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Analytical Computation of the Maximum Power Point of Solar Cells Using Perturbation Theory

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  • José G. Tirado-Serrato

    (Programa de Graduados e Investigación en Ingeniería Eléctrica, Instituto Tecnológico de Morelia, Tecnológico Nacional de Mexico, Campus Morelia, Avenida Tecnológico No. 1500, Lomas de Santiaguito, Morelia 58120, Michoacán, Mexico)

  • Alfredo Sanchez Garcia

    (Sustainable Energy Technology, SINTEF AS, 7465 Trondheim, Norway)

  • Serguei Maximov

    (Programa de Graduados e Investigación en Ingeniería Eléctrica, Instituto Tecnológico de Morelia, Tecnológico Nacional de Mexico, Campus Morelia, Avenida Tecnológico No. 1500, Lomas de Santiaguito, Morelia 58120, Michoacán, Mexico)

Abstract

To compute the maximum power point (MPP) from physical parameters of the single-diode model (SDM), it is necessary to solve a transcendental equation using numerical methods. This is computationally expensive and can lead to divergence problems. An alternative is to develop analytical approximations which can be accurate enough for engineering problems and simpler to use. Therefore, this paper presents approximations for computing the MPP of single-junction solar cells. Two special cases are considered: (i) SDM with only series resistance, and (ii) SDM with only shunt resistance. Power series closed-form expressions for the MPP are obtained using perturbation theory and the Lagrange inversion theorem. Validation of the formulas is performed using experimental data from six different technologies obtained from the NREL database and comparing the results with the numerical solution of the SDM and three approximations from the literature. The results show an absolute percentage error (APE) of less than 0.035% with respect to the real MPP measurements. In cases with limited computational resources, this value could be further improved by using a higher- or lower-order power-series approximation.

Suggested Citation

  • José G. Tirado-Serrato & Alfredo Sanchez Garcia & Serguei Maximov, 2024. "Analytical Computation of the Maximum Power Point of Solar Cells Using Perturbation Theory," Energies, MDPI, vol. 17(23), pages 1-19, November.
    • Handle: RePEc:gam:jeners:v:17:y:2024:i:23:p:6035-:d:1533954
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    References listed on IDEAS

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    1. Luis Fernando Grisales-Noreña & Oscar Danilo Montoya & Brandon Cortés-Caicedo & Farhad Zishan & Javier Rosero-García, 2023. "Optimal Power Dispatch of PV Generators in AC Distribution Networks by Considering Solar, Environmental, and Power Demand Conditions from Colombia," Mathematics, MDPI, vol. 11(2), pages 1-20, January.
    2. Li, Shaowu, 2016. "Linear equivalent models at the maximum power point based on variable weather parameters for photovoltaic cell," Applied Energy, Elsevier, vol. 182(C), pages 94-104.
    3. Kumar, Gaurav & Panchal, Ashish K., 2014. "Geometrical prediction of maximum power point for photovoltaics," Applied Energy, Elsevier, vol. 119(C), pages 237-245.
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