Stability and Interaction Effects of Grid-Forming Virtual Synchronous Machines within an IEEE 9-Bus System

The transition to converter-interfaced generation presents new challenges for maintaining power system stability. Stability problems can be caused by interactions induced by converter controls. This paper examines the impact of different grid-forming (GFM) virtual synchronous machine (VSMs) designs on the stability and interactions within an IEEE 9-Bus benchmark system, comprising two voltage source converters (VSCs) and a Thévenin equivalent. A mathematical representation of the system enables eigenvalue and participation factor analyses, offering deeper insights into the causes of interactions and stability issues.The small-signal stability analyses reveal that VSMs based on the Current-Controlled Quasi-Stationary Electrical Model (CC-QSEM) are prone to instability in weak grid conditions due to interactions with current and grid states. In contrast, VSMs using the Transient Virtual Resistor (TVR) design exhibit greater robustness and reduced sensitivity of the eigenvalue movement to varying grid strengths. Nonlinear time-domain simulations confirm these findings, highlighting the importance of virtual impedance configuration in enhancing system robustness.This paper provides recommendations for selecting VSM strategies to improve stability across a range of operating conditions. Furthermore, it highlights the necessity of considering a minimum of two converters to take interactions between the converters into account.