Structure and Stability of the Indian Power Transmission Network

We present the study on the Indian power transmission network using the framework of a complex network and quantify its structural properties. For this, we build the network structure underlying the Indian power grid, using two of its most prevalent power lines. We construct an equivalent model of an exponential network and study its structural changes with changes in two parameters related to redundancy and dead-ends. Then we analyze its stability against cascading failures by varying these two parameters using the link failure model. This helps to gain insight into the relation of network topology to its stability, and indicates how the optimum choice of these parameters can result in a power grid structure with minimum failed links. We apply the same model to study the robustness of the Indian power grid against such failures. In this case, we find that when a link connected to a generator fails, it results in a cascade that spreads in the grid until it is split into two separate stable clusters of generators and consumers, with over one-third of its nodes nonfunctionaComment: 19 pages, 11 figure

Identification of key players in networks using multi-objective optimization and its applications

Identification of a set of key players, is of interest in many disciplines such as sociology, politics, finance, economics, etc. Although many algorithms have been proposed to identify a set of key players, each emphasizes a single objective of interest. Consequently, the prevailing deficiency of each of these methods is that, they perform well only when we consider their objective of interest as the only characteristic that the set of key players should have. But in complicated real life applications, we need a set of key players which can perform well with respect to multiple objectives of interest. In this dissertation, a new perspective for key player identification is proposed, based on optimizing multiple objectives of interest. The proposed approach is useful in identifying both key nodes and key edges in networks. Experimental results show that the sets of key players which optimize multiple objectives perform better than the key players identified using existing algorithms, in multiple applications such as eventual influence limitation problem, immunization problem, improving the fault tolerance of the smart grid, etc. We utilize multi-objective optimization algorithms to optimize a set of objectives for a particular application. A large number of solutions are obtained when the number of objectives is high and the objectives are uncorrelated. But decision-makers usually require one or two solutions for their applications. In addition, the computational time required for multi-objective optimization increases with the number of objectives. A novel approach to obtain a subset of the Pareto optimal solutions is proposed and shown to alleviate the aforementioned problems. As the size and the complexity of the networks increase, so does the computational effort needed to compute the network analysis measures. We show that degree centrality based network sampling can be used to reduce the running times without compromising the quality of key nodes obtained

Percolation Centrality: Quantifying Graph-Theoretic Impact of Nodes during Percolation in Networks

A number of centrality measures are available to determine the relative importance of a node in a complex network, and betweenness is prominent among them. However, the existing centrality measures are not adequate in network percolation scenarios (such as during infection transmission in a social network of individuals, spreading of computer viruses on computer networks, or transmission of disease over a network of towns) because they do not account for the changing percolation states of individual nodes. We propose a new measure, percolation centrality, that quantifies relative impact of nodes based on their topological connectivity, as well as their percolation states. The measure can be extended to include random walk based definitions, and its computational complexity is shown to be of the same order as that of betweenness centrality. We demonstrate the usage of percolation centrality by applying it to a canonical network as well as simulated and real world scale-free and random networks. © 2013 Piraveenan et al.published_or_final_versio

Space Weather and Power Grids - A Vulnerability Assessment

Strong geomagnetic disturbances resulting from solar activity can have a major impact on ground-based infrastructures, such as power grids, pipelines and railway systems. The high voltage transmission network is particularly affected as currents induced by geomagnetic storms, so-called GICs, can severely damage network equipment possibly leading to system collapse. Therefore, increasing attention has been devoted to understanding the vulnerability of power grids to space weather conditions. In this study, we aim at analysing the vulnerability of power grids to extreme space weather. By means of complex network theory, we propose an analysis approach to understand how geomagnetically induced currents are driven through the power network based on its structural and physical characteristics. As a test network we used the Finnish power grid for which a study using network centrality measures was carried out to understand which components are the most critical for the system when exposed to an electric field of 1V/km. This information is helpful as the identification and ranking of critical components can help to identify where and how mitigation measures should be implemented to increase the system’s resilience to space weather impact. We have also subjected the grid to varying angles of the electric field. In addition, we have carried out a scoping study adding load flow to the GICs induced in the system. The preliminary results suggest that the benchmark system can resist GICs induced from high intensity electric fields. Moreover, the simplified network seems more prone to collapse if the electric field is oriented northward. Work is underway to further validate and expand our approach with the aim to eventually carry out a risk assessment of space weather impact on the power grid at EU level.JRC.G.5-Security technology assessmen

Markov Tensor Theory and Cascade, Reachability, and Routing in Complex Networks

University of Minnesota Ph.D. dissertation. 2017. Major: Electrical Engineering. Advisor: Zhi-Li Zhang. 1 computer file (PDF); 180 pages.In this dissertation, we study and characterize the networks as the medium and substrate for communications, interactions, and flows by addressing various crucial problems under the general topics of cascade, reachability, and routing. These are general problem domains common in several applications and from a variety of networks. We address these problems in a unified way by a theoretical platform that we have developed in this research, which we call Markov Tensor Theory. How does a phenomena, influence, or a failure cascade in a network and what are the key factors in this cascade? We study the influence cascade in social networks and introduce the Heat Conduction (HC) Model which captures both social influence and non-social influence, and extends many of the existing non-progressive models. We then prove that selecting the optimal seed set of influential nodes for maximizing the influence spread is NP-hard for HC, however, by establishing the submodularity of influence spread, we tackle the influence maximization problem with a scalable and provably near-optimal greedy algorithm. We also study failure cascade in inter-dependent networks where we considered the effects of cascading failures both within and across different layers. In this study, we investigate how different couplings (i.e., inter-dependencies) between network elements across layers affect the cascading failure dynamics. How failures or disruptions affect the network in terms of reachability of entities from each other, how to identify the reachabilities efficiently after failures, and who are the pivotal players in the reachabilities? We develop an oracle to answer dynamic reachabilities efficiently for failure-prone networks with frequent reachability query requirement. Founded on the concept of reachability, we also introduce and provide a formulation for finding articulation points, measuring network load balancing, and computing pivotality ranking of nodes. Once the reachabilities are determined, how to quickly and robustly route a flow from a part of the network to the other part of a network under the failures? To avoid solely relying on the shortest path and generate alternative paths on one hand, and to correct the degeneracy of hitting time distance, on the other hand, we develop a novel routing continuum method from shortest-path routing to all-path routing which provides both a closed form formulation for computing the continuum distances and an efficient routing strategy. We also devise an oracle for efficiently answering to single-source shortest path queries as well as finding the replacement paths in the case of multiple failures. For these studies, we develop Markov Tensor Theory as a platform of powerful theories and tools founded on Markov chain theory and random walk methods which supports the general weighted and directed networks

Resilience of the Critical Communication Networks Against Spreading Failures: Case of the European National and Research Networks

A backbone network is the central part of the communication network, which provides connectivity within the various systems across large distances. Disruptions in a backbone network would cause severe consequences which could manifest in the service outage on a large scale. Depending on the size and the importance of the network, its failure could leave a substantial impact on the area it is associated with. The failures of the network services could lead to a significant disturbance of human activities. Therefore, making backbone communication networks more resilient directly affects the resilience of the area. Contemporary urban and regional development overwhelmingly converges with the communication infrastructure expansion and their obvious mutual interconnections become more reciprocal. Spreading failures are of particular interest. They usually originate in a single network segment and then spread to the rest of network often causing a global collapse. Two types of spreading failures are given focus, namely: epidemics and cascading failures. How to make backbone networks more resilient against spreading failures? How to tune the topology or additionally protect nodes or links in order to mitigate an effect of the potential failure? Those are the main questions addressed in this thesis. First, the epidemic phenomena are discussed. The subjects of epidemic modeling and identification of the most influential spreaders are addressed using a proposed Linear Time-Invariant (LTI) system approach. Throughout the years, LTI system theory has been used mostly to describe electrical circuits and networks. LTI is suitable to characterize the behavior of the system consisting of numerous interconnected components. The results presented in this thesis show that the same mathematical toolbox could be used for the complex network analysis. Then, cascading failures are discussed. Like any system which can be modeled using an interdependence graph with limited capacity of either nodes or edges, backbone networks are prone to cascades. Numerical simulations are used to model such failures. The resilience of European National Research and Education Networks (NREN) is assessed, weak points and critical areas of the network are identified and the suggestions for its modification are proposed