54 research outputs found
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
Structural transition in interdependent networks with regular interconnections
Networks are often made up of several layers that exhibit diverse degrees of
interdependencies. A multilayer interdependent network consists of a set of
graphs that are interconnected through a weighted interconnection matrix , where the weight of each inter-graph link is a non-negative real number . Various dynamical processes, such as synchronization, cascading failures
in power grids, and diffusion processes, are described by the Laplacian matrix
characterizing the whole system. For the case in which the multilayer
graph is a multiplex, where the number of nodes in each layer is the same and
the interconnection matrix , being the identity matrix, it has
been shown that there exists a structural transition at some critical coupling,
. This transition is such that dynamical processes are separated into
two regimes: if , the network acts as a whole; whereas when , the network operates as if the graphs encoding the layers were isolated. In
this paper, we extend and generalize the structural transition threshold to a regular interconnection matrix (constant row and column sum).
Specifically, we provide upper and lower bounds for the transition threshold in interdependent networks with a regular interconnection matrix
and derive the exact transition threshold for special scenarios using the
formalism of quotient graphs. Additionally, we discuss the physical meaning of
the transition threshold in terms of the minimum cut and show, through
a counter-example, that the structural transition does not always exist. Our
results are one step forward on the characterization of more realistic
multilayer networks and might be relevant for systems that deviate from the
topological constrains imposed by multiplex networks.Comment: 13 pages, APS format. Submitted for publicatio
Context-Independent Centrality Measures Underestimate the Vulnerability of Power Grids
Power grids vulnerability is a key issue in society. A component failure may
trigger cascades of failures across the grid and lead to a large blackout.
Complex network approaches have shown a direction to study some of the problems
faced by power grids. Within Complex Network Analysis structural
vulnerabilities of power grids have been studied mostly using purely
topological approaches, which assumes that flow of power is dictated by
shortest paths. However, this fails to capture the real flow characteristics of
power grids. We have proposed a flow redistribution mechanism that closely
mimics the flow in power grids using the PTDF. With this mechanism we enhance
existing cascading failure models to study the vulnerability of power grids.
We apply the model to the European high-voltage grid to carry out a
comparative study for a number of centrality measures. `Centrality' gives an
indication of the criticality of network components. Our model offers a way to
find those centrality measures that give the best indication of node
vulnerability in the context of power grids, by considering not only the
network topology but also the power flowing through the network. In addition,
we use the model to determine the spare capacity that is needed to make the
grid robust to targeted attacks. We also show a brief comparison of the end
results with other power grid systems to generalise the result.Comment: Pre-Proceedings of CRITIS '1
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
Limit cycles in the Holling-Tanner model
This paper deals with the following question: does the asymptotic stability of the positive equilibrium of the Holling-Tanner model imply it is also globally stable? We will show that the answer to this question is negative. The main tool we use is the computation of Poincaré-Lyapunov constants in case a weak focus occurs. In this way we are able to construct an example with two limit cycles
Measuring and Controlling Unfairness in Decentralized Planning of Energy Demand
Demand-side energy management improves robustness and efficiency in Smart Grids. Load-adjustment and load-shifting are performed to match demand to available supply. These operations come at a discomfort cost for consumers as their lifestyle is influenced when they adjust or shift in time their demand. Performance of demand-side energy management mainly concerns how robustness is maximized or discomfort is minimized. However, measuring and controlling the distribution of discomfort as perceived between different consumers provides an enriched notion of fairness in demand-side energy management that is missing in current approaches. This paper defines unfairness in demand-side energy management and shows how unfairness is measurable and controllable by software agents that plan energy demand in a decentralized fashion. Experimental evaluation using real demand and survey data from two operational Smart Grid projects confirms these findings. © 2014 IEEE
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