# An Advanced and Robust Approach to Maximize Solar Photovoltaic Power Production

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{p}rooftop SPV system is also presented in the paper. Energy production is increased by 8.55% using the proposed approach to the practical system.

## 1. Introduction

## 2. Mathematical Modelling

#### 2.1. SPV Array

^{2}, respectively. Whereas, ${\mathrm{T}}_{\mathrm{c}}$ is the temperature of the SPV cell and $\mathrm{G}$ is the irradiance incident on the plane of the SPV cell. ${\mathrm{I}}_{\mathrm{sc}}$ is the short-circuit current and ${\mathrm{K}}_{\mathrm{i}}$ is the temperature coefficient of the SPV cell. ${\mathrm{V}}_{\mathrm{to}}$ is thermal voltage at STC, ${\mathrm{E}}_{\mathrm{g}}$ and ${\mathrm{E}}_{\mathrm{go}}$ is the energy bandgap of the semiconductor and energy band at $\mathrm{T}=0\mathrm{K}$. $\mathrm{s}$ is the number of SPV cells in series and $\mathrm{p}$ is the number of SPV cells in parallel.

#### 2.2. Configuration/Topologies of the SPV System

## 3. Methodology

_{p}SPV panel during the uneven distribution of irradiance.

#### Hybrid Grey Wolf Optimizer-Based MPPT

_{dc}) is converted in three-phase AC with the help of inverter gating pulses. Here, duty cycle ($\mathrm{d})$ is the grey wolf, and to find the optimal value of D is the main aim of the algorithm. During dynamic changing conditions, the current sensed by the HGWO–MPPT Algorithm changes with every change in irradiance. The proposed algorithm updates the optimum duty cycle value for the boost converter to extract maximum power at that instance. The robustness and versatility of the developed hybrid meta-heuristic MPPT algorithm, coupled with fast voltage and current sensors, are the key in avoiding the condition of ‘MPPT failure’ [49]. Figure 7 shows the flowchart for the proposed algorithm; it is divided into four stages:

## 4. Results and Discussion

#### 4.1. Simulation Results

_{p}rating. The performance is analyzed on the basis of rise time $\left({\mathrm{t}}_{\mathrm{rs}}\right)$, settling time $\left({\mathrm{t}}_{\mathrm{st}}\right)$, maximum power extracted $\left({\mathrm{P}}_{\mathrm{mp}}\right)$, shading loss $\left({\mathrm{P}}_{\mathrm{sl}}\right)$, and efficiency $\left(\mathsf{\eta}\right)$. The above-mentioned parameters define the dynamic and steady-state performance of the MPPT controllers. On the basis of these parameters, the performance of the HGWO, PSO and INC MPPT controllers is assessed for three types of configurations of the SPV system (as mentioned in Section 3). In this work, the effectiveness and robustness in tracking MPP is addressed, as the MPPT techniques are tested for different shading conditions, as shown in Figure 4. Table 3 presents the different control parameter values for the discussed MPPT algorithms. These values for PSO and HGWO were chosen by a trial-and-error method, such that, a common optimum value can suffice for the optimal performance for each scenario. Meanwhile, the values of ${\mathrm{K}}_{\mathrm{p}}$ and ${\mathrm{K}}_{\mathrm{i}}$ are the values of the proportional and integral controller for INC-based MPPT.

**Scenario 1—No Shading (NS):**During this scenario, as for all the configurations, ${\mathrm{P}}_{\mathrm{n}\mathrm{m}\mathrm{p}}$ is 11,250 W as a constant irradiance of 1000 $\mathrm{W}/{\mathrm{m}}^{2}$ is incident on each of the 25 panels. Since this scenario is also known as STC, the performance of the MPPTs for each of the configurations is similar and MPP from the controllers is also the same. The performance for no shading is presented in Figure 8 and Table 4.

**Scenario 2—Column Shading (CS):**In this scenario, two columns, C4 and C5, of the 5 × 5 SPV system are shaded. The irradiance incident on the panels of columns C4 and C5 is 600 W/m

^{2}and 400 W/m

^{2}, respectively. Figure 9 shows the performance of different MPPT controllers for each type of configuration. The proposed HGWO controller extracts the maximum power for each of the arrangements of the SPV system. The performance parameters for scenario 2 are presented in Table 5.

**Scenario 3—Row Shading (RS):**In this scenario, two rows, R4 and R5, of the 5 × 5 SPV system are shaded. The irradiance incident on the panels of column R4 and R5 is 600 W/m

^{2}and 400 W/m

^{2}, respectively. Figure 10 shows the performance of different MPPT controllers for each type of configuration. The performance parameters for scenario 2 are presented in Table 6. During the RS scenario, the steady-state response of the INC controller is not free from oscillations; similarly, PSO also has oscillations in tracking the power, whereas the MPP extracted from HGWO is free from oscillations and is more in comparable with PSO and INC. The GWOBLTCT-type of configuration of the PSO controller performs better than scenario 2.

**Scenario 4—Diagonal Shading (DS):**In this scenario, the primary diagonal of the 5 × 5 SPV system is partially shaded. The irradiance incident on the panels of the diagonal is 800 W/m

^{2}, 600 W/m

^{2}and 400 W/m

^{2}. Figure 11 shows the performance of different MPPT controllers for each type of configuration. The proposed HGWO controller has an average efficiency of 92.59% across all the topologies. This average efficiency in tracking the MPP is better in comparison to 76.74% for INC and 88.28% for PSO techniques. Here, PSO has irregular behavior in transient state and INC during steady-state. Both INC and PSO have fluctuations while trying to track the maximum power during DS-type of shade. The performance parameters for scenario 4 are presented in Table 7.

**Scenario 5—Corner Shading (CNRS):**In this scenario, all the panels present in the corner of the 5 × 5 SPV system are partially shaded, as shown in Figure 4e. The irradiance incident on the panels of diagonal is 800 W/m

^{2}, 600 W/m

^{2}and 400 W/m

^{2}. Figure 12 shows the performance of different MPPT controllers for each type of configuration. During this scenario, the controllers INC, PSO and HGWO have an average efficiency of 78.34%, 90.33% and 92.05%. The proposed HGWO has comparatively better transient and steady characteristics of tracking MPP. INC still suffers from oscillations while trying to track the maximum power during CNRS-type of shade, whereas PSO performs significantly well under this challenging scenario. ${\mathrm{P}}_{\mathrm{m}{\mathrm{p}}_{\mathrm{pso}}}$ is better than INC and very close to ${\mathrm{P}}_{{\mathrm{mp}}_{\mathrm{hgwo}}}$. The performance parameters for scenario 5 are presented in Table 8.

#### 4.2. Practical Assessment

_{p}SPV system. This system is a combination of fourteen 450 W

_{p}SPV modules in a 7 × 2 arrangement on the rooftop of the Qassim University, KSA. This assessment is performed by collecting the data from the installed SPV system; this data includes irradiance incident on the system, module temperature, power and energy produced by the system. The recorded data for irradiance and temperature of a day are presented in Figure 13. These required data are collected through current sensors, voltage sensors, an irradiance meter and a wattmeter.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature and Abbreviations

$\mathsf{\eta}$ | Efficiency |

${\mathrm{C}}_{\mathrm{f}}$ | Convergence factor |

${\mathrm{E}}_{\mathrm{g}},{\mathrm{E}}_{\mathrm{go}}$ | Energy bandgap of semiconductor and energy band at $\mathrm{T}=0\mathrm{K}$ |

$\mathrm{G}$ | Irradiance incident on the plane of SPV cell |

${\mathrm{G}}_{\mathrm{ref}}$ | 1000 W/m^{2} |

${\mathrm{I}}_{\mathrm{PH}}$ | Photogenerated controlled current source |

${\mathrm{I}}_{\mathrm{sc}}$ | Short circuit current |

${\mathrm{I}}_{\mathrm{o}}$ | Reverse saturation current |

${\mathrm{K}}_{\mathrm{i}}$ | Temperature coefficient of the SPV cell |

$\mathrm{n}$ | Diode ideality factor |

${\mathrm{P}}_{\mathrm{mp}}$ | Power at maximum power point |

${\mathrm{P}}_{\mathrm{sl}}$ | Shading loss |

${\mathrm{R}}_{\mathrm{s}},{\mathrm{R}}_{\mathrm{sh}}$ | Series and shunt resistance for power loss |

${\mathrm{t}}_{\mathrm{rs}}$ | Rise time |

${\mathrm{t}}_{\mathrm{st}}$ | Settling time |

${\mathrm{T}}_{\mathrm{ref}}$ | 25 deg. C |

${\mathrm{T}}_{\mathrm{c}}$ | Temperature of the SPV cell |

${\mathrm{V}}_{\mathrm{t}}$ | Thermal voltage |

${\mathrm{V}}_{\mathrm{to}}$ | Thermal voltage at STC |

ANFIS | Adaptive Neuro Fuzzy Inference System |

BLTCT | Bridge Linked Total Cross Tied |

CS | Column Shading |

CNRS | Corner Shading |

DS | Diagonal Shading |

GWO | Grey Wolf Optimizer |

HGWO | Hybrid Grey Wolf Optimizer |

INC | Incremental Conductance |

IT-2 FL | Interval Type 2 Fuzzy Logic |

MPPT | Maximum Power Point Tracking |

NS | No Shading |

PSO | Particle Swarm Optimization |

RS | Row Shading |

S | Series |

SP | Series Parallel |

SPV | Solar Photovoltaic |

TCT | Total Cross Tied |

## References

- Bojek, P.; Bahar, H. Solar PV Tracking Report: November 2021; International Energy Agency: Paris, France, 2021; Available online: https://www.iea.org/reports/solar-pv (accessed on 11 February 2022).
- Esram, T.; Chapman, P.L. Comparison of Photovoltaic Array Maximum Power Point Tracking Techniques. IEEE Trans. Energy Convers.
**2007**, 22, 439–449. [Google Scholar] [CrossRef] [Green Version] - Danandeh, M.A.; Mousavi, G.S.M. Comparative and Comprehensive Review of Maximum Power Point Tracking Methods for PV Cells. Renew. Sustain. Energy Rev.
**2018**, 82, 2743–2767. [Google Scholar] [CrossRef] - Ram, J.P.; Babu, T.S.; Rajasekar, N. A Comprehensive Review on Solar PV Maximum Power Point Tracking Techniques. Renew. Sustain. Energy Rev.
**2017**, 67, 826–847. [Google Scholar] [CrossRef] - Kumar, A.; Rizwan, M.; Nangia, U. Development of ANFIS-Based Algorithm for MPPT Controller for Standalone Photovoltaic System. Int. J. Adv. Intell. Paradig.
**2021**, 18, 247–264. [Google Scholar] [CrossRef] - Yang, B.; Zhu, T.; Wang, J.; Shu, H.; Yu, T.; Zhang, X.; Yao, W.; Sun, L. Comprehensive Overview of Maximum Power Point Tracking Algorithms of PV Systems under Partial Shading Condition. J. Clean. Prod.
**2020**, 268, 121983. [Google Scholar] [CrossRef] - Li, X.; Wang, Q.; Wen, H.; Xiao, W. Comprehensive Studies on Operational Principles for Maximum Power Point Tracking in Photovoltaic Systems. IEEE Access
**2019**, 7, 121407–121420. [Google Scholar] [CrossRef] - Iqbal, B.; Nasir, A.; Murtaza, A.F. Stochastic Maximum Power Point Tracking of Photovoltaic Energy System under Partial Shading Conditions. Prot. Control Mod. Power Syst.
**2021**, 6, 30. [Google Scholar] [CrossRef] - Elgendy, M.A.; Zahawi, B.; Atkinson, D.J. Operating Characteristics of the P&O Algorithm at High Perturbation Frequencies for Standalone PV Systems. IEEE Trans. Energy Convers.
**2015**, 30, 189–198. [Google Scholar] [CrossRef] - Kamran, M.; Mudassar, M.; Fazal, M.R.; Asghar, M.U.; Bilal, M.; Asghar, R. Implementation of Improved Perturb & Observe MPPT Technique with Confined Search Space for Standalone Photovoltaic System. J. King Saud Univ. Eng. Sci.
**2020**, 32, 432–441. [Google Scholar] [CrossRef] - Elgendy, M.A.; Zahawi, B.; Atkinson, D.J. Assessment of the Incremental Conductance Maximum Power Point Tracking Algorithm. IEEE Trans. Sustain. Energy
**2013**, 4, 108–117. [Google Scholar] [CrossRef] - Safari, A.; Mekhilef, S. Simulation and Hardware Implementation of Incremental Conductance MPPT with Direct Control Method Using Cuk Converter. IEEE Trans. Ind. Electron.
**2011**, 58, 1154–1161. [Google Scholar] [CrossRef] - Bidram, A.; Davoudi, A.; Balog, R.S. Control and Circuit Techniques to Mitigate Partial Shading Effects in Photovoltaic Arrays. IEEE J. Photovolt.
**2012**, 2, 532–546. [Google Scholar] [CrossRef] - Li, X.; Wen, H.; Hu, Y.; Jiang, L.; Xiao, W. Modified Beta Algorithm for GMPPT and Partial Shading Detection in Photovoltaic Systems. IEEE Trans. Power Electron.
**2018**, 33, 2172–2186. [Google Scholar] [CrossRef] - Zhang, J.H.; Wei, X.Y.; Hu, L.; Ma, J.G. A MPPT Method Based on Improved Fibonacci Search Photovoltaic Array. Teh. Vjesn.
**2019**, 26, 163–170. [Google Scholar] [CrossRef] - Li, H.; Yang, D.; Su, W.; Lu, J.; Yu, X. An Overall Distribution Particle Swarm Optimization MPPT Algorithm for Photovoltaic System under Partial Shading. IEEE Trans. Ind. Electron.
**2019**, 66, 265–275. [Google Scholar] [CrossRef] - Suyanto, S.; Mohammad, L.; Setiadi, I.C.; Roekmono, R. Analysis and Evaluation Performance of MPPT Algorithms: Perturb Observe (PO), Firefly, and Flower Pollination (FPA) in Smart Microgrid Solar Panel Systems. In Proceedings of the 2019 International Conference on Technologies and Policies in Electric Power and Energy, TPEPE, Yogyakarta, Indonesia, 21–22 October 2019. [Google Scholar] [CrossRef]
- Krishnan, G.S.; Kinattingal, S.; Simon, S.P.; Nayak, P.S.R. MPPT in PV Systems Using Ant Colony Optimisation with Dwindling Population. IET Renew. Power Gener.
**2020**, 14, 1105–1112. [Google Scholar] [CrossRef] - Hussaian Basha, C.; Bansal, V.; Rani, C.; Brisilla, R.M.; Odofin, S. Development of Cuckoo Search MPPT Algorithm for Partially Shaded Solar PV SEPIC Converter. In Advances in Intelligent Systems and Computing; Springer: Singapore, 2020; Volume 1048. [Google Scholar] [CrossRef]
- Assad, A.; Deep, K. A Hybrid Harmony Search and Simulated Annealing Algorithm for Continuous Optimization. Inf. Sci.
**2018**, 450, 246–266. [Google Scholar] [CrossRef] - Eltamaly, A.M. A Novel Musical Chairs Algorithm Applied for MPPT of PV Systems. Renew. Sustain. Energy Rev.
**2021**, 146, 111135. [Google Scholar] [CrossRef] - Hamza Zafar, M.; Mujeeb Khan, N.; Feroz Mirza, A.; Mansoor, M.; Akhtar, N.; Usman Qadir, M.; Ali Khan, N.; Raza Moosavi, S.K. A Novel Meta-Heuristic Optimization Algorithm Based MPPT Control Technique for PV Systems under Complex Partial Shading Condition. Sustain. Energy Technol. Assess.
**2021**, 47, 101367. [Google Scholar] [CrossRef] - Firdaus, A.A.; Yunardi, R.T.; Agustin, E.I.; Nahdliyah, S.D.N.; Nugroho, T.A. An Improved Control for MPPT Based on FL-PSo to Minimize Oscillation in Photovoltaic System. Int. J. Power Electron. Drive Syst.
**2020**, 11, 1082–1087. [Google Scholar] [CrossRef] - Priyadarshi, N.; Bhaskar, M.S.; Padmanaban, S.; Blaabjerg, F.; Azam, F. New CUK–SEPIC Converter Based Photovoltaic Power System with Hybrid GSA–PSO Algorithm Employing MPPT for Water Pumping Applications. IET Power Electron.
**2020**, 13, 2824–2830. [Google Scholar] [CrossRef] - Nugraha, D.A.; Lian, K.L.; Suwarno, S. A Novel Mppt Method Based on Cuckoo Search Algorithm and Golden Section Search Algorithm for Partially Shaded Pv System. Can. J. Electr. Comput. Eng.
**2019**, 42, 173–182. [Google Scholar] [CrossRef] - Bhukya, L.; Nandiraju, S. A Novel Photovoltaic Maximum Power Point Tracking Technique Based on Grasshopper Optimized Fuzzy Logic Approach. Int. J. Hydrog. Energy
**2020**, 45, 9416–9427. [Google Scholar] [CrossRef] - Eltamaly, A. A novel particle swarm optimization optimal control parameter determination strategy for maximum power point trackers of partially shaded photovoltaic systems. Eng. Optim.
**2021**, 54, 634–650. [Google Scholar] [CrossRef] - Eltamaly, A. A Novel Strategy for Optimal PSO Control Parameters Determination for PV Energy Systems. Sustainability
**2021**, 13, 1008. [Google Scholar] [CrossRef] - Eltamaly, A.; Farh, H.; Abokhalil, A. A novel PSO strategy for improving dynamic change partial shading photovoltaic maximum power point tracker. Energy Sources Part A Recovery Util. Environ. Eff.
**2020**, 42, 1–15. [Google Scholar] [CrossRef] - Eltamaly, A. An improved cuckoo search algorithm for maximum power point tracking of photovoltaic systems under partial shading conditions. Energies
**2021**, 14, 953. [Google Scholar] [CrossRef] - Cherukuri, S.K.; Rayapudi, S.R. Enhanced Grey Wolf Optimizer Based MPPT Algorithm of PV System Under Partial Shaded Condition. Int. J. Renew. Energy Dev.
**2017**, 6, 203–212. [Google Scholar] [CrossRef] [Green Version] - Belhachat, F.; Larbes, C. PV Array Reconfiguration Techniques for Maximum Power Optimization under Partial Shading Conditions: A Review. Sol. Energy
**2021**, 230, 558–582. [Google Scholar] [CrossRef] - Venkateswari, R.; Rajasekar, N. Power Enhancement of PV System via Physical Array Reconfiguration Based Lo Shu Technique. Energy Convers. Manag.
**2020**, 215, 112885. [Google Scholar] [CrossRef] - Tatabhatla, V.M.R.; Agarwal, A.; Kanumuri, T. A Generalized Chaotic Baker Map Configuration for Reducing the Power Loss under Shading Conditions. Electr. Eng.
**2020**, 102, 2227–2244. [Google Scholar] [CrossRef] - Kumar, A.; Rizwan, M.; Nangia, U.; Alaraj, M. Grey Wolf Optimizer-Based Array Reconfiguration to Enhance Power Production from Solar Photovoltaic Plants under Different Scenarios. Sustainability
**2021**, 13, 13627. [Google Scholar] [CrossRef] - Kumar Pachauri, R.; Thanikanti, S.B.; Bai, J.; Kumar Yadav, V.; Aljafari, B.; Ghosh, S.; Haes Alhelou, H. Ancient Chinese Magic Square-Based PV Array Reconfiguration Methodology to Reduce Power Loss under Partial Shading Conditions. Energy Convers. Manag.
**2022**, 253, 115148. [Google Scholar] [CrossRef] - Yousri, D.; Thanikanti, S.B.; Balasubramanian, K.; Osama, A.; Fathy, A. Multi-Objective Grey Wolf Optimizer for Optimal Design of Switching Matrix for Shaded PV Array Dynamic Reconfiguration. IEEE Access
**2020**, 8, 159931–159946. [Google Scholar] [CrossRef] - Karmakar, B.K.; Karmakar, G. A Current Supported PV Array Reconfiguration Technique to Mitigate Partial Shading. IEEE Trans. Sustain. Energy
**2021**, 12, 1449–1460. [Google Scholar] [CrossRef] - Babu, T.S.; Ram, J.P.; Dragičević, T.; Miyatake, M.; Blaabjerg, F.; Rajasekar, N. Particle Swarm Optimization Based Solar PV Array Reconfiguration of the Maximum Power Extraction under Partial Shading Conditions. IEEE Trans. Sustain. Energy
**2018**, 9, 74–85. [Google Scholar] [CrossRef] - Zhu, Z.; Hou, M.; Ding, L.; Zhu, G.; Jin, Z. Optimal Photovoltaic Array Dynamic Reconfiguration Strategy Based on Direct Power Evaluation. IEEE Access
**2020**, 8, 210267–210276. [Google Scholar] [CrossRef] - Fares, D.; Fathi, M.; Shams, I.; Mekhilef, S. A Novel Global MPPT Technique Based on Squirrel Search Algorithm for PV Module under Partial Shading Conditions. Energy Convers. Manag.
**2021**, 230, 113773. [Google Scholar] [CrossRef] - Aldosary, A.; Ali, Z.M.; Alhaider, M.M.; Ghahremani, M.; Dadfar, S.; Suzuki, K. A Modified Shuffled Frog Algorithm to Improve MPPT Controller in PV System with Storage Batteries under Variable Atmospheric Conditions. Control Eng. Pract.
**2021**, 112, 104831. [Google Scholar] [CrossRef] - Shams, I.; Mekhilef, S.; Tey, K.S. Improved-Team-Game-Optimization-Algorithm-Based Solar MPPT with Fast Convergence Speed and Fast Response to Load Variations. IEEE Trans. Ind. Electron.
**2021**, 68, 7093–7103. [Google Scholar] [CrossRef] - Koad, R.B.A.; Zobaa, A.F.; El-Shahat, A. A Novel MPPT Algorithm Based on Particle Swarm Optimization for Photovoltaic Systems. IEEE Trans. Sustain. Energy
**2017**, 8, 468–476. [Google Scholar] [CrossRef] [Green Version] - Silvestre, S. Strategies for Fault Detection and Diagnosis of PV Systems. In Advances in Renewable Energies and Power Technologies; Elsevier: Amsterdam, The Netherlands, 2018. [Google Scholar] [CrossRef]
- Saxena, H.; Singh, A.; Rai, J.N. Design and Performance Analysis of Generalised Integrator-Based Controller for Grid Connected PV System. Int. J. Electron.
**2018**, 105, 1079–1096. [Google Scholar] [CrossRef] - Kumar, A.; Alaraj, M.; Rizwan, M.; Nangia, U. Novel AI Based Energy Management System for Smart Grid with RES Integration. IEEE Access
**2021**, 9, 162530–162542. [Google Scholar] [CrossRef] - Bilal, M.; Rizwan, M. Integration of Electric Vehicle Charging Stations and Capacitors in Distribution Systems with Vehicle-to-Grid Facility. Energy Sources Part A Recovery Util. Environ. Eff.
**2021**, 43, 1–30. [Google Scholar] [CrossRef] - Chen, M.; Ma, S.; Wu, J.; Huang, L. Analysis of MPPT Failure and Development of an Augmented Nonlinear Controller for MPPT of Photovoltaic Systems under Partial Shading Conditions. Appl. Sci.
**2017**, 7, 95. [Google Scholar] [CrossRef] [Green Version] - Kumar, A.; Bilal, M.; Rizwan, M.; Nangia, U. Grey Wolf Optimization Inspired Maximum Power Extraction from SPV System for Water Pumping Application. In Proceedings of the 2022 International Conference for Advancement in Technology (ICONAT), Goa, India, 21–22 January 2022. [Google Scholar] [CrossRef]
- Verma, P.; Garg, R.; Mahajan, P. Asymmetrical Interval Type-2 Fuzzy Logic Control Based MPPT Tuning for PV System under Partial Shading Condition. ISA Trans.
**2020**, 100, 251–263. [Google Scholar] [CrossRef]

**Figure 3.**SPV array configurations. (

**a**) Series (S), (

**b**) Series Parallel (SP), (

**c**) Total Cross Tied (TCT).

**Figure 4.**Representation of different PSCs on 5 × 5 SPV system. (

**a**) No Shading (NS), (

**b**) Column Shading (CS), (

**c**) Row Shading (RS), (

**d**) Diagonal Shading (DS) and (

**e**) Corner Shading (CNRS).

**Figure 9.**Performance of HGWO, INC and PSO MPPT during scenario 2 for different topologies. (

**a**) SP, (

**b**) TCT, (

**c**) GWOBLTCT.

**Figure 10.**Performance of HGWO, INC and PSO MPPT during scenario 3 for different topologies. (

**a**) SP, (

**b**) TCT, (

**c**) GWOBLTCT.

**Figure 11.**Performance of HGWO, INC and PSO MPPT during scenario 4 for different topologies. (

**a**) SP, (

**b**) TCT, (

**c**) GWOBLTCT.

**Figure 12.**Performance of HGWO, INC and PSO MPPT during scenario 5 for different topologies. (

**a**) SP, (

**b**) TCT (

**c**), GWOBLTCT.

Specification | Data |
---|---|

Cell Type | Mono-crystalline |

Cell Arrangement | 144 [2 × (12 × 6)] |

${\mathrm{P}}_{\mathrm{peak}}$ | 450 W |

${\mathrm{I}}_{\mathrm{M}\mathrm{P}}$ | 11.12 A |

${\mathrm{V}}_{\mathrm{M}\mathrm{P}}$ | 40.5 V |

${\mathrm{I}}_{\mathrm{SC}}$ | 11.65 A |

${\mathrm{V}}_{\mathrm{OC}}$ | 48.7 V |

Operating Temperature | −40 °C to 85 °C |

Power Tolerance | 0 to 5 W |

**Table 2.**Nominal Maximum Power $\left({\mathrm{P}}_{\mathrm{n}\mathrm{m}\mathrm{p}}\right)$ For Each Configuration Under Various Shading Scenarios.

Shading | Configuration of 5 × 5 SPV System | |||
---|---|---|---|---|

S | SP | TCT | GWO–BLTCT | |

NS | 11,250 | 11,250 | 11,250 | 11,250 |

CS | 6645 | 8972 | 8972 | 9102 |

RS | 6644 | 6644 | 6645 | 6877 |

DS | 6277 | 7004 | 8570 | 8896 |

CNRS | 5052 | 6096 | 7129 | 7262 |

Algorithms | Parameters |
---|---|

INC | ${\mathrm{K}}_{\mathrm{p}}=$1.93, ${\mathrm{K}}_{\mathrm{i}}=$ 2.35 |

PSO | ${\mathrm{w}}_{\mathrm{pso}}$$=0.83\left(\mathrm{fixed}\right),{\mathrm{c}}_{1}$$=2,{\mathrm{c}}_{2}$$=2.4,{\mathrm{r}}_{\mathrm{pso}1}={\mathrm{r}}_{\mathrm{pso}2}$= rand (0,1) |

HGWO | ${\mathrm{w}}_{\mathrm{pso}}$$\mathrm{given}\mathrm{by}\mathrm{Equations}.10\left(\mathrm{variable}\right),{\mathrm{c}}_{1}$$=1.4,{\mathrm{c}}_{2}$$=1,{\mathrm{c}}_{3}$$=1,{\mathrm{r}}_{\mathrm{pso}1}={\mathrm{r}}_{\mathrm{pso}2}={\mathrm{r}}_{\mathrm{pso}3}$= rand (0, 1) |

Common Parameters for Optimization Algorithms | |

Iterations | 1000 |

Tolerance | 10^{−3} |

Population Size | 5 |

Sampling Time | 10^{−5} s |

Configuration | MPPT | Performance Parameters | ||||
---|---|---|---|---|---|---|

${\mathbf{P}}_{\mathbf{m}\mathbf{p}}\left(\mathbf{W}\right)$ | ${\mathbf{P}}_{\mathbf{s}\mathbf{l}}\left(\mathbf{W}\right)$ | $\mathsf{\eta}(\%)$ | ${\mathbf{t}}_{\mathbf{r}\mathbf{s}}\left(\mathbf{s}\right)$ | ${\mathbf{t}}_{\mathbf{s}\mathbf{t}}\left(\mathbf{s}\right)$ | ||

SP/TCT/GWOBLTCT | INC | 10073 | 1177 | 89.54 | 0.04 | 0.14 |

PSO | 10685 | 565 | 94.97 | 0.03 | 0.06 | |

HGWO | 10856 | 394 | 96.59 | 0.05 | 0.06 |

Configuration | MPPT | Performance Parameters | ||||
---|---|---|---|---|---|---|

${\mathbf{P}}_{\mathbf{m}\mathbf{p}}\left(\mathbf{W}\right)$ | ${\mathbf{P}}_{\mathbf{s}\mathbf{l}}\left(\mathbf{W}\right)$ | $\mathsf{\eta}(\%)$ | ${\mathbf{t}}_{\mathbf{r}\mathbf{s}}\left(\mathbf{s}\right)$ | ${\mathbf{t}}_{\mathbf{s}\mathbf{t}}\left(\mathbf{s}\right)$ | ||

SP | INC | 7291 | 1681 | 81.26 | 0.03 | 0.10 |

PSO | 7425 | 1547 | 82.75 | 0.02 | 0.10 | |

HGWO | 8256 | 716 | 92.02 | 0.08 | 0.12 | |

TCT | INC | 7339 | 1633 | 81.79 | 0.03 | 0.10 |

PSO | 7967 | 1005 | 88.80 | 0.02 | 0.10 | |

HGWO | 8288 | 684 | 92.38 | 0.08 | 0.12 | |

GWOBLTCT | INC | 7567 | 1535 | 83.13 | 0.03 | 0.10 |

PSO | 8133 | 969 | 89.35 | 0.02 | 0.10 | |

HGWO | 8561 | 541 | 94.06 | 0.07 | 0.08 |

Configuration | MPPT | Performance Parameters | ||||
---|---|---|---|---|---|---|

${\mathbf{P}}_{\mathbf{m}\mathbf{p}}\left(\mathbf{W}\right)$ | ${\mathbf{P}}_{\mathbf{s}\mathbf{l}}\left(\mathbf{W}\right)$ | $\mathsf{\eta}(\%)$ | ${\mathbf{t}}_{\mathbf{r}\mathbf{s}}\left(\mathbf{s}\right)$ | ${\mathbf{t}}_{\mathbf{st}}\left(\mathbf{s}\right)$ | ||

SP | INC | 5695 | 949 | 85.72 | 0.03 | 0.18 |

PSO | 6227 | 417 | 93.72 | 0.03 | 0.16 | |

HGWO | 6441 | 203 | 96.94 | 0.07 | 0.08 | |

TCT | INC | 5894 | 751 | 88.68 | 0.03 | 0.18 |

PSO | 6298 | 347 | 94.77 | 0.03 | 0.16 | |

HGWO | 6488 | 157 | 97.65 | 0.07 | 0.08 | |

GWOBLTCT | INC | 6126 | 751 | 89.08 | 0.03 | 0.18 |

PSO | 6527 | 350 | 94.91 | 0.04 | 0.08 | |

HGWO | 6738 | 139 | 97.98 | 0.07 | 0.08 |

Configuration | MPPT | Performance Parameters | ||||
---|---|---|---|---|---|---|

${\mathbf{P}}_{\mathbf{mp}}\left(\mathbf{W}\right)$ | ${\mathbf{P}}_{\mathbf{sl}}\left(\mathbf{W}\right)$ | $\mathsf{\eta}(\%)$ | ${\mathbf{t}}_{\mathbf{rs}}\left(\mathbf{s}\right)$ | ${\mathbf{t}}_{\mathbf{st}}\left(\mathbf{s}\right)$ | ||

SP | INC | 5267 | 1737 | 75.19 | 0.04 | 0.11 |

PSO | 6125 | 879 | 87.45 | 0.03 | 0.14 | |

HGWO | 6347 | 657 | 90.61 | 0.07 | 0.08 | |

TCT | INC | 6651 | 1919 | 77.60 | 0.04 | 0.11 |

PSO | 7563 | 1007 | 88.21 | 0.03 | 0.14 | |

HGWO | 7969 | 601 | 92.98 | 0.07 | 0.08 | |

GWOBLTCT | INC | 6887 | 2009 | 77.41 | 0.04 | 0.11 |

PSO | 7932 | 964 | 89.16 | 0.03 | 0.14 | |

HGWO | 8377 | 519 | 94.16 | 0.07 | 0.08 |

Configuration | MPPT | Performance Parameters | ||||
---|---|---|---|---|---|---|

${\mathbf{P}}_{\mathbf{mp}}\left(\mathbf{W}\right)$ | ${\mathbf{P}}_{\mathbf{sl}}\left(\mathbf{W}\right)$ | $\mathsf{\eta}(\%)$ | ${\mathbf{t}}_{\mathbf{rs}}\left(\mathbf{s}\right)$ | ${\mathbf{t}}_{\mathbf{st}}\left(\mathbf{s}\right)$ | ||

SP | INC | 4531 | 1565 | 74.32 | 0.06 | 0.10 |

PSO | 5439 | 657 | 89.22 | 0.02 | 0.06 | |

HGWO | 5567 | 529 | 91.32 | 0.07 | 0.08 | |

TCT | INC | 5693 | 1436 | 79.85 | 0.06 | 0.10 |

PSO | 6403 | 726 | 89.81 | 0.02 | 0.06 | |

HGWO | 6537 | 592 | 91.69 | 0.07 | 0.08 | |

GWOBLTCT | INC | 5871 | 1391 | 80.84 | 0.06 | 0.10 |

PSO | 6678 | 584 | 91.95 | 0.02 | 0.06 | |

HGWO | 6764 | 498 | 93.14 | 0.07 | 0.08 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Alaraj, M.; Kumar, A.; Alsaidan, I.; Rizwan, M.; Jamil, M.
An Advanced and Robust Approach to Maximize Solar Photovoltaic Power Production. *Sustainability* **2022**, *14*, 7398.
https://doi.org/10.3390/su14127398

**AMA Style**

Alaraj M, Kumar A, Alsaidan I, Rizwan M, Jamil M.
An Advanced and Robust Approach to Maximize Solar Photovoltaic Power Production. *Sustainability*. 2022; 14(12):7398.
https://doi.org/10.3390/su14127398

**Chicago/Turabian Style**

Alaraj, Muhannad, Astitva Kumar, Ibrahim Alsaidan, Mohammad Rizwan, and Majid Jamil.
2022. "An Advanced and Robust Approach to Maximize Solar Photovoltaic Power Production" *Sustainability* 14, no. 12: 7398.
https://doi.org/10.3390/su14127398