Unified Loadability Quality Factor (ULQF): A bounded and interpretable voltage stability index

Abstract

Voltage stability assessment remains a critical challenge in evolving power networks, which are increasingly influenced by load variability, renewable energy integration, and distributed energy resources. Traditional indices such as the Loadability Quality Power (LQP) index exhibit significant limitations under stressed or complex conditions, frequently producing unbounded or misleading values. To address these shortcomings, this paper introduces the Unified Loadability Quality Factor (ULQF). This normalized and bounded voltage stability index quantifies line stress on a [0, 1] scale, offering improved interpretability and consistency for steady-state security assessment. ULQF incorporates a dynamic normalization framework that accounts for real and reactive capacity margins, ensuring applicability across both radial and meshed topologies. Its performance is validated on four benchmark systems, Garver 6-bus, IEEE 14, 30, and 118-bus, across more than 160,000 load scenarios, including nodal overloading, contingency stress testing, Monte Carlo uncertainty analysis, and comparisons against classical indices such as FVSI and L- index. Results show that ULQF reliably tracks proximity to voltage collapse and aligns with PV curve behavior, outperforming existing methods under conditions of congestion and increased demand. Its lightweight computational design and compatibility with SCADA measurements highlight its potential for practical integration into control-center workflows. While this study focuses on classical benchmark networks, future work will extend the framework to converter- dominated and renewable-rich systems, further supporting resilience and reliability in evolving power grids.