Control methods for network dynamics and criticality phenomena

This dissertation studies the role of the network structure on the emergence and mitigation of critical phenomena in complex power networks. In particular, the event to consider is the emergence of cascading failures due to congestion mechanism. The main contributions of this thesis are the proposal of a vulnerability analysis framework to study network influence on critical phenomena and the design of a control framework combining Network theory with Markov Decision Processes and Stochastic Games in order to choose best strategies to reduce the impact of cascading failures. The vulnerability analysis framework includes the identification of main properties influencing cascading failures triggering and propagation, the study of the central role of cut-sets in cascading propagation and the proposal of new metrics to evaluate global and local vulnerability. The control framework includes control strategies to generate worst-case failure scenarios and optimal solutions for damage control on those scenarios employing the dynamic setting of transmission lines capacity. This dissertation is developed around these two contributions, as is described in the following. The first part of this thesis studies the influence of the network connectivity in failure triggering and propagation. Network science theory had been used to study relevant network connectivity properties. A methodology based on the connectivity properties is evaluated to measure the network robustness. A cascading failures model based on hybrid systems theory is proposed to define the congestion mechanism and describe the structure-function power network interdependence. The network Cut-sets (CS) identified as central elements for failures propagation are used to propose a critical link identification algorithm evaluated over the Quasy Stable State (QSS) approach of the proposed cascading failures model. The second part of this dissertation proposes a network-based vulnerability analysis framework and propose a control framework to integrate network properties, electric properties, eventtriggered failures, and control. Several algorithms are developed to evaluate different triggers and propagation events. The framework is developed analytically by the integration of Networks theory with Markov Decision Processes and Stochastic Games. Finally, using the previously obtained results about connectivity and vulnerability, a control strategy is designed to mitigate the damage of failures propagation by dynamically control the transmission lines capacity. An attacker-defender stochastic game framework is used to formulate the control problem. In the problem, the defender selects lines which are the best candidates to apply transmission capacity control as a response to the imminent risk of cascading failures related to the attacker actions. To solve the control problem, we propose a system of multi-population state-dependent replicator dynamics where their fitness change with the long term discounted expected reward in the game. The solution of the replicator equations converges to the Nash equilibrium of the game and coincides with the best strategy for control the cascading failures damage related to worst scenarios produced by optimal attacks.