  Small-signal instability of grid-connected power converters may arise when
the converters use a phase-locked loop (PLL) to synchronize with a weak grid.
Commonly, this stability problem (referred as PLL-synchronization stability in
this paper) was studied by employing a single-converter system connected to an
infinite bus, which however, omits the impacts of power grid structure and the
interactions among multiple converters. Motivated by this, we investigate how
the grid structure affects PLL-synchronization stability of multi-converter
systems. By using Kron reduction to eliminate the interior nodes, an equivalent
reduced network is obtained which contains only the converter nodes. We
explicitly show how the Kron-reduced multi-converter system can be decoupled
into its modes. This modal representation allows us to demonstrate that the
smallest eigenvalue of the grounded Laplacian matrix of the Kron-reduced
network dominates the stability margin. We also carry out a sensitivity
analysis of this smallest eigenvalue to explore how a perturbation in the
original network affects the stability margin. On this basis, we provide
guidelines on how to improve the PLL-synchronization stability of
multi-converter systems by PLL-retuning, proper placement of converters or
enhancing some weak connection in the network. Finally, we validate our
findings with simulation results based on a 39-bus test system.
