Value Set Method for Robust Stability Analysis of Microgrids with Multiple Uncertain Time Delays

This brief proposes a value set-based robust stability analysis method to compute the time delay stability boundary of microgrids (MGs) with centralized power sharing control and with inclusion of multiple uncertain time delays. The method consists of three steps. First, construct the characteristic quasi-polynomial in the space of the multiplication between frequency and time delays (FDM) instead of the time delay space. Second, compute the external and internal approximations of the corresponding value set and discriminate their zero exclusion/inclusion. Finally, subdivide the parameter space according to the zero exclusion principle to obtain the time delay stability boundary with the given resolution. By utilizing conciseness, regularity, and periodicity of $2\pi$ of the stability boundary in the FDM space, the proposed value set method is endowed with high accuracy and efficiency, and independent of the magnitude of the time delay intervals. A numerical case is offered to prove the efficiency of the proposed method, while a typical MG case is presented to demonstrate its accuracy and practical applicability.