On Modeling Adequacy and Stability Analysis of IBR-related Subsynchronous Oscillations in Multimachine Systems

Time-varying phasor-based analysis of subsynchronous oscillations (SSOs) involving grid-following converters (GFLCs) and its benchmarking with electromagnetic transient (EMT) models have so far been restricted to highly simplified grid models with constant voltage sources behind series R-L circuits. In this paper, modeling adequacy of bulk power systems with synchronous generators (SGs), transmission systems, loads, and GFLCs are considered. To this end, we revisit the notions of time-varying phasor calculus, highlighting the distinction between space-phasor-calculus (SPC) and two often interchangeably used frameworks namely baseband-abc and generalized averaging. We present the models of grids in SPC framework that include transmission line dynamics, load dynamics, and SG stator transients. Next, we propose a generic approach to study modeling adequacy in small-signal sense by (a) identifying critical modes through eigenvalue and singular value analysis followed by (b) using weighted maximum singular value error magnitudes as metrics, and (c) further cross-validation. Using a modified 4-machine IEEE benchmark model with up to 3 GFLCs we show that SPC framework can be used for analysis of SSOs. Further, we consider the quasistationary phasor calculus (QPC) framework that neglects transmission line, load, and SG stator dynamics to show its adequacy in SSO modeling and analysis. Time-domain and frequency-domain results with EMT models are also presented.