Interaction Modeling and Stability Analysis of Grid-Forming Energy Storage System Based on SISO Transfer Functions

With the rapid expansion of photovoltaic (PV), grid-forming energy storage systems (GFM-ESS) have been widely employed for inertia response and voltage support to enhance the dynamic characteristics. Converters with different synchronization methods represent significant differences in dynamic behavior. The interactions between grid-forming (GFM) and grid-following (GFL) devices with multi-time scale control may lead to small-signal instability in hybrid systems. This paper investigates a grid-connected system comprising a grid-forming energy storage system and a grid-following PV system (GFL-PV). Based on single-input-single-output (SISO) transfer functions, a dynamic interaction model for the PV-ESS system is established. Combining the open-loop transfer functions of full-loop and sub-loop, the proposed model reveals how GFM-ESS modifies the dynamic characteristics of GFL-PV under weak grid conditions. Subsequently, the impact of different control loops and parameters on the small-signal stability of the system is analyzed. The stability margins of both devices are also compared through the SISO model. Electromagnetic transient simulation results in MATLAB/Simulink and experiments validate the effectiveness of the proposed models and analyses.