A network approach for power grid robustness against cascading failures

Cascading failures are one of the main reasons for blackouts in electrical power grids. Stable power supply requires a robust design of the power grid topology. Currently, the impact of the grid structure on the grid robustness is mainly assessed by purely topological metrics, that fail to capture the fundamental properties of the electrical power grids such as power flow allocation according to Kirchhoff's laws. This paper deploys the effective graph resistance as a metric to relate the topology of a grid to its robustness against cascading failures. Specifically, the effective graph resistance is deployed as a metric for network expansions (by means of transmission line additions) of an existing power grid. Four strategies based on network properties are investigated to optimize the effective graph resistance, accordingly to improve the robustness, of a given power grid at a low computational complexity. Experimental results suggest the existence of Braess's paradox in power grids: bringing an additional line into the system occasionally results in decrease of the grid robustness. This paper further investigates the impact of the topology on the Braess's paradox, and identifies specific sub-structures whose existence results in Braess's paradox. Careful assessment of the design and expansion choices of grid topologies incorporating the insights provided by this paper optimizes the robustness of a power grid, while avoiding the Braess's paradox in the system.Comment: 7 pages, 13 figures conferenc

Robustness Can Evolve Gradually in Complex Regulatory Gene Networks with Varying Topology

The topology of cellular circuits (the who-interacts-with-whom) is key to understand their robustness to both mutations and noise. The reason is that many biochemical parameters driving circuit behavior vary extensively and are thus not fine-tuned. Existing work in this area asks to what extent the function of any one given circuit is robust. But is high robustness truly remarkable, or would it be expected for many circuits of similar topology? And how can high robustness come about through gradual Darwinian evolution that changes circuit topology gradually, one interaction at a time? We here ask these questions for a model of transcriptional regulation networks, in which we explore millions of different network topologies. Robustness to mutations and noise are correlated in these networks. They show a skewed distribution, with a very small number of networks being vastly more robust than the rest. All networks that attain a given gene expression state can be organized into a graph whose nodes are networks that differ in their topology. Remarkably, this graph is connected and can be easily traversed by gradual changes of network topologies. Thus, robustness is an evolvable property. This connectedness and evolvability of robust networks may be a general organizational principle of biological networks. In addition, it exists also for RNA and protein structures, and may thus be a general organizational principle of all biological systems

An Optimal and Distributed Method for Voltage Regulation in Power Distribution Systems

This paper addresses the problem of voltage regulation in power distribution networks with deep-penetration of distributed energy resources, e.g., renewable-based generation, and storage-capable loads such as plug-in hybrid electric vehicles. We cast the problem as an optimization program, where the objective is to minimize the losses in the network subject to constraints on bus voltage magnitudes, limits on active and reactive power injections, transmission line thermal limits and losses. We provide sufficient conditions under which the optimization problem can be solved via its convex relaxation. Using data from existing networks, we show that these sufficient conditions are expected to be satisfied by most networks. We also provide an efficient distributed algorithm to solve the problem. The algorithm adheres to a communication topology described by a graph that is the same as the graph that describes the electrical network topology. We illustrate the operation of the algorithm, including its robustness against communication link failures, through several case studies involving 5-, 34-, and 123-bus power distribution systems.Comment: To Appear in IEEE Transaction on Power System

Distributed Estimation and Control of Algebraic Connectivity over Random Graphs

In this paper we propose a distributed algorithm for the estimation and control of the connectivity of ad-hoc networks in the presence of a random topology. First, given a generic random graph, we introduce a novel stochastic power iteration method that allows each node to estimate and track the algebraic connectivity of the underlying expected graph. Using results from stochastic approximation theory, we prove that the proposed method converges almost surely (a.s.) to the desired value of connectivity even in the presence of imperfect communication scenarios. The estimation strategy is then used as a basic tool to adapt the power transmitted by each node of a wireless network, in order to maximize the network connectivity in the presence of realistic Medium Access Control (MAC) protocols or simply to drive the connectivity toward a desired target value. Numerical results corroborate our theoretical findings, thus illustrating the main features of the algorithm and its robustness to fluctuations of the network graph due to the presence of random link failures.Comment: To appear in IEEE Transactions on Signal Processin

Structure and topology of transcriptional regulatory networks and their applications in bio-inspired networking

Biological networks carry out vital functions necessary for sustenance despite environmental adversities. Transcriptional Regulatory Network (TRN) is one such biological network that is formed due to the interaction between proteins, called Transcription Factors (TFs), and segments of DNA, called genes. TRNs are known to exhibit functional robustness in the face of perturbation or mutation: a property that is proven to be a result of its underlying network topology. In this thesis, we first propose a three-tier topological characterization of TRN to analyze the interplay between the significant graph-theoretic properties of TRNs such as scale-free out-degree distribution, low graph density, small world property and the abundance of subgraphs called motifs. Specifically, we pinpoint the role of a certain three-node motif, called Feed Forward Loop (FFL) motif in topological robustness as well as information spread in TRNs. With the understanding of the TRN topology, we explore its potential use in design of fault-tolerant communication topologies. To this end, we first propose an edge rewiring mechanism that remedies the vulnerability of TRNs to the failure of well-connected nodes, called hubs, while preserving its other significant graph-theoretic properties. We apply the rewired TRN topologies in the design of wireless sensor networks that are less vulnerable to targeted node failure. Similarly, we apply the TRN topology to address the issues of robustness and energy-efficiency in the following networking paradigms: robust yet energy-efficient delay tolerant network for post disaster scenarios, energy-efficient data-collection framework for smart city applications and a data transfer framework deployed over a fog computing platform for collaborative sensing --Abstract, page iii

Robustness Measure of China’s Railway Network Topology Using Relative Entropy

This study focused on China’s railway network topology issue from a robustness measure perspective. Relative entropy is used in the study as a measurement of robustness of railway network topology. It is found that the entropy-based measure provides more informative analyses compared to a traditional graph measure. The results indicate that the railway network in the 12th five-year plan has improved robustness when compare to 2008 with respect to deliberate and random attacks