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The defence will be in French.
Abstract: The massive integration of renewable energy sources is making the power grid more complex, unstable and fragile. New numerical methods are needed to calculate the state of the grid more quickly, and to better understand the observed trends. For that purpose, we propose the use of methods derived from condensed matter theory.
First, the network equations are rewritten in a Hamiltonian formalism. Then, the Lanczos algorithm is used to calculate the steady-state load flow. This numerical method is particularly effective when a locality principle is verified, i.e. only certain states located in a bounded region of the network are involved in the solution. Compared with conventional approaches, we achieve considerable time savings when performing contingency analyses (line outages).
For the dynamic regime, the classical modal approach describes how groups of generators oscillate coherently at a given frequency. Here, we propose to go beyond this description to better model the intrinsic superposition of modes in the dynamic response. The mean-field approximation, in this case Shiba’s theory, is used to understand dynamic interactions within power systems. Disturbance propagations are characterized by two lengths. The mean free path is the distance over which a signal propagates ballistically in the network, before being scattered by its inhomogeneities. The localization length characterizes the average size of the mode support at a given frequency. Anderson’s localization theory is also used for the latter.
The results are illustrated on model lattices (Lieb and Honeycomb-Kagomé lattices well known for the study of crystalline materials) before being successfully extended to a model of the European grid.
