Frequency-Domain Large Signal Modeling and Stability Analysis of Grid-Forming Converters: an Unified Approach Scalable for Large Scale Multi-Converter Systems

Driven by the large-scale integration of renewable energy, voltage source converters (VSCs) are increasingly expected to provide grid-forming functionalities. While various time-domain large-signal analysis methods for single gridforming VSC have been proposed, it is difficult to extend these methods to the systems with multiple converters. For the first time, this paper proposes a unified nonlinear large-signal modeling and non-conservative stability analysis method for multiple grid-forming VSCs in the frequency-domain. By transforming the grid-forming control from rotating dq frame to stationary <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha \beta$</tex> frame, it allows accurate and unified modeling of the control nonlinearities as memoryless sectors, and enables the system-level model integration without relying on a global dq frame. Then sufficient and necessary condition for global asymptotic stability of the multi-converter system is obtained by the proposed virtual clamping technique together with multivariable circle criterion. The critical stability boundary identified by the proposed method has been accurately validated by experimental results on the multi-converter system, consisting of two grid-forming VSCs with different control parameters and transmission lines connected to the weak grid. This frequency-domain approach can be readily applied to large-scale systems, which provides a crucial foundation to secure the stable operation of future power electronics-based power systems.