Modeling and control of power systems in microgrids

This thesis addresses several problems related to modeling and control of power systems in microgrids. First, a method is established to measure the effect of the addition of output impedances on the inductivity of a power network. We define a network inductivity measure, and compute it for homogeneous networks with RL output impedances. Second, we propose a master-slave architecture for microgrids, in which the source with the highest generation capacity acts as the master. In this scheme, power sharing can be achieved among the sources, without the need to any communication network. Third, we derive an improved swing model for synchronous generators which, compared to the swing equation, predicts better the behavior of the system, and yet it is easy to use. Incremental passivity properties of this model paves the path for a controller design. As a fourth problem, we look into the problem of lack of inertia in networks with dominant renewable energies. We model the power converters with large capacitors acting as inertia, and show stability and frequency regulation for a network of these converters. Fifth, we investigate the shifted passivity property of port-Hamiltonian systems with strictly convex Hamiltonian. We establish conditions under which the system is shifted passive, and guarantee stability of forced equilibria of pH systems. Finally, a subclass of port-Hamiltonian systems is developed, where the control input or disturbance is acting on the power entering the system. We investigate the shifted passivity of such pH systems, and characterize a region of attraction for stability of the equilibrium