Bifurcation Analysis of Inverter-Based Microgrids Using Poincaré Map Theory

The integration of numerous power electronic inverters into AC microgrids has introduced strong nonlinear dynamic characteristics. This poses challenges to the accuracy and effectiveness of traditional linearization analysis methods. Therefore, this paper conducts a nonlinear dynamic stability analysis of inverter-based microgrids using Poincaré map theory, specifically focusing on bifurcation behavior analysis. First, we develop state-space models for each component of the microgrid and construct a complete system dynamic model based on their input-output relationships. Then, by using Poincaré map theory, we derive the system periodic map equation and obtain an explicit expression for its Jacobian matrix. By analyzing the evolutions of the Jacobian matrix's eigenvalues and bifurcation diagrams, we comprehensively investigate the impacts of droop control parameters on the system's nonlinear dynamic behaviors, like Neimark-Sacker bifurcation. Finally, time-domain simulations validate the accuracy of the theoretical analysis.