  The modern power grid features the high penetration of power converters,
which widely employ a phase-locked loop (PLL) for grid synchronization.
However, it has been pointed out that PLL can give rise to small-signal
instabilities under weak grid conditions. This problem can be potentially
resolved by operating the converters in grid-forming mode, namely, without
using a PLL. Nonetheless, it has not been theoretically revealed how the
placement of grid-forming converters enhances the small-signal stability of
power systems integrated with large-scale PLL-based converters. This paper aims
at filling this gap. Based on matrix perturbation theory, we explicitly
demonstrate that the placement of grid-forming converters is equivalent to
increasing the power grid strength and thus improving the small-signal
stability of PLL-based converters. Furthermore, we investigate the optimal
locations to place grid-forming converters by increasing the smallest
eigenvalue of the weighted and Kron-reduced Laplacian matrix of the power
network. The analysis in this paper is validated through high-fidelity
simulation studies on a modified two-area test system and a modified 39-bus
test system. This paper potentially lays the foundation for understanding the
interaction between PLL-based (i.e., grid-following) converters and
grid-forming converters, and coordinating their placements in future
converter-dominated power systems.
