with expansion and contraction linked to cyclical wind and tidal regimes, giving the reefal system a signature pulse in circulation. Strengthening of the circulation around the reef resulted in closure of looping circulation, increased recirculation rate of particles, increased gyre current speeds and broadening of the circulation's spatial extent.

A reef-centered circulation driven by wind, tides and over-the-reef flow;

A CRC that was persistent because it is always present and localized;

A CRC with a spatial pulse indicated by cycles of expansion and contraction;

ribbon reef. The channel in the reefal bay is the main conduit of back-reef water exiting to the sea, and therefore sets up the hydrodynamics to produce jet currents that help complete the circum-reef current. This CRC has been shown to either close in on itself , which is when gyres are formed that cause particles to re-circulate on the reef, or to flow along the fore-reef and join the general long-shore flow, causing particles to leave the system.

Fig. 13. Spatial 3D model of Wreck Bay (A) and Engine Head Bay (B) revealing their differences in topography. In Wreck Bay, reef arms are emergent at high tide and the deepest part of the system is its prominent channel. This is topographically more complex than the open, non-reefal Engine Head Bay (spatial 3D Models are exaggerated vertically).

Bathymetric characterization includes the reef arms, where their presence localizes the CRC and relative size becomes an important factor. The larger reef arm generates the more expansive gyres and therefore greatest emanations of the bay. This geomorphology is typical of many Caribbean reefal bays. By over-generalization, however, bays have been classified geomorphologically by variations in their coastlines' indented shape (Rea & Komar, 1975; Silvester et al., 1980). This has been applied to systems for which the circulation can be persistent or temporary. Gently-sloping shorelines, for example, exposed to wave action may contain gyre circulations, similar to the CRC, that comprise a seaward rip current diffusing beyond the breaker zone and returning landward as slow mass drift under wave action (Carter 1988). Unlike the reefal-bay system, however, the stability of these gyres is heavily dependent on high energy wave action and so rip features are hardly permanent or in the same location. Ultimately, the bathymetry unique to these reefal-bay systems is principal in forming and maintaining the CRC, as seen in the simulation of the longer-lasting gyres when both the wind and tidal contributions are reduced.

### **6.6 Reliability of the hydrodynamic model**

The hydrodynamic model used flow over-the-reef along a boundary line to simulate wave breaking and captured the effects of shorter period wind-wave driven flow important in driving channel currents. Current simulations in the channel were therefore in good agreement with S4 field data and are considered most important in these models since they form the main link in the CRC formation, in addition to being the direct driver of CRC emanation and contraction. Simulations, however, fell short in capturing some effects caused by the reef flat (Cetina-Heredia et al., 2008), and the contribution of longer period swell, seiching and infra-gravity waves (Lugo-Fernandez et al., 1998; Pequignet, 2008). This affected the back-reef outputs where currents were faster and less variable than simulated by the RMA model. Results from the model, however, were sufficient for simulating the bay circulation around the reef, revealing signature patterns, and deriving the contributions of wind and tide regimes to driving gyre emanations.


*2.10. Statistical Analyses*

The significance of the treatment effects (Ecs), storage days and their interaction on the determined variables was estimated by two-way ANOVA. In controls, one-way ANOVA was also performed. During the last two sampling dates and also when denoted, partial analysis of data was performed in addition to two-way ANOVA of all data from day 7. Mean comparisons were performed using the Tukey-HSD multiple range test (α = 0.05) with standard error (SE) values calculated from the residual variances. Data of weight loss (WL), pedicel removal force (PRF), and the analyses of respiration rates (RR) of controls, hue angle of controls and pedicel removal force of controls were transformed to log10, while c-3-glc and analyses of controls of c-3-rut, catechin, epicatechin, chlorogenic and neochlorogenic acids were transformed to the square root. The data presented were back transformed. Decay data were analyzed without transformation after checking the residuals for normality, according to the Shapiro–Wilk test, and the plot of the residuals for homoscedasticity. All statistical analyses were performed using STATGRAPHICS Plus (Statgraphics Technologies Inc., The Plains, VA, USA).


**Author details**

Megha Gupta Fred Hutchinson Cancer Research Center, Seattle, WA, USA

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