Mitigation of cascade failures in complex networks: theory and application

Complex networks such as transportation networks, the Internet, and electrical power grids are fundamental parts of modern life, and their robustness under any attack or fault has always been a concern. Failure and intentional removal of components in complex networks might affect the flow of information and change balance of flows in the network. This phenomenon may require load redistribution all over the network. Component overloaded can act as a trigger for a chain of overload failures. This overload, could, for example, increase the amount of information a router must transmit and ultimately make internet congestion. One of the major applications of complex network theory is to study power systems. Power systems are the most complex human-made infrastructures, and almost every individual's life is dependent on electrical energy and resilient functioning of power systems. Recently, there have been many reports about massive power outages leaving vast areas without power that sometimes takes a few days to have the power back. One of the most critical areas in the power system is the root cause analysis of such catastrophes and trying to resolve them. From an electrical engineering point of view, these power outages occur following an initial failure due to problems, such as generators tripping, transformers overheating, faulty power generation units, damage to the transmission system, substations or distribution systems, or overloading of the power system. A faulty protection relay or malicious attack to control centres can also trigger it. In any of these cases, the failed component will be out of service immediately and to keep the robust power delivery to all customers, their loads should be redistributed across the power system, and henceforth some of them might become overloaded as well, and accordingly get out of service. This chain of failures can be propagated all over the system and lead to a catastrophic blackout. This thesis conducts a full study on how to mitigate cascade failures in complex networks. First, cascade depth is applied to quantify nodes criticality for cascade failures. Then, a wide range of node centrality parameters is considered to find out the relationship between the node vitality and these centralities. To discover the structure of cascade propagation in complex networks, the edge geodesic distance is considered for computing the structural distance between two arbitrary edges in the network. Then, starting with the single edge removal events, the route that cascade tends to spread is studied. In the next step, the impact of two or three concurrent edge removals on the way the cascade spreads are examined. Besides, the power system vulnerability is studied using the maximum flow algorithm based on Ford-Fulkerson method and critical capacity parameters are identified. A synthetic model with the same properties as a real power system is generated and examined. For a power line, to be overloaded, a new method is developed to overpass across the network and shortlist the busbars for load reduction. Next, a novel sensitivity method is formulated based on AC load flow analysis to rank the loads according to their effect on the lines power flow