Resilience Revisited: A Multidimensional Framework Derived from Realistic Attack Scenarios

TL;DR

This paper introduces a Multidimensional Resilience Index (MDRI) for power systems, capturing cross-dimensional effects under cyberattack scenarios to better assess system degradation.

Contribution

It proposes a novel MDRI framework that explicitly models interactions among physical, operational, digital-cyber, climatic, and regulatory dimensions, validated on a standard system.

Findings

Multi-vector attacks cause 5.6 times more degradation than linear models predict.

Coupling effects contribute an additional 60.6% to system failure.

External factors amplify degradation by 84%.

Abstract

Power systems are increasingly vulnerable to high-impact, low-probability (HILP) events, including coordinated cyberattacks targeting inverter-based resources. Existing resilience frameworks rely on single-dimensional metrics that fail to capture cross-dimensional coupling effects, underestimating real system degradation under multi-vector attack conditions. This study proposes a Multidimensional Resilience Index (MDRI) that decomposes power system degradation into five interacting dimensions: physical, operational, digital-cyber, climatic, and regulatory, explicitly separating independent and coupled contributions via a calibrated multiplicative interaction term. The framework is validated on the IEEE 39-bus system under two attack scenarios derived from the December 2025 cyberattack on the Polish energy infrastructure. MDRI results show that multi-vector attacks produce degradation exceeding linear expectations by a factor of 5.6, with simultaneous dimensional failures contributing an additional 60.6% through endogenous coupling, and exogenous factors amplifying it by an additional 84%.