45,495 research outputs found
Optimizing the robustness of electrical power systems against cascading failures
Electrical power systems are one of the most important infrastructures that
support our society. However, their vulnerabilities have raised great concern
recently due to several large-scale blackouts around the world. In this paper,
we investigate the robustness of power systems against cascading failures
initiated by a random attack. This is done under a simple yet useful model
based on global and equal redistribution of load upon failures. We provide a
complete understanding of system robustness by i) deriving an expression for
the final system size as a function of the size of initial attacks; ii)
deriving the critical attack size after which system breaks down completely;
iii) showing that complete system breakdown takes place through a first-order
(i.e., discontinuous) transition in terms of the attack size; and iv)
establishing the optimal load-capacity distribution that maximizes robustness.
In particular, we show that robustness is maximized when the difference between
the capacity and initial load is the same for all lines; i.e., when all lines
have the same redundant space regardless of their initial load. This is in
contrast with the intuitive and commonly used setting where capacity of a line
is a fixed factor of its initial load.Comment: 18 pages including 2 pages of supplementary file, 5 figure
A simple beam model for the shear failure of interfaces
We propose a novel model for the shear failure of a glued interface between
two solid blocks. We model the interface as an array of elastic beams which
experience stretching and bending under shear load and break if the two
deformation modes exceed randomly distributed breaking thresholds. The two
breaking modes can be independent or combined in the form of a von Mises type
breaking criterion. Assuming global load sharing following the beam breaking,
we obtain analytically the macroscopic constitutive behavior of the system and
describe the microscopic process of the progressive failure of the interface.
We work out an efficient simulation technique which allows for the study of
large systems. The limiting case of very localized interaction of surface
elements is explored by computer simulations.Comment: 11 pages, 13 figure
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