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Mathematical modelling of photovoltaic panels

Fco. Javier Toledo Melero, Universidad Miguel Hernández
The behavior of a photovoltaic panel can be mathematically modeled by an equivalent electrical circuit. Depending on the electrical components of this circuit, number of diodes and resistors in series and in parallel, Kirchoff's laws give rise to a mathematical equation that relates voltage and current. This equation is the mathematical model of the panel and depends on some parameters that must be determined so that the equation can correctly predict the value of the current for a given value of the voltage or vice versa. The number of parameters of the model/equation depends on the number of components of the equivalent electrical circuit, the more components the more parameters and the more complicated it is to obtain. It has been verified that, under minimum conditions of temperature and irradiance, the equivalent electrical model with a single diode, a resistance in series and a resistance in parallel, called Single-Diode Model, correctly describes the behavior of the solar panel, therefore, it is one of the most used models in the literature. This model is described by an implicit equation with five parameters to be determined. The complexity of its resolution means that several decades after its first use it continues to be the subject of investigation. In this talk some resolution techniques of the model with different types of data (voltage and current values) will be described and, in particular, it will be shown the methodology that has provided the best accuracy documented until now in two important case studies usually used in the literature as well as in a large-scale I-V curve repository with more than one million of samples.