Small-Signal Stability Modal Analysis Template

Small-signal stability refers to a power system's ability to maintain synchronism under small disturbances—such as minor load changes or generator perturbations—through inherent damping of rotor angle oscillations. Modal analysis decomposes the linearized system dynamics into decoupled oscillatory modes via eigenanalysis of the state matrix A; each eigenvalue λ_i = σ_i + jω_i encodes mode frequency (ω_i), damping (σ_i), and stability (Re(λ_i) < 0 for stable modes). The Excel template automates key post-processing steps: computing damping ratio ζ_i = −σ_i / |λ_i|, natural frequency f_n,i = ω_i / (2π), mode shape vectors (eigenvectors), and participation factors that quantify how strongly each state variable (e.g., rotor angle, speed, exciter voltage) contributes to a given mode. It typically integrates with industry-standard simulation outputs (e.g., PSS/E .raw + .dyr files or MATLAB/Simulink linearization exports) and includes built-in validation checks (e.g., matrix rank, controllability observability flags) and interactive dashboards for mode clustering, time-domain validation links, and sensitivity tagging. This resource bridges theoretical modal analysis with practical engineering workflows—enabling rapid screening of inter-area vs. local modes, tuning of Power System Stabilizers (PSS), and compliance assessment against grid codes (e.g., NERC MOD-025, ENTSO-E RfG Annex 4).