Stability Boundary Analysis for Grid-Following and Grid-Forming Inverters

Studying the dynamics and stability of inverter-driven power systems has become a top priority for grid operators in view of the massive renewable energy deployment. The simplest and most widely used model for stability analysis for such networks is the single-inverter single- bus (SISB) equivalent model. Although quite insightful, SISB models with an L-filter for the inverter suffer from implementation difficulties due to algebraic loops. This paper develops a closed-form SISB model for grid-following (GFL) and grid-forming (GFM) inverters and derives symbolic formulation for the linearized system, which resolves algebraic loops and obtains fast results with uncompromised precision. This model is then used in an N-Dimensional Stability Boundary Tracking (ND-SBT) algorithm, which identifies the stability boundary for GFL and GFM inverters. This is the first method to infer the stability region for an arbitrary number of dimensions in a computationally efficient and software-agnostic manner while preserving accuracy. A detailed sensitivity analysis yields useful findings on the stability impact of individual parameters, while the results are validated using the IEEE 14- bus system.