Stability Analysis Method of a Hierarchical Control Structure Microgrid Based on a Small-Signal Model and Hopf Bifurcation Theory

•In this paper, through the following highlights, a hierarchical control structure microgrid based on a small-signal model and Hopf bifurcation theory are used.•Combining linear damping analysis method and nonlinear Hopf bifurcation analysis method, a stability analysis method based on oscillating trajectory is proposed.•Considering the oscillation phenomenon caused by changes the system model and control structure, and study the influence of microgrid secondary control on system stability under different oscillating trajectories and abrupt loads.•Using Hopf bifurcation theory and oscillation trajectory to delineate the parameter trajectories stable region, and analyze the changes of track stability region before and after hierarchical control. To the oscillation and stability problem caused by multi-scale and broadband electromagnetic dynamics among many isomerized power electronic devices in a microgrid, a small-signal model of hierarchical control structure microgrid and stability analysis method based on oscillation trajectories are proposed. Moreover, a hierarchical control structure is used as the research object in microgrid, and the analysis is performed based on the small-signal model and Hopf bifurcation theory. First, the small-signal model of the hierarchical control structure microgrid is established, combining the dominant eigenvalue and participation factor analysis methods, to analyze the influence of the controller and related sensitive parameters on the dynamic performance of the system. Then, based on the small-signal model and Hopf bifurcation theory, a stability analysis method based on oscillation trajectories is proposed. The relationship between different oscillation modes and limit cycles in the microgrid system and the influence of the sag control parameter values on the oscillation trajectory and stability domain of the system are researched on. Combining Hopf bifurcation theory and oscillation trajectory to delineate the stable domain of parameter trajectories, the influence of secondary control on the system stability is analyzed under different oscillation trajectories and load disturbances, revealing the corresponding relationship between the state trajectories of different oscillation modes and system stability of a hierarchical control structure microgrid. Based on the proposed oscillating trajectories, the stability analysis method has sufficient universality for studying the impact of system stability, establishing the pa