Voltage-Regulated Sparse Optimization for Proactive Diagnosis of Voltage Collapses

This paper aims to proactively diagnose and manage the voltage collapse risks, i.e., the risk of bus voltages violating the safe operational bounds, which can be caused by extreme events and contingencies. We jointly answer two resilience-related research questions: (Q1) Survivability: Upon having an extreme event/contingency, will the system remain feasible with voltage staying within a (preferred) safe range? (Q2) Dominant Vulnerability: If voltage collapses, what are the dominant sources of system vulnerabilities responsible for the failure? This highlights some key locations worth paying attention to in the planning or decision-making process. To address these questions, we propose a voltage-regulated sparse optimization that finds a minimal set of bus locations along with quantified compensations (corrective actions) that can simultaneously enforce AC network balance and voltage bounds. Results on transmission systems of varying sizes (30-bus to 2383-bus) demonstrate that the proposed method effectively mitigates voltage collapses by compensating at only a few strategically identified nodes, while scaling efficiently to large systems, taking on average less than 4 min for 2000+ bus cases. This work can further serve as a backbone for more comprehensive and actionable decision-making, such as reactive power planning to fix voltage issues.