This thesis addresses the problem of reactive power scheduling in a power system with several areas controlled by independent transmission system operators (TSOs). To design a fair method for optimizing the control settings in the interconnected multi-TSO system, two types of schemes are developed.<br />First, a centralized multi-TSO optimization scheme is introduced, and it is shown that this scheme has some properties of fairness in the economic sense.<br />Second, the problem is addressed through a decentralized optimization scheme with no information exchange between the TSOs. In this framework, each TSO assumes an external network equivalent in place of its neighboring TSOs and optimizes the objective function corresponding to its own control area regardless of the impact that its choice may have on the other TSOs.<br />The thesis presents simulation results obtained with the IEEE 39 bus system and IEEE 118 bus systems partitioned between three TSOs. It also presents some results for a UCTE-like 4141 bus system with seven TSOs. The decentralized control scheme is applied to both time-invariant and time-varying power systems. Nearly optimal performance is obtained in those contexts.

Confronté à un contexte de stagnation globale de la consommation d'électricité mais avec un potentiel important de développement de nouveaux usages, ainsi qu'à l'apparition d'unités de production dispersée sur le territoire, le principal gestionnaire de réseau de distribution français a besoin d'expliciter ce que sont ses grands choix de structure et de règles d'exploitation, et de les comparer avec les distributeurs étrangers. Les principes de construction du réseau ont un impact sur la capacité à intégrer les nouvelles installations de consommation ou de production à moindre cout, et à assurer les exigences sociétales,notamment pour ce qui concerne la continuité de fourniture. Cette thèse permet de comparer ces choix techniques majeurs avec les pratiques rencontrées à l'étranger, pour situer le réseau français et ses spécificités dans un environnement technique international.Après avoir arrêté une perspective de développement des usages et des productions en France sur la base notamment des textes législatifs, l'architecture du réseau de distribution français est décrite. Les différences fonctionnelles de choix de structure dans le monde sont alors analysés, en soulignant les conséquences dans le dimensionnement par rapport au cas français. Puis l'équilibre entre niveaux de tension est questionné, ainsi que les effet des caractéristiques du territoire sur le réseau. Enfin, des choix techniques nouveaux sont proposés après analyse des points forts et des points faibles des variantes existant dans le monde. / Faced to a context of a global lack of growth in electricity consumption, but with many potential development of new uses, added with the appearance of more and more dispersed generation, the main French distribution grid utility needs to question and compare its choicesconcerning grid structure and exploitation practices. Grid building principles have a greatimpact over its capacity to integrate at low cost consumption and production facilities, whilemeeting society needs, mainly continuity of supply. This work allows to compare thosetechnical choices between France and other countries, to determine where French utilitystands and what are its specific features in a worldwide technical environment.After setting a perspective about uses and production development, mainly on the basis of French legislation, the overall distribution grid architecture is described. Functional differences in structure choices in the world are then analysed, their consequences in thesizing of equipments is underlined. Then the equilibrium between voltage levels is questioned,as the effect of territorial features on the grid. Finally, new technical choices are proposed after advantages and drawbacks analysis of existing world grids.

[pt] Para combater as alterações climáticas, os sistemas energéticos modernos estão a passar por uma transição baseada na descarbonização, envolvendo uma vasta implantação de fontes de energia renováveis e a electrificação das sociedades. Para que esta transição seja bem sucedida, vários desafios associados à produção de energia renovável precisam de ser abordados nas operações do sistema energético. Esses desafios decorrem da alta variabilidade de produção, juntamente com previsibilidade e controlabilidade limitadas, levando a necessidades de flexibilidade nas operações do sistema de energia. O fluxo de potência ideal (OPF) e o comprometimento da unidade (UC) estão entre as ferramentas computacionais mais importantes para os operadores do sistema determinarem o estado do sistema de potência. Este cálculo é realizado para otimizar diversas decisões na rede, para despachar os componentes da rede e para reconfigurá-los. Além disso, o cálculo é utilizado para precificar os serviços prestados por geradores de grande escala e, progressivamente, por entidades descentralizadas como famílias e pequenas empresas que, além de consumirem, também geram e armazenam energia, e assim, têm um papel no equilíbrio energético através de sua flexibilidade. Várias simplificações são feitas no OPF e no UC para lidar com a carga computacional dos modelos, que tende a ser elevada para sistemas realistas. A imprecisão do modelo devido à simplificação das equações de fluxo de potência ou ao ignorar a estocasticidade, está causando cada vez mais altos custos para as operações do sistema, à medida que a situação real se desvia da previsão, implicando ações dispendiosas por parte dos operadores do sistema em tempo real. Esta tese centra-se nos desafios das operações dos sistemas de energia modernos, tais como gestão coordenada de congestionamento e tensão, programação de energia e reservas, bem como cálculo de preços. Em primeiro lugar, a tese constrói métodos e algoritmos para melhorar a capacidade computacional e a precisão do modelo para problemas de UC e OPF com restrita de rede e corrente alternada (AC) através do desenvolvimento de uma aproximação melhorada das leis físicas que governam os fluxos de potência. Em segundo lugar, aplica estes métodos e algoritmos ao problema de coordenação entre múltiplos Operadores de Redes de Distribuição (DSO) e Operadores de Redes de Transmissão (TSO), introduzindo novas técnicas de optimização descentralizada para gerir problemas de congestionamento e tensão, bem como abordar aspectos de troca de informação de rede. Por fim, a tese propõe novos mecanismos de precificação, abordando endogenamente as decisões operacionais não convexas de energia e programação de reservas para o planejamento do dia seguinte, considerando a estocasticidade da geração de energia renovável. Os benefícios computacionais e de precisão são ilustrados em estudos de caso, empregando diversas métricas desenvolvidas. / [en] To counter climate change, modern power systems are undergoing a decarbonisation-based transition involving vast deployment of renewable energy sources and electrification of societies. For this transition to succeed, various challenges associated with renewable power production need to be addressed in power system operations. These challenges stem from high output variability along with limited predictability and controllability, leading to flexibility needs in power system operations. Optimal power flow (OPF) and unit commitment (UC) are amongst the most important computational tools for system operators to determine the state of the power system. This computation is performed to optimise various decisions on the grid, to dispatch the components in the network, and to reconfigure them. Additionally, the computation is used to price the services provided by large scale generators and, progressively, by decentralised entities such as households and small enterprises which, apart from consuming, also generate and store power, and thus, have a role in energy balancing through their flexibility. Various simplifications are made in OPF and UC to tackle the computational burden of the models, which tends to be high for realistic systems. Model inaccuracy due to simplification of power flow equations or ignoring stochasticity, is increasingly causing high costs for system operations, as the real situation deviates from the forecast implying costly actions by system operators in real-time. This thesis focuses on challenges in modern power system operations, such as coordinated congestion and voltage management, energy and reserve scheduling as well as price computation. Firstly, the thesis constructs methods and algorithms to enhance computational capability and model accuracy for Alternating Current (AC) Network-Constrained UC and OPF problems through devising an improved approximation of the physical laws governing power flows. Secondly, it applies these methods and algorithms to the coordination problem amongst multiple Distribution System Operators (DSO) and Transmission System Operators (TSO), introducing novel decentralised optimisation techniques for managing congestion and voltage problems as well as addressing network information exchange aspects. Finally, the thesis proposes new pricing mechanisms, endogenously tackling the non-convex operational decisions for energy and reserve scheduling for day-ahead planning, considering stochasticity of renewable energy generation. Computational and accuracy benefits are illustrated in case studies by employing various metrics developed.