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Open AccessArticle

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

1
Escuela de Ingenierías Eléctrica, Electrónica y de Telecomunicaciones, Universidad Industrial de Santander, Bucaramanga 680003, Colombia
2
Departamento de Ingeniería Eléctrica, Electrónica y Computación, Universidad Nacional de Colombia, Manizales 170003, Colombia
3
Departamento de Electromecánica y Mecatrónica, Instituto Tecnológico Metropolitano, Medellín 050013, Colombia
4
Departamento de Electrónica y Telecomunicaciones, Instituto Tecnológico Metropolitano, Medellín 050013, Colombia
*
Author to whom correspondence should be addressed.
Energies 2020, 13(4), 801; https://doi.org/10.3390/en13040801
Received: 19 December 2019 / Revised: 23 January 2020 / Accepted: 30 January 2020 / Published: 12 February 2020
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. View Full-Text
Keywords: implicit model solution; photovoltaic array; series–parallel; global optimization; partial shading; deterministic optimization algorithm; metaheuristic optimization algorithm implicit model solution; photovoltaic array; series–parallel; global optimization; partial shading; deterministic optimization algorithm; metaheuristic optimization algorithm
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MDPI and ACS Style

Pérez Archila, L.M.; Bastidas-Rodríguez, J.D.; Correa, R.; Trejos Grisales, L.A.; Gonzalez-Montoya, D. A Solution of Implicit Model of Series-Parallel Photovoltaic Arrays by Using Deterministic and Metaheuristic Global Optimization Algorithms. Energies 2020, 13, 801.

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