Abstract
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.
Highlights
The stability analysis of a synchronverter-dominated microgrid based on bifurcation theory was presented in [18]; in this work, the system is modeled in DQ frame and an eigenvalue analysis is performed considering three different bifurcation paramenters, the results show that the modification of the reactive power coefficient provokes a Hopf bifurcation in the system
Note in this Figure that the solution forms a torus, as in the first case, which means that the instability is given by a supercritical Neimark–Sacker bifurcation; observe that both phase portraits from the first case and this case are not similar, this is because, as discussed before from the Floquet multipliers results, the system dynamics before and after enabling the commutation process in the distributed generation unit (DG) units are different and the unstable solution has a different dynamic, showing again the need to consider detailed system models for the system assessment
A detailed microgrid system, considering multiple aspects such as, nonlinearities, unbalances and closed-loop controls was used as case study in order to perform stability analyzes based on an autonomous shooting method
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. In [20], the computation of stability regions in an islanded droop-controlled microgrid is performed through a bifurcation analysis software called MATONT; the system is modeled in DQ reference frame, and different load types are considered. By removing the explicit time dependency, the steady-state solution can be obtained with a shooting method and the stability of the system calculated such that the shooting methods can compute the steady-state solution even with variable and unknown frequency In this way, in this contribution, by including a mathematical system transformation, a shooting method is used to perform the bifurcation analysis, which allows the consideration of the system nonlinear dynamics, unbalances, and the harmonic content.
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