Application of frequency-domain fitting and descriptor state-space modeling for the analysis of sub-synchronous oscillations in multi-IBR systems

Due to the growing complexity of power system topologies and the proprietary nature of inverter-based resource (IBR) controls, developing accurate state-space models (SSMs) for large-scale power systems with high IBR penetration is challenging. To address these, a combined Loewner Matrix (LM)-Vector Fitting (VF) method is proposed to accurately fit black-box IBRs to SSMs, while an improved descriptor state-space modeling (DSSM) approach is developed to efficiently construct SSMs of white-box networks and integrate them with black-box IBRs SSMs. The approach introduces two key innovations: First, new metrics, cumulative energy and its rate of change, are developed to quantify the significance of singular values derived from the LM pencil function. These metrics enable selection of a sufficient model order, so VF only needs to be performed once, without trial-and-error order tuning. Second, the enhanced DSSM approach introduces novel virtual state variables for black-box IBRs. While these variables lack physical meaning, they create a unified state-space representation that overcomes the challenges of integrating different SSMs. Furthermore, the improved DSSM approach constructs detailed SSMs of white-box networks. Building on this, system-level SSMs can be obtained through the feedback interconnection between IBRs and networks. Two test systems (a radial network with a single IBR and a meshed network with multiple IBRs) are employed to validate the proposed modeling approach, demonstrating its effectiveness.