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Implicit Mathematical Model of Photovoltaic Arrays with Improved Calculation Speed Based on Inflection Points of the Current–Voltage Curves

Author

Listed:
  • Juan David Bastidas-Rodriguez

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

  • Carlos Andres Ramos-Paja

    (Facultad de Minas, Universidad Nacional de Colombia, Medellin 050041, Colombia
    These authors contributed equally to this work.)

  • Andres Julian Saavedra-Montes

    (Facultad de Minas, Universidad Nacional de Colombia, Medellin 050041, Colombia
    These authors contributed equally to this work.)

Abstract

Dynamic reconfiguration, the monitoring of power production, and the fault diagnosis of photovoltaic arrays, among other applications, require fast and accurate models of photovoltaic arrays. In the literature, some models use the Lambert-W function to represent each module of the array, which increases the calculation time. Other models that use implicit equations to avoid the Lambert-W function do not use the inflection voltages to simplify the system of nonlinear equations that represent the array, increasing the computational burden. Therefore, this paper proposes mathematical models for series-parallel (SP) and total-cross-tied (TCT) photovoltaic arrays based on the implicit equations of the single-diode model and the inflection points of the current–voltage curves. These models decrease the calculation time by reducing the complexity of the nonlinear equation systems that represent each string of SP arrays and the whole TCT. Consequently, the calculation process that solves the model speeds up in comparison with processes that solve traditional explicit models based on the Lambert-W function. The results of several simulation scenarios using the proposed SP model with different array sizes show a reduction in the computation time by 82.97 % in contrast with the traditional solution. Additionally, when the proposed TCT model for arrays larger than 2 × 2 is used, the reduction in the computation time is between 47.71 % and 92.28 % . In dynamic reconfiguration, the results demonstrate that the proposed SP model provides the same optimal configuration but 7 times faster than traditional solutions, and the TCT model is solved at least 4 times faster than classical solutions.

Suggested Citation

  • 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.
  • Handle: RePEc:gam:jeners:v:16:y:2023:i:13:p:4875-:d:1176948
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    References listed on IDEAS

    as
    1. Luis Miguel Pérez Archila & Juan David Bastidas-Rodríguez & Rodrigo Correa & Luz Adriana Trejos Grisales & Daniel Gonzalez-Montoya, 2020. "A Solution of Implicit Model of Series-Parallel Photovoltaic Arrays by Using Deterministic and Metaheuristic Global Optimization Algorithms," Energies, MDPI, vol. 13(4), pages 1-22, February.
    2. Ko, Suk Whan & Ju, Young Chul & Hwang, Hye Mi & So, Jung Hun & Jung, Young-Seok & Song, Hyung-Jun & Song, Hee-eun & Kim, Soo-Hyun & Kang, Gi Hwan, 2017. "Electric and thermal characteristics of photovoltaic modules under partial shading and with a damaged bypass diode," Energy, Elsevier, vol. 128(C), pages 232-243.
    3. Orozco-Gutierrez, M.L. & Ramirez-Scarpetta, J.M. & Spagnuolo, G. & Ramos-Paja, C.A., 2013. "A technique for mismatched PV array simulation," Renewable Energy, Elsevier, vol. 55(C), pages 417-427.
    4. 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.
    5. Orozco-Gutierrez, M.L. & Spagnuolo, G. & Ramos-Paja, C.A. & Ramirez-Scarpetta, J.M & Ospina-Agudelo, B., 2019. "Enhanced simulation of total cross tied photovoltaic arrays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 158(C), pages 49-64.
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