Modeling and Stability Analysis of Single-Phase Microgrids Controlled in Stationary Frame

Modern microgrids are transitioning toward having an increasing portion of grid-forming (GFM) converters to support nontraditional sources, such as renewable energy and energy storage systems, while aiming to improve system stability, reliability, power rating, and flexibility. Understanding the interaction among parallel GFM converters to guarantee the microgrid stability within various operating conditions is necessary. For single-phase systems, when the controllers are implemented in the rotating frame to facilitate the stability analysis and design, the required orthogonal signal generation (OSG) units degrade the system stability. On the other hand, when the controllers are implemented in the stationary frame to avoid OSG-related problems, the stability analysis becomes particularly challenging due to nonlinearities and mixed dc and ac state variables. In this article, an approach is proposed to systematically model and perform stability analysis for a single-phase microgrid with stationary frame controllers. The approach is based on defining a complementary system that allows transformation to the synchronous rotating frame without introducing time-varying (double-frequency) terms and without altering the stability properties. The accuracy of the proposed modeling approach is verified using simulations and experimental results.