Placing Grid-Forming Converters to Enhance Small Signal Stability of PLL-Integrated Power Systems

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