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A digital-twin and machine-learning framework for the design of multiobjective agrophotovoltaic solar farms


This work develops a computational Digital-Twin framework to track and optimize the flow of solar power through complex, multipurpose, solar farm facilities, such as Agrophotovoltaic (APV) systems. APV systems symbiotically cohabitate power-generation facilities and agricultural production systems. In this work, solar power flow is rapidly computed with a reduced order model of Maxwell’s equations, based on a high-frequency decomposition of the irradiance into multiple rays, which are propagated forward in time to ascertain multiple reflections and absorption for various source-system configurations, varying multi-panel inclination, panel refractive indices, sizes, shapes, heights, ground refractive properties, etc. The method allows for a solar installation to be tested from multiple source directions quickly and uses a genomic-based Machine-Learning Algorithm to optimize the system. This is particularly useful for planning of complex next-generation solar farm systems involving bifacial (double-sided) panelling, which are capable of capturing ground albedo reflection, exemplified by APV systems. Numerical examples are provided to illustrate the results, with the overall goal being to provide a computational framework to rapidly design and deploy complex APV systems.

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  1. 1.

    APV systems can involve a variety of aspects, even utilizing pollinating insects, such as bees, to ‘solar grazing’ systems.

  2. 2.

    Resolving diffraction (which ray theory is incapable of describing) is unimportant for the applications of interest.

  3. 3.

    The free space electric permittivity is \(\epsilon _o=\frac{1}{c^2\mu _o}=8.8542\times 10^{-12}\) C N\(^{-1}\) m\(^{-1}\) and the free space magnetic permeability is \(\mu _o=4\pi \times 10^{-7}\) Wb A\(^{-1}\) m\(^{-1}=1.2566\times 10^{-6}\)  Wb A\(^{-1}\) m\(^{-1}\).

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    By combining the relations in Eq. 5 one obtains \(||{\varvec{k}}||=\frac{\omega }{c}\).

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    Throughout the analysis we assume that \(\hat{n}\ge 1\).

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    The limiting case \(\frac{sin \theta ^*_i}{\hat{n}}=1\), is the critical angle (\(\theta ^*_i\)) case.

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    Note that algorithmically, we can the set total initial irradiance via \(\sum _{i=1}^{N_r}I^{inc}_i(t=0)\mathcal{A}_r=P\) Watts. To achieve this distribution, one would first place rays randomly in the plane, and then scale the individual \(I^{inc}\) by \(e^{-ad}\) and the normalized the average so that the total was P Watts.


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This work has been partially supported by the UC Berkeley College of Engineering and the USDA AI Institute for Next Generation Food Systems (AIFS), USDA award number 2020-67021-32855.

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Zohdi, T.I. A digital-twin and machine-learning framework for the design of multiobjective agrophotovoltaic solar farms. Comput Mech 68, 357–370 (2021).

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  • Agrophotovoltaics
  • Digital-twin
  • Machine-learning