A Dynamic Phasor Framework for Analysis of IBR-Induced SSOs in Multi-Machine Systems

Abstract

We propose a generalized dynamic phasor (DP) framework to analyze inverter-based resources (IBRs) connected to multi-machine systems under balanced and unbalanced conditions. It captures subsynchronous oscillations (SSOs) induced by grid-following (GFL) IBRs. The linearizability and time invariance of the framework enables us to perform eigen decomposition, which is a powerful tool for root-cause analysis of the SSO modes and damping controller design. The same framework also enables analysis of excitation of the SSO modes in presence of data center (DC) loads. The GFL IBRs are modeled in their respective $dq$-frame DPs and the detailed model of synchronous generators (SGs) along with dynamic transmission network models are represented in $pnz$-frame DPs. Several case studies are performed on the modified IEEE two-area benchmark system, where $2$ SGs are replaced by GFL IBRs and validated with EMTDC/PSCAD simulations. First, time- and frequency-domain analyses of the SSO mode are presented followed by the design of a robust decentralized $\mathcal{H}_\infty$ damping controller based on local signals of the GFL IBRs. Second, the dynamic behavior of the system following an unbalanced fault is demonstrated that is damped by the proposed damping controller. Finally, excitation of the SSO mode in presence of DC load is exhibited and its locational impact is analytically quantified.