Small‐Signal Weak‐Grid Instability of Grid‐Forming Converters Considering DC‐Capacitor Voltage Dynamics

ABSTRACT

Most of studies on the grid‐forming (GFM) converter grid‐tied systems ignored DC‐capacitor voltage dynamics (DVD) and reported that the systems show a perfect weak‐grid adaptability. To answer the question whether the GFM converters can lose stability under weak grids by considering or ignoring the DVD, this article systematically investigates five typical GFM converters, including the well‐known droop, virtual synchronous generator control, DC capacitor self‐synchronization control, etc. and analyses their small‐signal weak‐grid instability conditions. First, based on the eigenvalue analysis and participation factor calculations on the full‐order linearized systems, the system dominant modes including the synchronization loop and/or the DC voltage loop are uncovered and the reduced‐order models are obtained. Next, the classical Routh–Hurwitz criterion is employed to obtain the weak‐grid critical stability conditions explicitly. They well demonstrate that under an ideal condition of ignoring the DVD, the small‐signal stability condition is the same as the equilibrium point existence condition, under the short‐circuit ratio (SCR) being 1. In contrast, under a more realistic condition of considering the DVD, the small‐signal stability condition becomes stricter, under the SCR being slightly larger than 1. Finally, all these explicit analytical results are verified by wide MATLAB/Simulink simulations and hardware‐in‐the‐loop experiments. These time‐domain studies and theoretical analyses provide comprehensive and rigorous results in a unified manner and demonstrate that the small‐signal weak‐grid instability of GFM systems considering DC‐capacitor voltage dynamics is general and it works for all grid‐tied converter systems.