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This thesis, supported by the ANR project HISPALIS, aims at developing theoretical results in the field of Automatic Control to provide controllers for microgrids in order to guarantee high reliability, energy efficiency and robustness. The main objective is to propose new paradigms for the design of several layers of control laws for the microgrid levels, by using Hybrid Dynamical Systems [1] and Multi-Agent Systems theories [2]. In a first stage, an intensive attention will be paid to an inner control level for the regulation of the electronic power converters. These electronic devices can be modeled as a Hybrid Dynamical Systems, and more particularly as switching affine systems [3],[4]. The use of the Hybrid Dynamical System theory will be crucial to formulate the control problem and define the switching control signals in view of reducing the dissipated energy and improving the system lifespan of the devices. Indeed, this recent theory is well suited for analysis of power electronic converters, since they combine continuous (voltage and currents) and discrete (on-off state of switches) signals avoiding, in this way, the use of averaged models. Likewise, an outer control level for controlling the microgrid will be developed to provide a distributed strategy that makes the microgrid scalable and robust with respect to blackouts of sources and/or loads, following the principle of the theory of Multi-Agent System. In this distributed strategy, there are several crucial and innovative aspects to be regarded such as the heterogeneity and the hybrid and nonlinear nature of these converters. The objectives are here to provide robust consensus algorithms with respect to the parameter variations.
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