Stochastic Dynamic Modeling and Stability Analysis Method for DC Microgrids Under Gaussian–Poisson Hybrid Excitations

ABSTRACT To address the problem that the deterministic modeling of a direct‐current (DC) microgrid and its stability analysis method are insufficient for DC microgrid characterization when multiple types of stochastic perturbations are considered, a stochastic dynamic model of a DC microgrid under Gaussian–Poisson mixed excitation and a stability analysis method are proposed. Existing research has primarily focused on the impact of deterministic disturbances on the stability of DC microgrids, while lacking in‐depth exploration of system‐level modeling and stability mechanisms under hybrid random excitation. To address this, this paper models continuous random disturbances as Gaussian random excitation and discrete random disturbances as Poisson random excitation, thereby constructing a stochastic dynamic model for DC microgrids under hybrid excitation. By employing the Heun numerical algorithm to solve this stochastic dynamic model and conduct stability analysis, a theoretical proof is provided for the system's mean and mean‐square stability when combined Gaussian and Poisson small excitation intensities are present. By analyzing the system response trajectories under varying excitation intensities, this study elucidates the impact mechanism of hybrid stochastic excitations on DC microgrid stability. The simulation results validate the effectiveness of the proposed model and method in characterizing mixed random disturbances and analyzing system stability.