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The power plants and the coupling in space and time of their distribution and fields of consumption, lead electrical networks of being "complex systems". Such systems are characterized by dynamic singularities under the control of entangled causalities which condemn any intuitive mastery of sometimes chaotic and even catastrophic behaviors. Facing them, the intuitive rational control must give way to a simulation which has especially to take into account the multi-evaluation of response functions. This feature, leads however to refer the behavior of these systems to the dynamics on hyperbolic manifolds, and especially on their most common physical archetype: the fractal geometries. We show that the singularities are distributed according to scaling laws associated to these geometries. The experimental relevance of these laws is confirmed and with it, the efficiency of simulation tools developed to give to the technical and political actors, the tools required to monitor, manage and anticipate the network behavior.