Abstract: The goal of this thesis is to provide modelling and control solutions for the optimal energy management of a DC (direct current) microgrid under constraints and some uncertainties. The studied microgrid system includes electrical storage units (e.g., batteries, supercapacitors), renewable sources (e.g., solar panels) and loads (e.g., an electro-mechanical elevator system). These interconnected components are linked to a three phase electrical grid through a DC bus and its associated converters. The optimal energy management is usually formulated as an optimal control problem which takes into account the system dynamics, cost, constraints and reference profiles. An optimal energy management for the microgrid is challenging with respect to classical control theories. Needless to say, a DC microgrid is a complex system due to its heterogeneity, distributed nature (both spatial and in sampling time), nonlinearity of dynamics, multi-physic characteristics, presences of constraints and uncertainties. Not in the least, the power-preserving structure and the energy conservation of a microgrid are essential for ensuring a reliable operation. These challenges are tackled through the combined use of PH (Port-Hamiltonian) formulations, differential flatness and economic MPC (Model Predictive Control). The PH formalism allows to explicitly describe the power-preserving structure and the energy conservation of the microgrid and to connect heterogeneous components under the same framework. The strongly non-linear system is then translated into a flat representation. Taking into account differential flatness properties, reference profiles are generated such that the dissipated energy is minimized and the various physical constraints are respected. Lastly, the modelling approach is extended to PH formalism on graphs which is further used in an economic MPC formulation for minimizing the purchasing/selling electricity cost within the DC microgrid. The proposed control strategies are validated through extensive simulation results over the elevator DC microgrid system using real profiles data.
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