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An improved Fractional MPPT Method by Using a Small Circle Approximation of the P–V Characteristic Curve

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Listed:
  • Ernesto Bárcenas-Bárcenas

    (Academic Coordination of the Altiplano-Region Campus, Autonomous University of San Luis Potosi, Matehuala, San Luis Potosi 78700, Mexico)

  • Diego R. Espinoza-Trejo

    (Academic Coordination of the Altiplano-Region Campus, Autonomous University of San Luis Potosi, Matehuala, San Luis Potosi 78700, Mexico)

  • José A. Pecina-Sánchez

    (Academic Coordination of the Altiplano-Region Campus, Autonomous University of San Luis Potosi, Matehuala, San Luis Potosi 78700, Mexico)

  • Héctor A. Álvarez-Macías

    (Academic Coordination of the Altiplano-Region Campus, Autonomous University of San Luis Potosi, Matehuala, San Luis Potosi 78700, Mexico)

  • Isaac Compeán-Martínez

    (Academic Coordination of the Altiplano-Region Campus, Autonomous University of San Luis Potosi, Matehuala, San Luis Potosi 78700, Mexico)

  • Ángel A. Vértiz-Hernández

    (Academic Coordination of the Altiplano-Region Campus, Autonomous University of San Luis Potosi, Matehuala, San Luis Potosi 78700, Mexico)

Abstract

This paper presents an analytical solution to the maximum power point tracking (MPPT) problem for photovoltaic (PV) applications in the form of an improved fractional method. The proposal makes use of a mathematical function that describes the relationship between power and voltage in a PV module in a neighborhood including the maximum power point (MPP). The function is generated by using only three points of the P–V curve. Next, by using geometrical relationships, an analytical value for the MPP can be obtained. The advantage of the proposed technique is that it provides an explicit mathematical expression for calculation of the voltage at the maximum power point ( v M P P ) with high accuracy. Even more, complex calculations, manufacturer data, the measurements of short circuit current ( i S C ) and open-circuit voltage ( v O C ) are not required, making the proposal less invasive than other solutions. The proposed method is validated using the P–V curve of one PV module. Experimental work demonstrates the speed in the calculation of v M P P and the feasibility of the proposed solution. In addition, this MPPT proposal requires only the typical and available measurements, namely, PV voltage and current. Consequently, the proposed method could be implemented in most PV applications.

Suggested Citation

  • Ernesto Bárcenas-Bárcenas & Diego R. Espinoza-Trejo & José A. Pecina-Sánchez & Héctor A. Álvarez-Macías & Isaac Compeán-Martínez & Ángel A. Vértiz-Hernández, 2023. "An improved Fractional MPPT Method by Using a Small Circle Approximation of the P–V Characteristic Curve," Mathematics, MDPI, vol. 11(3), pages 1-15, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:526-:d:1040191
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    References listed on IDEAS

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    1. Pindado, Santiago & Cubas, Javier, 2017. "Simple mathematical approach to solar cell/panel behavior based on datasheet information," Renewable Energy, Elsevier, vol. 103(C), pages 729-738.
    2. Victor Andrean & Pei Cheng Chang & Kuo Lung Lian, 2018. "A Review and New Problems Discovery of Four Simple Decentralized Maximum Power Point Tracking Algorithms—Perturb and Observe, Incremental Conductance, Golden Section Search, and Newton’s Quadratic Int," Energies, MDPI, vol. 11(11), pages 1-25, November.
    3. Fathi Troudi & Houda Jouini & Abdelkader Mami & Nidhal Ben Khedher & Walid Aich & Attia Boudjemline & Mohamed Boujelbene, 2022. "Comparative Assessment between Five Control Techniques to Optimize the Maximum Power Point Tracking Procedure for PV Systems," Mathematics, MDPI, vol. 10(7), pages 1-15, March.
    4. Santiago Pindado & Javier Cubas & Elena Roibás-Millán & Francisco Bugallo-Siegel & Félix Sorribes-Palmer, 2018. "Assessment of Explicit Models for Different Photovoltaic Technologies," Energies, MDPI, vol. 11(6), pages 1-22, May.
    5. Carlos Restrepo & Nicolas Yanẽz-Monsalvez & Catalina González-Castaño & Samir Kouro & Jose Rodriguez, 2021. "A Fast Converging Hybrid MPPT Algorithm Based on ABC and P&O Techniques for a Partially Shaded PV System," Mathematics, MDPI, vol. 9(18), pages 1-25, September.
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