In the modern power grid, the increasing penetration of intermittent energy sources like solar and wind into the comes with unsought challenges. With increasing smart grid directcurrent (DC) deployments in distribution feeders, microgrids, smart buildings, and highvoltage transmission, there is a need for better understanding the landscape of power flow (PF) solutions as well as for efficient PF solvers with performance guarantees. This thesis puts forth three approaches with complementary strengths towards coping with the PF task, consisting of solving a system on non-linear equations, in DC power systems. We consider a possibly meshed network hosting ZIP loads and constant-voltage/power generators. Uncertainty is another inevitable side-effect of a modern power grid with vast deployments of renewable generation. Since energy storage systems (ESS) can be employed to mitigate the effect of uncertainties, their energy and power ratings along with their charging control strategies become of vital importance for renewable energy producers. This thesis also deals with the task of sizing ESS under a model predictive control (MPC) operation for a single ESS used to smoothen out a random energy signal. To account for correlations in the energy signal and enable charging adjustments in response to real-time fluctuations, we adopt a linear charging policy, designed by minimizing the initial ESS investment plus the average operational cost. Since charging decisions become random, the energy and power limits are posed as chance constraints. The chance constraints are enforced in a distributionally robust fashion. The proposed scheme is contrasted to a charging policy under Gaussian uncertainties and a deterministic formulation. / M.S. / Power systems are undergoing major changes as more renewable energy resources are being deployed across their networks. Two of the major changes are the increase in direct-current (DC) generation and loads and making up for the uncertainty introduced by these resources. In this thesis, we have tackled these two important aspects; a DC power flow (PF) solver and an energy storage system (ESS) sizing under uncertainty. The three DC PF solvers proposed in this thesis exhibit complementary values and can handle a wide range of loads and generation types. We have also proposed a distributionally robust ESS sizing under model predictive control framework, capable of handling worst-case uncertainties.

Cette thèse a été consacrée à l'étude des réseaux multi-terminaux haute tension à courant continu (MTDC). Les principales contributions étaient dans le domaine du contrôle automatique non linéaire, appliquées aux systèmes électriques, électronique de puissance et les sources d'énergie renouvelables. Le travail de recherche a été lancé avec l'intention de combler certaines lacunes entre la théorie et la pratique, en particulier: 1) d'enquêter sur diverses approches de contrôle pour le but d'améliorer la performance des systèmes MTDC; 2) d'établir des connexions entre la conception du contrôle empiriques existantes et analyse théorique; 3) d'améliorer la compréhension du comportement multi-échelle de temps des systèmes MTDC caractérisés par la présence de transitoires lents et rapides en réponse aux perturbations externes. En conséquence, ce travail de thèse peut être mis en trois domaines, à savoir la conception non linéaire de commande de systèmes MTDC, analyse des comportements dynamiques de système MTDC et l'application de systèmes MTDC pour le contrôle de fréquence des systèmes de climatisation. / This dissertation was devoted to the study of multi-terminal high voltage direct current (MTDC) networks. The main contributions were in the field of nonlinear automatic control, applied to power systems, power electronics and renewable energy sources. The research work was started with the intention of filling some gaps between the theory and the practice, in particular: 1) to investigate various control approaches for the purpose of improving the performance of MTDC systems; 2) to establish connections between existing empirical control design and theoretical analysis; 3) to improve the understanding of the multi-time-scale behavior of MTDC systems characterized by the presence of slow and fast transients in response to external disturbances. As a consequence, this thesis work can be put into three areas, namely nonlinear control design of MTDC systems, analysis of MTDC system's dynamic behaviors and application of MTDC systems for frequency control of AC systems.