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.
Highlights
The continuous effects of climate change and environmental contamination have motivated a growing interest in the use of renewable energies to replace conventional energy sources based on fossil fuels
The small generator used for the experimental validation was formed by one string of three submodules, which was evaluated for homogeneous (C-1) and partial shading (C-2) defined by the
The simulations show that the deterministic optimization methods can solve the optimization problem for small, medium and large generators operating in homogeneous and partial shading conditions; with these algorithms, it is possible to reproduce the generator I–V curves
Summary
The continuous effects of climate change and environmental contamination have motivated a growing interest in the use of renewable energies to replace conventional energy sources based on fossil fuels. When the irradiance and temperature of all the submodules in the generator are the same, it can be said that the generator operates under homogeneous conditions [6] In these conditions, the whole generator can be represented by the single-diode model (SDM) scaled in voltage, according to the number of modules in the string, and scaled in current, according to the number of strings in parallel [7]. The whole generator can be represented by the single-diode model (SDM) scaled in voltage, according to the number of modules in the string, and scaled in current, according to the number of strings in parallel [7] In this case, the current vs voltage (I–V) curve has a single knee and the power vs voltage (P-V) curve has a single maximum power point (MPP), which can be tracked The current vs. voltage (I–V) curve has a single knee and the power vs. voltage (P-V) curve has a single maximum power point (MPP), which can be tracked
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