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Abstract This paper presents a unified framework forconverter-driven stability assessment in large-scale power systems. The approach builds on two resonance mode analysis-based criteria: the Lanczos-based positive-mode-damping (L_PMD) and the Arnoldi-based smallest eigenvalue logarithmic derivative (A_SELD). Both methods estimate the smallest eigenvalues of the nodal admittance matrix across a frequency range using sparse techniques, thus enabling efficient identification of oscillatory modes. Their theoretical relationship with state-space eigenvalues is clarified, and their respective strengths and limitations are systematically analysed. Based on this, a combined application strategy is proposed, where L_PMD provides robust oscillatory mode detection and participation factors, while A_SELD enables accurate damping estimation. In addition, parallel computation is implemented to enhance scalability, achieving significant reductions in computational time in large-scale systems. The framework is validated on IEEE and synthetic test power systems, demonstrating accurate stability assessment and substantial improvements in efficiency compared to conventional approaches. Key words: Large-scale power system, Parallel computation, Positive-mode-damping, Resonance mode analysis, Smallest eigenvalue logarithmic derivative, Stability assessment.
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