Cascading failures in interdependent systems under a flow redistribution model

TL;DR

This paper introduces a flow redistribution model for interdependent systems that captures cascading failures caused by load overloading, revealing complex transition behaviors and the nuanced impact of interdependence on system robustness.

Contribution

It develops a novel flow redistribution model for interdependent networks, analyzing how load transfer affects cascading failures and robustness, which differs from traditional percolation-based models.

Findings

Final system collapse is always first-order.

Transitions can include both first and second-order phases.

Interdependence can enhance individual network robustness.

Abstract

Robustness and cascading failures in interdependent systems has been an active research field in the past decade. However, most existing works use percolation-based models where only the largest component of each network remains functional throughout the cascade. Although suitable for communication networks, this assumption fails to capture the dependencies in systems carrying a flow (e.g., power systems, road transportation networks), where cascading failures are often triggered by redistribution of flows leading to overloading of lines. Here, we consider a model consisting of systems $A$ and $B$ with initial line loads and capacities given by $\{L_{A,i},C_{A,i}\}_{i=1}^{n}$ and $\{L_{B,i},C_{B,i}\}_{i=1}^{n}$, respectively. When a line fails in system $A$, $a$-fraction of its load is redistributed to alive lines in $B$, while remaining $(1-a)$-fraction is redistributed equally among all functional lines in $A$; a line failure in $B$ is treated similarly with $b$ giving the fraction to be redistributed to $A$. We give a thorough analysis of cascading failures of this model initiated by a random attack targeting $p_1$-fraction of lines in $A$ and $p_2$-fraction in $B$. We show that (i) the model captures the real-world phenomenon of unexpected large scale cascades and exhibits interesting transition behavior: the final collapse is always first-order, but it can be preceded by a sequence of first and second-order transitions; (ii) network robustness tightly depends on the coupling coefficients $a$ and $b$, and robustness is maximized at non-trivial $a,b$ values in general; (iii) unlike existing models, interdependence has a multi-faceted impact on system robustness in that interdependency can lead to an improved robustness for each individual network.