Contribuições para a resolução do problema de extração dos parâmetros do modelo fotovoltaico de um diodo

Abstract

The single diode model is the leading physical–mathematical framework for representing the electrical behavior of photovoltaic generators, supporting both performance simulation and component characterization. However, practical application requires adjusting the five parameters of its characteristic equation. The most consistent approach involves extracting these parameters from a current–voltage (I–V) curve of the generator under study, ensuring the characteristic equation accurately mirrors the observed behavior. This process presents a challenging optimization problem, characterized by nonlinearity, transcendence, nonconvexity, numerical sensitivity, and a strong dependence on the chosen formulation and calculation approach. Through a comprehensive literature review and critical analysis of existing treatments, it was established that a formal approach to the model—based on the explicit rewriting of the characteristic equation using the Lambert W function—combined with a formulation incorporating coherent boundary constraints, constitutes the most appropriate and promising alternative for obtaining high-quality solutions. This insight led to the proposal of an integrated methodological framework developed along two complementary lines. The first focuses on efficient computation of the Lambert W function within the physically relevant domain of the single-diode model, culminating in a self-started predictor–corrector method capable of delivering solutions with machine-precision accuracy and low computational cost. The second line focused on an initiative that, to the best of the author’s knowledge, has no precedent in the literature: the proposal of a deterministic local search method specifically designed for the direct solution of the problem. Consequently, the tailored exterior-point method (TEPM) was conceived, whose architecture combines mechanisms specifically designed to address the structural and numerical challenges, such as a modified logarithmic barrier, inertial regularization, and symmetric matrix scaling. Through case studies widely reported in the literature, both proposed methods were shown to be highly competitive, standing out among state-of-the-art alternatives in terms of efficacy and robustness. Moreover, in a large-scale application involving the solution of more than one million parameter extraction problems from I–V curves, these performances were further corroborated: the high accuracy potential of the TEPM was evidenced, while the self-started predictor–corrector method proved suitable by providing reduced simulation times compatible with the application’s requirements. In summary, the original contributions of this thesis consist primarily in the proposal of two dedicated methods—the self-started predictor–corrector method and the TEPM—which constitute concrete tools for the effective, reproducible, and technically grounded solution of the single diode model parameter extraction problem from an I–V curve, with direct value for both the scientific community and the photovoltaic industry.