Transient and Static Stability Analysis in Power Systems

Power system stability analysis serves as the core technology for ensuring secure grid operation, primarily encompassing transient and static analytical dimensions.

Transient stability focuses on the system's ability to maintain synchronous operation within a few cycles after major disturbances (such as short-circuit faults or generator tripping). The critical indicator is the critical clearing time—if the fault is cleared within this time window, the power angle swing curves of generating units will converge; otherwise, the system may lose synchronization. SIMULINK simulations can model rotor dynamic responses under different fault durations by constructing modules for generators, excitation systems, and network impedances. Implementation typically involves using Simscape Electrical components to build synchronous machine models with governor controls, where ode45 solver configurations help capture electromechanical transients accurately.

Static stability examines the system's capability to maintain steady-state operating points under small disturbances, typical scenarios including gradual load increases or line switching. The analytical method commonly employs power flow calculations combined with Jacobian matrix eigenvalue determination. When operating points approach power transmission limits, voltage collapse or angle instability may occur. Code implementation often involves MATPOWER-based潮流计算 with eig() function analysis to identify stability margins, where singularity of the Jacobian matrix indicates proximity to stability boundaries.

Engineers utilize simulation results from both analyses to identify grid vulnerabilities, optimize protection device setting thresholds, and provide theoretical basis for operational adjustments. The calculation of critical clearing time is particularly crucial as it directly determines relay protection system settings, serving as the primary defense against cascading failures. Automated scripting approaches (e.g., MATLAB batch processing with fault scenario loops) enable systematic sensitivity analysis for protection coordination studies.