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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.
The grid-forming converter is an important unit in the future power system with more inverter-interfaced generators. However, improving its performance is still a key challenge. This paper proposes a generalized architecture of the grid-forming conve
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 st
The renewable energy is connected to the power grid through power electronic converters, which are lack of make the inertia of synchronous generator/machine (SM) be lost. The increasing penetration of renewable energy in power system weakens the freq
Having sufficient grid-forming sources is one of the necessary conditions to guarantee the stability in a power system hosting a very large share of inverter-based generation. The grid-forming function has been historically fulfilled by synchronous m
The modern power system features high penetration of power converters due to the development of renewables, HVDC, etc. Currently, the controller design and parameter tuning of power converters heavily rely on rich engineering experience and extrapola