Stability Boundary Analysis of Islanded Droop-Based Microgrids Using an Autonomous Shooting Method

This paper presents a stability analysis for droop-based islanded AC microgrids via an autonomous shooting method based on bifurcation theory. Shooting methods have been used for the periodic steady-state analysis of electrical systems with harmonic or unbalanced components with a fixed fundamental frequency; however, these methods cannot be directly used for the analysis of microgrids because, due to the their nature, the microgrids frequency has small variations depending on their operative point. In this way, a new system transformation is introduced in this work to change the droop-controlled microgrid mathematical model from an non-autonomous system into an autonomous system. By removing the explicit time dependency, the steady-state solution can be obtained with a shooting methods and the stability of the system calculated. Three case studies are presented, where unbalances and nonlinearities are included, for stability analysis based on bifurcation analysis; the bifurcations indicate qualitative changes in the dynamics of the system, thus delimiting the operating zones of nonlinear systems, which is important for practical designs. The model transformation is validated through time-domain simulation comparisons, and it is demonstrated through the bifurcation analysis that the instability of the microgrid is caused by supercritical Neimark–Sacker bifurcations, and the dynamical system phase portraits are presented.