Vulnerability Analysis Evaluating Bilevel Optimal Power Flow Approaches for Multiple Load Cases

TL;DR

This work tackles vulnerability assessment under high-impact, low-probability events in power systems by using bilevel attacker–defender interdiction models with lower-level OPF. It develops two key contributions: (i) an evaluation procedure that compares DC OPF and a linearized AC OPF (LAC) formulation to determine whether the commonly used DC model misses critical vulnerabilities or merely reorders them, and (ii) a multi-load-case scoring framework that identifies critical attack vectors (CAVs) that remain impactful across multiple load/generation scenarios. Case studies on a SimBench HV grid show that the DC approach misses more than 15% of CAVs detected by LAC, and that vulnerability depends strongly on time step and load pattern, underscoring the need for multi-case analysis. These methodologies provide a practical basis for selecting OPF formulations and for prioritizing defense strategies to improve grid resilience against HILP events.

Abstract

This work presents two methodologies to enhance vulnerability assessment in power systems using bilevel attacker-defender network interdiction models. First, we introduce a systematic evaluation procedure for comparing different optimal power flow formulations in the lower-level problem. We demonstrate the procedure for a comparison of the widely used DC approximation and a linearized AC optimal power flow model. Second, we propose a novel scoring methodology to identify and prioritize critical attack vectors across diverse load and generation scenarios. Both methodologies go beyond traditional worst-case analysis. Case studies on a SimBench high-voltage test grid show that the DC approach fails to detect a significant portion of critical vulnerabilities. The scoring methodology further demonstrates the dependency of vulnerabilities on the considered load case and time step, highlighting the importance of assessing multiple scenarios and going beyond worst-case solutions. The proposed methodologies enhance power system vulnerability assessment and can support the effective development of robust defense strategies for future power systems.

Figures (4)

• Figure 1: General scheme of a BNI model.
• Figure 2: SimBench high-voltage test grid topology with the best five CAVs for the DC and LAC approach (red numbers indicate attacked line indices).
• Figure 3: Sum of lost load $\zeta^{(n)}_{\text{LAC},2}$ for LAC CAVs that remain undetected with the DC approach (blue bars), sum of lost load underestimated with the DC approach for identified CAVs $\Delta \zeta^{(n)}_{\text{abs},2}$ (orange bars) and absolute number of undetected LAC CAVs per time step (dots).
• Figure 4: Objective and rank score of best 10 attack vectors for 1, 2 and 3 possible attacks, indexed by the $1^{\text{st}}$ to $10^{\text{th}}$ best combination per $\overline Z$.