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Mathematical Model of a Series-Parallel (SP) photovoltaic (PV) generator represents each module through an equivalent electrical circuit denominated single diode model, this model has associated a nonlinear equation system that describes the electrical behavior of SP generator. This paper presents a solution of this system using optimization methods widely using: Trust Region Dogleg and Particle swarm optimization (PSO) for solving the electrical model of PV generator operating under homogeneous or non-homogeneous conditions, changing the number of submodules and shading pattern. It has been made simulations about generators composed by 3 and 15 series submodules, operating under different partial shading conditions. Between the implemented methods, Trust Region Dogleg show a better performance than other methods, with 2 and 14 times less computation time than the reference method and PSO, respectively, and a RMSE equal or 50% lower than PSO. [ABSTRACT FROM AUTHOR]

As the classical water-supply looped-network optimization problem is mathematically nonconvex and multimodal, the resulting solution of most approaches is uncertain in the sense of how close it is to the "best" solution. In many cases, this "best"' or "global" solution is invoked and pursued without a clear understanding of its meaning. This paper discusses what is involved in "global" solutions and the role that pipe flow distribution can play to deal with nonconvexity and multimodality in a new context. The author has introduced this new context recently after formulating a new objective function capable of finding that a looped network can be economically more attractive than its related branched one. Therefore, the convenience of an approach dealing with flows and heads, as relevant decision variables, is encouraged in this paper and its advantages enumerated under the new concepts. The entropy approach is studied critically and an example is provided for comparison with the proposed approach. [ABSTRACT FROM AUTHOR]