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Mathematical Model for Regular and Irregular PV Arrays with Improved Calculation Speed

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  • Luz Adriana Trejos-Grisales

    (Departamento de Electromecánica y Mecatrónica, Instituto Tecnológico Metropolitano, Medellín 050013, Colombia
    These authors contributed equally to this work.)

  • Juan David Bastidas-Rodríguez

    (Facultad de Ingeniería y Arquitectura, Universidad Nacional de Colombia, Manizales 170003, Colombia
    These authors contributed equally to this work.)

  • Carlos Andrés Ramos-Paja

    (Facultad de Minas, Universidad Nacional de Colombia, Medellín 050013, Colombia
    These authors contributed equally to this work.)

Abstract

Photovoltaic (PV) systems are usually developed by configuring the PV arrays with regular connection schemes, such as series-parallel, total cross-tied, bridge-linked, among others. Such a strategy is aimed at increasing the power that is generated by the PV system under partial shading conditions, since the power production changes depending on the connection scheme. Moreover, irregular and non-common connection schemes could provide higher power production for irregular (but realistic) shading conditions that aere caused by threes or other objects. However, there are few mathematical models that are able to predict the power production of different configurations and reproduce the behavior of both regular and irregular PV arrays. Those general array models are slow due to the large amount of computations that are needed to find the PV current for a given PV voltage. Therefore, this paper proposes a general mathematical model to predict the power production of regular and irregular PV arrays, which provides a faster calculation in comparison with the general models that were reported in the literature, but without reducing the prediction accuracy. The proposed modeling approach is based on detecting the inflection points that are caused by the bypass diodes activation, which enables to narrow the range in which the modules voltages are searched, thus reducing the calculation time. Therefore, this fast model is useful in designing the fixed connections of PV arrays that are subjected to shading conditions, in order to reconfigure the PV array in real-time, depending on the shading pattern, among other applications. The proposed solution is validated by comparing the results with another general model and with a circuital implementation of the PV system.

Suggested Citation

  • Luz Adriana Trejos-Grisales & Juan David Bastidas-Rodríguez & Carlos Andrés Ramos-Paja, 2020. "Mathematical Model for Regular and Irregular PV Arrays with Improved Calculation Speed," Sustainability, MDPI, vol. 12(24), pages 1-28, December.
    • Handle: RePEc:gam:jsusta:v:12:y:2020:i:24:p:10684-:d:465882
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    References listed on IDEAS

    as
    1. Manoharan Premkumar & Umashankar Subramaniam & Thanikanti Sudhakar Babu & Rajvikram Madurai Elavarasan & Lucian Mihet-Popa, 2020. "Evaluation of Mathematical Model to Characterize the Performance of Conventional and Hybrid PV Array Topologies under Static and Dynamic Shading Patterns," Energies, MDPI, vol. 13(12), pages 1-37, June.
    2. Jeisson Vélez-Sánchez & Juan David Bastidas-Rodríguez & Carlos Andrés Ramos-Paja & Daniel González Montoya & Luz Adriana Trejos-Grisales, 2019. "A Non-Invasive Procedure for Estimating the Exponential Model Parameters of Bypass Diodes in Photovoltaic Modules," Energies, MDPI, vol. 12(2), pages 1-20, January.
    3. Daniel Gonzalez Montoya & Juan David Bastidas-Rodriguez & Luz Adriana Trejos-Grisales & Carlos Andres Ramos-Paja & Giovanni Petrone & Giovanni Spagnuolo, 2018. "A Procedure for Modeling Photovoltaic Arrays under Any Configuration and Shading Conditions," Energies, MDPI, vol. 11(4), pages 1-17, March.
    4. Pal, Rudra Sankar & Mukherjee, V., 2020. "Metaheuristic based comparative MPPT methods for photovoltaic technology under partial shading condition," Energy, Elsevier, vol. 212(C).
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    Cited by:

    1. Mariana Durango-Flórez & Daniel González-Montoya & Luz Adriana Trejos-Grisales & Carlos Andres Ramos-Paja, 2022. "PV Array Reconfiguration Based on Genetic Algorithm for Maximum Power Extraction and Energy Impact Analysis," Sustainability, MDPI, vol. 14(7), pages 1-14, March.
    2. Jae-Sub Ko & Dae-Kyong Kim, 2021. "Localization of Disconnection Faults in PV Installations Using the Multiple Frequencies Injection Method," Energies, MDPI, vol. 14(21), pages 1-28, November.
    3. Jangyoul You & Myungkwan Lim & Kipyo You & Changhee Lee, 2021. "Wind Coefficient Distribution of Arranged Ground Photovoltaic Panels," Sustainability, MDPI, vol. 13(7), pages 1-19, April.
    4. Juan David Bastidas-Rodriguez & Carlos Andres Ramos-Paja & Andres Julian Saavedra-Montes, 2023. "Implicit Mathematical Model of Photovoltaic Arrays with Improved Calculation Speed Based on Inflection Points of the Current–Voltage Curves," Energies, MDPI, vol. 16(13), pages 1-29, June.

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