Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2409.04590

On Graph Theory vs. Time-Domain Discrete Event Simulation for Topology-Informed Assessment of Power Grid Cyber Risk

Khandaker Akramul Haque·Leen Al Homoud·Xin Zhuang·Mariam Elnour·Ana Goulart·Katherine Davis
View original source ↗Read source document ↗Export metadata ↓

Abstract

The shift toward more renewable energy sources and distributed generation in smart grids has underscored the significance of modeling and analyzing modern power systems as cyber-physical systems (CPS). This transformation has highlighted the importance of cyber and cyber-physical properties of modern power systems for their reliable operation. Graph theory emerges as a pivotal tool for understanding the complex interactions within these systems, providing a framework for representation and analysis. The challenge is vetting these graph theoretic methods and other estimates of system behavior from mathematical models against reality. High-fidelity emulation and/or simulation can help answer this question, but the comparisons have been understudied. This paper employs graph-theoretic metrics to assess node risk and criticality in three distinct case studies, using a Python-based discrete-event simulation called SimPy. Results for each case study show that combining graph theory and simulation provides a topology-informed security assessment. These tools allow us to identify critical network nodes and evaluate their performance and reliability under a cyber threat such as denial of service threats.

Explore related subjects

math.NAcs.NA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Khandaker Akramul Haque, Leen Al Homoud, Xin Zhuang, Mariam Elnour, Ana Goulart, Katherine Davis. 2024-09-06. On Graph Theory vs. Time-Domain Discrete Event Simulation for Topology-Informed Assessment of Power Grid Cyber Risk. https://arxiv.org/abs/2409.04590

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Fully spectral scheme for the linear BGK equation on the whole space

In this article, we design a fully spectral method in both space and velocity for a linear inhomogeneous kinetic equation with mass, momentum and energy conservation. We focus on the linear BGK equation with a confinement potential $Φ$, even if the method could be applied to different collision operators. It is based upon the projection on Hermite polynomials in velocity and orthonormal polynomials with respect to the weight $e^{-$Φ$}$ in space. The potential $Φ$ is assumed to be a polynomial. It is, to the author's knowledge, the first scheme which preserves hypocoercive behavior in addition to the conservation laws. These different properties are illustrated numerically on both quadratic and double well potential.

math.NA↗
arXiv2026

Inverse inequalities for kernel-based approximation on bounded domains and Riemannian manifolds

This paper establishes inverse inequalities for kernel-based approximation spaces defined on bounded Lipschitz domains in $\mathbb{R}^d$ and compact Riemannian manifolds. While inverse inequalities are well-studied for polynomial spaces, their extension to kernel-based trial spaces poses significant challenges. For bounded Lipschitz domains, we extend prior Bernstein inequalities, which only apply to a limited range of Sobolev orders, to the full range of lower and upper orders, and derive Nikolskii inequalities that bound $L_\infty$ norms by $L_2$ norms. For compact Riemannian manifolds, we focus on restricted kernels, which are defined as the restriction of positive definite kernels from the ambient Euclidean space to the manifold, and prove their counterparts.

math.NA↗
arXiv2026

Error Estimates for Hyperbolic Scaling Limits of Linear Kinetic Models on Networks

This paper studies linear discrete kinetic models on networks and their asymptotic behavior in the small Knudsen number limit. For coupling conditions at an n-edge junction under a symmetric formulation, we introduce a change of variables that reformulates the system into n independent initial-boundary value problems. The asymptotic expansions are then constructed and rigorously justified by deriving an error estimate based on the energy method.

math.NA↗