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A method to calculate array spacing and potential system size of photovoltaic arrays in the urban environment using vector analysis

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  • Copper, J.K.
  • Sproul, A.B.
  • Bruce, A.G.

Abstract

The standard mathematical approach used to calculate photovoltaic (PV) array spacing contains a number of assumptions that limits its use to PV arrays installed on horizontal surfaces. This paper utilises vector analysis to develop a new method to calculate array spacing and potential system size for any combination of PV array and surface tilt and orientation. This approach is validated by comparing the vector results with ray-tracing shadow visualisations utilising the Ecotect software package. The vector method is presented as an approach compatible with online solar/PV mapping tools after a review of the existing online tools indicated that rack mounted array functionalities were rarely included. The methodology is further demonstrated via results from the Australian PV Institute’s (APVI’s) Solar Potential Tool which utilises the array spacing method presented. This paper also applies the methodology to a general analysis of array spacing and power density (installed capacity/unit area) for an optimally tilted equator facing array on roof surfaces of a variety of tilts and orientations.

Suggested Citation

  • Copper, J.K. & Sproul, A.B. & Bruce, A.G., 2016. "A method to calculate array spacing and potential system size of photovoltaic arrays in the urban environment using vector analysis," Applied Energy, Elsevier, vol. 161(C), pages 11-23.
    • Handle: RePEc:eee:appene:v:161:y:2016:i:c:p:11-23
    DOI: 10.1016/j.apenergy.2015.09.074
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    References listed on IDEAS

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    1. Freitas, S. & Catita, C. & Redweik, P. & Brito, M.C., 2015. "Modelling solar potential in the urban environment: State-of-the-art review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 41(C), pages 915-931.
    2. Castellano, Nuria Novas & Gázquez Parra, José Antonio & Valls-Guirado, Juan & Manzano-Agugliaro, Francisco, 2015. "Optimal displacement of photovoltaic array’s rows using a novel shading model," Applied Energy, Elsevier, vol. 144(C), pages 1-9.
    3. Sproul, Alistair B., 2007. "Derivation of the solar geometric relationships using vector analysis," Renewable Energy, Elsevier, vol. 32(7), pages 1187-1205.
    4. Martinez-Rubio, A. & Sanz-Adan, F. & Santamaria, J., 2015. "Optimal design of photovoltaic energy collectors with mutual shading for pre-existing building roofs," Renewable Energy, Elsevier, vol. 78(C), pages 666-678.
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    Cited by:

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    2. Appelbaum, Joseph & Aronescu, Avi, 2022. "Inter-row spacing calculation in photovoltaic fields - A new approach," Renewable Energy, Elsevier, vol. 200(C), pages 387-394.
    3. Rodrigo, Pedro M. & Mouhib, Elmehdi & Fernandez, Eduardo F. & Almonacid, Florencia & Rosas-Caro, Julio C., 2024. "Comprehensive ground coverage analysis of large-scale fixed-tilt bifacial photovoltaic plants," Renewable and Sustainable Energy Reviews, Elsevier, vol. 192(C).
    4. Chen, X.M. & Li, Y. & Zhao, B.Y. & Wang, R.Z., 2020. "Are the optimum angles of photovoltaic systems so important?," Renewable and Sustainable Energy Reviews, Elsevier, vol. 124(C).
    5. Saeed Swaid & Joseph Appelbaum & Avi Aronescu, 2021. "Shading and Masking of PV Collectors on Horizontal and Sloped Planes Facing South and North—A Comparative Study," Energies, MDPI, vol. 14(13), pages 1-15, June.
    6. Huang, Lin & Song, Zihao & Dong, Qichang & Song, Ye & Zhao, Xiaoqing & Qi, Jiacheng & Shi, Long, 2024. "Surface temperature and power generation efficiency of PV arrays with various row spacings: A full-scale outdoor experimental study," Applied Energy, Elsevier, vol. 367(C).
    7. Roberts, M.B. & Bruce, A. & MacGill, I., 2019. "Opportunities and barriers for photovoltaics on multi-unit residential buildings: Reviewing the Australian experience," Renewable and Sustainable Energy Reviews, Elsevier, vol. 104(C), pages 95-110.
    8. Rehman, Naveed ur & Uzair, Muhammad & Allauddin, Usman, 2020. "An optical-energy model for optimizing the geometrical layout of solar photovoltaic arrays in a constrained field," Renewable Energy, Elsevier, vol. 149(C), pages 55-65.
    9. Hu, Jing & Harmsen, Robert & Crijns-Graus, Wina & Worrell, Ernst, 2019. "Geographical optimization of variable renewable energy capacity in China using modern portfolio theory," Applied Energy, Elsevier, vol. 253(C), pages 1-1.
    10. Ma, Chao & Deng, Zexing & Xu, Ximeng & Pang, Xiulan & Li, Xiaofeng & Wu, Runze & Tian, Zhuojun, 2024. "Space optimization of utility-scale photovoltaic power plants considering the impact of inter-row shading," Applied Energy, Elsevier, vol. 370(C).
    11. Sameh Monna & Adel Juaidi & Ramez Abdallah & Mohammed Itma, 2020. "A Comparative Assessment for the Potential Energy Production from PV Installation on Residential Buildings," Sustainability, MDPI, vol. 12(24), pages 1-17, December.

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