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

José G. Tirado-Serrato, Alfredo Sanchez Garcia () and Serguei Maximov
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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

Energies, 2024, vol. 17, issue 23, 1-19

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.

Keywords: analytical solution; maximum power point; photovoltaic module; power series (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2024
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