Extended modal analysis of internal dynamics in grid-following inverters based on impedance model

• An extended modal analysis based on impedance framework is proposed to decouple synchronous and electromagnetic dynamics within grid-following inverters. • Participation ratios and explicit parameter participation factors are derived to quantify control loop contributions and pinpoint critical parameters for stability enhancement. • The method overcomes black-box limitations, and its scalability for large-scale grids is validated on modified IEEE 14-bus and 68-bus systems. With the increasing integration of Grid-Following inverters (GFLs), the dynamic behavior of power systems is undergoing significant changes. To evaluate the interaction between GFLs and the grid, impedance-based modal analysis is commonly employed, using impedance or admittance participation factors. However, conventional impedance-based modal analysis treats the GFL as a black box based on port characteristics, which masks the internal coupling mechanisms among different control loops. To address this limitation, this paper proposes an extended modal analysis based on impedance method. This approach decouples the equivalent dynamics of the GFL into two distinct parts: synchronous dynamics dominated by the phase-locked loop and electromagnetic dynamics dominated by the current control loop. By calculating the participation ratios of these components, the dominant dynamics affecting system stability can be effectively identified. Furthermore, explicit parameter participation factors are derived to locate critical control parameters, providing direct guidance for stability enhancement. Simulations on modified IEEE 14-bus and 68-bus systems validate the effectiveness of the proposed method. Unlike state space model, the proposed method analyzes internal control loops using only impedance models, ensuring scalability and broad applicability for large-scale power grids.