Abstract-In this paper, we study the robustness of interdependent networks, in which the state of one network depends on the state of the other network and vice versa. In particular, we focus on the interdependency between the power grid and communication networks, where the grid depends on communications for its control, and the communication network depends on the grid for power. A real-world example is the Italian blackout of 2003, when a small failure in the power grid cascaded between the two networks and led to a massive blackout. In this paper, we study the minimum number of node failures needed to cause total blackout (i.e., all nodes in both networks to fail). In the case of unidirectional interdependency between the networks we show that the problem is NP-hard, and develop heuristics to find a near-optimal solution. On the other hand, we show that in the case of bidirectional interdependency this problem can be solved in polynomial time. We believe that this new interdependency model gives rise to important, yet unexplored, robust network design problems for interdependent networked infrastructures.

Abstract-In this paper, we study the interdependency between the power grid and the communication network used to control the grid. A communication node depends on the power grid in order to receive power for operation, and a power node depends on the communication network in order to receive control signals for safe operation. We demonstrate that these dependencies can lead to cascading failures, and it is essential to consider the power flow equations for studying the behavior of such interdependent networks. We propose a twophase control policy to mitigate the cascade of failures. In the first phase, our control policy finds the non-avoidable failures that occur due to physical disconnection. In the second phase, our algorithm redistributes the power so that all the connected communication nodes have enough power for operation and no power lines overload. We perform a sensitivity analysis to evaluate the performance of our control policy, and show that our control policy achieves close to optimal yield for many scenarios. This analysis can help design robust interdependent grids and associated control policies.

We study the interaction between the power grid and the communication network used for its control. We design a centralized emergency control scheme under both full and partial communication support, to improve the performance of the power grid. We use our emergency control scheme to model the impact of communication loss on the grid. We show that unlike previous models used in the literature, the loss of communication does not necessarily lead to the failure of the correspondent power nodes; i.e. the "point-wise" failure model is not appropriate. In addition, we show that the impact of communication loss is a function of several parameters such as the size and structure of the power and communication failure, as well as the operating mode of power nodes disconnected from the communication network. Our model can be used to design the dependency between the power grid and the communication network used for its control, so as to maximize the benefit in terms of intelligent control, while minimizing the risks due to loss of communication.