# Optimization of Photovoltaic Panel Array Configurations to Reduce Lift Force Using Genetic Algorithm and CFD

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Proposed Methodology

#### 2.1. Problem Formulation

- $\rho $: density of air.
- ${A}_{pi}$: projected area calculated using Equation (3).
- ${C}_{Li}$: lift coefficient computed from CFD.
- θ
_{1}: tilt angle of the first row. - θ
_{2}: tilt angle of the second row. - P: pitch between rows.
- ${x}_{1},{y}_{1},{x}_{2}$,${y}_{2}$: tilt angles limits.
- $a,b$: pitch limits.

#### 2.2. Optimization Process Using Genetic Algorithm

#### 2.3. Performance Ratio Calculations

#### 2.4. Model

^{2}was considered, as shown in Figure 3a. A 1:1 Scale model was developed using an ANSYS Fluent geometry tool. For each type of configuration, two rows of solar panels wereconsidered in a 2-D domain (Figure 3a,b). The size of the panels considered was 2 m × 1 m × 40 mm. The parametric design approach was used in which the tilt angle of each row and the pitch between them wereparameterized and couldbe adjusted according to the requirement. Simulations werecarried out using the two-equation k-Ɛ model. The computation domain was subdivided into control volumes for better mesh generation. A multi-zone Quad/Tri mesh was generated. Grid independence study results are presented in Table 2. Three types of mesh, coarse, medium, and fine, wereused to calculate the lift coefficient. The results formedium and fine mesh wereapproximately the same. Therefore, the medium mesh was used for the final results evaluation. Furthermore, to obtain better results, near-wall treatment was performed around the photovoltaicpanels, and refinement was done in the region of interest, i.e., the area around the solar panel, as shown in Figure 3b.

## 3. Results and Discussion

#### 3.1. Case I—Single-Row Landscape Configuration

_{1}, θ

_{2}, and P were parameterized in the range of 15 to 30 degrees for the tilt angle of both rows, and 1m to 1.5m for the pitch between the two rows. The total population size, in this case, was 1536. The genetic algorithm method was used to find the optimum configuration. Around 10% of the population (200 individuals) was used as convergence criteria for achieving an optimum configuration. Figure 5 shows the results obtained for each iteration.

_{1}, θ

_{2}, and P, which result in minimum and maximum lift force configurations.

#### 3.2. Case II—Two-Row Landscape Configuration

_{1}and θ

_{2}were altered from a 15-degree to 30-degree tilt angle, and pitch (P) was varied from 2 m to 3 m insearch ofan optimum configuration. The total population size, in this case, was 2816. The genetic algorithm method was used to find the optimum configuration. Around 10% of the individuals as convergence criteria were analyzed before achieving an optimum configuration. Figure 8 shows the results obtained for each iteration.

_{1}, θ

_{2}, and P, which result in minimum and maximum lift force configurations for this case.

#### 3.3. Case III—Three-Row Landscape Configuration

_{1}, θ

_{2}, and P, which resulted in minimum and maximum lift force configurations for this case.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- ReferencesPing, Y.; Yifan, Z.; Peng, W. Rooftop photovoltaic potential assessment: A framework to integrate technological, economic, environmental and social. Renew. Energy
**2019**, 149, 101016. [Google Scholar] - O’Brien, C.; Banks, D. Wind Load Analysis for Commercial Roof-Mounted Arrays. SolarPro
**2012**, 5, 72–92. [Google Scholar] - Radu, A.; Axinte, E.; Theohari, C. Steady Wind Pressures on Solar Collectors on Flat-roofed Buildings. J. Wind. Eng. Ind. Aerodyn.
**1986**, 23, 249–258. [Google Scholar] [CrossRef] - Peterka, J.A.; Bienkiewicz, B.; Hosoya, N.; Cermak, J.E. Performance Heliostat mean wind load reduction. Energy
**1987**, 12, 261–267. [Google Scholar] [CrossRef] - Maffei, J.; Telleen, K.; Ward, R.; Kopp, G.A.; Schellenberg, A. Wind Design Practice and Recommendations for Solar Arrays on Low-Slope Roofs. J. Struct. Eng.
**2014**, 140, 04013040. [Google Scholar] [CrossRef] - Chou, C.-C.; Chung, P.-H.; Yang, R.-Y. Wind Loads on a Solar Panel at High Tilt Angles. Appl. Sci.
**2019**, 9, 1594. [Google Scholar] [CrossRef] [Green Version] - Ginger, J.D.; Bodhinayake, G.G.; Ingham, S. Wind Loads for Designing Ground-Mounted Solar-Panel Arrays. Aust. J. Struct. Eng.
**2019**, 20, 204–218. [Google Scholar] [CrossRef] - Wang, J.; Van Phuc, P.; Yang, Q.; Tamura, Y. LES Study of Wind Pressure and Flow Characteristics of Flat-Roof-Mounted Solar Arrays. J. Wind. Eng. Ind. Aerodyn.
**2020**, 198, 104096. [Google Scholar] [CrossRef] - Marwood, R.; Wood, C.J. Conical vortex movement and its effect on roof pressures. J. Wind. Eng. Ind. Aerodyn.
**1997**, 69, 589–595. [Google Scholar] [CrossRef] - Aly, A.M.; Bitsuamlak, G. Wind-Induced Pressures on Solar PanelsMounted on Residential Homes. J. Archit. Eng.
**2014**, 20, 04013003. [Google Scholar] [CrossRef] - Erwin, J.; Bitsuamlak, G.; Chowdhury, A.G.; Barkaszi, S.; Gamble, S. Full Scale and Wind Tunnel Testing of a Photovoltaic Panel Mounted on Residential Roofs. Adv. Hurric. Eng.
**2013**, 471–482. [Google Scholar] - Geurts, C.P.W.; Bentum, C.A.V. Wind loads on solar energy roofs. Heron J.
**2007**, 52, 201–222. [Google Scholar] - Shademan, M.; Hangan, H. Wind Loading on Solar Panels at Different Azimuthal and Inclination Angles. In Proceedings of the the Fifth International Symposium on Computational Wind Engineering, Chapel Hill, CA, USA, 23–27 May 2010. [Google Scholar]
- Warsido, W.P.; Bitsuamlak, G.T.; Barata, J.; Chowdhury, A.G. Influence of Spacing Parameters on the Wind Loading of Solar Array. J. Fluids Struct.
**2014**, 48, 295–315. [Google Scholar] [CrossRef] - Ghosh, D.; Behera, S.; Mittal, A.K. Numerical Simulation of Wind Effect on a Rooftop Solar Array. J. Energy Power Sources
**2015**, 2, 317–322. [Google Scholar] - Nagadurga, T.; Narasimham, P.V.R.L.; Vakula, V.S.; Devarapalli, R.; Márquez, F.P.G. Enhancing Global Maximum Power Point of Solar Photovoltaic Strings under Partial Shading Conditions Using Chimp Optimization Algorithm. Energies
**2021**, 14, 4086. [Google Scholar] [CrossRef] - VATANDAŞ, E.; ÖZKOL, İ.; NASc, S. Implementation of Genetic Algorithm on The Design of a Transonic Wing by Using Parallel Processing. Signal Process. ICSP
**2004**, 2004, 17–19. [Google Scholar] - Dina, A.; Danaila, S.; Pricop, M.-V.; Bunescu, I. Using Genetic Algorithms to Optimize Airfoils in Incompressible Regime. INCAS Bulletin
**2019**, 11, 79–90. [Google Scholar] [CrossRef] - Doyle, J.B.; Hartfield, R.J. Aerodynamic Optimization for Freight Trucks using a Genetic Algorithm and CFD. In Proceedings of the 46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, USA, 7–10 January 2008; pp. 1–20. [Google Scholar]
- Flórez, M.D.; Montoya, D.G.; Grisales, L.A.T.; Paja, C.A.R. PV Array Reconfiguration Based on Genetic Algorithm for Maximum Power Extraction and Energy Impact Analysis. Sustainability
**2022**, 14, 3764. [Google Scholar] [CrossRef] - Meerimatha, G.; Rao, B.L. Genetic algorithm based PV array reconfiguration for improving power output under partial shadings. Int. J. Renew. Energy Res.
**2020**, 10, 803–812. [Google Scholar] - Rajan, N.; Kulkarni, D.; Dhanalakshmi, B.; Natarajan, R. Solar PV array reconfiguration using the concept of Standard deviation and Genetic Algorithm. Energy Procedia
**2017**, 117, 1062–1069. [Google Scholar] [CrossRef] - Akram, M.T.; Kim, M.-H. CFD Analysis and Shape Optimization of Airfoils Using Class Shape Transformation and Genetic Algorithm—Part I. Appl. Sci.
**2021**, 11, 3791. [Google Scholar] [CrossRef] - Sharma, D.K.; Verma, V.; Sharma, S. Performance Ratio and Losses Analysis of 1MW Grid-Connected Photovoltaic System. In Impending Power Demand and Innovative Energy Paths; Excellent Publishing House: New Delhi, India, 2014; ISBN 978-93-83083-84-8. [Google Scholar]
- Decker, B.; Jahn, U. Performance of 170 Grid Connected PV Plants in Northern Germany—Analysis of Yields and Optimization Potentials. Sol. Energy
**1997**, 59, 127–133. [Google Scholar] [CrossRef] - Reich, N.H.; Mueller, B.; Armbruster, A.; Van Sark, W.G.; Kiefer, K.; Reise, C. Performance Ratio Revisited: Is PR> 90% Realistic? Prog. Photovolt. Res. Appl.
**2012**, 20, 717–726. [Google Scholar] [CrossRef] - Ghabuzyan, L.; Pan, K.; Fatahi, A.; Kuo, J.; Baldus-Jeursen, C. Thermal Effects on Photovoltaic Array Performance: Experimentation, Modeling, and Simulation. Appl. Sci.
**2021**, 11, 1460. [Google Scholar] [CrossRef] - Manual, U.D.F.; ANSYS Fluent 12.0. Theory Guide. 2009. Available online: https://www.afs.enea.it/project/neptunius/docs/fluent/html/th/main_pre.htm (accessed on 20 November 2022).

**Figure 6.**Case I—CFD simulation results for optimum configuration (

**a**) velocity contour; (

**b**) pressure contour.

**Figure 9.**Case II—CFD simulation results for optimum configuration (

**a**) velocity contour; (

**b**) pressure contour.

**Figure 12.**Case III—CFD simulation results for optimum configuration (

**a**) velocity contour; (

**b**) pressure contour.

Design Parameter | Details |
---|---|

System Location Met Data | Lahore, Pakistan MeteoNorm 7.1 Station |

Solar PV Module | Trina Solar 445 W, 34 V, Si-mono, TSM-445DE17M |

Solar Inverter | Sungrow 5.0 kW, SG5KTL-EC, 200–900 V, TL, 50 HZ |

Shading 3D fields | 2 Tables, total rough area, 54 m^{2} |

PV modules: | 2 strings of 12 modules in series, 24 total |

Inverters (5.00 kWa) | 1 MPPT input, Total of 10 kWa |

Sr. No. | Mesh Type | No. of Nodes | Coefficient of Lift |
---|---|---|---|

1 | Coarse | 0.92 × 10^{4} | 2.0492534 |

2 | Medium | 1.2 × 10^{4} | 2.2486291 |

3 | Fine | 1.7 × 10^{4} | 2.2467382 |

RESULTS | Lift Force 1 (N) | Parameters | ||
---|---|---|---|---|

θ_{1} (Degrees) | θ_{2} (Degrees) | P (m) | ||

Maximum lift | 741.5 | 16 | 30 | 1.5 |

Minimum lift | 250.4 | 18 | 15 | 1.5 |

Results | Lift Force 1 (N) | Parameters | ||
---|---|---|---|---|

θ_{1} (Degrees) | θ_{2} (Degrees) | P (m) | ||

Maximum lift | 4903.1 | 25 | 30 | 3.0 |

Minimum lift | 2045.7 | 15 | 15 | 2.4 |

Results | Lift Force 1 (N) | Parameters | ||
---|---|---|---|---|

θ_{1} (Degrees) | θ_{2}(Degrees) | P (m) | ||

Maximum lift | 11,876.7 | 24 | 30 | 4.4 |

Minimum lift | 5507.6 | 15 | 15 | 3.7 |

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**MDPI and ACS Style**

Khan, A.Y.; Ahmad, Z.; Sultan, T.; Alshahrani, S.; Hayat, K.; Imran, M.
Optimization of Photovoltaic Panel Array Configurations to Reduce Lift Force Using Genetic Algorithm and CFD. *Energies* **2022**, *15*, 9580.
https://doi.org/10.3390/en15249580

**AMA Style**

Khan AY, Ahmad Z, Sultan T, Alshahrani S, Hayat K, Imran M.
Optimization of Photovoltaic Panel Array Configurations to Reduce Lift Force Using Genetic Algorithm and CFD. *Energies*. 2022; 15(24):9580.
https://doi.org/10.3390/en15249580

**Chicago/Turabian Style**

Khan, Asfand Y., Zeshan Ahmad, Tipu Sultan, Saad Alshahrani, Khazar Hayat, and Muhammad Imran.
2022. "Optimization of Photovoltaic Panel Array Configurations to Reduce Lift Force Using Genetic Algorithm and CFD" *Energies* 15, no. 24: 9580.
https://doi.org/10.3390/en15249580