A General Linear Framework for Analysis of Islanded Inverter-Based Microgrids

Simulation and stability analysis of power systems are challenging topics due to nonlinear models. Fortunately, most power components are weakly nonlinear and by taking the advantages of this characteristic and also using the first-order term of the Taylor expansion, a general linear time-variant model for such systems is derived. Specifically, this article analyzes islanded inverter-based microgrids (IBMGs) using the proposed linear model driven directly from a general nonlinear model of IBMGs, and it is just as comprehensive as the reference one. Two methods to linearize the weakly and severely nonlinear state-space models are presented. A new time-step simulation is developed to modify the model dynamically and to calculate time-domain response as well as eigenvalues directly, which are much faster and more efficient than numerical methods and small-signal stability analyses. The capabilities of the proposed models make it possible to easily develop a time-saving eigenvalue calculator as well as a fast- and low computational direct power flow analysis. Different time-domain simulations in MATLAB/Simulink and other tests are investigated to verify the performance of the proposed simulations and their applications.