Optimizing heliostat solar power plant field design: using the golden ratio of the Fibonacci sequence
Corresponding Author(s) : Ahmad Hajinezhad
Future Energy,
Vol. 4 No. 4 (2025): November 2025 Issue
Abstract
Considering the importance of achieving sustainable development and using the potential of clean and renewable energy resources, such as solar energy with the highest efficiency, this research aims to optimize the design of the Heliostat solar power plant field with a central tower using the golden ratio of the Fibonacci sequence and investigate the effect of this ratio on the designed field results. The reference pattern used in this paper is the radial staggered pattern. The field under study is located in Naypyitaw (the capital of Myanmar). In this paper, with the approach of optimizing the heliostat field design, using the equations available in the design of solar power plants, the results of the new field pattern calculated using the golden ratio are investigated. The results of this research show that using the golden ratio increases the area required for the placement of heliostats by 27%, while increasing the optical efficiency by 77%. Also, in this case, it will be possible to increase the number of heliostats by 11% without increasing the current area.
Keywords
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- Jisoo Shim, Doosam Song, Unveiling energy inefficiencies: A study on building energy consumption in single-person households, Renewable and Sustainable Energy Reviews, Volume 214, 2025, doi: https://doi.org/10.1016/j.rser.2025.115546.
- S. F. Moosavian, A. Hajinezhad, R. Fattahi, and A. Shahee, "Evaluating the effect of using nanofluids on the parabolic trough collector's performance," Energy Science & Engineering, vol. 11, no. 10, pp. 3512–3535, 2023.
- Guixian Tian, Irfan Khan, Impact of energy end-uses and efficiency indicators on the environmental policy stringency index, Energy, Volume 326, 2025, 136232, doi: ttps://doi.org/10.1016/j.energy.2025.136232.
- K. R. Abbasi, M. Shahbaz, J. Zhang, M. Irfan, and R. Alvarado, "Analyze the environmental sustainability factors of China: The role of fossil fuel energy and renewable energy," Renewable Energy, vol. 187, pp. 390–402, 2022.
- H. H. Pourasl, R. V. Barenji, and V. M. Khojastehnezhad, "Solar energy status in the world: A comprehensive review," Energy Reports, vol. 10, pp. 3474–3493, 2023.
- S. F. Moosavian, N. Mirzaei, A. Hajinezhad, H. Yousefi, R. Fattahi, and M. R. Golshadi, "Thermodynamic, Economic, and Environmental Evaluation of Municipal Waste Incinerator to Produce Power and Fresh Water," Energy Science & Engineering, 2025. doi: https://doi.org/10.1002/ese3.70263
- T. Falope, L. Lao, D. Hanak, and D. Huo, "Hybrid energy system integration and management for solar energy: A review," Energy Conversion and Management: X, p. 100527, 2024.
- M. Arun, Susmita Samal, Debabrata Barik, Sreejesh S.R. Chandran, Kapura Tudu, Seepana Praveenkumar, Integration of energy storage systems and grid modernization for reliable urban power management toward future energy sustainability, Journal of Energy Storage, Volume 114, Part B, 2025, https://doi.org/10.1016/j.est.2025.115830.
- A. Kumler et al., "Potential effects of climate change and solar radiation modification on renewable energy resources," Renewable and Sustainable Energy Reviews, vol. 207, p. 114934, 2025.
- R. M. Elavarasan, M. Nadarajah, and G. Shafiullah, "Multi-criteria decision analysis of clean energy technologies for envisioning sustainable development goal 7 in Australia: Is solar energy a game-changer?," Energy conversion and management, vol. 321, p. 119007, 2024.
- M. Cellura, L. Q. Luu, F. Guarino, and S. Longo, "A review on life cycle environmental impacts of emerging solar cells," Science of The Total Environment, vol. 908, p. 168019, 2024.
- Ugur Korkut Pata, Umit Bulut, Daniel Balsalobre-Lorente, Jana Chovancová, Does income growth affect renewable energy or carbon emissions first? A Fourier-based analysis for renewable and fossil energies, Energy Strategy Reviews, Volume 57, 2025, https://doi.org/10.1016/j.esr.2024.101615.
- D. C. Nath et al., "Internet of Things integrated with solar energy applications: a state-of-the-art review," Environment, Development and Sustainability, vol. 26, no. 10, pp. 24597–24652, 2024.
- G. Li, M. Li, R. Taylor, Y. Hao, G. Besagni, and C. Markides, "Solar energy utilisation: Current status and roll-out potential," Applied Thermal Engineering, vol. 209, p. 118285, 2022.
- José L. Torres-Madroñero, Julian D. Osorio, César Nieto-Londoño, Juan C. Ordonez, Impact of molten salt inflow on the temperature distribution in thermal energy storage tanks at startup for central receiver concentrating solar power plants, Journal of Energy Storage, Volume 117, 2025, https://doi.org/10.1016/j.est.2025.116069.
- A. N. Yerudkar, D. Kumar, V. H. Dalvi, S. V. Panse, V. R. Gaval, and J. B. Joshi, "Economically feasible solutions in concentrating solar power technology specifically for heliostats–A review," Renewable and Sustainable Energy Reviews, vol. 189, p. 113825, 2024.
- L. A. Omeiza et al., "Application of solar thermal collectors for energy consumption in public buildings–An updated technical review," Journal of Engineering Research, 2023.
- S. Wang et al., "Co-optimisation of the heliostat field and receiver for concentrated solar power plants," Applied Energy, vol. 348, p. 121513, 2023.
- C. J. Noone, M. Torrilhon, and A. Mitsos, "Heliostat field optimization: A new computationally efficient model and biomimetic layout," Solar Energy, vol. 86, no. 2, pp. 792–803, 2012/02/01/ 2012, doi: https://doi.org/10.1016/j.solener.2011.12.007.
- S. M. Besarati and D. Yogi Goswami, "A computationally efficient method for the design of the heliostat field for solar power tower plant," Renewable Energy, vol. 69, pp. 226–232, 2014/09/01/ 2014, doi: https://doi.org/10.1016/j.renene.2014.03.043.
- A. Mutuberria, J. Pascual, M. Guisado, and F. Mallor, "Comparison of heliostat field layout design methodologies and impact on power plant efficiency," Energy Procedia, vol. 69, pp. 1360–1370, 2015.
- P. Richter, D. Laukamp, L. Gerdes, M. Frank, and a. E. Abrah´am, "Heliostat Field Layout Optimization
- with Evolutionary Algorithms," Artificial Intelligence, p. 13, 2016. https://doi.org/10.29007/7p6t
- Deng et al., "Rose pattern for heliostat field optimization with a dynamic speciation-based mutation differential evolution," Int. J. Energy Res, 2020. https://doi.org/10.1002/er.5048
- Q. Xie, Z. Guo, D. Liu, Z. Chen, Z. Shen, and X. Wang, "Optimization of heliostat field distribution based on improved Gray Wolf optimization algorithm," Renewable Energy, vol. 176, pp. 447–458, 2021/10/01/ 2021, doi: https://doi.org/10.1016/j.renene.2021.05.058.
- E. Ghirardi, G. Brumana, G. Franchini, and A. Perdichizzi, "Heliostat layout optimization for load-following solar tower plants," Renewable Energy, vol. 168, pp. 393–405, 2021/05/01/ 2021, doi: https://doi.org/10.1016/j.renene.2020.12.066.
- K. Ali and S. Jifeng, "Research on modeling simulation and optimal layout of heliostat field optical efficiency for Solar Power Tower Plant," Applied Solar Energy, vol. 59, no. 6, pp. 957–977, 2023.
- S. Babatunde and O. Abiola, "The Golden Ratio and Fibonacci Sequence in Nature." https://www.researchgate.net/profile/Abiola-Oyetoro/publication/378125611_The_Golden_Ratio_and_Fibonacci_Sequence_in_Nature/links/65c7cd6e34bbff5ba7fb8143/The-Golden-Ratio-and-Fibonacci-Sequence-in-Nature.pdf
- Benguar, Alliah Nicole D., et al. "Golden ratio applied in the orientation of solar cells in a golden spiral solar panel." International Journal of Development Research 8.05 (2018): 20416-20420.
- T. Nishiwaki and T. Yachi, "Arrangement of Fibonacci number photovoltaic modules for power generation woods," in 2014 International Conference on Renewable Energy Research and Application (ICRERA), 2014: IEEE, pp. 142–146.
- H. Habibi, M. Zoghi, A. Chitsaz, K. Javaherdeh, M. Ayazpour, and E. Bellos, "Working fluid selection for regenerative supercritical Brayton cycle combined with bottoming ORC driven by molten salt solar power tower using energy–exergy analysis," Sustainable Energy Technologies and Assessments, vol. 39, p. 100699, 2020/06/01/ 2020, doi: https://doi.org/10.1016/j.seta.2020.100699.
- B. Panbechi, A. Hajinezhad, S. F. Moosavian, and R. Fattahi, "Enhancing the enviro-economic viability of biogas-solar hybrid systems: Strategies for sustainable energy development in Iran," Energy Strategy Reviews, vol. 58, p. 101671, 2025/03/01/ 2025, doi: https://doi.org/10.1016/j.esr.2025.101671.
- Hamid Hawi Ogaili, Shahram Khalilarya, Ata Chitsaz, Parisa Mojaver, Energy, exergy, and economic performance analysis of integrated parabolic trough collector with organic rankine cycle and ejector refrigeration cycle, Energy Conversion and Management: X, Volume 25, 2025, https://doi.org/10.1016/j.ecmx.2024.100843.
- A. Herez, H. El Hage, T. Lemenand, M. Ramadan, and M. Khaled, "Review on photovoltaic/thermal hybrid solar collectors: Classifications, applications and new systems," Solar Energy, vol. 207, pp. 1321–1347, 2020.
- Andi S. Ekariansyah, Martin Muwonge, M. Rifqi Saefuttamam, Yophie Dikaimana, Nasruddin, Energy, exergy, and exergy-economic optimization of a multigeneration system driven by geothermal primary heat source using multi-objective genetic algorithm (MOGA), Energy, Volume 330, 2025, https://doi.org/10.1016/j.energy.2025.136653.
- J. B. Blackmon, "Heliostat size optimization for central receiver solar power plants," in Concentrating solar power technology: Elsevier, 2021, pp. 585–631.
- J. Carballo et al., "Reinforcement learning for heliostat aiming: Improving the performance of Solar Tower plants," Applied Energy, vol. 377, p. 124574, 2025.
- M. Maiga, K. E. N’Tsoukpoe, A. Gomna, and Y. K. Fiagbe, "Sources of solar tracking errors and correction strategies for heliostats," Renewable and Sustainable Energy Reviews, vol. 203, p. 114770, 2024.
- C. B. Anderson, G. Picotti, M. E. Cholette, B. Leslie, T. A. Steinberg, and G. Manzolini, "Heliostat-field soiling predictions and cleaning resource optimization for solar tower plants," Applied Energy, vol. 352, p. 121963, 2023.
- J. Baigorri, F. Zaversky, and D. Astrain, "Massive grid-scale energy storage for next-generation concentrated solar power: A review of the potential emerging concepts," Renewable and Sustainable Energy Reviews, vol. 185, p. 113633, 2023.
- A. H. Alami et al., "Concentrating solar power (CSP) technologies: Status and analysis," International Journal of Thermofluids, vol. 18, p. 100340, 2023.
- F. J. Collado and J. Guallar, "Campo: Generation of regular heliostat fields," Renewable energy, vol. 46, pp. 49–59, 2012.
- M. Saghafifar, "Thermo-economic optimization of hybrid combined power cycles using heliostat field collector," 2016. http://hdl.handle.net/11073/8103.
- M. Atif and F. A. Al‐Sulaiman, "Development of a mathematical model for optimizing a heliostat field layout using differential evolution method," International Journal of Energy Research, vol. 39, no. 9, pp. 1241–1255, 2015.
- C. Shen, Y.-L. He, Y.-W. Liu, and W.-Q. Tao, "Modelling and simulation of solar radiation data processing with Simulink," Simulation Modelling Practice and Theory, vol. 16, no. 7, pp. 721–735, 2008.
- K. Jazayeri, S. Uysal, and M. Jazayeri, "MATLAB/simulink based simulation of solar incidence angle and the sun's position in the sky with respect to observation points on the Earth," in 2013 International Conference on Renewable Energy Research and Applications (ICRERA), 2013: IEEE, pp. 173–177.
- Y. Yao, Y. Hu, and S. Gao, "Heliostat field layout methodology in central receiver systems based on efficiency-related distribution," Solar energy, vol. 117, pp. 114–124, 2015.
- X. Wei, Z. Lu, Z. Wang, W. Yu, H. Zhang, and Z. Yao, "A new method for the design of the heliostat field layout for solar tower power plant," Renewable Energy, vol. 35, no. 9, pp. 1970–1975, 2010/09/01/ 2010, doi: https://doi.org/10.1016/j.renene.2010.01.026.
References
Jisoo Shim, Doosam Song, Unveiling energy inefficiencies: A study on building energy consumption in single-person households, Renewable and Sustainable Energy Reviews, Volume 214, 2025, doi: https://doi.org/10.1016/j.rser.2025.115546.
S. F. Moosavian, A. Hajinezhad, R. Fattahi, and A. Shahee, "Evaluating the effect of using nanofluids on the parabolic trough collector's performance," Energy Science & Engineering, vol. 11, no. 10, pp. 3512–3535, 2023.
Guixian Tian, Irfan Khan, Impact of energy end-uses and efficiency indicators on the environmental policy stringency index, Energy, Volume 326, 2025, 136232, doi: ttps://doi.org/10.1016/j.energy.2025.136232.
K. R. Abbasi, M. Shahbaz, J. Zhang, M. Irfan, and R. Alvarado, "Analyze the environmental sustainability factors of China: The role of fossil fuel energy and renewable energy," Renewable Energy, vol. 187, pp. 390–402, 2022.
H. H. Pourasl, R. V. Barenji, and V. M. Khojastehnezhad, "Solar energy status in the world: A comprehensive review," Energy Reports, vol. 10, pp. 3474–3493, 2023.
S. F. Moosavian, N. Mirzaei, A. Hajinezhad, H. Yousefi, R. Fattahi, and M. R. Golshadi, "Thermodynamic, Economic, and Environmental Evaluation of Municipal Waste Incinerator to Produce Power and Fresh Water," Energy Science & Engineering, 2025. doi: https://doi.org/10.1002/ese3.70263
T. Falope, L. Lao, D. Hanak, and D. Huo, "Hybrid energy system integration and management for solar energy: A review," Energy Conversion and Management: X, p. 100527, 2024.
M. Arun, Susmita Samal, Debabrata Barik, Sreejesh S.R. Chandran, Kapura Tudu, Seepana Praveenkumar, Integration of energy storage systems and grid modernization for reliable urban power management toward future energy sustainability, Journal of Energy Storage, Volume 114, Part B, 2025, https://doi.org/10.1016/j.est.2025.115830.
A. Kumler et al., "Potential effects of climate change and solar radiation modification on renewable energy resources," Renewable and Sustainable Energy Reviews, vol. 207, p. 114934, 2025.
R. M. Elavarasan, M. Nadarajah, and G. Shafiullah, "Multi-criteria decision analysis of clean energy technologies for envisioning sustainable development goal 7 in Australia: Is solar energy a game-changer?," Energy conversion and management, vol. 321, p. 119007, 2024.
M. Cellura, L. Q. Luu, F. Guarino, and S. Longo, "A review on life cycle environmental impacts of emerging solar cells," Science of The Total Environment, vol. 908, p. 168019, 2024.
Ugur Korkut Pata, Umit Bulut, Daniel Balsalobre-Lorente, Jana Chovancová, Does income growth affect renewable energy or carbon emissions first? A Fourier-based analysis for renewable and fossil energies, Energy Strategy Reviews, Volume 57, 2025, https://doi.org/10.1016/j.esr.2024.101615.
D. C. Nath et al., "Internet of Things integrated with solar energy applications: a state-of-the-art review," Environment, Development and Sustainability, vol. 26, no. 10, pp. 24597–24652, 2024.
G. Li, M. Li, R. Taylor, Y. Hao, G. Besagni, and C. Markides, "Solar energy utilisation: Current status and roll-out potential," Applied Thermal Engineering, vol. 209, p. 118285, 2022.
José L. Torres-Madroñero, Julian D. Osorio, César Nieto-Londoño, Juan C. Ordonez, Impact of molten salt inflow on the temperature distribution in thermal energy storage tanks at startup for central receiver concentrating solar power plants, Journal of Energy Storage, Volume 117, 2025, https://doi.org/10.1016/j.est.2025.116069.
A. N. Yerudkar, D. Kumar, V. H. Dalvi, S. V. Panse, V. R. Gaval, and J. B. Joshi, "Economically feasible solutions in concentrating solar power technology specifically for heliostats–A review," Renewable and Sustainable Energy Reviews, vol. 189, p. 113825, 2024.
L. A. Omeiza et al., "Application of solar thermal collectors for energy consumption in public buildings–An updated technical review," Journal of Engineering Research, 2023.
S. Wang et al., "Co-optimisation of the heliostat field and receiver for concentrated solar power plants," Applied Energy, vol. 348, p. 121513, 2023.
C. J. Noone, M. Torrilhon, and A. Mitsos, "Heliostat field optimization: A new computationally efficient model and biomimetic layout," Solar Energy, vol. 86, no. 2, pp. 792–803, 2012/02/01/ 2012, doi: https://doi.org/10.1016/j.solener.2011.12.007.
S. M. Besarati and D. Yogi Goswami, "A computationally efficient method for the design of the heliostat field for solar power tower plant," Renewable Energy, vol. 69, pp. 226–232, 2014/09/01/ 2014, doi: https://doi.org/10.1016/j.renene.2014.03.043.
A. Mutuberria, J. Pascual, M. Guisado, and F. Mallor, "Comparison of heliostat field layout design methodologies and impact on power plant efficiency," Energy Procedia, vol. 69, pp. 1360–1370, 2015.
P. Richter, D. Laukamp, L. Gerdes, M. Frank, and a. E. Abrah´am, "Heliostat Field Layout Optimization
with Evolutionary Algorithms," Artificial Intelligence, p. 13, 2016. https://doi.org/10.29007/7p6t
Deng et al., "Rose pattern for heliostat field optimization with a dynamic speciation-based mutation differential evolution," Int. J. Energy Res, 2020. https://doi.org/10.1002/er.5048
Q. Xie, Z. Guo, D. Liu, Z. Chen, Z. Shen, and X. Wang, "Optimization of heliostat field distribution based on improved Gray Wolf optimization algorithm," Renewable Energy, vol. 176, pp. 447–458, 2021/10/01/ 2021, doi: https://doi.org/10.1016/j.renene.2021.05.058.
E. Ghirardi, G. Brumana, G. Franchini, and A. Perdichizzi, "Heliostat layout optimization for load-following solar tower plants," Renewable Energy, vol. 168, pp. 393–405, 2021/05/01/ 2021, doi: https://doi.org/10.1016/j.renene.2020.12.066.
K. Ali and S. Jifeng, "Research on modeling simulation and optimal layout of heliostat field optical efficiency for Solar Power Tower Plant," Applied Solar Energy, vol. 59, no. 6, pp. 957–977, 2023.
S. Babatunde and O. Abiola, "The Golden Ratio and Fibonacci Sequence in Nature." https://www.researchgate.net/profile/Abiola-Oyetoro/publication/378125611_The_Golden_Ratio_and_Fibonacci_Sequence_in_Nature/links/65c7cd6e34bbff5ba7fb8143/The-Golden-Ratio-and-Fibonacci-Sequence-in-Nature.pdf
Benguar, Alliah Nicole D., et al. "Golden ratio applied in the orientation of solar cells in a golden spiral solar panel." International Journal of Development Research 8.05 (2018): 20416-20420.
T. Nishiwaki and T. Yachi, "Arrangement of Fibonacci number photovoltaic modules for power generation woods," in 2014 International Conference on Renewable Energy Research and Application (ICRERA), 2014: IEEE, pp. 142–146.
H. Habibi, M. Zoghi, A. Chitsaz, K. Javaherdeh, M. Ayazpour, and E. Bellos, "Working fluid selection for regenerative supercritical Brayton cycle combined with bottoming ORC driven by molten salt solar power tower using energy–exergy analysis," Sustainable Energy Technologies and Assessments, vol. 39, p. 100699, 2020/06/01/ 2020, doi: https://doi.org/10.1016/j.seta.2020.100699.
B. Panbechi, A. Hajinezhad, S. F. Moosavian, and R. Fattahi, "Enhancing the enviro-economic viability of biogas-solar hybrid systems: Strategies for sustainable energy development in Iran," Energy Strategy Reviews, vol. 58, p. 101671, 2025/03/01/ 2025, doi: https://doi.org/10.1016/j.esr.2025.101671.
Hamid Hawi Ogaili, Shahram Khalilarya, Ata Chitsaz, Parisa Mojaver, Energy, exergy, and economic performance analysis of integrated parabolic trough collector with organic rankine cycle and ejector refrigeration cycle, Energy Conversion and Management: X, Volume 25, 2025, https://doi.org/10.1016/j.ecmx.2024.100843.
A. Herez, H. El Hage, T. Lemenand, M. Ramadan, and M. Khaled, "Review on photovoltaic/thermal hybrid solar collectors: Classifications, applications and new systems," Solar Energy, vol. 207, pp. 1321–1347, 2020.
Andi S. Ekariansyah, Martin Muwonge, M. Rifqi Saefuttamam, Yophie Dikaimana, Nasruddin, Energy, exergy, and exergy-economic optimization of a multigeneration system driven by geothermal primary heat source using multi-objective genetic algorithm (MOGA), Energy, Volume 330, 2025, https://doi.org/10.1016/j.energy.2025.136653.
J. B. Blackmon, "Heliostat size optimization for central receiver solar power plants," in Concentrating solar power technology: Elsevier, 2021, pp. 585–631.
J. Carballo et al., "Reinforcement learning for heliostat aiming: Improving the performance of Solar Tower plants," Applied Energy, vol. 377, p. 124574, 2025.
M. Maiga, K. E. N’Tsoukpoe, A. Gomna, and Y. K. Fiagbe, "Sources of solar tracking errors and correction strategies for heliostats," Renewable and Sustainable Energy Reviews, vol. 203, p. 114770, 2024.
C. B. Anderson, G. Picotti, M. E. Cholette, B. Leslie, T. A. Steinberg, and G. Manzolini, "Heliostat-field soiling predictions and cleaning resource optimization for solar tower plants," Applied Energy, vol. 352, p. 121963, 2023.
J. Baigorri, F. Zaversky, and D. Astrain, "Massive grid-scale energy storage for next-generation concentrated solar power: A review of the potential emerging concepts," Renewable and Sustainable Energy Reviews, vol. 185, p. 113633, 2023.
A. H. Alami et al., "Concentrating solar power (CSP) technologies: Status and analysis," International Journal of Thermofluids, vol. 18, p. 100340, 2023.
F. J. Collado and J. Guallar, "Campo: Generation of regular heliostat fields," Renewable energy, vol. 46, pp. 49–59, 2012.
M. Saghafifar, "Thermo-economic optimization of hybrid combined power cycles using heliostat field collector," 2016. http://hdl.handle.net/11073/8103.
M. Atif and F. A. Al‐Sulaiman, "Development of a mathematical model for optimizing a heliostat field layout using differential evolution method," International Journal of Energy Research, vol. 39, no. 9, pp. 1241–1255, 2015.
C. Shen, Y.-L. He, Y.-W. Liu, and W.-Q. Tao, "Modelling and simulation of solar radiation data processing with Simulink," Simulation Modelling Practice and Theory, vol. 16, no. 7, pp. 721–735, 2008.
K. Jazayeri, S. Uysal, and M. Jazayeri, "MATLAB/simulink based simulation of solar incidence angle and the sun's position in the sky with respect to observation points on the Earth," in 2013 International Conference on Renewable Energy Research and Applications (ICRERA), 2013: IEEE, pp. 173–177.
Y. Yao, Y. Hu, and S. Gao, "Heliostat field layout methodology in central receiver systems based on efficiency-related distribution," Solar energy, vol. 117, pp. 114–124, 2015.
X. Wei, Z. Lu, Z. Wang, W. Yu, H. Zhang, and Z. Yao, "A new method for the design of the heliostat field layout for solar tower power plant," Renewable Energy, vol. 35, no. 9, pp. 1970–1975, 2010/09/01/ 2010, doi: https://doi.org/10.1016/j.renene.2010.01.026.