Optimization of Fixed and Seasonal Tilt Angles for Photovoltaic Systems under Clear-Sky Conditions

Shivan Shkur Mahmood; Alaa M. Abdulrahman; Ghamgeen I. Rashed

doi:10.24017/science.2026.2.6

Authors

Shivan Shkur Mahmood Department of Electrical Engineering, College of Engineering, University of Sulaimani, Sulaymaniyah, Iraq. Author https://orcid.org/0009-0005-9179-9173
Alaa M. Abdulrahman Department of Electrical Engineering, College of Engineering, University of Sulaimani, Sulaymaniyah, Iraq. Author https://orcid.org/0000-0002-4361-7292
Ghamgeen I. Rashed School of Electrical Engineering and its Automation, Wuhan University, Wuhan, China. Author

DOI:

https://doi.org/10.24017/science.2026.2.6

Keywords:

Photovoltaic systems, Solar energy, Tilt-angle optimization, Clear-sky conditions, Renewable energy

Abstract

This study investigates the optimal fixed and seasonal tilt angles for photovoltaic systems in Sulaymaniyah, Iraq, under clear-sky conditions. A mathematical model based on solar geometry was developed to estimate annual solar irradiation, and the generalized reduced gradient nonlinear optimization method was used to determine the optimal fixed and seasonal tilt angles. Annual fixed, biannual, quarterly, and monthly tilt-angle strategies were compared to identify the most suitable approach for maximizing annual solar irradiation. For each strategy, the model simulated the annual irradiation received by the panels and identified the tilt angles that maximized this value. The annual analysis identified a fixed tilt angle of approximately 34° as the optimal year-round setting. A biannual adjustment strategy, using tilt angles of 10° in summer and 55° in winter, provided a practical and efficient alternative to conventional fixed installations. Its annual irradiation was comparable to that achieved through quarterly and monthly adjustments, with differences of only approximately 1–2%. The additional irradiation gained through more frequent adjustments was therefore relatively small compared with the biannual approach. These results indicate that two adjustments per year offer a practical balance between irradiation gains and adjustment frequency under the modeled conditions. The findings demonstrate the value of selecting appropriate tilt angles to maximize the annual solar irradiation received by photovoltaic panels and provide practical guidance for the design and optimization of photovoltaic systems in Iraq and regions with similar climates.

References

[1] J. A. Duffie and W. A. Beckman, Solar Engineering of Thermal Processes, 4th ed. Hoboken, NJ, USA: Wiley, 2013, doi: 10.1002/9781118671603. DOI: https://doi.org/10.1002/9781118671603

[2] H. Mousazadeh, A. Keyhani, H. Mobli, A. Javadi, A. Sharifi, and K. Abrinia, “A review of principle and sun-tracking methods for maximizing solar systems output,” Renewable and Sustainable Energy Reviews, vol. 13, no. 8, pp. 1800–1818, Oct. 2009, doi: 10.1016/j.rser.2009.01.022. DOI: https://doi.org/10.1016/j.rser.2009.01.022

[3] S. Rehman and I. M. El-Amin, “Study of a solar PV–diesel–battery hybrid power system for a remotely located popula-tion near Rafha, Saudi Arabia,” Energy, vol. 35, no. 12, pp. 4986–4995, 2010, doi: 10.1016/j.energy.2010.08.025. DOI: https://doi.org/10.1016/j.energy.2010.08.025

[4] International Renewable Energy Agency, Renewable Power: Sharply Falling Generation Costs in 2017. Abu Dhabi, UAE: IRENA, 2017.

[5] W. A. M. Al-Shohani, A. J. Khaleel, H. J. Dakkama, and A. Q. Ahmed, “Optimum tilt angle of the photovoltaic modules in Baghdad, Iraq,” Applied Solar Energy, vol. 58, no. 4, pp. 517–525, 2022, doi: 10.3103/S0003701X22040028. DOI: https://doi.org/10.3103/S0003701X22040028

[6] S. A. Kadhim, M. K. S. Al-Ghezi, and W. Y. Shehab, “Optimum orientation of non-tracking solar applications in Bagh-dad City,” International Journal of Heat and Technology, vol. 41, no. 1, pp. 125–134, 2023, doi: 10.18280/ijht.410113. DOI: https://doi.org/10.18280/ijht.410113

[7] A. A. K. Al-Waeli, K. A. Al-Asadi, and M. M. Fazleena, “The impact of Iraq climate condition on the use of solar energy applications in Iraq: A review,” International Journal of Science and Engineering Investigations, vol. 6, pp. 64–73, 2017.

[8] A. George and R. Anto, “Analytical and experimental analysis of optimal tilt angle of solar photovoltaic systems,” In-ternational Conference on Green Technologies, Coimbatore, India, Dec. 2012, pp. 234–239, doi: 10.1109/ICGT.2012.6477978. DOI: https://doi.org/10.1109/ICGT.2012.6477978

[9] M. Benghanem, “Optimization of tilt angle for solar panel: Case study for Madinah, Saudi Arabia,” Applied Energy, vol. 88, no. 4, pp. 1427–1433, Apr. 2011, doi: 10.1016/j.apenergy.2010.10.001. DOI: https://doi.org/10.1016/j.apenergy.2010.10.001

[10] K. Skeiker, “Optimum tilt angle for solar collectors used in Syria,” Energy Conversion and Management, vol. 50, no. 9, pp. 2439–2443, Sep. 2009, doi: 10.1016/j.enconman.2009.05.031. DOI: https://doi.org/10.1016/j.enconman.2009.05.031

[11] I. Daut, M. Irwanto, Y. M. Irwan, N. Gomesh, and N. S. Ahmad, “Clear sky global solar irradiance on tilt angles of pho-tovoltaic module in Perlis, Northern Malaysia,” in 2011 International Conference on Electrical, Control and Computer Engi-neering (InECCE), Kuantan, Malaysia, 2011, pp. 445–450, doi: 10.1109/INECCE.2011.5953923. DOI: https://doi.org/10.1109/INECCE.2011.5953923

[12] A. Zurfi, A. A. R. Altahir, and A. Ibrahim, “Investigation of optimal tilt, orientation, and tracking of a solar PV system in Iraq,” International Journal of Power Electronics and Drive Systems, vol. 16, no. 3, pp. 1914–1925, 2025, doi: 10.11591/ijpeds. v16.i3. pp1914-1925. DOI: https://doi.org/10.11591/ijpeds.v16.i3.pp1914-1925

[13] H. M. Taha and S. M. Hameed, “Optimization of tilt angle of a PV system to get maximum generated power: A case study,” Kurdistan Journal of Applied Research, vol. 5, no. 2, pp. 71–81, 2020, doi: 10.24017/science.2020.2.7. DOI: https://doi.org/10.24017/science.2020.2.7

[14] F. A. Ali, "Optimum tilt angle of photovoltaic panels for some Iraq cities," Journal of University of Babylon for Engineering Sciences, vol. 26, no. 1, pp. 155–163, 2018. [Online]. Available: https://www.journalofbabylon.com/index.php/JUBES/article/view/1191.

[15] M. Guo, Z. Zang, N. Gao, T. Liang, and T. Zhu, “Optimal tilt angle and orientation of photovoltaic modules using har-mony search algorithm in different climates of China,” Applied Sciences, vol. 7, no. 10, Art. no. 1028, 2017, doi: 10.3390/app7101028. DOI: https://doi.org/10.3390/app7101028

[16] S. A. Al-Shammari, A. A. Karamallah, and S. Aljabair, “Optimization of tilt angle and experimental study of standalone PV system for clean energy home supply in Baghdad,” FME Transactions, vol. 49, no. 3, pp. 664–672, 2021, doi: 10.5937/fme2103664A. DOI: https://doi.org/10.5937/fme2103664A

[17] I. Shariah, M. A. Al-Akhras, and I. A. Al-Omari, “Optimizing the tilt angle of solar collectors,” Renewable Energy, vol. 26, no. 4, pp. 587–598, 2002, doi: 10.1016/S0960-1481(01)00106-9. DOI: https://doi.org/10.1016/S0960-1481(01)00106-9

[18] T. O. Kaddoura, M. A. M. Ramli, and Y. A. Al-Turki, “On the estimation of the optimum tilt angle of PV panel in Saudi Arabia,” Renewable and Sustainable Energy Reviews, vol. 65, pp. 626–634, 2016, doi: 10.1016/j.rser.2016.07.032. DOI: https://doi.org/10.1016/j.rser.2016.07.032

[19] A. A. Ashetehe, B. B. Gessesse, and F. Shewarega, “Development of optimal tilt angle models of a photovoltaic module for maximum power production: Ethiopia,” International Journal of Photoenergy, vol. 2022, Art. no. 8729570, 2022, doi: 10.1155/2022/8729570. DOI: https://doi.org/10.1155/2022/8729570

[20] R. Melhem and Y. Shaker, “Optimum tilt angle and solar radiation of photovoltaic modules for Gulf Collaboration Council countries,” International Journal of Energy Research, vol. 2023, Art. no. 8381696, 2023, doi: 10.1155/2023/8381696. DOI: https://doi.org/10.1155/2023/8381696

[21] M. Tamoor, A. R. Bhatti, M. Farhan, A. Rasool, and A. Sherefa, “Optimizing tilt angle of PV modules for different loca-tions using isotropic and anisotropic models to maximize power output,” Scientific Reports, vol. 14, Art. no. 30197, 2024, doi: 10.1038/s41598-024-81826-9. DOI: https://doi.org/10.1038/s41598-024-81826-9

[22] Y. Liu et al., “Spatial estimation of the optimum PV tilt angles in China by incorporating ground with satellite data,” Renewable Energy, vol. 189, pp. 1249–1258, 2022, doi: 10.1016/j.renene.2022.03.072. DOI: https://doi.org/10.1016/j.renene.2022.03.072

[23] A. K. Abdelaal and A. El-Fergany, “Estimation of optimal tilt angles for photovoltaic panels in Egypt with experimental verifications,” Scientific Reports, vol. 13, Art. no. 3268, 2023, doi: 10.1038/s41598-023-30375-8. DOI: https://doi.org/10.1038/s41598-023-30375-8

[24] N. Lu and J. Qin, “Optimization of tilt angle for PV in China with long-term hourly surface solar radiation,” Renewable Energy, vol. 229, Art. no. 120741, 2024, doi: 10.1016/j.renene.2024.120741. DOI: https://doi.org/10.1016/j.renene.2024.120741

[25] A. A. Teyabeen and F. Mohamed, “Estimation of the optimum tilt angle of solar PV panels to maximize incident solar radiation in Libya,” Energies, vol. 17, no. 23, Art. no. 5891, 2024, doi: 10.3390/en17235891. DOI: https://doi.org/10.3390/en17235891

[26] Z. Ibrahim and M. Aljanabi, “Influence of tilt angle on PV output for solar energy optimization in Iraq,” Salud, Ciencia y Tecnología – Serie de Conferencias, vol. 3, Art. no. 871, 2024, doi: 10.56294/sctconf2024871. DOI: https://doi.org/10.56294/sctconf2024871

[27] H. U. Manzoor, S. M. Aaqib, T. Manzoor, F. Azeem, M. W. Ashraf, and S. Manzoor, “Effect of optimized tilt angle of PV modules on solar irradiance for residential and commercial buildings in different cities of Pakistan: Simulation-based study,” Energy Science & Engineering, vol. 13, no. 4, pp. 1831–1845, 2025, doi: 10.1002/ese3.70004. DOI: https://doi.org/10.1002/ese3.70004

[28] E. Coffari, “The sun and the celestial vault,” in Solar Energy Engineering, A. A. M. Sayigh, Ed. New York, NY, USA: Aca-demic Press, 1977, pp. 5-36. DOI: https://doi.org/10.1016/B978-0-12-620850-4.50008-9

[29] R. A. Messenger and A. Abtahi, Photovoltaic Systems Engineering, 4th ed. Boca Raton, FL, USA: CRC Press, 2017.

[30] H. Muslim, “Solar tilt angle optimization of PV systems for different case studies,” EAI Endorsed Transactions on Ener-gy Web, vol. 6, pp. 1–8, 2019, doi: 10.4108/eai.13-7-2018.157038. DOI: https://doi.org/10.4108/eai.13-7-2018.157038

[31] A. K. S. Al-Sayyab and M. K. Taher, “Optimum tilted angle of photovoltaic cell located in northern Iraq cities to get max-imum generated electric power,” in Proc. National Renewable Energies Conference and Their Applications, 2013. Accessed: Aug. 30, 2026. [Online]. Available: https://www.researchgate.net/publication/313726087.

[32] European Commission, Joint Research Centre, “Photovoltaic Geographical Information System (PVGIS), version 5.3,” PVGIS-SARAH3 solar radiation database. Accessed: Aug. 16, 2026. [Online]. Available: https://re.jrc.ec.europa.eu/pvg_tools/en/tools.html.