Resilience Revisited: A Multidimensional Framework Derived from Realistic Attack Scenarios

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%.