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A Solution of Implicit Model of Series-Parallel Photovoltaic Arrays by Using Deterministic and Metaheuristic Global Optimization Algorithms

Author

Listed:
  • Luis Miguel Pérez Archila

    (Escuela de Ingenierías Eléctrica, Electrónica y de Telecomunicaciones, Universidad Industrial de Santander, Bucaramanga 680003, Colombia)

  • Juan David Bastidas-Rodríguez

    (Departamento de Ingeniería Eléctrica, Electrónica y Computación, Universidad Nacional de Colombia, Manizales 170003, Colombia)

  • Rodrigo Correa

    (Escuela de Ingenierías Eléctrica, Electrónica y de Telecomunicaciones, Universidad Industrial de Santander, Bucaramanga 680003, Colombia)

  • Luz Adriana Trejos Grisales

    (Departamento de Electromecánica y Mecatrónica, Instituto Tecnológico Metropolitano, Medellín 050013, Colombia)

  • Daniel Gonzalez-Montoya

    (Departamento de Electrónica y Telecomunicaciones, Instituto Tecnológico Metropolitano, Medellín 050013, Colombia)

Abstract

The implicit model of photovoltaic (PV) arrays in series-parallel (SP) configuration does not require the LambertW function, since it uses the single-diode model, to represent each submodule, and the implicit current-voltage relationship to construct systems of nonlinear equations that describe the electrical behavior of a PV generator. However, the implicit model does not analyze different solution methods to reduce computation time. This paper formulates the solution of the implicit model of SP arrays as an optimization problem with restrictions for all the variables, i.e., submodules voltages, blocking diode voltage, and strings currents. Such an optimization problem is solved by using two deterministic (Trust-Region Dogleg and Levenberg Marquard) and two metaheuristics (Weighted Differential Evolution and Symbiotic Organism Search) optimization algorithms to reproduce the current–voltage (I–V) curves of small, medium, and large generators operating under homogeneous and non-homogeneous conditions. The performance of all optimization algorithms is evaluated with simulations and experiments. Simulation results indicate that both deterministic optimization algorithms correctly reproduce I–V curves in all the cases; nevertheless, the two metaheuristic optimization methods only reproduce the I–V curves for small generators, but not for medium and large generators. Finally, experimental results confirm the simulation results for small arrays and validate the reference model used in the simulations.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jeners:v:13:y:2020:i:4:p:801-:d:319781
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    References listed on IDEAS

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    Cited by:

    1. 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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