Distributed optimization methods for the management of the security of interconnected power systems

Our societies are more dependent on electricity than ever, thus any disturbance in the power transmission and delivery has major economic and social impact. The reliability and security of power systems are then crucial to keep, for power system operators, in addition to minimizing the system operating cost. Moreover, transmission systems are interconnected to decrease the cost of operation and improve the system security. One of the main challenges for transmission system operators is therefore to coordinate with interconnected power systems, which raises scalability, interoperability and privacy issues. Hence, this thesis is concerned with how TSOs can operate their networks in a decentralized way but coordinating their operation with other neighboring TSOs to find a cost-effective scheduling that is globally secure.The main focus of this thesis is the security of power systems, this is why the evolution of the main characteristics of the blackouts that are failures in power system security, of the period 2005-2016 is studied. The approach consists in determining what the major characteristics of the incidents of the past 10 years are, to identify what should be taken into account to mitigate the risk of incidents. The evolution have been studied and compared with the characteristics of the blackouts before 2005. The study focuses on the pre-conditions that led to those blackouts and on the cascades, and especially the role of the cascade speed. Some important features are extracted and later integrated in our work.An algorithm that solve the preventive Security Constrained Optimal Power Flow (SCOPF) problem in a fully distributed manner, is thus developed. The preventive SCOPF problem consists in adding constraints that ensure that, after the loss of any major device of the system, the new steady-state reached, as a result of the primary frequency control, does not violate any constraint. The developed algorithm uses a fine-grained decomposition and is implemented under the multi-agent system paradigm based on two categories of agents: devices and buses. The agents are coordinated with the Alternating Direction method of multipliers in conjunction with a consensus problem. This decomposition provides the autonomy and privacy to the different actors of the system and the fine-grained decomposition allows to take the most of the decomposition and provides a good scalability regarding the size of the problem. This algorithm also have the advantage of being robust to any disturbance of the system, including the separation of the system into regions.Then, to account for the uncertainty of production brought by wind farms forecast error, a two-step distributed approach is developed to solve the Chance-Constrained Optimal Power Flow problem, in a fully distributed manner. The wind farms forecast errors are modeled by independent Gaussian distributions and the mismatches with the initials are assumed to be compensated by the primary frequency response of generators. The first step of this algorithm aims at determining the sensitivity factors of the system, needed to formulate the problem. The results of this first step are inputs of the second step that is the CCOPF. An extension of this formulation provides more flexibility to the problem and consists in including the possibility to curtail the wind farms. This algorithm relies on the same fine-grained decomposition where the agents are again coordinated by the ADMM and a consensus problem. In conclusion, this two-step algorithm ensures the privacy and autonomy of the different system actors and it is de facto parallel and adapted to high performance platforms.