232 research outputs found
A Topological Investigation of Phase Transitions of Cascading Failures in Power Grids
Cascading failures are one of the main reasons for blackouts in electric
power transmission grids. The economic cost of such failures is in the order of
tens of billion dollars annually. The loading level of power system is a key
aspect to determine the amount of the damage caused by cascading failures.
Existing studies show that the blackout size exhibits phase transitions as the
loading level increases. This paper investigates the impact of the topology of
a power grid on phase transitions in its robustness. Three spectral graph
metrics are considered: spectral radius, effective graph resistance and
algebraic connectivity. Experimental results from a model of cascading failures
in power grids on the IEEE power systems demonstrate the applicability of these
metrics to design/optimize a power grid topology for an enhanced phase
transition behavior of the system
Collective frequency variation in network synchronization and reverse PageRank
A wide range of natural and engineered phenomena rely on large networks of
interacting units to reach a dynamical consensus state where the system
collectively operates. Here we study the dynamics of self-organizing systems
and show that for generic directed networks the collective frequency of the
ensemble is {\it not} the same as the mean of the individuals' natural
frequencies. Specifically, we show that the collective frequency equals a
weighted average of the natural frequencies, where the weights are given by an
out-flow centrality measure that is equivalent to a reverse PageRank
centrality. Our findings uncover an intricate dependence of the collective
frequency on both the structural directedness and dynamical heterogeneity of
the network, and also reveal an unexplored connection between synchronization
and PageRank, which opens the possibility of applying PageRank optimization to
synchronization. Finally, we demonstrate the presence of collective frequency
variation in real-world networks by considering the UK and Scandinavian power
grids
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
Resistance distance, information centrality, node vulnerability and vibrations in complex networks
We discuss three seemingly unrelated quantities that have been introduced in different fields of science for complex networks. The three quantities are the resistance distance, the information centrality and the node displacement. We first prove various relations among them. Then we focus on the node displacement, showing its usefulness as an index of node vulnerability.We argue that the node displacement has a better resolution as a measure of node vulnerability than the degree and the information centrality
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