# Biblio

The previous consideration of power grid focuses on the power system itself, however, the recent work is aiming at both power grid and communication network, this coupling networks are firstly called as interdependent networks. Prior study on modeling interdependent networks always extracts main features from real networks, the model of network A and network B are completely symmetrical, both degree distribution in intranetwork and support pattern in inter-network, but in reality this circumstance is hard to attain. In this paper, we deliberately set both networks with same topology in order to specialized research the support pattern between networks. In terms of initial failure from power grid or communication network, we find the remaining survival fraction is greatly disparate, and the failure initially from power grid is more harmful than failure initially from communication network, which all show the vulnerability of interdependency and meantime guide us to pay more attention to the protection measures for power grid.

Cascading failure is an intrinsic threat of power grid to cause enormous cost of society, and it is very challenging to be analyzed. The risk of cascading failure depends both on its probability and the severity of consequence. It is impossible to analyze all of the intrinsic attacks, only the critical and high probability initial events should be found to estimate the risk of cascading failure efficiently. To recognize the critical and high probability events, a cascading failure analysis model for power transmission grid is established based on complex network theory (CNT) in this paper. The risk coefficient of transmission line considering the betweenness, load rate and changeable outage probability is proposed to determine the initial events of power grid. The development tendency of cascading failure is determined by the network topology, the power flow and boundary conditions. The indicators of expected percentage of load loss and line cut are used to estimate the risk of cascading failure caused by the given initial malfunction of power grid. Simulation results from the IEEE RTS-79 test system show that the risk of cascading failure has close relations with the risk coefficient of transmission lines. The value of risk coefficient could be useful to make vulnerability assessment and to design specific action to reduce the topological weakness and the risk of cascading failure of power grid.

The vulnerability analysis is vital for safely running power grids. The simultaneous attack, which applies multiple failures simultaneously, does not consider the time domain in applying failures, and is limited to find unknown vulnerabilities of power grid networks. In this paper, we discover a new attack scenario, called the sequential attack, in which the failures of multiple network components (i.e., links/nodes) occur at different time. The sequence of such failures can be carefully arranged by attackers in order to maximize attack performances. This attack scenario leads to a new angle to analyze and discover vulnerabilities of grid networks. The IEEE 39 bus system is adopted as test benchmark to compare the proposed attack scenario with the existing simultaneous attack scenario. New vulnerabilities are found. For example, the sequential failure of two links, e.g., links 26 and 39 in the test benchmark, can cause 80% power loss, whereas the simultaneous failure of them causes less than 10% power loss. In addition, the sequential attack is demonstrated to be statistically stronger than the simultaneous attack. Finally, several metrics are compared and discussed in terms of whether they can be used to sharply reduce the search space for identifying strong sequential attacks.

The security issue of complex networks has drawn significant concerns recently. While pure topological analyzes from a network security perspective provide some effective techniques, their inability to characterize the physical principles requires a more comprehensive model to approximate failure behavior of a complex network in reality. In this paper, based on an extended topological metric, we proposed an approach to examine the vulnerability of a specific type of complex network, i.e., the power system, against cascading failure threats. The proposed approach adopts a model called extended betweenness that combines network structure with electrical characteristics to define the load of power grid components. By using this power transfer distribution factor-based model, we simulated attacks on different components (buses and branches) in the grid and evaluated the vulnerability of the system components with an extended topological cascading failure simulator. Influence of different loading and overloading situations on cascading failures was also evaluated by testing different tolerance factors. Simulation results from a standard IEEE 118-bus test system revealed the vulnerability of network components, which was then validated on a dc power flow simulator with comparisons to other topological measurements. Finally, potential extensions of the approach were also discussed to exhibit both utility and challenge in more complex scenarios and applications.