Stability and Sensitivity Analysis of a Freedom-Based Microgrid

Stability and sensitivity analysis was performed for the freedom-based microgrid system. During stability analysis, we implemented numerical simulation algorithms to evaluate system behavior under various operating conditions and disturbance scenarios. The approach involved modeling the microgrid using state-space representation and applying Lyapunov stability criteria through MATLAB/Simulink simulations. Key functions included eigenvalue computation to assess dynamic stability margins and transient response analysis to verify system robustness. For sensitivity analysis, we developed parameter perturbation algorithms using partial derivative calculations to quantify how system performance metrics (voltage stability, frequency regulation) respond to changes in input parameters like load variations and renewable generation fluctuations. The implementation involved Monte Carlo simulations and Sobol sequence sampling to comprehensively explore the parameter space. Critical components were identified through sensitivity indices calculated using variance-based methods. The analytical framework incorporated power flow algorithms and dynamic modelling techniques to simulate various operational scenarios. Results from these analyses provide crucial insights for microgrid design optimization, enabling parameter tuning and control strategy refinement to ensure reliable operation that meets user requirements. The code implementation utilized iterative solvers for power flow calculations and numerical integration methods for time-domain simulations.