Abstract：In China, the current renewable energy resources mainly use grid-following converters as grid-connected interfaces, which cannot provide inertia and damping support for power systems. In order to enhance the support capacity of renewable energy resources, grid-forming inverters are emerging as a promising solution as they can emulate the dynamic property of synchronous generator and provide support. However, the grid-forming inverter faces significant risks of transient synchronous instability. Current research primarily focuses on single grid-forming inverter systems, which cannot be applied to multi-machine systems due to complex interactions between converters. Quantitative transient analysis and the method of stability region estimation for multiple paralleled grid-forming inverter systems are absent. To fill this gap, taking transient interaction and power coupling into consideration, the large-signal equivalent model of multiple grid-forming inverters system is established. Based on this model, a set of Lyapunov functions is constructed, which accounts for damping dissipation, reactive power loop dynamics, and transient interactions, enabling intuitively and accurately plotting the stability region for multi-machine system. Then, by comparing the sizes of the stability regions, the impact of control parameters and grid parameters on the stability boundaries of grid-forming multi-machine systems is quantified. Furthermore, the influence of damping dissipation, reactive power loop dynamics, and transient interactions on the transient stability margin is explored. Finally, hardware-in-the-loop experiments validate the accuracy of the estimated maximum stability region. The following conclusions can be drawn from the analysis in this paper: (1) Due to the complex interaction, the equivalence model and transient characteristics of multi-machine system are more complex than those of single-machine system. (2) The Lyapunov function set, which takes into account voltage dynamics, damping dissipation and transient interaction, can accurately estimate the maximum stability region of multiple grid-forming inverter systems, and predict the transient synchronization stability via the location of the fault clearing point. (3) By comparing the size of the stability region, the increase of reference power, fault depth, and line impedance will reduce the stability region, and the increase of damping coefficient, inertia, and reactive droop coefficient will enlarge the stability region. The voltage dynamics and damping dissipation can increase the stability margin of the system, and the transient interaction between units can reduce the stability margin.
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